Claude Universite

Bernard -Lyon

M Le Professeur

Frédéric Fleury

Hamda Ben

Hadid M Le Professeur Didier

Revel M Le Professeur

Philippe Chevalier

M Fabrice

Vallée Mme

Dominique Marchand

Composantes Sante

G Rode

La Mme

C Professeure

Burillon

D Bourgeois

Vinciguerra

M X Perrot

A-M Professeure

Schott

Laura Kamal

T Gayet

E Baubet

S Devillard

L Say

S Brandt

C Pélabon

B-E Saether

Keywords: Harvesting, Mating system, Paternity analysis, Population genetic, Ungulate polyandry, multiple paternity, multiple male mating, mating system variation, harvesting, food resource Does multiple paternity explain phenotypic variation among offspring in wild boar? fetus mass, paternity analysis, phenotypic polymorphism, siblings

de Biométrie et Biologie Evolutive, LBBE), which is an academic research laboratory, and the ONCFS. The ONCFS is divided in several departments with specific missions. I belonged to the Expertise and Research Department, whose missions are to acquire knowledge on wildlife species by conducting field studies and to provide expert counseling and technical support for field managers. Therefore, you will find two popularization articles (in French) in the last two appendices aiming to give feedbacks to

COMPOSANTES ET DEPARTEMENTS DE SCIENCES ET TECHNOLOGIE

Doctor of Philosophy

A mon oncle Aimé, amateur de la bête noire

Résumé

Le sanglier (Sus scrofa scrofa) est une espèce à part entière. C'est une espèce de gibier particulièrement appréciée des chasseurs, un cauchemar pour les agriculteurs et un sujet de débat pour la société en général. La multiplication par dix des populations au cours des dernières décennies en France et dans toute l'Europe, malgré une pression de chasse accrue, a engendré de nombreux conflits entre les humains et la faune sauvage. Le sanglier est responsable de grandes pertes économiques dues aux dommages aux cultures, aux collisions avec les véhicules, à la transmission de maladies et aux dégradations des écosystèmes. L'amélioration des stratégies de gestion devient un intérêt majeur pour éviter, ou contrôler, de tels conflits. La récolte d'informations sur l'espèce problématique est un premier pas vers de bonnes stratégies de gestion.

L'objectif de mon travail est, dans un premier temps, de caractériser le système d'appariement du sanglier à l'aide d'outils génétiques (marqueurs microsatellites) et d'identifier certains paramètres influençant les processus de reproduction, notamment la chasse. Dans un deuxième temps, mon travail se concentre sur l'étude de l'influence du système d'appariement sur les traits d'histoire de vie du sanglier. Mes recherches sont basées sur l'étude de plusieurs populations contrastées dans leurs pratiques de chasse et sur des données longitudinales d'une population intensivement suivie. L'étude est basée sur des données recueillies sur des sangliers tués à la chasse. Les génotypes ont été obtenus pour les femelles gestantes et leur portée et des analyses de paternité ont été réalisées pour mesurer le nombre de pères dans une portée et estimer les taux de paternité multiples (proportion de portées engendrées par plus d'un père). J'ai été en mesure de montrer que le système d'appariement est principalement de la promiscuité (plusieurs mâles s'accouplent avec plusieurs femelles) contrastant avec la polygynie (un mâle dominant monopolisant un groupe de femelles) habituellement décrite chez cette espèce. De plus, les processus de reproduction, estimés par le nombre de partenaires d'une femelle et les taux de paternité multiples, sont influencés par les variations de chasse dans une population. J'ai aussi montré que le nombre de pères avait un effet positif sur la fécondité des femelles. Des taux élevés de paternité multiple et une grande diversité génétique ont été constatés ensemble dans une population fortement chassée, ce qui suggère que la paternité multiple peut tamponner les goulots d'étranglement annuels. Cependant, l'augmentation du nombre de père n'est pas associée à une augmentation de la variation intraportée.

Mots-clés : Analyse de paternité, Génétique des populations, Ongulés, Prélèvement, Système de reproduction. In this chapter, I introduce a general context of my thesis. I start by presenting problems arising from overabundant species. Then, I present theoretical context of causes explaining multiple male mating behavior of females. I further describe known consequences of multiple paternity ensuing from such behavior by focusing on studies about mammals and birds. The aim of my thesis was to investigate modifications of wild boar reproductive processes in relation to hunting and understanding the evolutionary consequences on the species, focusing especially on multiple paternity.

List of figures

List of tables

General context

Biotic homogenization refers to the actual trends of the decline of multitude of species in favor of great increase in distribution range and density of few species sharing special traits like high fecundity and variability, broad diet and adaptability to human disturbances [START_REF] Mckinney | Biotic homogenization: a few winners replacing many loosers in the next mass extinction[END_REF][START_REF] Jeschke | Determinants of vertebrate invasion success in Europe and North America[END_REF]. It is often associated to invasiveness of nonindigenous species introduced by humans in new biota that outcompete or directly prey on local species. However, environmental disturbances can also alter ecological equilibrium and promotes local species able to face, or even benefiting from, the changes [START_REF] Garrott | Overabundance: an issue for conservation biologists?[END_REF].

They are the so-called "Winners" of [START_REF] Baskin | Winners and losers in a changing world[END_REF], impacting negatively other species. Their reproduction and/or expansion are increased due to the changes and they become overabundant, meaning they affect human well-being, reduce density of other species and/or cause ecosystems dysfunctions [START_REF] Caughley | Overpopulation[END_REF]. Overabundance often results of anthropogenic modifications of the environment, as the focus species take advantage over less adaptable ones in the modified landscape [START_REF] Garrott | Overabundance: an issue for conservation biologists?[END_REF]). To avoid detrimental effects of such species considered as pests, management strategies aiming at controlling population growth are implemented. Variety of techniques were applied ranging from culling with traps or poison [START_REF] Bosch | Short-term efects of culling on the ecology and population dynamics of the yellow-legged gull[END_REF], increased hunting when the species is a game species [START_REF] Vercauteren | Regulated commercial harvest to manage overabundant white-tailed deer: An idea to consider?[END_REF][START_REF] Koons | Effects of exploitation on an overabundant species: The lesser snow goose predicament[END_REF], to fertility control considered more ethical in order to respond to social pressure [START_REF] Herbert | Long-acting contraceptives: A new tool to manage overabundant kangaroo populations in nature reserves and urban areas[END_REF] or combination of several technics [START_REF] Cooper | Genetics, biotechnology and population management of overabundant mammalian wildlife in Australasia[END_REF]. Contrasted results were obtained due to high adaptability of the species or compensatory mechanisms [START_REF] Bosch | Short-term efects of culling on the ecology and population dynamics of the yellow-legged gull[END_REF][START_REF] Cooper | Genetics, biotechnology and population management of overabundant mammalian wildlife in Australasia[END_REF][START_REF] Shuster | Is hunting an effective tool to control overabundant deer? A test using an experimental approach[END_REF]. However modeling approaches showed that management strategies can be improved by adapting culling to respond to population fluctuations but it requires knowledge about the focused population of the species [START_REF] Chee | Linking modelling, monitoring and management: An integrated approach to controlling overabundant wildlife[END_REF].

The success of overabundant species is associated to life history traits that promote their demography. They show high fecundity due to large litter size and frequent reproduction events [START_REF] Capellini | The role of life history traits in mammalian invasion success[END_REF], broad diet [START_REF] Jeschke | Determinants of vertebrate invasion success in Europe and North America[END_REF], good dispersal abilities [START_REF] Hulme | Grasping at the routes of biological invasions: A framework for integrating pathways into policy[END_REF]) and high plasticity allowing them to tolerate environmental variations and establish in new habitats [START_REF] Rosecchi | Can life-history traits predict the fate of introduced species? A case study on two cyprinid fish in southern France[END_REF]). These traits are the most commonly identified ones that help species to reach locally abundant densities, but also to increase their distribution range.

Moreover, during the invasion process, in addition to phenotypic plasticity, species may display significant evolutionary changes that favor their adaptation to newly colonized habitats [START_REF] Shine | Invasive species as drivers of evolutionary change: Cane toads in tropical Australia[END_REF]. Other species-specific factors can influence both life history traits and evolutionary changes, particularly the mating system. Indeed, mating system can affect genetic diversity, which influences the rate of occurrence of evolutionary changes, and fecundity. Many studies addressed these topic in plants [START_REF] Sun | Mating system of yellow starthistle (Centaurea solstitialis), a successful colonizer in North America[END_REF][START_REF] Rambuda | Breeding systems of invasive alien plants in South Africa: Does Baker's rule apply?[END_REF]Barrett et al. 2008), probably due to the wide range of mating systems existing in plants. However, studies in animals remain scarce, especially mammals, although mating system is known to influence their demography [START_REF] Holman | The consequences of polyandry for population viability, extinction risk and conservation[END_REF].

Monogamy, polygamy, multiple paternity

Across species, a wide range of behaviors exists to find a mating partner and access to reproduction. These behavioral strategies displayed by individuals of a species to obtain mates define its mating system (sensu [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF]. It includes the number of mates of an individual, the way it acquires mating, the social interactions between the pair of individuals and the parental cares. Several classifications were proposed over time depending on the ability to monopolize mates directly or indirectly by protecting ressource [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF], on the social bonds between partners [START_REF] Davies | Mating systems[END_REF], on the number of mates [START_REF] Shuster | Is hunting an effective tool to control overabundant deer? A test using an experimental approach[END_REF], or a combination of several of these parameters [START_REF] Clutton-Brock | Mammalian Mating Systems[END_REF][START_REF] Shuster | Is hunting an effective tool to control overabundant deer? A test using an experimental approach[END_REF]. [START_REF] Shuster | Is hunting an effective tool to control overabundant deer? A test using an experimental approach[END_REF] identified 12 major groups themselves divided in a total of 42 subcategories, in order to describe precisely each mating system. If this allows a fine description of the mating system of a species based on its social and behavioral characteristics, it does not influence the outcomes of the reproduction. Hereafter, for a matter of clarity, we will only consider mating systems based on the number of mates (Box 1). Indeed, whether a male mates with several females because he was able to monopolize a group of females, a territory including several female territories or because he was the most successful male in a lek, he still reproduces with several females and the variance in number of mating partners is higher between males than if each male reproduce with one female (variance of 0) or if all males reproduce with all females (Figure I 1).

It is interesting to highlight that these classifications are mostly based on behavioral observations. With the rise of genetic studies, due to lower costs of molecular techniques, this classification became subject of debate. Initially, more than 90% of bird species were considered to be monogamous (strictly, i.e. lifelong paring of two individuals, or sequentially) as couple were observed to provide biparental cares to their offspring [START_REF] Lack | Ecological adaptations for breeding in birds[END_REF]). However, in the end of the last century, evidences of extra-pair copulations started to undermine this conclusion [START_REF] Birkhead | Sperm competition in birds[END_REF]. In their review, [START_REF] Griffith | Extra pair paternity in birds: A review of interspecific variation and adaptive function[END_REF] showed that monogamy occurs in 14% of the species and only 25% of species previously considered monogamous.

They obtain the diametrically opposed conclusion of [START_REF] Lack | Ecological adaptations for breeding in birds[END_REF] that monogamy is more the exception than the rule. Similarly, mammal species were described as mainly polygynous but genetic analyses tend to show that the reproductive processes are more complicated [START_REF] Clutton-Brock | Mammalian Mating Systems[END_REF][START_REF] Soulsbury | Genetic patterns of paternity and testes size in mammals[END_REF]. Low ranking males also access to reproduction and observed mating behavior can be a poor predictor of male reproductive success [START_REF] Coltman | Male reproductive success in a promiscuous mammal: behavioural estimates compared with genetic paternity[END_REF][START_REF] Hoelzel | Alpha-male paternity in elephant seals[END_REF]. This lead to distinguish between social mating system (the mating system identified by behavioral studies) and genetic mating system which corresponds to the measured number of partners based on successful mating producing offspring. Each mating system, social or genetic, depends on ecological parameters depending on species-specific traits and on the environment.

Initially, it was accepted that reproductive success increases more for males than for females with the number of mating partners [START_REF] Bateman | Intra-sexual selection in Drosophila[END_REF]. From males point of view, monogamy was puzzling and questioned male advantages to mate with only one female. Latter, [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF] stated that monogamy occurs if mating partners are not able to monopolize any other individuals of the opposite sex. This is the case when (i) individuals are very dispersed in space due to large territories and/or resource scattered in the environment (no ecological potential for polygamy) or (ii) because life history traits of the species prevent the acquisition of additional mating despite environmental potential (biological constraints for polygyny). The later depends on traits such as the synchrony of estrus in females or biparental care requirement for the offspring. Indeed, many birds, reproducing in large colonies (ecological potential for polygamy or promiscuity) and producing only one offspring (monotocous) like greater flamingo (Phoenicopterus roseus) or northern garnet (Morus bassanus), display social monogamy. Often, if not always, long biparental cares are required to raise the brood (species-specific constraints) and the desertion of a parent would reduce the probability of successful reproduction [START_REF] Bart | Importance of monogamous male birds in determining reproductive success -Evidence for house wrens and a review of male-removal studies[END_REF]. Thus, losing the brood due to desertion of a parent would be costly considering the time and energy invested to find a mate and reproduce, except if the defecting parent did not sire the brood [START_REF] Hamilton | The genetical evolution of social behaviour[END_REF][START_REF] Trivers | Parental investment and sexual selection[END_REF]. Consequently, biparental cares are maintained in species where the risk of cuckoldry is low [START_REF] Griffin | Why do cuckolded males provide paternal care?[END_REF]. Overall, fitness of parents is increased if the couple stays together to raise their brood.

Box 1: Classification of mating systems based on number of mates, synthetized from [START_REF] Davies | Mating systems[END_REF] and [START_REF] Shuster | Is hunting an effective tool to control overabundant deer? A test using an experimental approach[END_REF].

Monogamy: Each sex mates with a single partner for life. When partner changes between reproductive events, this is called serial monogamy or sequential polygamy.

Polygamy: Males and/or females mate with varying number of partners divided in three main types:

-Polygyny: Females mate permanently with a single male, males mate with varying number of females.

-Polyandry: Males mate permanently with a single female, females mate with varying number of males.

-Polygynandry * : Males mate exclusively with several females and vice versa.

Promiscuity * : Males and females mate with any females and any males respectively without any pair bond (random mating).

*Both polygynandry and promiscuity define multiple-partner mating in both sexes, however the notion of social bond is implied in polygynandry (higher probability of mating with some individuals than others). It is not the case for promiscuity where mating is all individuals have the same probability to mate with any individuals of the other sex).

Figure I 1 Means and variances of fitness of polygamous, promiscuous and monogamous males assuming that the mean litter size is five. Mean fitness is five for females in all cases (from [START_REF] Wolff | Promiscuous females protect their offspring[END_REF]).

Among other traits, mammals are characterized by mammary glands, developed in females, producing milk to feed their young. The high proportion of mammal species displaying polygynous mating system (around 90%, see Clutton-Brock 1989) was explained by the fact that parental cares can be assumed by females alone. As male are relieved from paternal cares, their reproductive success will mainly depend on the number of females they will reproduce with. This lead to high competition between males to access reproduction and thus increased of sexual selection [START_REF] Wade | Sexual selection and variance in reproductive success[END_REF]. This is especially true if operational sex-ratio (relative proportion of males to females available for mating during a breeding event [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF]) is balanced or biased toward females. Males that are able to monopolize females and reproduce obtain high reproductive success (Figure I 1), while other males who do not reproduce at all obtain a null reproductive success [START_REF] Wade | Sexual selection: harem size and the variance in male reproductive success[END_REF]. This is why social polygyny is associated with a high variance in male reproductive success and a lower one for female, as all females can be fertilized by few males. Indeed virtually, only one male produces enough spermatozoids to fertilize all available females. However, as observed by [START_REF] Clutton-Brock | Mammalian Mating Systems[END_REF] mating systems are not as fixed as their definitions suggest and several strategies tend to coexist, which was later confirmed by genetic analyses. Reproductive processes are influenced by individual decisions that may change with time [START_REF] Gowaty | Reproductive decisions under ecological constraints: It's about time[END_REF]. That is why, despite their attempt to monopolize females, dominant males do not necessarily sire all offspring of all females he mated with because females may mate with several males [START_REF] Coltman | Male reproductive success in a promiscuous mammal: behavioural estimates compared with genetic paternity[END_REF][START_REF] Heckel | Extra-harem paternity in the white-lined bat Saccopteryx bilineata (Emballonuridae)[END_REF][START_REF] Hoelzel | Alpha-male paternity in elephant seals[END_REF].

Independently of the mating system, when females of polytocous species (species producing more than one offspring at a reproductive event) mate with several males, they can produce litters/broods sired by more than one male. This is true only if spermatozoids from several males lead to successful fecundation. The occurrence of such litters is multiple paternity, and by definition, it does not exist in monotocous species as one offspring can only have one father. We will not consider sequential polygamy of monotocous species as multiple paternity. Progenies produced over the lifetime of monotocous females include half-siblings (sibling with the same mother and different fathers) and, sometimes, some full-siblings (same mother and same father) but there is only one father per reproductive event. Also, by definition, multiple paternity should not occur in monogamous and polygynous species as females mate with only one male. On the other hand, females from polytocous species displaying social polyandry mating systems should mainly produce multiple sired litters/broods (considering all mating produce at least one offspring). It is now clear that mating system are more complex than their definitions. When multiple paternity occurs in monogamous species, it is often referred as extra-pair paternity (but for monogamous monotocous species, it also includes offspring sired by a male which is not the social mate). It is noteworthy that when considering social polygyny strictly, in theory all offspring produced by all females monopolized by a single male are half-siblings (same father, different mothers). Offspring produced by females monopolized by other males are not siblings. When multiple paternity occurs or in polyandrous and promiscuous species, the half-sibling relationships get more complicated as offspring from different females can share the same father and offspring from a male can be found in different females while some offspring are full-siblings. As one male can sire the whole offspring of a female for a breeding event, multiple paternity was subject of numerous studies to understand why this observation is so widespread in animals [START_REF] Griffith | Extra pair paternity in birds: A review of interspecific variation and adaptive function[END_REF][START_REF] Uller | Multiple paternity in reptiles: patterns and processes[END_REF][START_REF] Eccard | Effects of brood size on multiple-paternity rates: a case for 'paternity share' as an offspring-based estimate[END_REF]. The following parts will focus on explaining why and what are the consequences of multiple paternity in mammals.

Proximal causes of multiple paternity

The trivial answer to the question 'Why does multiple paternity exist?' would be 'because some females mate with several males'. While this answers the question, it does not give any insight to understand this observation. Thus, investigating the causes of multiple paternity is equivalent to understanding why females engage in multi-male mating. Indeed, this behavior is thought to be costly for females due to energetic losses and increased risks of contracting sexually and non-sexually transmitted diseases due to increased contact with conspecifics [START_REF] Parker | Polyandry: the history of a revolution[END_REF]. However, on a meta-analysis including 48 species, [START_REF] Lemaître | Polyandry has no detectable mortality cost in female mammals[END_REF] showed that multi-male mating has no cost on female mortality, acknowledging the fact that such study does not allow to detect if costs in some species are offset by benefits in others.

Over the years, several causes for multi-male mating were identified and review studies attached to detail them [START_REF] Wolff | Promiscuous females protect their offspring[END_REF][START_REF] Parker | Polyandry: the history of a revolution[END_REF]. [START_REF] Darwin | The descent of man and selection in relation to sex[END_REF] already noted that males are more eager to mate than females and, especially in mammals, they pursue them to do so. This behavior was later described as sexual coercion and mainly occurs when females are not guarded by males. Females engage in mating with several males because resisting sexual harassment is energetically costly. This strategy is referred as convenience polyandry. Several studies showed that females are lead to exhaustion by males chasing them or are directly injured by males attempting to mate [START_REF] Garshelis | Social organization of sea otters in Prince William Sound, Alaska[END_REF][START_REF] Réale | Female-biased mortality induced by male sexual harassment in a feral sheep population[END_REF][START_REF] Endo | Multiple copulations and post-copulatory guarding in a free-living population of sika deer (Cervus nippon)[END_REF]. When female mammals do not protect themselves, they may still engage in multi-male mating to protect their offspring [START_REF] Klemme | Polyandry enhances offspring survival in an infanticidal species[END_REF]. Indeed, infanticide is widespread in mammals [START_REF] Hrdy | Infanticide among animals: a review, classification, and examination of the implications for the reproductive strategies of females[END_REF]. There are several advantages for males to kill unrelated offspring, including, but non-exhaustingly, that cannibalism can provide food resources for the perpetrator, decreases competition for its own offspring (reduction of maternal allocation to offspring from another male or their absence also mean more resources for its offspring when weaned), and also because lactation is often associated with anestrus [START_REF] Trivers | Parental investment and sexual selection[END_REF][START_REF] Hrdy | Infanticide among animals: a review, classification, and examination of the implications for the reproductive strategies of females[END_REF]). Thus, the death of its offspring may lead the female to be receptive again for mating. As killing its own offspring induces great costs for a male (waste of time and energy allocated to reproduction for example), female may solicit several males to mate with them in order to create an uncertainty of paternity. In several species, females were observed to mate while already pregnant confirming that the behavior is adaptive to prevent infanticide, but obviously, this will not induce multiple paternity [START_REF] Van Noordwijk | Reproductive patterns in eutherian mammals: adaptations against infanticide?[END_REF].

However, multiple paternity may appear when this behavior is expressed during estrus. Female may also mate with multiple males in order to secure their own reproductive success. Indeed, males may be sterile due to genetic defect [START_REF] Wu | Haldane's rule and its legacy: why are there so many sterile males?[END_REF], but they may also suffer from sperm depletion if they mate with a lot of females in a short period of time, frequent when estrus are synchronized, or if the sex-ratio is strongly biased [START_REF] Preston | Dominant rams lose out by sperm depletion[END_REF][START_REF] Milner-Gulland | Reproductive collapse in saiga antelope harems[END_REF]. It is noteworthy that, for domestic animal husbandry, guidelines are set for the different species concerning semen collection for artificial insemination to maintain high fecundation rates [START_REF] Schilling | Frequency of semen collection in boars and quality of ejaculates as evaluated by the osmotic resistance of acrosomal membranes[END_REF][START_REF] Leboeuf | Production and storage of goat semen for artificial insemination[END_REF]. The time recommended between two sampling often exceed 24h proving that sperm quality is not optimal after few mating (e.g. maximum of 3 samplings a week for the pig, [START_REF] Frangež | Frequency of boar ejaculate collection and its influence on semen quality, pregnancy rate and litter size[END_REF]). Moreover, it was shown that males can modulate the quantity of sperm provided in their ejaculate, suggesting they could preserve themselves with a female in favor of another one [START_REF] Wedell | Sperm competition, male prudence and sperm-limited females[END_REF]. By mating with several males, females increase their chance to mate with at least one male able to guaranty the fecundation of all ovules. Marginally, multi-male mating can favor the offspring survival if it increases the number of males providing material benefits or paternal care, but both traits are rather rare among mammals [START_REF] Wolff | Promiscuous females protect their offspring[END_REF]. Moreover, and, as shown in birds, this may induce more costs due to desertion of the social father than benefits provided by other males. Finally, it was suggested that females mate with several males by chance, when they meet several males during their receptive period, if no cost is associated with multiple mating, resulting in random mating [START_REF] Sutherland | Chance can produce a sex difference in variance in mating success and explain Bateman's data[END_REF][START_REF] Hubbell | Environmental variance in lifetime mating success, mate choice, and sexual selection[END_REF]. [START_REF] Kokko | Multiple mating by females is a natural outcome of a null model of mate encounters[END_REF] also suggested it can be advantageous for females to mate with every males they meet if the probability of finding a mate is low. Indeed, in such ecological context, it would be very costly to refuse a mating opportunity and die virgin, so multi-male mating could be favored.

Evolutionary consequences of multiple paternity

Independently of its causes, multiple paternity is not neutral and may be the source of evolutionary changes in populations. By mating with several males and reducing the variance in their reproductive success, female allows greater contribution of males to the next generation.

Multiple paternity allows transmission of more genetic diversity from a generation to another than single-male mating [START_REF] Sugg | Effective population sizes with multiple paternity[END_REF][START_REF] Pearse | Multiple paternity increases effective population size[END_REF]. This is true at the population level, but it is also verified at individual scale. It is suggested that female engage in multi-male mating to increase the genetic diversity of their offspring, as it is often associated with fitness benefits [START_REF] Thonhauser | Does multiple paternity influence offspring disease resistance?[END_REF]). As female tend to reduce the variation of their reproductive success by increasing the variability of the offspring to maximize their fitness, this process is often referred as 'genetic bet-hedging' [START_REF] Fox | Bet-hedging and the evolution of multiple mating[END_REF][START_REF] Holman | Bet hedging via multiple mating: A meta-analysis[END_REF].

Multiple paternity may also increase female fitness in species where sperm competition occurs.

Male-male competition for reproduction is not over when they mate with a female. It goes on in female genital tract to fecund the ovule. The male with the sperm of better quality (concentration and velocity of spermatozoa) outcompetes males with lower sperm quality and has a higher reproductive success [START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF][START_REF] Malo | Antlers honestly advertise sperm production and quality[END_REF]. In species where multiple paternity is frequent, relative size of the testes is higher [START_REF] Soulsbury | Genetic patterns of paternity and testes size in mammals[END_REF], and increase of testes size is associated with higher production of sperm in order to maximize fecundation and the paternity share (the proportion of offspring produced by a male in a litter). The male winning the sperm competition should sire a larger proportion of the litter. Females can also influence the competition by removing sperm of less desirable male after mating to maximize the chance of being impregnated by favored males (female-female mating behavior are reported in the pig to expell ejaculate, see [START_REF] Aguilera-Reyes | Multiple mating and paternity determinations in domestic swine (Sus scrofa)[END_REF]. As females choose after copulation to bias paternity in favor of some preferred males, this strategy is often associated as 'good gene' effect on offspring fitness. Multiple paternity was also associated with increased litter size for females. Indeed, studies found that multiple sired litters tend to be larger than single-sired litters [START_REF] Hoogland | Why do female Gunnison's prairie dogs copulate with more than one male?[END_REF][START_REF] Stockley | Female multiple mating behaviour, early reproductive failure and litter size variation in mammals[END_REF]. This can be linked to multiple mating of female trying to overcome sperm depletion. Thus, multiple-male mating can influence life history traits of females and could be a factor enhancing population dynamic, in particular in invasive species.

Context of the study

The wild boar (Sus scrofa) raises serious concerns due to its proliferation in all countries where it is present. Also, it is an important game species which was initially hunted for meat consumption and it still represents an important food resource for some human communities [START_REF] Sales | Meat from wild boar (Sus scrofa L.): A review[END_REF]. In Europe, even if wild boar meat is still consumed, it is mainly a sport hunting species where big males are appreciated for their tusks used as trophy. Hunting bags from all European countries show clear positive evolution of the number of wild boars killed since 1980 (Figure I 2), with five years mean population growth rates above 1.40 over the study period [START_REF] Massei | Wild boar populations up, numbers of hunters down? A review of trends and implications for Europe[END_REF]. Only in France, from 35,893 wild boars shot in 1973, when the French Hunting and Wildlife Agency started recording wild boar hunting bags, the number increased progressively to the highest value ever recorded of 693,613 in 2016. Such demographic increase leads to important human-wildlife conflicts. The species can cause severe damages in a variety of agricultural crops such as maize, wheat, grapes and potatoes [START_REF] Schley | Diet of wild boar Sus scrofa in Western Europe, with particular reference to consumption of agricultural crops[END_REF]. Damage occur more frequently in cultivated fields located near forest [START_REF] Calenge | Efficiency of spreading maize in the garrigues to reduce wild boar (Sus scrofa) damage to Mediterranean vineyards[END_REF]) and may lead to important economic losses for farmers [START_REF] Pimentel | Update on the environmental and economic costs associated with alien-invasive species in the United States[END_REF][START_REF] Linkie | Patterns and perceptions of wildlife crop raiding in and around Kerinci Seblat National Park, Sumatra[END_REF][START_REF] Schley | Patterns of crop damage by wild boar (Sus scrofa) in Luxembourg over a 10-year period[END_REF]. Costs of compensation associated to damaged crops range from more than €500.000 for small countries such as Luxembourg or Slovenia to €32 million in France [START_REF] Massei | Wild boar populations up, numbers of hunters down? A review of trends and implications for Europe[END_REF]. Grassland are not spared. If rooting behavior displayed by wild boar foraging for underground food resources can have a positive effect on plant richness and diversity when moderate, it strongly reduced plant cover and alter soil properties when too intensive [START_REF] Massei | The environmental impact of wild boar[END_REF][START_REF] Barrios-Garcia | Impact of wild boar (Sus scrofa) in its introduced and native range: a review[END_REF][START_REF] Bueno | Occurrence and intensity of wild boar disturbances, effects on the physical and chemical soil properties of alpine grasslands[END_REF]. Increase in wild boar number also raises health concerns as high densities are associated with higher contact rates and disease transmission [START_REF] Rossi | Incidence and persistence of classical swine fever in free-ranging wild boar (Sus scrofa)[END_REF][START_REF] Acevedo | Estimation of European wild boar relative abundance and aggregation: a novel method in epidemiological risk assessment[END_REF]. Moreover, the species carries numerous diseases, as reservoir or as host, susceptible to be transmitted to other animal species, especially to pigs (leading once again to great economical losses for farmers) and then indirectly, or directly, to humans [START_REF] Rosvold | A review of viral diseases of the European wild boar: Effects of population dynamics and reservoir rôle[END_REF]. Indeed, wild boar-human contacts greatly increased over the last decades. Sightings of wild boars roaming in urban areas become more and more common, including in big cities like Berlin or Barcelona [START_REF] Cahill | Characteristics of wild boar (Sus scrofa) habituation to urban areas in the Collserola Natural Park (Barcelona) and comparison with other locations[END_REF][START_REF] Stillfried | Do cities represent sources, sinks or isolated islands for urban wild boar population structure?[END_REF]). As hunting is forbidden close to habitations, wild boars identify these protected areas and tend to concentrate locally [START_REF] Tolon | Responding to spatial and temporal variations in predation risk : space use of a game species in a changing landscape of fear[END_REF]). These concentrations of individuals often lead to conflicts when wild boars degrade private gardens and public parks while foraging for food or when they are responsible of collisions with vehicles, which may lead to people injury or death. Costs associated to these accidents are very high and were estimated to be on average more than €45 million per year in Spain and over €100 million in France [START_REF] Vignon | Collisions entre véhicules et ongulés sauvages : quel coût économique ? Une tentative d'évaluation[END_REF][START_REF] Sáenz-De-Santa-María | Wildlife-vehicle collisions in Spain[END_REF].

The ecological and economic impact of the high number of wild boar does not need to be demonstrated any further. It is noteworthy that all these disturbances lead to societal conflicts, mostly involving hunters. Farmers suffering from great economic losses blame hunters for inadequate hunting practices that aim to maintain high densities of games species. Hunters argue in response that damage would not occur if farmers manage their lands better by fencing their crops for example [START_REF] Storie | Wildlife management conflicts in rural communities: a casestudy of wild boar (Sus scrofa) management in Ērgļu Novads, Latvia[END_REF]. Debates also occur within society in a broader scale, especially in recently recolonized areas. They are nourished by news articles that often focus on the negative effects of wild boar, especially the danger it represents to humans when attacked [START_REF] Goulding | Press responses to the presence of free-living Wild Boar (Sus scrofa) in southern England[END_REF][START_REF] Van Herzele | Wildlife comeback in Flanders: tracing the fault lines and dynamics of public debate[END_REF]. Rare accidents may happen raising public concerns. Generally, hunters are accused of releasing farm animals not afraid of human and facilitating overpopulation to kill for pleasure, while conservationists denounce senseless behavior of people and proliferation of game species due to the lack of predators [START_REF] Van Herzele | Wildlife comeback in Flanders: tracing the fault lines and dynamics of public debate[END_REF]. Despite the critics, recreational hunting have been proven to, if not decrease, at least regulate wild boar population growth locally [START_REF] Geisser | Efficacy of hunting, feeding, and fencing to reduce crop damage by wild boars[END_REF][START_REF] Quirós-Fernández | Hunters serving the ecosystem: the contribution of recreational hunting to wild boar population control[END_REF], especially when harvesting is wisely planned, and slight increase of hunting effort targeting the most influential individuals can have significant demographic consequences [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF]). However, even high hunting mortality is not always enough and heavily hunted populations can still display positive growth rates [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]. Moreover, the number of hunters is decreasing and they are aging in most European countries and even with increased of wild boar harvested per capita, the wild boar population keeps growing [START_REF] Massei | Wild boar populations up, numbers of hunters down? A review of trends and implications for Europe[END_REF]. Altogether, the disturbances raise the wild boar as an ecological, economic and societal problematic species.

Reasons for wild boar proliferation have already been investigated and some were identified explaining this demography. First of all, wild boar is peculiar among ungulates. It has the highest reproductive potential of them all, together with a rather low natural adult mortality [START_REF] Massei | Diet, food availability and reproduction of wild boar in a Mediterranean coastal area[END_REF][START_REF] Bieber | Population dynamics in wild boar Sus scrofa : ecology, elasticity of growth rate and implications for the management of pulsed resource consumers[END_REF][START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF][START_REF] Keuling | Mortality rates of wild boar Sus scrofa L. in central Europe[END_REF]. [START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF] also showed that wild boar adapts to high hunting pressure by advancing their reproduction allowing progeny to reproduce at one year of age. Moreover, mild winters allow to maintain better body condition leading to increased winter survival in adults. With climate change, mild winters tend to be more frequent making the environment more favorable for the species [START_REF] Jedrzejewski | Wolf predation and snow cover as mortality factors in the ungulate community of the Białowieża National Park, Poland[END_REF][START_REF] Vetter | What is a mild winter? Regional differences in within-species responses to climate change[END_REF]. Survival and reproduction are also favored by change in agricultural practices, improving food resources availability, and rural desertion, reducing human disturbances [START_REF] Sáez-Royuela | The increased population of the wild boar (Sus scrofa L .) in Europe[END_REF][START_REF] Schley | Diet of wild boar Sus scrofa in Western Europe, with particular reference to consumption of agricultural crops[END_REF][START_REF] Massei | The environmental impact of wild boar[END_REF]. Also, female fertility is increased for hybrids where hybridization with the domestic pig occurs, as pig selected traits genes are introduced in wild boar (Fulgione et al. 2016). To face such an adaptable species, improving management strategies is of great importance. As explained before, the first step to good management strategies is good knowledge of the focus species.

Aim of the thesis

The European wild boar is hunted all over its distribution range but its demography does not seem influenced despite locally high hunting efforts. Hunting is known to induce great changes on structure and genetic characteristics of populations [START_REF] Harris | Genetic consequences of hunting: what do we know and what should we do?[END_REF][START_REF] Allendorf | Human-induced evolution caused by unnatural selection through harvest of wild animals[END_REF]. Understanding how wild boar reacts and adapts to the high hunting pressure is of prime interest. In this species, the hunting targets mostly big males for their trophies. Males grow overdeveloped canines all along their life, so oldest males have the longest teeth and are the most favored individuals of hunters (Kierdorf et al. 2004). In heavily hunted populations, such males can be rare because, firstly, intensive hunting leads to reduced survival and very few males reach old age, and, secondly the few individuals reaching old age are easily recognized and preferentially harvested. During my thesis, I investigated if the removal of such males by hunting disrupts the polygynous mating system. As big males are removed from the populations, female monopolization should decrease and their number of mating partners increase, reducing variance in male reproductive success as the mating systems tend toward promiscuity (Figure I 1).

To measure how removal of males from the population influences reproductive processes and to understand how reproduction is shared among remaining males, the study was realized at two different scales. Firstly, a large scale where I compared five populations of wild boars contrasting mostly in their hunting pressure. The contribution of males to reproduction was estimated from proportions of litters sired by more than one male (multiple paternity rates) and from number of fathers within litters (Chapter IIIA). Secondly, at a narrower scale, as longitudinal study is not possible in all populations, I focused on one of them which was already monitored for several years. This allowed me to evaluate between year variations of the contribution of males to reproduction and to include in the analysis other factors, especially yearly variations of resources availability (Chapter IIIB). Proportions of big males in hunting bag were also registered as it is inversely linked to the number of big males remaining in the population. I expected that mating system disruption should increase with the intensity of hunting and the proportion of big males killed at hunting. Thus, I predicted higher multiple paternity rates and number of fathers within a litter in the most heavily hunted populations and/or years. Concerning the influence of resources on the mating systems, I expected that years of high resource availability would favor female monopolization by males as female groups are more concentrated. As part of my work, I also tried to identify the consequences of the increase of number of sires on life history traits of the species. As explained before, multiple paternity is known to be a female strategy to increase their fecundity and to produce more diverse genetically, and thus, phenotypically offspring (genetic bet-hedging). These hypotheses were tested by measuring the relation between the number of fathers and the number of fetuses within a litter (Chapter IVA) and their phenotypic variations (Chapter IVB). Finally, as fathers of the fetuses are known from previous analyses, I also investigated if their genetic characteristics and body mass were linked to their mating success and reproductive success (number of partners and number of offspring respectively, Chapter V). Biggest males are the most competitive and should be the most able to monopolize females and father high number of offspring. Also, males displaying higher genetic diversity and higher differentiation from the mother, allow females to diversify their litters increasing the fitness of their offspring. They should be favored in detriment of males with lower genetic diversity. Thus, both the number of partners and offspring should increase with male body weight and individual heterozygosity.

Chapter II

Material and methods

In this chapter, I will present information that are common to the following chapters. I start by the general presentation of the wild boar species, including its classification, distribution and biology. Then, I give a description of the study sites with some details about the monitoring realized as part of the data collection for my thesis in the different wild boar populations. I finish with information about the genetic markers used in this study and the number of genotyped individuals. The genetic and statistical analyses description will be provided in each corresponding chapters.

Wild boar

Classification

The wild boar (Sus scrofa) belong to the Suidae family which is part of the order Cetartiodactyla (Figure II 1). The species includes 16 wild subspecies recognized by the world conservation union IUCN, distinguished by geographical and morphological characteristics [START_REF] Oliver | Sus scrofa. IUCN Red List Threat[END_REF][START_REF] Keuling | Eurasian wild boar Sus scrofa[END_REF]. They are divided in four main groups (Table II 1).

The domestic pig can also be added because it is the domestic subspecies (Sus scrofa domesticus). Surprisingly, the number of chromosomes varies in the species, from 2n=36 in Europe to 2n=38 in central Europe, Asia and in the pig (Fang et al. 2006). Despite the variation in chromosome number, hybridization between the different subspecies is possible and offspring are viable and fertile. and is now recovering [START_REF] Booth | Wild boar farming in the united kingdom[END_REF][START_REF] Rosvold | A review of viral diseases of the European wild boar: Effects of population dynamics and reservoir rôle[END_REF]. Similarly, over the last centuries, it colonized all other continents due to intentional introduction by human and/or escape from farms (Figure II 2), whether it was with the classic wild form (S. scrofa scrofa), the domestic pigs (S. s. domesticus) that form feral population or hybrid swarm of those two, like in Australia and USA [START_REF] Gabor | Demography, sociospatial behaviour and genetics of feral pigs (Sus scrofa) in a semi-arid environment[END_REF][START_REF] Dexter | The influence of pasture distribution, and temperature on adult body wieght of feral pigs in a semi-arid environment[END_REF]. It was able to adapt to a wide variety of habitats and climates starting from temperate forests, to latter colonized areas ranging from semi-arid taiga to tropical forests [START_REF] O'brien | Crouching tigers, hidden prey: Sumatran tiger and prey populations in a tropical forest landscape[END_REF][START_REF] Barrios-Garcia | Impact of wild boar (Sus scrofa) in its introduced and native range: a review[END_REF][START_REF] Bengsen | Impacts and management of wild pigs Sus scrofa in australia[END_REF]. This shows the great plasticity of the species.

Biology

The wild boar is a medium size and sexually dimorphic ungulate. The body weight ranges from 35 to 350 kg for biggest subspecies and a height varying between 55 et 110 cm, but high variations exist depending of the environment [START_REF] Spitz | Variation in body mass of wild boars from southern France[END_REF][START_REF] Powell | Pigs (Suidae)[END_REF]. In the population of Châteauvillain, wild boar mean adult weight is 72 ± 11 kg for females and 102 ±16 kg for males [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]. It can live up to 10 years but its life expectancy is often greatly reduced by hunting [START_REF] Jezierski | Longevity and mortality rate in a population of wild boar[END_REF][START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]. The structures of wild boar populations reported in the literature often show high proportions of young individuals as hunting occurs everywhere, with few or complete absence of old individuals (Fernández-llario and Mateosquesada 2003;[START_REF] Herrero | Reproductive and demographic parameters in two Iberian wild boar Sus scrofa populations[END_REF]. The mortality during the first months of life can be high leading to relatively low juvenile survival [START_REF] Náhlik | Birth rate and offspring survival in a free-ranging wild boar Sus scrofa population[END_REF][START_REF] Bieber | Population dynamics in wild boar Sus scrofa : ecology, elasticity of growth rate and implications for the management of pulsed resource consumers[END_REF].

Except hunting, the main causes of wild boar mortality are vehicle collisions, disease, starvation, especially where snow cover limits foraging in winter, and finally predation by wolves where they co-occur [START_REF] Jedrzejewski | Wolf predation and snow cover as mortality factors in the ungulate community of the Białowieża National Park, Poland[END_REF][START_REF] Okarma | The roles of predation, snow cover, acorn crop, and man-related factors on ungulate mortality in Białowieża Primeval Forest, Poland[END_REF].

The wild boar is not a territorial species, but females are philopatric. They live in small matriarchal groups of close relatives with their piglets and/or yearlings [START_REF] Dardaillon | Wild boar social groupings and seasonal changes in the Camargue, southern France[END_REF][START_REF] Kaminski | Life-history patterns in female wild boars (Sus scrofa): mother-daughter postweaning associations[END_REF][START_REF] Podgórski | Next of kin next door -philopatry and socio-genetic population structure in wild boar[END_REF]. The composition of the group can change throughout the year especially during the breeding season, when male wild boars usually solitary join female groups for mating [START_REF] Mauget | Régulation écologiques, comportementales et physiologiques (fonction de reproduction) de l'adaptation du sanglier[END_REF]. The size of home range of an individual or group varies depending of the resource in the forest, the time of the year and hunting. Its size ranges from few dozen hectares to few thousands [START_REF] Maillard | Effects of shooting with hounds on size of resting range of wild boar (Sus scrofa L.) groups in mediterranean habitat[END_REF][START_REF] Massei | Factors influencing home range and activity of wild boar (Sus scrofa) in a Mediterranean coastal area[END_REF]Keuling et al. 2008a). The home range is wider during hunting period which also often corresponds to the mating period of the species. Females tend to remain in, or close to, the group where they are born while males have a higher probability of dispersing. Moreover, when they disperse, males disperse on average further than females (mean of 3.8km versus 1.6km, [START_REF] Keuling | Hunter feedback of individually marked wild boar Sus scrofa L.: Dispersal and efficiency of hunting in northeastern Germany[END_REF]. It is mainly a nocturnal species, with highest activity around sunset, but as for its home range, its behavior may change depending on factors such as the time of year and the hunting pressure [START_REF] Russo | Daily home range and activity of wild boar in a mediterranean area free from hunting[END_REF][START_REF] Powell | Pigs (Suidae)[END_REF]Keuling et al. 2008b).

Diet

The wild boar is omnivore. It is an opportunistic feeder which includes a wide variety of food in its diet depending of available resources in its environment and in time (Figure II 3).

This eases its establishment and colonization of new habitats. Vegetable matters are the most important part of its diet, with great proportion of acorn and beechnut during years of high production [START_REF] Schley | Diet of wild boar Sus scrofa in Western Europe, with particular reference to consumption of agricultural crops[END_REF]. Maize can also represent a significant part of the alimentation as it is often used for supplementary feeding to maintain wild boars in the forest when forest fruit production is low, thus protecting crops [START_REF] Calenge | Efficiency of spreading maize in the garrigues to reduce wild boar (Sus scrofa) damage to Mediterranean vineyards[END_REF]). Food from animal origin is also consumed such as earthworms, eggs, small animals (rodents, birds, amphibian, etc…). Wild boar can also scavenge on bigger carcasses, including conspecific carcasses, and also, predatory behaviors on fawns of wild ungulates and livestock have been reported [START_REF] Ballari | A review of wild boar Sus scrofa diet and factors affecting food selection in native and introduced ranges[END_REF]. Around cities, it was also observed to forage on garbage and food for pets [START_REF] Cahill | Characteristics of wild boar (Sus scrofa) habituation to urban areas in the Collserola Natural Park (Barcelona) and comparison with other locations[END_REF]. The wild boar shows great plasticity concerning its diet which allowed it to settle in very different environments as explained above. From continental forests with high food availability, it also adapts to environments like Mediterranean forests where oaks are scarce, leading to very low forest fruits availability [START_REF] Massei | Diet, food availability and reproduction of wild boar in a Mediterranean coastal area[END_REF].

It is noteworthy that the main influential food items remains forest fruits in forest habitat [START_REF] Geisser | The influence of food and temperature on population density of wild boar Sus scrofa in the Thurgau (Switzerland)[END_REF] and pulsed productions of acorn and beechnut influence reproductive outputs of females [START_REF] Gamelon | Reproductive allocation in pulsed-resource environments : a comparative study in two populations of wild boar[END_REF]. Also, breeding strategy changes between the two populations studied and depends on the kind of forest fruits produced, highlighting again the great plasticity of the species.

Figure II 3 Proportions of food items in the autumn-winter (rutting period) wild boar diet from various habitats (adapted from [START_REF] Keuling | Eurasian wild boar Sus scrofa[END_REF].

Reproduction

As suggested by the sexual dimorphism, the mating system of the wild boar is polygynous, with males competing to monopolize a group of females showing synchronized estrous cycle [START_REF] Graves | Behavior and ecology of wild and feral swine (Sus Scrofa)[END_REF][START_REF] Delcroix | Existence of synchronization of reproduction at the level of the social group of the European wild boar (Sus scrofa)[END_REF]). Males are sexually mature and start producing sperm at 7 months but usually do not access reproduction before 3 years while females can start reproduce around one year of age when they reach about 37% of their adult body mass [START_REF] Mauget | Seasonal changes in testis weight and testosterone concentration in the european wild boar (Sus scrofa L.)[END_REF][START_REF] Servanty | Pulsed resources and climate-induced variation in the reproductive traits of wild boar under high hunting pressure[END_REF]. Also, the species adapts to the hunting with females starting to reproduce earlier in life when the hunting pressure is high [START_REF] Herrero | Reproductive and demographic parameters in two Iberian wild boar Sus scrofa populations[END_REF][START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF]. The rutting period spreads from October to January with a pic around mid-December [START_REF] Kozdrowski | The effect of season on the properties of wild boar (Sus scrofa L.) semen[END_REF]. Farrowing occurs 115 days after mating (3 months, 3 weeks, 3 days), in a nest constructed by the female [START_REF] Baubet | Tagging piglets at the farrowing nest in the wild : some preliminary guidelines[END_REF], so a birth pic generally occurs around mid-April. The number of piglets produced per female averages 5 but it also depends on the mother age, its body weight and the population [START_REF] Bieber | Population dynamics in wild boar Sus scrofa : ecology, elasticity of growth rate and implications for the management of pulsed resource consumers[END_REF][START_REF] Servanty | Litter size and fetal sex ratio adjustment in a highly polytocous species: the wild boar[END_REF][START_REF] Bywater | Litter size and latitude in a large mammal: The wild boar Sus scrofa[END_REF]Gamelon et al. 2013b). Neonatal phase is poorly known (survival, stillbirth) because disturbances can induce a desertion of the litter by the mother [START_REF] Baubet | Tagging piglets at the farrowing nest in the wild : some preliminary guidelines[END_REF]. Between 2 weeks and 6 months piglets grow fast (around 100g/day), without difference of growth rate between males and females [START_REF] Gaillard | Sex differentiation in postnatal growth rate: a test in a wild boar population[END_REF].

They are weaned at 4 months old but females remain in the group while males leave at 14 months of age [START_REF] Jensen | When to wean -Observations from free-ranging domestic pigs[END_REF][START_REF] Kaminski | Life-history patterns in female wild boars (Sus scrofa): mother-daughter postweaning associations[END_REF].

Data collection

Châteauvillain-Arc-en-Barrois

The main wild boar population of the study is from the 11,000ha The mean monthly temperature ranged from 1.9 ± 2.1°C in January to 18.9 ± 1.8°C in July (Météo France) while the average monthly precipitation was 75.1 ± 37.5mm over the study period (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016). The forest is mainly composed of oak (Quercus petraea, 41%) and beech (Fagus sylvatica, 30%) and surrounded by agricultural fields. Acorn and beechnut production fluctuates greatly among years, with a year of very high production followed by several years of low production [START_REF] Liebhold | Within-population spatial synchrony in mast seeding of North American oaks[END_REF]). Wild boars favored these food resources when available, but they can also cause severe crop damages, especially years of low production. To maintain wild boar in the forest and avoid agricultural damages, hunters spread maize in the forest as supplementary food resource. Also, most part of the forest is surrounded by electric fences to prevent wild boars from going in surrounding crop fields. Fences are also used around the corn crop close to the forest. Obtaining precise estimations of wild boar density in a population remains a challenge [START_REF] Engeman | Monitoring wild pig populations: A review of methods[END_REF] and no data was available for most of the populations. The main criteria used to get a proxy of population density remains hunting bag [START_REF] Maillard | Ungulates and their management in France[END_REF].

Considering the number of wild boars killed per unit of space, the highest densities are found

Sampling

Wild boars are hunted in each of these study sites between October and February with variations according to the year and the study sites. In Châteauvillain, hunting events are very frequent as they take place every week-end during this period. [START_REF] Baubet | Valeur de l'examen de la denture pour la détermination de l'âge chez le sanglier (Sus scrofa)[END_REF]) are recorded. Stomach contents are sampled for diet analysis (see [START_REF] Baubet | Diet of the wild boar in the french Alps[END_REF] for details). For each female, genital tract and ovaries are observed to assess her reproductive status. When she is pregnant, fetuses are removed from the uterus to be weighed and measured. A piece of the ear of the mother and of each fetus (or the whole fetus, depending on its size) of the litter are sampled and stored in alcohol in an individual tube. Some males were also sampled for paternity analysis (usually heavier than 50kg, and mostly over 70kg in Chambord). Some non-reproductive adult females were also sampled for another study (see Table II 5). They were included in analysis for population estimation of genetic parameters (Table II 2,Table II 5). Overall, around 6000 individuals were sampled all populations and all years combined (Table II 2).

Presentation of the set of microsatellites

An initial set of 13 microsatellites markers was used in this study but the marker S0386

was removed due to a lot of individuals displaying amplification failure (Table II 3). Ten out of these twelve markers were chosen from a larger set of 27 markers initially designed for pig (Sus scrofa domesticus), which is the domestic sub-species of the wild boar. This initial set was developed by a working group of the Food and Agriculture Organization of the United Nations (ISAG/FAO Standing Committee 2004). The aim was to develop species specific markers allowing to measure the genetic diversity within domestic animal. The markers were chosen from previous studies with strict characteristics. They needed to be identified in mapping studies to avoid linked markers (at least separate by more than 35cM when not possible), exhibit

Mendelian inheritance, and be high quality marker (low allelic dropout, low mismatch rate).

The last two markers (SW2021 and SW2496) were also selected from pig diversity analysis studies [START_REF] Vernesi | The genetic impact of demographic decline and reintroduction in the wild boar (Sus scrofa) : A microsatellite analysis[END_REF]. Finally, an additional marker, AMEL, was used for sex determination [START_REF] Fontanesi | Differences of the porcine amelogenin X and Y chromosome genes (AMELX and AMELY) and their application for sex determination in pigs[END_REF], especially important for small fetuses where genital organs are not visible to the naked eye. More details about all markers are available on the following website that records genetic map and markers for the pig http://www.thearkdb.org/arkdb/.

Table II 3 Microsatellite markers information used for paternity study of the five wild boar populations including the name of the locus, its chromosome location, the sequences for the primers used for amplification and expected and observed size in our sample. The set of markers shows high variation of allele number (minA=6.17 ± 4.11 in Belval, maxA = 12.08 ± 8.07 in Châteauvillain) and genetic diversity (ranging from 0.58 in Chambord and La Petite Pierre to 0.61 in Châteauvillain) in all studied populations (Table II 4). Variation in allele number is important for paternity analysis. For example, some rare alleles can improve assignment of an offspring to its father if this allele is present in both individuals and high genetic diversity allows to distinguish individual from one another. In highly inbred populations, a lot of individuals may share the same genotype (combination of allele for loci studied). No population showed deviation from Hardy-Weinberg equilibrium (tested on adults for each hunting seasons and each populations) allowing to perform analysis with most genetic software (lack of deviation from Hardy-Weinberg equilibrium is a hypothesis to perform the statistical analysis). Estimated using GenALEx (Peakall andSmouse 2006, 2012), probabilities of identity (PID, the probability that two random individuals have exactly the same genotype)

were very low in all populations (the highest value being 8,1×10 -10 in Chambord) suggesting analyzing the genotype allows to discriminate one individuals from one the other beyond any doubt. Also, probabilities of identity for siblings (PIDsib, the probability that two sibling individuals have exactly the same genotype) were low. These values fit recommendations from literature that suggest value of below 0.0001 for wildlife forensic cases [START_REF] Waits | Estimating the probability of identity among genotypes in natural populations: cautions and guidelines[END_REF].

Also, they are similar to values of another study of parentage in wild boar [START_REF] Costa | Microsatellite markers for identification and parentage analysis in the European wild boar (Sus scrofa)[END_REF].

Altogether, results for this set of markers allow to be confident for the paternity analysis.

Moreover, as fetuses were sampled from pregnant mothers, mother-offspring relationships are known (except when sampling mistake occurs but they are easily detected). Including this information with certainty allows to greatly improve paternity analysis (Jones et al. 2010). Also, the comparison of genotype of mothers against their whole litter showed that genotyping errors are rare according to the marker selection (except when sampling mistake occurred highlighted by genotype incompatibility between the mother and all fetuses).

Table II 4 Number of individuals included (N), mean ± sd of number of alleles (A), allelic richness (Ar, calculated on 1000 subsampling of 96 individuals, based on minimum number of individuals in a population, found for Belval), observed (Ho) and expected heterozygosity (He) and differentiation index (Fis), difference from Hardy-Weinberg equilibrium (HW, NS for nonsignificant) tested with Fstat, probability of identity of random individuals (PID) and identity between full sibling (PIDsib) from Genalex, across the 12 microsatellite loci, calculated using adult individuals, for the five populations of wild boar.

Châteauvillain

Characterization of mating system in five wild boar populations subject to varying hunting pressure

Abstract: Intraspecific variations in mating system are reported in numerous species, especially when they live in broad ecological contexts. This induces between population variability in proportion of females engaging in multiple male mating, which depends on the number of male available. For hunted ungulates species, hunting is known to influence population structure, especially when males are preferentially targeted for trophy hunting. Here we investigated how variations in hunting pressure and yearly proportion of big males' removal impact probability of multiple paternity within a litter and the number of mating partners of females in five wild boar (Sus scrofa scrofa) populations. We found high rates of multiple paternity in all studied populations confirming the promiscuous mating system recently reported of wild boar with high within population variation. However, variations in hunting pressure and removal of big males did not influence the probability of multiple paternity neither the number of mating partners of females, once the population with the highest sample size was removed. The large magnitude of within population variations in mating systems of wild boar show the great plasticity already reported in the species.

Keywords: polyandry; multiple paternity; harvesting; reproduction monopolization; multiple male mating

Introduction

Multiple sired-litters are common in mammals. Females often mate with several males at a reproductive event [START_REF] Stockley | Female multiple mating behaviour, early reproductive failure and litter size variation in mammals[END_REF]. The proportion of females engaging multi-male mating varies among species, from close to 0% for monogamous species to 100% for highly promiscuous species [START_REF] Taylor | Polyandry in nature: A global analysis[END_REF], leading to inter-species variations of multiple paternity rates [START_REF] Eccard | Effects of brood size on multiple-paternity rates: a case for 'paternity share' as an offspring-based estimate[END_REF]. The number of males that females mate with also changes depending on species-specific characteristics. For example, mate guarding behaviors by male decrease the probability of multi-male mating of female [START_REF] Kokko | Mate guarding, male attractiveness, and paternity under social monogamy[END_REF].

However within-species variations also exist depending on the environmental context individuals live in. For domestic cat (Felis catus), proportion of litters sired by several males is lower in a low density population than in areas of higher density of cats [START_REF] Say | High variation in multiple paternity of domestic cats (Felis catus L.) in relation to environmental conditions[END_REF][START_REF] Say | The mating system of feral cats (Felis catus L.) in a sub-Antarctic environment[END_REF]. Indeed, in low density, males can more easily defend females against competitors and monopolize paternity of their whole litters. Also, by definition, in such ecological contexts, females have a lower probability of meeting several males than in high population densities leading to low multiple-male mating [START_REF] Kokko | Multiple mating by females is a natural outcome of a null model of mate encounters[END_REF]. In addition to population density, another important parameter influencing the encounter rate of potentials mating partners is the operational sex ratio [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF], consists of sex-ratio only considering reproducing males and females. Indeed, when the operational sex ratio is highly females skewed, only few males are available for reproduction and thus, multiple-male mating will be rare.

The age structure of animal populations changes over time. The range of variations is especially high for hunted populations as harvesting artificially reduces survival differentially in age classes [START_REF] Langvatn | Consequences of harvesting on age structure, sex ratio and population dynamics of red deer Cervus elaphus in central Norway[END_REF][START_REF] Solberg | Age-specific harvest mortality in a Norwegian moose Alces alces population[END_REF][START_REF] Frank | Indirect effects of bear hunting: a review from Scandinavia[END_REF]. Moreover, reducing female survival can influence their reproductive strategy. Low survival changes the trade-off between reproduction and survival [START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF]. In populations where hunting is intensive, females of iteroparous species (reproduction in several reproductive events) may not get more than one breeding occasion and should favor any strategy maximizing their reproductive output early in life [START_REF] Proaktor | Evolutionary responses to harvesting in ungulates[END_REF]. Multi-male mating can be favored in such context. It reduces the probability of reproductive failure compared to single-male mating and also increases the litter size [START_REF] Stockley | Female multiple mating behaviour, early reproductive failure and litter size variation in mammals[END_REF]. This is possible only if female have the opportunity to meet and mate with several males [START_REF] Martin | Environmental, social, morphological, and behavioral constraints on opportunistic multiple paternity[END_REF]. In polygynous species, females are monopolized by dominant males which try to maximize their reproductive success by preventing competing males to mate [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF]. Such species are characterized by strong sexual dimorphism with males displaying secondary sexual characters. Older males are often preferentially targeted by hunters because they have the biggest trophies. Their removal allows females to engage in multi-male mating as they are no longer maintained in harem.

Trophy hunting impacts the structure of the population leading to a decrease of their number [START_REF] Loveridge | The impact of sport-hunting on the population dynamics of an African lion population in a protected area[END_REF][START_REF] Douhard | Changes in horn size of Stone's sheep over four decades correlate with trophy hunting pressure[END_REF]. As few males are enough to fertilize many females, the consequences of their disappearance were neglected for a long time in population dynamic models. [START_REF] Rankin | Do males matter? The role of males in population dynamics[END_REF] showed that depending on populations characteristics, changes in sex ratio or absolute number of males can have important consequences. They also highlighted that selective harvesting can have severe consequences depending on the mating system of the population. Moreover, the change in population structure in trophy hunted populations leads to changes in its operational sex-ratio [START_REF] Milner | Demographic side effects of selective hunting in ungulates and carnivores[END_REF]).

Thus, through the reduction of the number of males in the population, trophy hunting can lead to change in its mating systems. [START_REF] Milner-Gulland | Reproductive collapse in saiga antelope harems[END_REF] reported a switch of mating system in an intensively hunted population of saiga antelope (Saiga tatarica tatarica) where mainly males are killed for their horns. Dominant females where anecdotally observed surrounding available males while normally males would defend a harem of up to 30 females. While this case is extreme, changes in operational sex ratio can release sexual competition between males and change reproductive patterns [START_REF] Singer | Influence of trophy hunting and horn size on mating behavior and survivorship of mountain sheep[END_REF].

The wild boar (Sus scrofa scrofa) is hunted all over its distribution range [START_REF] Massei | Wild boar populations up, numbers of hunters down? A review of trends and implications for Europe[END_REF]). The mating system of the species is polygyny [START_REF] Mauget | Régulation écologiques, comportementales et physiologiques (fonction de reproduction) de l'adaptation du sanglier[END_REF][START_REF] Dardaillon | Le sanglier et le milieu camarguais : dynamique coadaptative[END_REF]. Males feature tusks growing during their entire life, they used to fight other males to monopolize group of females. These tusks are appreciated trophies collected by hunters (Kierdorf et al. 2004).

Thus, old males are preferentially killed and the number of adult males in the population can be low in heavily hunted populations due to low survival and higher removal rates (Fernándezllario and Mateos-quesada 2003;[START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]. Multiple paternity was reported based on genetic studies in hunted populations of wild boars, highlighting multi-male mating behavior of females with variation in number of mates [START_REF] Delgado | Paternity assessment in free-ranging wild boar (Sus scrofa) -Are littermates full-sibs?[END_REF][START_REF] Pérez-González | Males and females contribute unequally to offspring genetic diversity in the polygynandrous mating system of wild boar[END_REF]Gayet et al. 2016). However, whether the proportion of female engaging in multi-male mating and the number of partners they mate with are linked to hunting pressure or not remains to be studied.

We characterized the mating system of wild boar in five different populations varying mainly in hunting pressure. We investigated how the removal of big males influenced multiple paternity rates in the population. We then measured the impacts of hunting and of the proportion of big males in the hunting bag on (i) the probability for a litter to be multiply-sired and (ii) the number of sires within a litter. We expected higher rates of multiple paternity in heavily hunted populations due to increased disruption of the population structure by harvesting. Finally, we expected increased probabilities for litters to be multiply sired together with increased number of fathers in a litter when the proportion of big males was high in the hunting bag. Indeed, female monopolization should decrease when big competitive males are removed from the population and allows medium males, still present, to get access to females.

Material and Methods

Samplings

Molecular and paternity analysis

All samples were genotyped for 12 microsatellite loci (see Chapter IVA for more details).

Individuals whose genotyping completely failed, were excluded from analysis and when the genotype of the mother or a fetus was not obtained, we excluded the whole mother-litter couples. This reduced the dataset to 511 litters across all populations (details in Table III 1). All genotypes obtained were analyzed using the software COLONY [START_REF] Jones | COLONY: A program for parentage and sibship inference from multilocus genotype data[END_REF]. As mothers were already known, it was used to identify fathers among putative males from the hunting bag or to assign a genotype if the father was not sampled. The analyses were performed for each population and each year. The population of Châteauvillain is well studied and we know that the probability of being killed each year for males is very high in this population (estimated survival of 0.23 [0.17; 0.30], [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]. Accordingly, all sampled males from year n, subadult and adult males killed year n+1 and adult males from year n+2 were included as possible fathers in COLONY analyses (Table III 1). Since the other populations are not as well studied, all males killed during the focused year and the following years were included as possible fathers in the analyses (Table III 1). We considered that 50% of reproductive males were sampled each year. We acknowledge this is speculative considering the variation of number of males sampled between years in different population. Nevertheless, our results were only slightly influenced by the proportion of males sampled when it varied between 20% and 70% (Figure III 2) and results of COLONY are known to be consistent across different values of this parameter [START_REF] Harrison | Relative accuracy of three common methods of parentage analysis in natural populations[END_REF]. For all analyses, we considered both sex polygynous, did not set population allele frequency, and used the full likelihood analysis method with a medium precision. The markers were chosen codominant, with an allelic dropout of 0.001 and a typing error of 0.01 for each locus. The default values were chosen for all other parameters. The results allowed us to estimate the number of fathers in each litter and then to know if the litter was sired by one or multiple males. Multiple paternity in a litter was coded as 0 (no multiple paternity) when only one male sired the litter and 1 (multiple paternity) when several males contributed to the litter.

Statistical analysis

Multiple paternity rates were measured in all five populations and were compared using Kruskal-Wallis test. In order to get information on the proportion of big males removed from each population and each year, we recorded the weight of all males killed a given year (except Belval and the year 2009 of La Petite Pierre for which information were not available). To focus only on sexually matured males, we removed males with a dressed body weight inferior to 30kg

(which correspond to full body mass of 38kg [START_REF] Mauget | Seasonal changes in testis weight and testosterone concentration in the european wild boar (Sus scrofa L.)[END_REF][START_REF] Baubet | Biologie du sanglier en montagne : biodémographie, occupation de l'espace et régime alimentaire[END_REF])), as the proportion of males producing sperm above this threshold weight is low [START_REF] Mauget | Seasonal changes in testis weight and testosterone concentration in the european wild boar (Sus scrofa L.)[END_REF]. For each population and each year, the weight of the biggest males in the hunting bag was used as reference. The yearly proportions of big males (Prop) were estimated as the proportion of males with a weight higher than the 80% percentile of the biggest male killed this year in all four populations (Figure III 3). To quantify the variance of the weight of males killed a given year, we also calculated the difference between the 80% percentile weight value and the median of the weight of sexually mature males (Diff). To measure the influence of these two parameters on mating system we performed two analyses. The first measured the probability of a litter to be multiply-sired using the litter status (pMP) as a dependent variable in a binomial regression model, while the number of fathers (Nf) of a litter was used as a dependent variable in a Poisson regression model. In both cases, the mother body mass (BMm), the proportion of big males (Prop) and the difference between the 80% percentile weight of the biggest males and the median value of mature males (Diff) and the number of wild boars killed per unit of space (Nha), were included as explanatory parameters. We also included the litter size (LS) for the second model as we know there is a positive relation between LS and Nf (Chapter IVA). Finally, we included the population as a random factor in all models. We acknowledge that we should include operational sex ratio. However, estimating population size of wild boar is difficult without heavy capture-mark-recapture protocol and the data were not available for all the focused populations [START_REF] Sweitzer | Estimating sizes of wild pig populations in the north and central coast regions of California[END_REF]. Analyses were performed including and excluding Châteauvillain population, as the big sample size of this population may weight on the outcome on the results. Correlation between parameters was verified using the Variance Inflation Factor (VIF). Parameters with highest VIF were gradually removed until all VIF were below 3 [START_REF] Zuur | Statistics for Biology and Health[END_REF]). The best model was selected based on AICc criterion and when several obtained ΔAICc < 2, we used model averaging to get the parameters estimates [START_REF] Burnham | Multimodel inference: understanding AIC and BIC in model selection[END_REF]. All statistical analyses were performed using R software version 3.3.3 (R Core Team 2017).

Results

Between populations variations of multiple paternity rates

All seasons combined, the number of fathers per litter ranged from one to four and up to seven depending of the population (Figure III 4a andFigure III 2). The highest numbers of fathers were found in Belval (median = 2 ± 2.08 SD) and Chambord (median = 2 ± 1.32 SD).

The maximum number of fathers reached six for both Châteauvillain (median = 2 ± 1.25 SD)

and La Petite Pierre (median = 2 ± 1.12 SD). The smallest maximal number of fathers per litters was found in Chizé (median = 2 ± 1.19 SD) reaching only four. In all populations, the majority of litters (more than 50%) were sired by one to three males (

Investigation of parameters influencing multiple paternity

Three models supported the data to explain pMP in a litter (ΔAICc < 2, Supplementary material Table III S3a). The averaged models included the proportion of big males in hunting bag (Prop), the difference of the median weight males killed and the threshold for big males (Diff), the mother body mass (BMm) and the number of wild boars killed per unit of space (Nha) when all population were included in analyses (Table III 2a). Only Prop showed a significant positive effect on the pMP (β = 0.374 ± 0.177, p = 0.035, Table III 2a), however when the population of Châteauvillain was removed, effects no longer exist and the best model was the null model (Table III 2b). When focusing on the number of fathers per litter, BMm, Diff, Nha and LS were included in the models best supported by the data whether Châteauvillain was included or not (Table III 2c and Supplementary material Table III S3b,Table III 2d). Prop was also in the averaged model including all four populations, however, the only significant parameter in both cases was the positive effect of the litter size (β = 0.113 ± 0.032, p < 0.001 with Châteauvillain, Table III 2c andβ = 0.113 ± 0.045, p = 0.013 when the population of Châteauvillain was removed, Table III 2d).

Discussion

Overall, multiple paternity rates estimated with COLONY are high in all five populations of wild boars. However, despite variations in hunting intensities between populations, results

did not show influence of the number of individuals killed per 100ha or the proportion of big males in the hunting bag on probability of multiple paternity or on the number of fathers within a litter once the population of Châteauvillain was removed from analysis.

High multiple paternity rates were observed in the five populations but there was no difference between populations. These rates are higher than most of those already reported in other populations of wild boars based on genetic studies (see Chapter IVA, Table IV 2). The genetic mating system of the species can be confidently defined as promiscuous, at least in hunted populations of dense deciduous forests. The disruption of population age structure by hunting is well documented [START_REF] Langvatn | Consequences of harvesting on age structure, sex ratio and population dynamics of red deer Cervus elaphus in central Norway[END_REF][START_REF] Milner | Demographic side effects of selective hunting in ungulates and carnivores[END_REF]). Moreover hunting may change individuals repartition in space and influence mating opportunity [START_REF] Milner-Gulland | Reproductive collapse in saiga antelope harems[END_REF]Keuling et al. 2008b;[START_REF] Davidson | Sociospatial behaviour of an African lion population following perturbation by sport hunting[END_REF]). Thus, even low hunting pressures may induce changes in the mating system. The lack of variation between populations does not fit with results obtain from some other polytocous species where multiple paternity rates change between populations [START_REF] Wakabayashi | Intraspecific variation in the frequency of multiple paternity in the Japanese intraspecific variation in the frequency of multiple paternity in the japanese wood mouse (Apodemus speciosus)[END_REF]) and other ungulate species where the mating systems varies according to the environmental context [START_REF] Gosling | The alternative mating strategies of male topi, Damaliscus lunatus[END_REF]. Besides, except for hunting, amplitude of variation of ecological context is rather low between our focus populations. Indeed, all populations are located in Northern France and the forest clump composition is rather favorable for wild boars. Investigating multiple paternity rates in populations with greater ranges of ecological contexts would be interesting to investigate precisely mating system of wild boar.

Variations of hunting were observed between populations considering the number of individuals killed by unit of space (Nha). This parameter allows to get information readily comparable between populations, but it is greatly sensitive to the density of populations. Two of the three enclosed populations showed very high values of Nha. Both are populations were wild boars are fed with maize (pers. com.) allowing high densities and bigger hunting bags.

Usually, in open populations, supplementary feeding is used by hunters to maintain wild boars in forest and protect crop fields [START_REF] Calenge | Efficiency of spreading maize in the garrigues to reduce wild boar (Sus scrofa) damage to Mediterranean vineyards[END_REF]) but in that case, maize is used to maintain individuals in good body conditions. High values of Nha can be explained by high population densities and be poor predictor of hunting intensity. However independently of the density, Nha remains meaningful to quantify disturbance induced by hunting in populations. However, obtaining good estimates of the number of individuals in each population, and proportions of reproductive wild boars removed, would greatly improve the confidence in the observed patterns. Such information is difficult to obtain especially for large study areas such as Châteauvillain or high-density population as Chambord. Despite great variations between populations, in this study, Nha did not influence neither pMP nor the number of fathers in a litter. This hunting parameter influences other population characteristics, but not those investigated in this study. Another possible explanation is that since we used population as a random factor, its effect may have been encompassed in the population effect. Once population effect removed, variations in Nha were not sufficient to influence significantly the explained variables. Investing influence of yearly variations of Nha within each population would be interesting. We were not able to perform these analyses here since, excepted for Châteauvillain, sampling did not cover enough years (Chizé, Chambord) or included enough litters per year (La Petite Pierre) to have good statistical power.

Probability of multiple paternity (pMP) within a litter was not significantly influenced by any parameter included in our analysis except when the Châteauvillain population, having the highest sample size, was part of the analysis. This showed two things. First, pMP does not change neither due to yearly variations of the removal of big males in the population of Chambord, Chizé and La Petite Pierre, nor due to the yearly changes of the variance of weight of the males killed at hunting. We did not include any time parameters in the models. Hunting takes place during the rut of wild boar, and males are preferentially targeted by hunters [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF]. The probability of multiple-male mating may change during the hunting season along with the decrease of the proportion of males in the population over the hunting period. Secondly, some variable in our models influenced pMP in the population of Châteauvillain enough to influence the results for the analysis including all populations.

Especially, Prop had a significant positive effect in average models where all populations were analyzed. The increase of the removal of big males induces a decrease in the number of males with the capacity to monopolize females. Females are more available for other males to mate with, and, without big males, the competition between males decreases [START_REF] Singer | Influence of trophy hunting and horn size on mating behavior and survivorship of mountain sheep[END_REF][START_REF] Kokko | Lonely hearts or sex in the city? Density-dependent effects in mating systems[END_REF]. However, the number of sire per litter was no significantly influenced by Prop whether Châteauvillain was part of the analysis or not. This suggested that more litters were sired by several males (increase of pMP) but litters were not sired by more males (no effect of the number of fathers) when big males disappeared from the population.

Indeed, high multiple paternity rates can be observed in populations where females reproduce with a maximum of two males but the number of fathers would only slightly change. The litter size showed a positive effect on the number of fathers. Indeed, the probability of detecting several fathers in large litters is higher than in small litters as the number of fathers ranges from one to a maximum corresponding to the number of fetuses in the litter. However, the increase of the number of mating partners can also induce an increase of female fertility by decreasing the number of unfertilized eggs [START_REF] Stockley | Female multiple mating behaviour, early reproductive failure and litter size variation in mammals[END_REF], also see Chapter IVA).

In conclusion, we did not find any influence of hunting on multiple paternity rates, or the number of fathers in our study populations when analyzed all together. However, the population of Châteauvillain seems apart from the others, as whether it was included or not in the analyses greatly influenced results. Investigating more precisely the mechanisms in this population could shed light in parameters influencing mating patterns in wild boar.

Acknowledgment

We are grateful to all people who helped collect harvested wild boars in the different study sites over the year. We thank the ONF, and F.

Supplementary Material

Model selection

Table III S3 Model selection to test the effect on (a.) the probability of occurrence of multiple paternity in a litter and (b.) the number of fathers in a litter of the proportion of males killed with a dressed weigh above the annual threshold (Prop), the difference between the median of dressed weigh of males killed and the annual threshold (Diff), the mother body mass (BMm), the litter size (LS) and the number of wild boars killed per surface unit (Nha) in four populations of wild boars in France. The model retained is in bold (ΔAICc<2). 'Χ' denotes that the explanatory variable was included in the model (nlitter-Chambord=166, nlitter-Châteauvillain =226, nlitter-Chizé=14, nlitter-La Petite Pierre=65).

a.

Hunting variations shape reproductive processes in a wild boar population

Abstract: Identifying origins of within population variations in reproductive strategies is an increasingly studied subject of research. Several mechanisms have already been described including female choice, male strategy, or ecological factors to explain variations of proportion of females engaging in multiple male mating. However, these mechanisms remain to be studied for many species. The wild boar (Sus scrofa scrofa) shows high rates of multiple paternity with within population yearly variations. In this study, we investigated how availability of food resources (proportion of forest fruits in stomach) and hunting processes (yearly number of animals killed, proportion of big males killed)

Introduction

The mating system of animal species or population is defined by ecological factors described and summarized by [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF]. While it is convenient to categorize the whole species/population, all individuals of a population do not exhibit the same mating strategy. Some females from monogamous species often produce multiple sired broods [START_REF] Ophir | Social but not genetic monogamy is associated with greater breeding success in prairie voles[END_REF][START_REF] Arct | Genetic similarity between mates predicts extrapair paternity-a meta-analysis of bird studies[END_REF] leading to the distinction between social and genetic monogamy. Also, some females from polygynandrous species produce single-sired broods, creating variations in multiple paternity rates (proportion of broods sired by more than one male) within and between species [START_REF] Trexler | Variation among populations of the sailfin molly in the rate of concurrent multiple paternity and its implications for mating-system evolution[END_REF][START_REF] Lank | High frequency of polyandry in a lek mating system[END_REF][START_REF] Mceachern | Another genetically promiscuous "polygynous" mammal: mating system variation in <i>Neotoma fuscipes<i[END_REF]). However, despite increasing interest in the subject, detangling if these variations of strategies are due to female choice, male strategy, ecological factors or a combination of one or more factors remain to be explored in many species (but, for a review in mammals, see [START_REF] Wolff | Promiscuous females protect their offspring[END_REF].

A recent study by [START_REF] Wells | Determinants of multiple paternity in a fluctuating population of ground squirrels[END_REF], in golden-mantled ground squirrels (Callospermophilus lateralis), tested three hypotheses to explain multiple paternity rate variations over a 18 years period: the encounter rate (i) where multiple paternity increases with the probability that females meet males [START_REF] Kokko | Lonely hearts or sex in the city? Density-dependent effects in mating systems[END_REF], male monopolization (ii) in which multiple paternity rates decrease with capacity of male to monopolize females [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF][START_REF] Shuster | Is hunting an effective tool to control overabundant deer? A test using an experimental approach[END_REF], female choice (iii) suggesting multiple paternity increase with female physical condition [START_REF] Cotton | Sexual selection and condition-dependent mate preferences[END_REF]. Yearly variations of multiple paternity rates were best explained by male monopolization hypothesis as it was mostly influenced by female aggregations and the number of competitors a male had to fight to monopolize a group of females.

Mating system of mammals is known to be influenced by population density, predation and food availability [START_REF] Say | High variation in multiple paternity of domestic cats (Felis catus L.) in relation to environmental conditions[END_REF][START_REF] Say | The mating system of feral cats (Felis catus L.) in a sub-Antarctic environment[END_REF][START_REF] Kamler | Variation in mating system and group structure in two populations of swift foxes, Vulpes velox[END_REF][START_REF] Martin | Resource distribution influences mating system in the bobuck (Trichosurus cunninghami: Marsupialia)[END_REF]. Also, food distribution in space and time is of great importance, especially in ungulates, as it shapes aggregation patterns of females and, in return, influences the capacity of males to defend group of females for reproduction [START_REF] Brashares | Role of forage, habitat and predation in the behavioural plasticity of a small African antelope[END_REF][START_REF] Pérez-González | Female aggregation interacts with population structure to influence the degree of polygyny in red deer[END_REF].

When resources distribution is sparse, females are expected to be scattered in the environment and increase their displacements when foraging [START_REF] Brashares | Role of forage, habitat and predation in the behavioural plasticity of a small African antelope[END_REF], decreasing the capacity of males to maintain them in group [START_REF] Clutton-Brock | Mammals, resources and reproductive strategies[END_REF]. Thus, social monogamy is often observed in such situations with one male siring the litter, as most ungulates are monotocous or only slightly polytocous (litter size ranging mainly between one and three, Gaillard et al. 2000a). But increased females movement can also increase their probability to meet different males, leading to serial monogamy (multiple male mating) (Kokko and Mappes 2013) and increase of multiple paternity rates. However, when resource are abundant and/or clumped, females are expected to remain in groups that a single male can more easily defend against competitors forming a harem [START_REF] Emlen | Ecology, sexual selection, and the evolution of mating systems[END_REF][START_REF] Clutton-Brock | Mammals, resources and reproductive strategies[END_REF].

The ensuing social mating system is polygyny with low multiple paternity rates as only one male should reproduce with the females of the group.

Unlike other ungulates, the wild boar (Sus scrofa scrofa) is a highly polytocous species with a litter size averaging five [START_REF] Servanty | Litter size and fetal sex ratio adjustment in a highly polytocous species: the wild boar[END_REF], offering great opportunity to detect multiple male mating. The reproduction of this species is influenced by forest fruits availability (acorn and beechnut mostly), which mainly shape reproductive outputs of females (Servanty et al. 2009;[START_REF] Gamelon | Reproductive allocation in pulsed-resource environments : a comparative study in two populations of wild boar[END_REF]. Despite high adaptability for its diet, acorns and beechnuts remain the main food items of wild boar [START_REF] Schley | Diet of wild boar Sus scrofa in Western Europe, with particular reference to consumption of agricultural crops[END_REF]. Forest fruits production is highly variable and unpredictable due to masting reproductive strategy of oaks (Quercus sp.) and beech (Fagus sp.). This strategy consists of massive production of fruits a given year followed by several years of low production, with high synchronization of trees of a same forest [START_REF] Liebhold | Within-population spatial synchrony in mast seeding of North American oaks[END_REF]). Thus, mast years represent years of abundant food resources distributed in space, in contrary of years without mast production where resources are scattered. As for other ungulates species, resources distribution in space and time can influence capacity of males to monopolize groups of females and in return multiple paternity rates. However, to our knowledge, no study investigated the link between resource and mating system in the wild boar so far. Moreover, as a game species, the wild boar is subject to intensive hunting with big males especially targeted for their tusk used as trophy (Kierdorf et al. 2004). Survival of male can be heavily impacted in population with intensive harvesting [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]). Disruption of the population structure ensuing from hunting was shown to influence reproductive processes differentially depending on the population (Chapter IIIA).

The wild boar shows between year variations in multiple paternity rates that exceed between population variations (Chapter IIIA, Figure III 4). However, factors influencing the proportion of females that mate with several males and their number of partners remain poorly investigated. We used long term monitoring of the wild boar population of Châteauvillain to investigate the influence of food resource availability and the effect of the population structure disruption on the mating system in this population. We expect high probability of multiple paternity (pMP) and high number of fathers (Nf) in a litter (promiscuous mating system) when both food resources are scarce and the number of big males in the population is low. When food resources are scarce, groups of females would be scattered in the environment and harder to monopolize by a single male leading to increased probabilities of multiple paternity. In mast production years, when resource are abundant, the movement of females groups should be narrower leading to low level of multiple paternity. Moreover, when big males are removed from the population, females are more available for other males creating opportunity for multiple paternity.

Material and Methods

Study site and sample collection

The wild boar population is located in the 11,000 ha Châteauvillain-Arc-en-Barrois forest (48°02′N; 4°55′E, France) and is described in detail in Gayet et al. (2016). During nine hunting seasons (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015), tissue samples were collected from 210 hunted pregnant females and their full litters with fetuses big enough to be measured (1092 fetuses, mean litter size = 5.2 ± 1.66 SD), 305 non-breeding females, females with putative missing fetuses due to bullet wound in the uterus or female with fetuses too small to be measured (those females were only included in the genetic diversity analyses), and from 895 putative reproductive males (also sampled in 2016) with a dressed body mass (i.e. without the digestive system, heart, lungs, liver, reproductive tract and blood) higher than 30kg. Crown-rump length of fetuses was measured (in millimeters) to calculate the gestation stage in days, from the average length of fetus within the litter, using relation from [START_REF] Henry | Fetal Development in European Wild Hogs[END_REF]. The Julian mating date (using the 1 st of July of each year as reference) was calculated by subtracting the gestation stage in days to the date of kill.

Stomach contents analysis were realized during the hunting period to identify wild boar diet as described in [START_REF] Baubet | Diet of the wild boar in the french Alps[END_REF]. The proportion of three major items, acorn, beechnut and corn was measured and pooled for each hunting month. Finally, for each year, the number of wild boars killed for 100ha and the weight of all sexually mature males killed a given year were recorded (above 30kg of dressed body mass corresponding to a full body mass of 38kg [START_REF] Mauget | Seasonal changes in testis weight and testosterone concentration in the european wild boar (Sus scrofa L.)[END_REF][START_REF] Baubet | Biologie du sanglier en montagne : biodémographie, occupation de l'espace et régime alimentaire[END_REF].

Molecular and paternity analysis

All samples were genotyped for 12 microsatellite loci (see Chapter IVA for more details). Individuals, whose genotyping failed, were excluded from analysis, including the whole mother-litter couples if the genotype of the mother or a fetus was not obtained. This reduced the dataset to 871 putative males, 202 litters and 1049 fetuses. All genotypes obtained were analyzed using the software COLONY [START_REF] Jones | COLONY: A program for parentage and sibship inference from multilocus genotype data[END_REF]. As mothers were already known, it was used to identify fathers among putative males from the hunting bag or to assign a genotype if the father was not sampled. The analyses were realized for each year, including as possible fathers all sampled males from year n, subadult and adult males killed year n+1 and adult males from year n+2 considering the probability of being killed each year for males is very high in this population [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]. This lead to include 141,233,307,355,417,273,161,120 and 89 sampled males in the analysis, from 2007 to 2015 respectively. We considered 50% of reproductive males were sampled each year. We performed analysis for other proportions of sampled males and the number of fathers was not influenced by the proportion between 20% and 70%. For all analyses, we considered both sex polygynous, did not set population allele frequency, and used the full likelihood analysis method with a medium precision. The markers were chosen codominant, with an allelic dropout of 0.001 and a typing error of 0.01 for each locus. The default values were chosen for all other parameters. The results allowed us to estimate the number of fathers in each litter and then to know if the litter was sired by one or multiple males.

Statistical analysis

To estimate the proportion of big males in the hunting bag each year, we choose to take advantage of the long-term monitoring realized by the French Hunting and Wildlife Agency on this population. As the weight of all adult males killed by hunting since 1982 was available, we determined the 80% percentile value of weight. This allowed us to estimate a historical threshold of the weight of the biggest adult males in the population. We then measured the proportion of sexually mature males killed each year with a weight higher than this threshold (Prop). This parameter quantifies the relative number of big males killed each year. As the threshold is fixed through years, we directly recorded the median dressed weight of sexually mature males killed at hunting (Medw) to measure how the weight of an average reproductive male varies between years.

We performed two types of generalized linear mixed-effect models to investigate parameters influencing the probability of a litter to be multiple sired and the number of males that sire a litter. Indeed, the proportion of litter displaying multiple paternity can vary greatly but the number of fathers may only slightly change. For the first, we used a binomial regression model using the litter status (MP) as response variable (0 for single sired litters, 1 for litters with multiple paternity). For the second, we used a Poisson regression model using the number of fathers (Nf) as response variable. We included the mother body mass (BMm), the Julian date of mating (D), and the proportion of each of the three items in stomach content of the month when mating occurred: acorn (A), beechnut, (B) and corn (C). This reduced the sample size to 149 litters as some litters where conceived out of the hunting period when information for stomach content is not available. We also added in the model the number of wild boars killed by surface unit (Nha) and the parameters Prop and Medw described above as biological effects.

The year was included as a random factor. The litter size (LS) was included as a confounding variable in the model investigating for the number of fathers as we know Nf and LS are linked (Chapter IVA). All numeric variable were scaled before analysis. The collinearity between variables in the models was verified using the Variation Inflation Factor (VIF) with a threshold of three [START_REF] Zuur | Statistics for Biology and Health[END_REF]. As stomach proportion of acorn and beechnut were highly correlated, we summed them to create a parameter forest fruits (FF). Parameters with a VIF value above 3 were removed from full models starting from the proportion of corn (C) as this parameter was included only as a co-factor, followed by parameters showing the highest VIF value. The model selection started with the full additive model and the best models explaining the data were selected based on AICc (ΔAICc < 2) and averaged [START_REF] Burnham | Multimodel inference: understanding AIC and BIC in model selection[END_REF]). All statistical analyses were performed using R software version 3.3.3 (R Core Team 2017).

Results

The proportions of forest fruits and corn in stomach content varied during the study period. When proportions of forest fruit where high, the proportions of corn was low and vice versa. Both the proportion of corn (C) and the proportion of forest fruits (FF) showed high colinearity with other parameters included in the models (VIF > 3), so they were excluded from the full models. Two models were best supported by the data (ΔAICc < 2) for the pMP and were averaged (supplementary material Table III S5a). They included all the parameters of the full model as it was the second best model. The Julian date of mating (D, β = 0.624 ± 0.223, p = 0.006, Table III 4a) and the yearly proportion of big males killed at hunting (Prop, β = 0.838 ± 0.246, p = 0.001, Table III 4a) showed significant positive effects on the pMP within a litter.

The yearly number of wild boars killed (Nha, β = -0.457 ± 0.207, p = 0.028, Table III 4a) and the median weight of reproductive males (Medw, β = -0.476 ± 0.227, p = 0.038, Table III 4a) had significantly negative effects. The mother body mass did not influence significantly (BMm,β = 0.116 ± 0.195,p = 0.553,Table III 4a) the pMP in a litter. Concerning the number of fathers in a litter, six models were best supported by the data and were averaged (supplementary material Table III S5b). Nha was excluded from the best models. Only the yearly proportion of big males killed showed a significantly positive effect (Prop, β = 0.374 ± 0.177, p = 0.035, Table III 4b). The other parameters did not show significant effect on the number of fathers within a litter (Table III 4b).

Table III 4 Estimates, standard errors, z statistics, and P values of parameters linked with the probability of occurrence of multiple paternity (a.) and the number of fathers (b.) in a litter. Values for the Julian date of mating (D), the proportion of males killed with a dressed weigh above the historical threshold (Prop) and median dressed weight of reproductive males (Medw), the number of wild boar killed per surface unit (Nha), the mother body mass (BMm) and the litter size (LS) were obtained from averaged models strongly supported by the data. Significant parameters are in bold (nlitters = 149).

Discussion

In the population of wild boars of Châteauvillain, we observed that Julian date of mating (D) and the yearly proportion of big males killed (Prop) showed a positive effect on the probability of multiple paternity (pMP) within a litter. The hunting intensity measured as the number of wild boars killed a given year (Nha) and the median weight of reproductive males (Medw) showed negative effects on multiple paternity probability. Only Prop had also a positive effect on number of fathers in a litter. Parameters included as confounding factors (BMm and LS) showed no significant effect on any parameters.

The resources proportion measured as the proportion of corn (C) and forest fruits (FF) in stomach contents were highly correlated with other parameters, especially the yearly median weight of reproductive males (Medw), so they were excluded from the models presented here.

This did not allowed to test the influence of resource availability on the mating system. To perform this analysis, we removed Medw from the full models and we obtained VIF values below three for FF (C was still removed based on VIF values). In this case, FF was maintained in averaged models but it did not influenced significantly the pMP within a litter, and neither the number of sires in a litter (supplementary material Table III S6). Despite studies demonstrating the link between resources and multiple paternity in mammals [START_REF] Asher | Large males dominate: Ecology, social organization, and mating system of wild cavies, the ancestors of the guinea pig[END_REF][START_REF] Cameron | Spatial variation in food availability predicts extrapair paternity in the arctic fox[END_REF], we did not find such effect in this wild boar population. This does not fit our prediction as these results show that variations in forest fruits availability does not influence the mating system. In this population, the range of variations of food availability may be buffered by supplementary feeding. In years of poor mast production, the proportion of corn increased in stomach contents and we know that hunters provide more corn in the forest to avoid crop damages. Thus, female wild boar may aggregate around feeding places the same way they aggregate to feed on forest fruits. Also, the wild boar is a highly opportunistic feeder contrary to other ungulates, so distribution of food resources may be a poor estimator of mating system variations.

Both the pMP within a litter and the number of fathers in a litter were positively associated with the yearly proportion of big males in the hunting bag Prop. This result fits our prediction.

As the proportion of big males killed increases, their number in the population decreases.

Moreover, big males are often killed at the beginning of the hunting season which start before of the rutting period of wild boar [START_REF] Mauget | Seasonal changes in testis weight and testosterone concentration in the european wild boar (Sus scrofa L.)[END_REF]. The positive effect of the mating date (D) on pMP supports this hypothesis. Indeed, it suggests that females are less monopolized as the hunting season progresses. As big males are the most suitable to monopolize females and defend them against competitors, their removal by hunting allows other males, that would not reproduce if big males were present, to have access to females [START_REF] Hogg | Mating in bighorn sheep: Frequent male reproduction via a high-risk "unconventional" tactic[END_REF]. The increase of pMP and Nf observed fit the theory of increased of number of possible mating partners over the hunting season. Positive effect of the males density has already been reported to influence multiple paternity rate [START_REF] Martin | Environmental, social, morphological, and behavioral constraints on opportunistic multiple paternity[END_REF][START_REF] Wells | Determinants of multiple paternity in a fluctuating population of ground squirrels[END_REF]). However, the lack of effect of the mating date on the number of fathers suggests that Nf does not increase with the opportunity of multiple male mating. This can be explained by the increasing removal of males during hunting. Females are less monopolized by big males but, in the same time, less males are available in the population for mating. However, it is noteworthy that high values of Prop could also reflect higher proportion of males in the population and hunting bag would be a proxy of the structure of the global population but Prop and the median weight of reproductive males (Medw) were not highly correlated based in VIF analysis. Thus, the proportion of big males killed is not linked to the yearly median weight of males, the positive effects of Prop on pMP and Nf is trustworthy.

We observed a negative effect of Medw on pMP but not on Nf. High median weight of males killed can be link to two different scenarios. First, high Medw values imply that heavy males are removed of the population and the proportion of small and/or light males remaining increases. This should release between male competition and be associated with higher multiple paternity rates [START_REF] Zedrosser | Genetic estimates of annual reproductive success in male brown bears: The effects of body size, age, internal relatedness and population density[END_REF]) contrary to what is observed here. Second, high Medw values can also be associated with high weight of males in the population a given year. In this scenario, the hunting bag reflect the population trend. This second possibility is supported by correlation between Medw and FF. Increase of median body mass of males means higher number of males of good quality. Good quality males are able to defend females against competitors, decreasing multiple male mating opportunity, leading to a decreased pMP [START_REF] Singer | Influence of trophy hunting and horn size on mating behavior and survivorship of mountain sheep[END_REF][START_REF] Zedrosser | Genetic estimates of annual reproductive success in male brown bears: The effects of body size, age, internal relatedness and population density[END_REF]). Moreover, Nha showed a similar pattern to Medw with a negative effect on pMP but no effect on Nf. This can be explain because years of mast production allow better body condition leading to increased survival of wild boar, especially for young males [START_REF] Focardi | Survival of wild boars in a variable environment: unexpected life-history variation in an unusual ungulate[END_REF], and then increased hunting bags. However, the lack of effect of both Medw and Nha on Nf shows that number of fathers does not varies with average males quality and number of animal killed in the population, which temper this previous deduction as we could expect a decrease of the number of father when pMP decreases. To verify more precisely mechanism influencing male access to females and their probability to reproduce, identifying all fathers (reproductive males achieving reproduction) and obtaining their morphologic characteristics at the time of mating would be required. However, our data do not allow that (but see Chapter V for exploratory analysis) and such study suggests intensive and costly sampling and analysis procedures in such a large population.

In this wild boar population, variations of availability of food resource did not directly influence mating system but may indirectly modulate male quality and the intra-sexual competition. Also, the yearly proportion of big males killed, which are the most suitable to monopolize females, lead to increase of both probability of multiple paternity and number of mating partners of females. Altogether, these results suggest that mating system in wild boar is mainly influenced by the capacity of males to defend females against competitors. This capacity depends on hunting which change intra-sexual competition between males. Investigating in detail which characteristics of male wild boars influence their reproductive success should highlight interesting results for both evolutionary biology and management researchers.

Supplementary Material

Model selection

Table III S5 Model selection to test the effect on (a.) the probability of occurrence of multiple paternity in a litter and (b.) the number of fathers in a litter of the Julian date of mating (D), the proportion of males killed with a dressed weigh above the historical threshold (Prop) and the median dressed weight of reproductive males (Medw), the mother body mass (BMm), the litter size (LS), and the number of wild boar killed per surface unit (Nha) in the population of Châteauvillain, France. The model retained is in bold (ΔAICc<2). 'Χ' denotes that the explanatory variable was included in the model (nlitters = 149).

a. Chapter IVA

Intercept

Consequences of multiple paternity

Laura Touzot

On the evolutionary consequences of increasing litter size with multiple paternity in wild boar (Sus scrofa scrofa)

Abstract: Understanding how some species may be able to evolve quickly enough to deal with anthropogenic pressure is of prime interest in evolutionary biology, conservation and management. Wild boar (Sus scrofa scrofa) populations keep growing all over Europe despite increasing hunting pressure. In wild boar populations subject to male-selective harvesting, the initially described polygynous mating system may switch to a promiscuous/polyandrous one. Such a change in the mating system, where potentially more males sire a litter at one reproductive event, may be associated with the retention of high genetic diversity and an increase of litter size. We tested these hypotheses by estimating the number of sires per litter based on a 6-year long monitoring of a wild boar population subject to particularly high harvesting pressure. Our results show a high and stable genetic diversity and high rates of multiple paternity compared to other populations, thus depicting a promiscuous/polyandrous mating system in this population. We also show that litter size is positively linked to the number of sires, suggesting that multiple paternity increases fecundity. We finally discuss that multiple paternity may be one of the factors allowing rapid evolution of this population by maintaining both genetic and phenotypic diversity. Keywords: harvesting; polyandry; mating system; selective hunting; fecundity Gayet T., S. Devillard, M. Gamelon, S. Brandt, L. Say, and E. Baubet. 2016. On the evolutionary consequences of increasing litter size with multiple paternity in wild boar (Sus scrofa scrofa). Evolution (N. Y). 70:1386-1397.

Introduction

Human exploitation, through hunting or fishing, affects the size of free-ranging populations. High harvesting pressures lead to the removal of a large proportion of individuals, inducing a strong yearly decline of population size. Since genetic diversity is linked to population size [START_REF] Frankham | Relationship of genetic variation to population size in wildlife[END_REF], intensively harvested populations undergo great genetic loss every year [START_REF] Harris | Genetic consequences of hunting: what do we know and what should we do?[END_REF]. This may affect their adaptive potential [START_REF] Amos | When does conservation genetics matter?[END_REF]Barrett and Schluter 2008) leading to a demographic decline and, in the worst case scenario, to extinction [START_REF] Gilpin | Minimum viable population: processes of species extinction[END_REF][START_REF] Rosser | Overexploitation and species extinctions[END_REF]; see [START_REF] Spielman | Most species are not driven to extinction before genetic factors impact them[END_REF] for a meta-analysis on 170 taxa) if the populations are unable to respond to the new selective pressures. For example, overexploitation is the main factor that induced the collapse of several fisheries in the past century [START_REF] Hutchings | The biological collapse of Atlantic cod off Newfoundland and Labrador: an exploration of historical changes in exploitation, harvesting technology, and management[END_REF][START_REF] Jackson | Historical overfishing and the recent collapse of coastal ecosystems[END_REF]). In addition, for populations facing anthropogenic pressures through exploitation, some modifications have also been observed in phenotypic traits [START_REF] Coltman | Undesirable evolutionary consequences of trophy hunting[END_REF][START_REF] Douhard | Changes in horn size of Stone's sheep over four decades correlate with trophy hunting pressure[END_REF], demography [START_REF] Milner | Demographic side effects of selective hunting in ungulates and carnivores[END_REF][START_REF] Servanty | Influence of harvesting pressure on demographic tactics: implications for wildlife management[END_REF] or genetic characteristics [START_REF] Harris | Genetic consequences of hunting: what do we know and what should we do?[END_REF][START_REF] Allendorf | Genetic effects of harvest on wild animal populations[END_REF].

Selective harvesting, the intensification of harvest efforts geared toward individuals

showing phenotypic traits favored by hunters [START_REF] Milner | Demographic side effects of selective hunting in ungulates and carnivores[END_REF], may affect the structure of populations. For instance, in populations subject to size-selective harvesting, where the largest adults are preferentially removed, the age and sex structure is biased toward the young and females [START_REF] Milner | Demographic side effects of selective hunting in ungulates and carnivores[END_REF]). Such a change in age and sex distribution may have strong consequences on the mating system [START_REF] Kokko | Lonely hearts or sex in the city? Density-dependent effects in mating systems[END_REF][START_REF] Milner | Demographic side effects of selective hunting in ungulates and carnivores[END_REF]). In ungulate populations, the mating system is known to be influenced by density of males and females [START_REF] Isvaran | Variation in male mating behaviour within ungulate populations: Patterns and processes[END_REF]. For species showing a polygynous mating system with female monopolization by males, intra-sexual competition is diminished when larger males are removed and younger males are more likely to obtain paternities by harassment of females [START_REF] Isvaran | Variation in male mating behaviour within ungulate populations: Patterns and processes[END_REF]). The mating system switches to a promiscuous/polyandrous one and the multiple paternity rate (defined as the proportion of litters showing more than one father) increases. As the number of males accessing reproduction grows, the variance of male reproductive success decreases, allowing greater genetic diversity to pass on from one year to the other compared to the polygynous mating system [START_REF] Nunney | The influence of mating system and overlapping generations on effective population size[END_REF][START_REF] Sugg | Effective population sizes with multiple paternity[END_REF][START_REF] Pearse | Multiple paternity increases effective population size[END_REF]. We hypothesize that these processes (promiscuous mating system and multiple paternity) may have the potential to buffer the loss of genetic diversity due to intensive harvesting. However, multiple paternity effects have been the topic of a debate. On the one hand, in their review, [START_REF] Jennions | Why do females mate multiply? A review of the genetic benefits[END_REF] described most of the genetic benefits for females, including the increase of genetic diversity within a litter, which tends to increase the genetic diversity at the population scale [START_REF] Pearse | Multiple paternity increases effective population size[END_REF]. On the other hand, [START_REF] Lotterhos | The context-dependent effect of multiple paternity on effective population size[END_REF] tempered this result by showing that the positive link between multiple paternity and effective population size, which reflects population genetic diversity, is not always true but depends on the litter size, the number of reproductive events and the female's number of mates over her lifetime. Surprisingly, wild boars (Sus scrofa scrofa) do not fit into the classical frame of reduced population size due to intensive harvesting. Their populations are growing all over Europe despite the continuous increase of hunting pressure [START_REF] Massei | Wild boar populations up, numbers of hunters down? A review of trends and implications for Europe[END_REF]). The mating system of this species has been originally described as polygynous [START_REF] Mauget | Régulation écologiques, comportementales et physiologiques (fonction de reproduction) de l'adaptation du sanglier[END_REF][START_REF] Dardaillon | Le sanglier et le milieu camarguais : dynamique coadaptative[END_REF]) which is consistent with the sexual dimorphism displayed by the species [START_REF] Ralls | Sexual dimorphism in mammals: avian models and unanswered questions[END_REF]. Interestingly, with the rise of molecular genetic techniques, a growing literature has shown that multiple paternity occurs [START_REF] Delgado | Paternity assessment in free-ranging wild boar (Sus scrofa) -Are littermates full-sibs?[END_REF][START_REF] Poteaux | Sociogenetic structure and mating system of a wild boar population[END_REF] and may be common in some populations of wild pigs [START_REF] Delgado-Acevedo | Promiscuous mating in feral pigs (Sus scrofa) from Texas, USA[END_REF][START_REF] Costa | Microsatellite markers for identification and parentage analysis in the European wild boar (Sus scrofa)[END_REF]. A positive effect of multiple paternity on litter size has even been highlighted in the domestic pig (Sus scrofa domesticus) which is the domestic counterpart of the wild boar. Due to its economic importance [START_REF] Orr | World pig production, opportunity or threat?[END_REF], the pig is the subject of many studies that aim at understanding the mechanisms underlying reproduction to improve production. The number of artificial insemination events is known to have a positive effect on litter size [START_REF] Kemp | Relationship of weaning-to-estrus interval to timing of ovulation and fertilization in sows[END_REF][START_REF] Corrêa | Reproductive performance of early-weaned female swine according to their estrus profile and frequency of artificial insemination[END_REF]. Moreover, several sires are commonly used in pig husbandry to increase litter size, hence productivity [START_REF] Badinel | Biology and genetics of reproduction[END_REF]. However, until now, only a few studies have focused on the link between litter size and number of fathers in the wild [START_REF] Dibattista | Are indirect genetic benefits associated with polyandry? Testing predictions in a natural population of lemon sharks[END_REF][START_REF] Thonhauser | Multiple paternity in wild house mice (Mus musculus musculus): Effects on offspring genetic diversity and body mass[END_REF], but see [START_REF] Waller | Effect of mating frequency on sow reproductive performance under field conditions and natural mating in large outdoor production units[END_REF] for evidence of larger litter sizes with increasing number of sires per litter in free-ranging pigs).

Recent studies conducted on the wild boar population of Châteauvillain-Arc-en-Barrois which suffers from a particularly high and male-selective harvesting pressure [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF][START_REF] Servanty | Influence of harvesting pressure on demographic tactics: implications for wildlife management[END_REF], have shown that selection for both earlier birth date and earlier sexual maturity in females could occur over just a few generations to adapt to the harvesting regime [START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF][START_REF] Servanty | Pulsed resources and climate-induced variation in the reproductive traits of wild boar under high hunting pressure[END_REF]. But whether multiple paternity may (i) have a positive effect on wild boar fecundity through larger litter size as shown in pigs, and (ii) maintain a high genetic diversity through time, which is then transmitted to each generation, thereby buffering yearly genetic loss and allowing a high ability to respond to new selective pressure, remain understudied questions. Hence, using six years of data sampling, we addressed these questions. We expected a high level of genetic diversity together with a high rate of multiple paternity in this population, compared to other populations of the same species, triggered by a likely disruption of the polygynous mating system. Moreover, we investigated how the litter size is related to the number of sires within litters and predicted a larger litter size when the number of sires increases.

Material and Methods

Study site and sample collection

The wild boar population is located in the 11,000 ha Châteauvillain-Arc-en-Barrois open forest (48°02′N; 4°55′E, France) surrounded by agricultural fields, thus immigration rate is low (unpublished data). The number of individuals was estimated to be between 1,200 and 1,500 [START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF]. In this heavily hunted population, wild boars have a 40% probability of being shot every year, rising to 70% for adult males [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]). Moreover, the population exhibits a particularly short generation time for an ungulate which was previously estimated to be 2.27 years [START_REF] Servanty | Influence of harvesting pressure on demographic tactics: implications for wildlife management[END_REF]. During six hunting seasons (2007)(2008)(2009)(2010)(2011)(2012), the number of wild boar killed annually ranged from 567 to 794 (mean 635). Tissue samples were collected from 165 hunted pregnant females and their full litters (845 fetuses, mean litter size = 5.1 ± 1.63 SD), 264 non-breeding females (included only in the genetic diversity analyses), and from 627 putative reproductive males with a dressed body mass (i.e. without the digestive system, heart, lungs, liver, reproductive tract and blood) higher than 30kg [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF]. Body mass has been shown to be a structuring factor, more appropriate than age for this species [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF], so weight was recorded for individuals.

Molecular analysis

All tissue samples were stored in alcohol in an individual hermetic straight container of 25ml and then genotyped for 12 microsatellite loci (Supplementary Material 1, Table IV S3).

For each sample, 20-80 ng/l of total genomic DNA was extracted using a buffer lyse. A few milligrams of tissue were pounded and then incubated first at 56°C for 2-3 hours and then at 72°C for 20 minutes in 200l volumes containing 4l of Tris HCL 1M, 0.3l of MgCl2 1M, 5l of KCl 1M, 1l of Tween 20 and 1l of K proteinase (20mg/ml, EUROBIO). Selective amplification was carried out for 12 microsatellite loci divided into 2 PCR multiplexes by polymerase chain reaction (PCR). PCR were conducted in 96-well microtitre plates in final were the five most variable ones overall. Among the 73 remaining mother-litter arrays, 45 were analyzed with one other locus, 19 using two other loci and nine with all loci showing no missing data. Within these constraints, we performed an exhaustive search for the number of possible combinations of fathers that could explain each progeny array and recorded the minimum number of sires for each litter NG. Since GERUD uses exclusion to estimate the number of male genotypes contributing to a given progeny array, estimates using this program are considered very conservative and should never overestimate the number of sires NG for a litter [START_REF] Jones | GERUD 2.0: a computer program for the reconstruction of parental genotypes from half-sib progeny arrays with known or unknown parents[END_REF].

To circumvent CERVUS failures to identify sires of all fetuses within a litter and GERUD conservatism, we complemented our analysis with a less conservative analytical approach based on the maximal number of paternal alleles. Each fetus inherits one allele from its father and one allele from its mother so that the maximum number of alleles in a monopaternal litter is four if both parents are heterozygous and a maximum of two paternal alleles would be identified if single paternity occurs. For each litter and each locus, we calculated the number of alleles, from which we retrieved the known number of maternal alleles to estimate the number of paternal alleles. The maximal number of paternal alleles over the 12 loci was retained to obtain NPA. We acknowledge that this number is also conservative, as only one allele in a litter at a given locus does not preclude multiple paternities.

Three different estimates of the multiple paternity rate (MPR) could thus be obtained, allowing us to evaluate consistency: the proportion of litters having more than one putative sire (CERVUS, MPRC), the proportion of litters having a minimum number of sires NG higher than one (GERUD, MPRG) and the proportion of litters having more than two paternal alleles for at least one locus (maximal number of paternal alleles approach, MPRPA).

Statistical analysis

To identify the key-variables driving the variability of the litter size LS across the litters, we performed a Poisson regression model where the response variable was LS and in which the locus-specific Ho and the observed number of alleles A for the locus showing the maximal number of paternal alleles in each litter were included as confounding variables. The mother dressed body mass BMm and, finally, the maximal number of paternal alleles NPA, as a proxy of the number of fathers, were included as main biological effects. We started model selection from the full additive model and then we selected the model with the lowest AICc in order to get estimates and standard error for each predictor variable.

To ensure that the pattern of relationship revealed between LS and NPA was not an artefact due to the positive structural relationship between NPA and LS (i.e. the impossibility to observe a NPA higher than LS), we used a permutation test. We performed 10,000 random permutations of NPA, Ho and A values kept together as a triplet against the pair of LS and BMm values in the range of possible values (permutations where NPA was higher than LS were not allowed). Each permutated dataset was analyzed using the model selected from the analysis of the observed dataset (model with the lowest AICc) to obtain the averaged coefficient associated to NPA. The effect of NPA, obtained with our observed dataset, was tested by calculating the exact p-value, against the distribution of permuted values, using the method described by [START_REF] Phipson | Permutation P-values should never be zero: calculating exact P-values when permutations are randomly drawn[END_REF].

The same analyses were performed using NG along with BMm as biological effect in the model to explain LS variability. The same permutation approach was also carried out by permuting NG values against LS and BMm values in the range of possible values. The analysis was not performed with CERVUS due to the few litters with all fathers identified. Moreover, litters with few fathers are more likely to be fully resolved than litters with a higher number of fathers. All analyses were performed in R 3.1.3 software (R Core Team 2017).

Results

Paternity analyses and multiple paternity rate

Overall, mean allelic diversity was A = 11.25 alleles per locus, ranging from two to 25 and mean expected heterozygosity was He = 0.602 ranging from 0.125 to 0.891 (Table IV 2, see Supplementary Material 1, Table IV S3 for details). Ten out of 12 loci showed very small deviations from expected heterozygosity and 11 out of 12 a low frequency of null alleles (<0.05 per locus) (Supplementary Material 1, Table IV S3).

Two mothers showed loci mismatches with all their presumed offspring, leading us to consider that a sampling mistake occurred at the collecting site. Therefore, they were removed from further analyses. Overall, the sire of 44.77% of the fetuses was identified among the set of candidate fathers by CERVUS and 10% of the litters (i.e. 16 out of 160) were fully resolved.

Factors explaining the variability of NPA and NG

One model including the mother body mass BMm, the observed number of alleles A for the locus showing the maximal number of paternal alleles and the maximal number of paternal allele NPA was supported by the data (ΔAICc < 2, Supplementary Material 3, Table IV S4). LS increased significantly with BMm ( = 0.010 ± 0.002, p < 0.001, Table 2a) and A ( = 0.017 ± 0.007, p = 0.021, Table IV 1a). Once the effect of BMm and A was removed, LS was positively linked to NPA ( = 0.112 ± 0.047, p = 0.018, Figure IV 2a). The probability for the random effect of NPA on LS to be greater than the observed effect of NPA was small (p(NPA permuted > NPA observed) = 0.002 with 10 000 values of beta from the permutated data set).

The positive influence of increasing value of NPA on LS was significantly higher than the basal link (Figure IV 2c). Only the full model was supported by the data with the GERUD approach (Supplementary Material 4, Table IV S5). BMm was positively linked with LS ( = 0.011 ± 0.002, p < 0.001, Table 2b). Again, LS increased significantly with the number of fathers ( = 0.132 ± 0.054, p = 0.015, Table IV 1b,Figure IV 2b) and the probability for the random effect of NG to be greater than the observed effect of NG on LS was small (p(NG permuted > NG observed) < 0.001, with 10 000 values of beta, Figure IV 2d). Thus, the positive effect of NG was significantly higher than the basal link between LS and the number of sires. Overall, the higher the number of sires in a litter, the larger the litter size.

Table IV 1 Estimates, standard errors, z statistics and p values of parameters linked with litter size (LS). a) Values for the number of alleles A, the mother dressed body mass BMm and the maximal number of paternal alleles NPA were obtained from the model strongly supported by the data (Table S3). b) Values for the mother dressed body mass BMm and the number of father estimated by GERUD (NG) were obtained from the model strongly supported by the data (Table S4). Significant parameters are in bold (nlitters = 160). The average number of alleles and the allelic richness we reported are the highest among all the studies dealing with multiple paternity in wild boar (Table IV 2). It is noteworthy that the average number of alleles is sensitive to the sample size (our sample size is twice as big as the largest dataset), and both the average number of alleles and the allelic richness may vary with the loci analyzed (Table IV 2). Regarding the average heterozygosity, we found a moderate value (He = 0.602) compared to other studies (Table IV 2). Remarkably, this value is closer to the average heterozygosity reported for 14 non-threatened taxa (He = 0.699) than to the one reported for their 14 taxonomically-related threatened taxa (He = 0.407) provided in [START_REF] Frankham | Introduction to conservation genetics[END_REF]. Therefore, despite the strong hunting pressure, the genetic characteristics of this population are similar to those of other wild boar populations (Table IV 2) characterized, for some of them, with a weaker hunting pressure. Thus, our studied population definitely does not show any characteristics of endangered taxa. However, we acknowledge that despite the fact that comparing heterozygosities is less sensitive to sample size than comparing allelic richness, the comparison may still be sensitive to the loci used. Interestingly, four microsatellite loci used in our study have also been used by [START_REF] Poteaux | Sociogenetic structure and mating system of a wild boar population[END_REF] Around 60.6% of the litters showed multiple paternity with GERUD, 43.7% with CERVUS, and this rate was only 33.8% with the maximal number of paternal alleles' approach.

This might suggest that the multiple paternity rate is underestimated with this last method for which at least three paternal alleles have to be identified within a litter to classify it as a litter with multiple paternity. However, in our dataset, most of the litters display two paternal alleles, which could be obtained with one or more fathers. To our knowledge, these rates of multiple paternity obtained from the first long-term study at the population level, are among the highest ever reported in the species (Table IV 2). Multiple paternity rates are high (Table IV 2) but they likely underestimate the proportion of females that mate with more than one male. Indeed, multiple paternity rates only measure the number of successful matings that lead to multiple sired litters, and do not correspond to the proportion of females that mate with more than one male. Such a proportion may potentially be higher than the reported multiple paternity rates, suggesting that the mating system in this population is predominantly promiscuous/polyandrous.

In this population where intensive hunting pressure, especially targeting males, occurs for a long time relative to the short generation time (2.27 years, [START_REF] Servanty | Influence of harvesting pressure on demographic tactics: implications for wildlife management[END_REF], we observed both promiscuous/polyandrous mating system and stable genetic characteristics. We raise the hypothesis that such a mating system might have appeared as an evolutionary response to high hunting pressure due to the lack of dominant males, and be preserved since it has the ability to maintain high genetic variability within a litter [START_REF] Pérez-González | Males and females contribute unequally to offspring genetic diversity in the polygynandrous mating system of wild boar[END_REF]. It is also possible that this mating system appeared due to a tendency for females to mate promiscuously in the absence of dominant males, and it is preserved by the continual removal of large dominant males from the population. Equations from [START_REF] Nunney | The influence of mating system and overlapping generations on effective population size[END_REF] showed that multiple paternity (likened through random union of gametes) can increase effective population size by 10% and up to 50% when compared to harem polygyny depending on the proportion of males in the population. This was measured considering a constant population size, a generation time of 2.5 years, harem sizes of 1 (monogamy) and 5 females, thus consistent with group size of female wild boars [START_REF] Dardaillon | Wild boar social groupings and seasonal changes in the Camargue, southern France[END_REF][START_REF] Podgórski | Next of kin next door -philopatry and socio-genetic population structure in wild boar[END_REF]. Thus, we hypothesize that the high rates of multiple paternity measured in our study favor the retention of a high genetic diversity through year. Unfortunately, without genetic monitoring of our population before the beginning of intensive hunting, it is impossible to quantify the change of the mating system and its influence on genetic diversity. Moreover, the population studied here is non-fenced and thus open to emigration and immigration. Even if the immigration rate is known to be low in our population (unpublished data), it is difficult to unravel the relative contribution of mating system and migration to the genetic diversity. We strongly encourage further studies to investigate the link between hunting pressure and mating systems. One exciting perspective could be to analyze multiple paternity rates among populations with different hunting pressures, as well as in non-hunted ones, to strengthen the link between hunting intensity and mating system.

After some evidence in domestic pigs (e.g. [START_REF] Waller | Effect of mating frequency on sow reproductive performance under field conditions and natural mating in large outdoor production units[END_REF], we provide here the first empirical evidence of a positive link between multiple paternity and litter size in a freeranging population. This finding was supported by the permutation tests, which showed that the observed relation is stronger than any structural relationship between litter size and the number of sires. The pig illustrates the capacity of this species to cope with strong directional selective pressures [START_REF] Gepts | Evolution during domestication[END_REF]. It is now well known that the time lapse for optimal fertilization is very short in domestic sows [START_REF] Soede | Effects of time of insemination relative to ovulation, as determined by ultrasonography, on fertilization rate and accessory sperm count in sows[END_REF][START_REF] Nissen | The influence of time of insemination relative to time of ovulation on farrowing frequency and litter size in sows, as investigated by ultrasonography[END_REF]. Therefore, the probability of presence of healthy sperm at ovulation time in the female genital tract increases with the number of artificial insemination events, thereby maximizing the number of fertilized ovules [START_REF] Kemp | Relationship of weaning-to-estrus interval to timing of ovulation and fertilization in sows[END_REF][START_REF] Corrêa | Reproductive performance of early-weaned female swine according to their estrus profile and frequency of artificial insemination[END_REF]. However, the sperm quality of the boar strongly decreases after one ejaculation for, at least, the next two days [START_REF] Frangež | Frequency of boar ejaculate collection and its influence on semen quality, pregnancy rate and litter size[END_REF]. Increasing the number of sires for a female is thus used in pig husbandry to obtain optimal fertilization and maximal litter sizes with natural reproduction [START_REF] Badinel | Biology and genetics of reproduction[END_REF]. The underlying behavioral and physiological mechanisms involved in free-ranging wild boars remain to be studied.

In conclusion, high rates of multiple paternity are measured under intensive harvesting regime where rapid evolutionary changes were previously observed [START_REF] Servanty | Pulsed resources and climate-induced variation in the reproductive traits of wild boar under high hunting pressure[END_REF][START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF]. This lead us to hypothesize that multiple paternity might be a key basis for exploited populations of wild boar to display evolution over just a few generations [START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF][START_REF] Servanty | Influence of harvesting pressure on demographic tactics: implications for wildlife management[END_REF]). It allows the population to withstand the harvesting pressure [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF]) through an increase in the number of reproductive males, an unusual pattern in ungulates [START_REF] Ginsberg | Sex-biased harvesting and population dynamics in ungulates: implications for conservation and sustainable use[END_REF], which, we show here, induces larger litter sizes. It is noteworthy that litter size is a key life history trait of fecundity, a major component in demography. Therefore, multiple paternity could be one of the factors contributing to the actual increase of wild boar abundance [START_REF] Massei | Wild boar populations up, numbers of hunters down? A review of trends and implications for Europe[END_REF]. However, the access to reproduction for younger and/or weaker males that would normally not garner matings may have long term negative consequences. Indeed, these males may carry and transmit poor quality genes that could be deleterious on the long run for the population. This study raises question about other ungulate species' strategies to buffer negative consequences of size and sex selective harvesting [START_REF] Hard | Genetic implications of reduced survival of male red deer Cervus elaphus under harvest[END_REF], since they are generally unable to modulate the number of offspring produced per reproductive event. Some changes of mating systems can be expected with a decrease of harem size allowing more males to reproduce each year when hunting is intensive. In contrast, many game species from birds to small mammals produce several offspring per reproductive event; investigating to what extent the pattern observed here apply to these species in intensive harvesting context is an interesting challenge.

Supplementary Material

Characteristics of the genetic markers

Estimation of confidence for paternity analysis with CERVUS and GERUD a) CERVUS analysis

A simulation of parentage analysis determines a critical likelihood score for several levels of confidence at the population level. Genotypes were simulated for 10 000 offspring, with 50% of candidate fathers sampled based on an estimated population size of 1200-1500 wild boars [START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF]) and the stable-age structure in this population [START_REF] Servanty | Influence of harvesting pressure on demographic tactics: implications for wildlife management[END_REF], and ≥5 loci used. A conservative overall genotyping error rate of 0.01 was assumed. Strict and relaxed confidence intervals of 95% and 80% were specified for population-level assignment probabilities.

b) GERUD analysis

To evaluate the power of our microsatellite loci to detect multiple paternity, we used the program GERUDsim 2.0 [START_REF] Jones | GERUD 2.0: a computer program for the reconstruction of parental genotypes from half-sib progeny arrays with known or unknown parents[END_REF]. Using the observed allele frequencies within the population, GERUDsim simulates sets of offspring genotypes based on user-specified litter sizes (in our case 5), draws a sample of offspring, and then estimates the number of sires present in each litter. We ran 1000 iterations of the simulation, each using a single multilocus maternal genotype and up to four randomly generated paternal multilocus genotypes (two fathers siring 4/1 and 3/2 fetuses, three fathers sharing paternity of 3/1/1 and 2/2/1 fetuses, four fathers siring 2/1/1 fetuses) to evaluate the probability of correctly determining the number of sires within litters. Simulations were conducted using the five most polymorphic loci. The reconstructed number of sires equaled the number assigned by the program in 94.4% and 97.6% of the twofather (sharing 4/1 and 3/2 offspring, respectively) simulations, in only 35.7% and 0% of the three-father (sharing 2/2/1 and 3/1/1 offspring respectively), and 0% of the four-father simulations performed in GERUDsim. Albeit in no circumstances was the number of real fathers overestimated by the heuristic search algorithm employed by GERUDsim. Given our GERUDsim simulations, our estimates of the minimum number of males contributing to litters in GERUD are very conservative.

Chapter IVB

Consequences of multiple paternity

Introduction

Natural selection on body size is generally positive [START_REF] Kingsolver | Phenotypic selection in natural populations: what limits directional selection?[END_REF], also during early life. For example, in mammals and birds, offspring with high body mass often exhibit high survival (see [START_REF] Ronget | Causes and consequences of variation in offspring body mass: meta-analyses in birds and mammals[END_REF] for meta-analyses). However, because of a tradeoff between size and number of offspring [START_REF] Smith | The optimal balance between size and number of offspring[END_REF][START_REF] Lloyd | Selection of offspring size at independence and other size-versus-number strategies[END_REF][START_REF] Winkler | Offspring size and number: a life history model linking effort per offspring and total effort[END_REF], producing many large offspring is not a sustainable reproductive tactic for polytocous species. Thus, maternal resources are either equi-allocated among offspring [START_REF] Smith | The optimal balance between size and number of offspring[END_REF], or differentially allocated among them (see e.g. [START_REF] Kühl | The 'big spenders' of the steppe: sex-specific maternal allocation and twinning in the saiga antelope[END_REF] in saiga antelope Saiga tatarica ) leading to within-litter/clutch variation in offspring mass. In variable and unpredictable environments, such a diversification of offspring phenotypes may contribute to minimizing variance in reproductive success among years [START_REF] Philippi | Hedging one's evolutionary bets, revisited[END_REF][START_REF] Starrfelt | Bet-hedging-a triple trade-off between means, variances and correlations[END_REF][START_REF] Saether | The concept of fitness in fluctuating environments[END_REF] and thus maximizing fitness [START_REF] Kaplan | The evolution of developmental plasticity in reproductive characteristics: an application of the "adaptive coin-flipping" principle[END_REF]Gamelon et al. 2013b). Interestingly, within-litter/clutch variation in offspring mass can result from multiple paternity if offspring from different fathers genetically differ in their ability to acquire and/or use maternal resources [START_REF] Watson | Multiple paternity as genetic bet-hedging in female sierra dome spiders, Linyphia litigiosa (Linyphiidae)[END_REF][START_REF] Yasui | The `genetic benefits' of female multiple mating reconsidered[END_REF][START_REF] Yasui | Female multiple mating as a genetic bet-hedging strategy when mate choice criteria are unreliable[END_REF][START_REF] Fox | Bet-hedging and the evolution of multiple mating[END_REF].

In wild boar (Sus scrofa), litter size increases with mother body mass. Heavy females produce large litters with a mixture of heavy and light offspring, whereas lighter females produce litters with similar-sized offspring (Gamelon et al. 2013b). In this polytocous species, contrary to other large mammalian species of herbivores (Gaillard et al. 2000b), piglet body mass has little influence on survival [START_REF] Baubet | Growth and survival in piglets[END_REF] allowing females to produce a large range of offspring phenotypes. Furthermore, by producing diversified offspring phenotypes, heavy females may match the mass of their offspring with teat productivity, thus decreasing within-litter competition to get access to maternal milk, and thereby increasing the chance of rearing many offspring at a given breeding event (Gamelon et al. 2013a). The species has been classically described as polygynous with female monopolization by males. However, multiple paternity has been reported suggesting a promiscuous mating system, and it has been shown that the number of fathers increases with litter size (Gayet et al. 2016). One can thus hypothesize that multiple paternity is the mechanism by which wild boar females increase within-litter variation in offspring mass. If mating with multiple males is the pathway by which females increase the phenotypic polymorphism of their offspring, differences in piglet mass should be partly determined by paternally derived alleles, and we expect a paternal genetic effect on offspring mass as well as more variable offspring in litters sired by many fathers.

Taking advantage of a unique long-term monitoring of a wild boar population, we tested the hypothesis that multiple paternity mediates within-litter diversification of offspring phenotypes. We extended previous works linking female body mass with diversification of offspring phenotypes (Gamelon et al. 2013b) by including paternity analyses. We identified fathers of fetuses from females killed during hunting and tested for a paternal effect on fetus mass. Moreover, we explored the pathways through which female body mass influences the diversification of offspring phenotypes by testing specifically a direct effect of the number of fathers per litter on phenotypic variation among offspring.

Material and methods

Study site and data collection

The study was conducted in northeastern France in the 11,000ha forest of Châteauvillain-Arc-en-Barrois. In this area, wild boars are heavily hunted each year between October and February and the annual survival of adult females is 0.48 [95% CI: 0.44; 0.51] and 0.23 [0.17; 0.30] for adult males [START_REF] Toïgo | Disentangling natural from hunting mortality in an intensively hunted wild boar population[END_REF]. Between 2007 and 2014, we recorded the dressed body mass (BM: body mass without digestive tract, heart, lungs, liver, reproductive tract and blood) of 136 pregnant females shot with the sampling date. For each female, we also recorded the litter size (LS) and each fetus (n=711) was weighed, measured (crown-rump length, in millimeters) and sexed. From the average fetus length within a litter (Length), we estimated gestation stage in days by applying the model of Henry [START_REF] Henry | Fetal Development in European Wild Hogs[END_REF]): gestation stage (in days)

= 23.43 + 0.32* Length (in mm) (Gamelon et al. 2013b). From this estimated gestation stage and the sampling date, we back-calculated the timing of mating. In order to account for yearly variation in the timing of the mating season, we expressed the timing of mating as the number of days elapsed since the first female has mated in each particular season (Timing). Thus, a Timing of zero characterizes the most precocious female in each given year. The average fetus length at sampling depends on both the timing of mating and the sampling date. Indeed, for a given timing of mating, a female will have short fetuses when killed soon after mating and longer fetuses when killed later. However, because both the mating season (ranging between July and January, see Results) and the sampling period (from October to February) are wide, there is no correlation between the timing of mating and the average fetus length within a litter when sampled.

Paternity assessment

Tissue samples were collected from all mothers, fetuses and from 762 putative fathers (i.e. putative reproductive males shot). Among the 136 litters, data of the full litters were available for 116 of them (617 fetuses, mean ± SD litter size = 5.32 ± 1.61). All tissue samples were genotyped at 12 microsatellite loci (see Gayet et al. 2016 and Supplementary Material 1 for details). The genotypes of mothers, offspring and putative reproductive males, as well as the known mother-offspring relationships were analyzed using COLONY 2.0.6.1 (Jones and

Wang 2010) and for each hunting season t, we identified the father (whether the male was sampled or not) of each fetus. Parentage among individuals was inferred by maximal likelihood. We analyzed all the litters considering as putative fathers all males sampled at season t, subadult (i.e., between one and two years of age) and adult (i.e., two years of age or older) males sampled at season t+1 and adult males sampled at season t+2. For the analysis in COLONY, the parameters were set as follow: both sex polygamous (because of the promiscuous mating system characterizing the studied population), unknown population allele frequency, full likelihood analysis method, medium precision, codominant markers, proportion of males sampled of 50% (this value is approximated but it only slightly influences results; [START_REF] Harrison | Relative accuracy of three common methods of parentage analysis in natural populations[END_REF], an allelic dropout of 0.001 and a typing error of 0.01 for each locus. Other parameters were set to their default values. This software allowed identifying fathers (n=235) of each fetus, whether the father was sampled or not. Thus, some of the fathers were identified from tissue samples while others, not sampled, were assigned by COLONY. The probability of identity that is the probability that two fathers drawn in the population have the same genotype at multiple loci, was estimated to be 7.9.10 -11 . For the offspring, the probability of identity was estimated to be 1.5.10 -4 . These values indicate high confidence for individual identification [START_REF] Waits | Estimating the probability of identity among genotypes in natural populations: cautions and guidelines[END_REF]. The probability of inferred father, which is the probability to infer correctly a sampled male as the father of a given offspring, was high: 0.974 ± 0.094.

Effect of father identity on fetus mass

For multiple paternity to translate into an increase in within-litter variation in offspring mass, father identity should affect offspring mass in utero. We estimated this effect for fathers that have produced more than one offspring (n = 148 fathers, 624 fetuses in total) using a linear mixed-effect model with individual fetus mass as response variable, fetus sex and mother identity as fixed factors and father identity as a random factor and assumed a Gaussian thus decrease the estimate of the paternal effect. Therefore, the response variable fetus mass was log-transformed to perform the analysis on a proportional scale. We ran 260,000 Markov Chain Monte Carlo iterations, with a burn-in of 10,000 iterations thinning every 250th observation, and non-informative priors were used (for the variance structures (R and G), we used an expected variance of 1 and 0.002 degree of belief parameter for the inverse-Wishart).

We computed the posterior modes and the 95% credible intervals of this ratio, of fetus sex and of the variance associated with the father identity with the "HPDinterval" function of the package MCMCglmm [START_REF] Hadfield | MCMC methods for multi-response generalized linear mixed models: the MCMCglmm R package[END_REF]) in R 3.4.0 (R Core Team 2017). We assessed convergence with the functions "heidel.diag" (Heidelberger and Welch´s convergence diagnostic) and "geweke.diag" (Geweke´s convergence diagnostic) in R and from visual inspection. We checked normality and homoscedasticity of the residuals.

Effect of the number of fathers on within-litter variation in fetus mass

To assess whether multiple paternity mediates the increase of within-litter variation, we estimated the within-litter variation in mass by calculating the coefficient of variation (CV = SD/mean) of fetus mass (on the natural scale) for each full litter (n=116), corrected for small samples as suggested by [START_REF] Haldane | The measurement of variation[END_REF]. Using confirmatory path analyses [START_REF] Shipley | Confirmatory path analysis in a generalized multilevel context[END_REF][START_REF] Shipley | The AIC model selection method applied to path analytic models compared using a d-separation test[END_REF], we then determined the causal pathways from mother body mass to within-litter variation, through the number of fathers (F) within a litter and/or litter size (LS). We included a correlation between F and LS (Gayet et al. 2016). Because mating ranged between July and January (see Results) and because females were killed from October to February, we observed litters at different periods of the year and at different gestation stages. Therefore, we included both the timing of mating (Timing) and the average fetus length (Length) (as a measure of gestation stage) in our models. We used the Akaike Information Criterion corrected for small sample size (AICc) for model selection among the ones presented inTable IV S6 and Supplementary Material Figure IV S5. We recovered the standardized regression coefficients and their associated SE. The analyses were implemented using the package piecewiseSEM [START_REF] Lefcheck | piecewiseSEM: Piecewise structural equation modelling in r for ecology, evolution, and systematics[END_REF]) in R version 3.4.0 (R Core Team 2017).

Results

Paternity assessment

Among the 116 litters analyzed, 15 had all fathers known (i.e. identified from sampled males), 30 had some fathers known while the others were assigned by COLONY, and 71 litters had all fathers assigned by COLONY. Fathers sired on average 3.03 ±2.54 (mean ± SD) offspring (Figure IV 3), with one (75.7% of the cases), two (18.3%), three (5.1%) or four (0.9%) partners.

The average number of fathers within a litter was 2.28 ±1.28 (mean ± SD) (Figure IV 3) and multiple paternity was observed in 63.8% of the litters.

Effect of father identity on fetus mass

The linear mixed-effect model evaluating paternal effect on fetus mass in utero showed no lack of convergence (Supplementary Material S3). After accounting for maternal effects, fetus mass was 5% [95% CRI: 0.04; 0.07] lighter in female offspring than in males, in accordance with previous studies [START_REF] Servanty | Litter size and fetal sex ratio adjustment in a highly polytocous species: the wild boar[END_REF]). The variance associated with paternal identity, σ Father

Effect of the number of fathers on within-litter variation in fetus mass

Although heavy females produced large litters sired by many fathers with diversified offspring mass, our path analysis did not indicate any direct link between the number of fathers per litter and the within-litter variation in fetus mass. Indeed, the best path models (Table IV S6), close in terms of AICc values, never included direct effect of the number of fathers per litter on CV of fetus mass. However, some of these models included indirect positive effects of mother body mass and number of fathers per litter on the within-litter variation through an Table IV S6 Model fit of the 13 competing path models exploring the relationship between female body mass (BM), number of fathers within the litter (F), litter size (LS), timing of mating (Timing), mean fetus length (Length) and within-litter variation in fetus mass (CV) for each litter (n=116). Displayed are the number of parameters (N), the AICc of the tested models, and the difference between each model and the best one (ΔAICc).

Model The earliest mating reported in our study occurred in mid-July (for 2014) and the latest in mid-January (for 2011) suggesting a particularly long mating season. We provided evidence that female body mass was negatively associated with Timing, a metric indicating how precocious was the mating for a female in a given season (Figure IV 4). Therefore, heavy females reproduced earlier than lighter ones during the mating season. Moreover, within-litter variation increased with gestation stage (defined as the average fetus length Length) (Figure IV 4). Because within-litter variation in offspring mass was estimated using the coefficient of variation (CV), this effect indicates that variation in offspring mass increases more during gestation than the expected proportional increase of the standard deviation with the mean.

Although based on cross-sectional data, this result suggests that offspring differ in their growth rate.

Figure IV 4 Path model with the best fit (see Table IV S6) showing how mother body mass (BM) and number of fathers per litter (F) influence the within-litter variation in fetus mass (CV) through litter size (LS), timing of mating (Timing) and mean fetus length (Length). Numbers indicate standardized regression coefficients and their associated SE.

Discussion

Our findings showed that, contrary to expectations, the diversification of offspring phenotypes within a litter did not directly result from multiple paternity and the genetic diversification of the offspring. Indeed, although larger litters were sired by more fathers as previously observed (Gayet et al. 2016) and contained fetuses of more variable mass than smaller litters, this within-litter variation in fetus mass did not directly result from the number of fathers siring the litter. This result is further supported by the lack of paternal effect on fetus mass in utero, as indicated by the small proportion of the within-litter variance explained by paternal identity. Although expected for early-life stages [START_REF] Wilson | Maternal genetic effects set the potential for evolution in a free-living vertebrate population[END_REF], this weak paternal effect on offspring mass strongly limits the possibly for the females to diversify the mass of their offspring by mating with several, genetically distinct, fathers. It is noteworthy that, due to increasing genetic diversity among offspring, other types of genetic effects such as dominance or epistatic interactions may also affect within-litter variance in offspring mass [START_REF] Neff | Genetic quality and sexual selection: an integrated framework for good genes and compatible genes[END_REF]. Exploring such effects would require repeated measurements of offspring mass produced by a given pair of mother and father, which is unfortunately impossible in our study system.

Our path analysis identifies the most likely pathways through which female body mass affects within-litter variation in fetus mass. Depending on their body mass, females mate at different periods during the rut. Heavy/old females mate earlier during the rut and have larger litters sired by a high number of fathers than lighter/younger ones. These findings suggest interindividual heterogeneity among females, with earlier mating and thus parturition dates in old and heavy females compared to young and light ones (see [START_REF] Feder | Never too late? Consequences of late birthdate for mass and survival of bighorn lambs[END_REF] for evidence on bighorn sheep Ovis canadensis). Because wild boar females having reached 33-41% of their full body mass are able to reproduce [START_REF] Servanty | Pulsed resources and climate-induced variation in the reproductive traits of wild boar under high hunting pressure[END_REF], it is likely that light/young females are primiparous, born in spring and reaching this threshold body mass to reproduce only later during the mating season. In turn, large litters produced by heavy females and gestation stage tended to directly influence within-litter variation in offspring mass.

The increase in CV of fetus mass during gestation indicates that initial differences in body mass among offspring are magnified during gestation most likely due to different growth rates among offspring. This differential growth is not affected by the fathers' genotype and the number of fathers in the litter. Indeed, if multiple paternity was involved in within-litter variation in offspring mass, through different abilities among half-sibs to acquire and/or use maternal resources, we would have detected a direct effect of the number of fathers on withinlitter diversification. This is not supported by our observations and we regard multiple paternity as an unlikely mechanism to explain diversification of offspring mass in large litters.

Differential maternal allocation among offspring might explain differences in offspring mass.

Indeed, mothers of long-lived iteroparous organisms may change the phenotype of their offspring by allocating resources differentially among them within a reproductive attempt [START_REF] Kühl | The 'big spenders' of the steppe: sex-specific maternal allocation and twinning in the saiga antelope[END_REF]). Several mechanisms, not mutually exclusive, could explain differential maternal allocation among offspring such as developmental constraints (e.g., position of the offspring in the uterus, [START_REF] Bautista | Intrauterine position as a predictor of postnatal growth and survival in the rabbit[END_REF], or sibling rivalry in utero to get access to maternal resources [START_REF] Mock | The Evolution of Sibling Rivalry[END_REF][START_REF] Hudson | Sibling competition and cooperation in mammals: challenges, developments and prospects[END_REF]. Whether differential maternal allocation among offspring is adaptive or results from developmental constraints remains to be carefully explored and offers promising avenues of research.

Microsatellite information.

Table IV S7 Number of alleles A, observed Ho and expected He heterozygosity, estimated frequency of null alleles for each locus F_Null provided by packages adegenet and PopGenReport, linkage disequilibrium LD obtained with Fstat software for each season with all other loci (NS for non-significant), P-values from 1920 randomizations of alleles among individuals within seasons to measure deviation from Hardy-Weinberg equilibrium HW for each season provided by Fstat (adjusted P-value at 5% was 0.00052), fluorescent dyes Dye used for the resolution of the PCR amplified products and their expected size Expected size for adult wild boars (n = 1244 genotypes). The set of markers, not linked to the sex, is known for a good quality of the loci and a low typing error rate. For more details on the microsatellites used, see Appendix 7 in FAO (FAO 2011) and [START_REF] Groenen | The use of microsatellite genotyping for population studies in the pig with individual and pooled DNA samples[END_REF]. The probabilities of identity between two random individuals and two siblings were estimated to be 7.9×10 -11 and 1.5×10 -4 respectively using Genalex. Table IV S8 Assessment of the convergence of the linear mixed-effect model linking individual fetus mass (log-transformed) as response variable, to fetus sex and mother identity as explanatory variables and father identity as a random effect through (a) Heidelberger and Welch´s convergence diagnostic and (b) Geweke´s convergence diagnostic. Note that because many mother identities were included in the analysis, only the convergence diagnostics for the intercept, sex and father identity are shown. In this chapter, I investigated if characteristics of male wild boars could influence their mating success and reproductive success. Despite intensive sampling, rather low proportion of fathers were identified among fetuses. The study is far from exhaustive and has several pitfalls, considering that sample males may sire offspring which are non-sampled, male characteristics when they are killed does not necessarily reflect their characteristics when they mate.

Loc us A Ho He F_ Nul l L D H W S1 H W S2 H W S3 H W S4 H W S5 H W S6 H W S7 H W S8 D ye
However, these results allow to get some highlights about which males reproduce in the population of Châteauvillain.

Introduction

Sexual dimorphism is often associated with intense intra-sexual competition to access reproduction for the sex displaying the most exaggerated characteristics [START_REF] Darwin | The descent of man and selection in relation to sex[END_REF]. In ungulates species where sexual dimorphism occurs, it is displayed by males. It takes a wide range of forms, from antlers in Cervidae, horns in Bovidae, elongated teeth in Suidae and few Cervidae species, to increased body size compared to females [START_REF] Jarman | Mating system and sexual dimorphism in large, terrestrial, mammalian herbivores[END_REF][START_REF] Emlen | The evolution of animal weapons[END_REF]. All these characteristics are used by males to access reproduction by outcompeting other males.

The sexual dimorphism is especially important in species with polygynous mating system (only one male reproduce with several females). As few males reproduce with many females, the variance in male mating success (number of mating) is high and competition is particularly intense [START_REF] Wolff | Promiscuous females protect their offspring[END_REF]. Only males able to monopolize group of females access copulation and increase their reproductive success (number of offspring sired, in other words, successful mating). However, sneaker reproductive strategies are described in male ungulates, with subordinate males waiting for a mating opportunity with a female instead of trying to monopolize a whole group [START_REF] Isvaran | Variation in male mating behaviour within ungulate populations: Patterns and processes[END_REF][START_REF] Simmons | Sperm wars and the evolution of male fertility[END_REF]. This explains why, in some species, genetic studies showed that observed number of mating can be a poor predictor of male reproductive success [START_REF] Amos | Male mating success and paternity in the grey seal, Halichoerus grypus: a study using DNA fingerprinting[END_REF][START_REF] Coltman | Male reproductive success in a promiscuous mammal: behavioural estimates compared with genetic paternity[END_REF][START_REF] Hoelzel | Alpha-male paternity in elephant seals[END_REF].

Genetic studies changed conclusions based on behavioral observations regarding mating processes for many species. This is especially true for species where females engage in multiple male mating. Genetic analyses of their offspring highlighted behavior that were never observed before, due to short male-female interaction, nocturnal mating or inaccessible mating place.

From there, studies compared male mating success from paternity analyses and from traditional methods including harem size and number of observed copulations with contrasting results. For example, for fallow deer (Dama dama) high number of observed mating lead to high number of fawns fathered [START_REF] Say | Genetic and behavioural estimates of reproductive skew in male fallow deer[END_REF], while elephant seal (Mirounga leonina) showed rather low reproductive success compared to number of mating for some dominant males (Rus [START_REF] Hoelzel | Alpha-male paternity in elephant seals[END_REF]. Paternity assignment also allowed to investigate characteristics of fathers. For example, [START_REF] Sorin | Paternity assignment for white-tailed deer (Odocoileus virginianus): mating across age classes and multiple paternity[END_REF] showed that in fallow deer older males have higher probability of reproducing but yearlings also father some fawns. [START_REF] Amos | When does conservation genetics matter?[END_REF] showed in a multiple species analysis that relatedness between parents has a negative impact on their reproductive success.

From the long-term monitoring of the wild boar population of Châteauvillain, we performed paternity analyses on litters of pregnant females killed at hunting to quantify number of mating partners and offspring for males. Paternity studies require intense sampling of females, but also of males to be able to identify which males access reproduction and which ones do not. Working on pregnant females from hunting bag allows to have good quality data regarding litter size and mother offspring relationships, however this does not give access to litters of female remaining alive in the population. This suggests that we do not know if males, that do not sire any offspring in our litter of sampled females, did not sire any offspring at all or if they only sire some in other females. However, we can have information regarding sampled males that sired offspring in sampled females. We evaluated if genetic characteristics or body mass of males influence their mating success and reproductive success. Despite the promiscuous mating system of wild boars, we expect a higher number of mating partners and offspring sired for big males. Also, we expect higher proportions of litters sired by males with higher genetic diversity.

Material and methods

We used results of COLONY analyses (Jones and Wang 2010) from the Chapter IIIA. In order to ensure sufficient samples numbers, only the population of Châteauvillain has been investigated in the present study. COLONY assigned a father to each fetus among sampled males.

If no sampled male's genotype explained the genotype of a fetus, a potential father identification was created for the reconstructed genotype. This analysis resulted in 347 fetuses assigned among 85 sampled males (832 fetuses were assigned among 280 different fathers inferred from COLONY).

Based on the 365 fathers (sampled and inferred from COLONY) and the 226 sampled mothers, we have calculated the mating success (number of partners) and the reproductive success (number of fetuses sired) of all these individuals (thus only wild boars that produced at least one progeny were included). Following [START_REF] Jones | On the opportunity for sexual selection, the bateman gradient and the maximum intensity of sexual selection[END_REF], we calculated the opportunity for sexual selection for each sex (Is) and the between sex difference (ΔI), describing the difference in strength of sexual selection [START_REF] Shuster | Is hunting an effective tool to control overabundant deer? A test using an experimental approach[END_REF]. The Bateman's gradients (βss) for males and for females was estimated by fitting linear models with the mating success as an explanatory variable and the reproductive success as an explained variable.

Focusing on sampled fathers (85 sampled males that sired at least one progeny for which the dressed body mass was known), we recorded the number of partners the males reproduced with and offspring produced per males and per year. Indeed, males that reproduced during several years are more likely to mate with more females and produce more offspring. We also estimated individual heterozygosity for each male using the GENHET function [START_REF] Coulon | Genhet: An easy-to-use R function to estimate individual heterozygosity[END_REF]) in R. The number of mating partner per year and of fetuses produced per year were log transformed and were used as explained variable in two different Gaussian regression models. The effect of individual heterozygosity (Ho) and of the body mass of males (BM) were included in both models

The pairwise relatedness was measured by the index of [START_REF] Queller | Estimating relatedness using genetic markers[END_REF].

They were calculated between mothers and fathers (rQ&G-pair) using SPAGeDI version 1.5 [START_REF] Hardy | SPAGeDi 1.5: a program for Spatial Pattern Analysis of Genetic Diversity[END_REF], when the father was identified among sampled males. We also calculated the relatedness between the mothers and all possible mating partners (males sampled included in COLONY analysis i.e. all sampled males killed the same year n as the mother, all adults and subadults of the year n-1 and only adults of the year n-2, Table III 1) to obtain the relatedness for random mating (rQ&G-possible). For each female, the values of relatedness with the fathers of its fetuses were compared to the values of relatedness with all other possible partners (random mating). The mating was considered to be with a male more related than random when the relatedness of the couple was higher than 97.5% of the relatedness values obtained with all possible matings (rQ&G-pair > rQ&G-possible-97.5) and with a male less related than random when the relatedness of the couple was below 2.5% of the relatedness values obtained with all possible mating (rQ&G-pair < rQ&G-possible-2.5).

Results

Males mated with one to five females killed at hunting (median = 1 ± 0.8 SD whether males were sampled or not, Figure V

Discussion

Comparison of males and females mating success and reproductive success showed that medians of both were higher for females, but variance of reproductive success was higher for males, with 1 to 23 fetuses sired by a male. Males gain higher reproductive success by increasing their number of mating partners compared to females, but the opportunity for sexual selection was not different between sexes. Male characteristics did not influence their mating success neither their reproductive success. Altogether, results highlight that mating seems to be random for wild boar of the population of Châteauvillain.

We observed a positive relationship between the number of mating partners and the number of offspring produced for both males and females. Such pattern was already reported in Eastern chipmunk (Tamias striatus), although with a less steeper slope for males [START_REF] Bergeron | Bateman gradients in a promiscuous mating system[END_REF]. This suggests that both males and females, but especially males, obtain fitness benefits from additional mates.

Contrary to what is reported in other ungulates, we did not find any influence of male body mass on their mating success or reproductive success [START_REF] Mcelligott | Sexual size dimorphism in fallow deer (Dama dama): Do larger, heavier males gain greater mating success?[END_REF][START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF]. However, wild boar can show great annual variation of body mass, especially rutting males. The body mass of the day they are killed may be a poor proxy of their competitive ability during the rut, especially if the time elapsed is long. Some males sired offspring more than one year before being killed at hunting. However, most males were sampled the same year as the mating was recorded suggesting that males have few mating opportunities before being killed at hunting. In this heavily hunted population, sneaker males may obtain many mating opportunities due to the disturbances caused by hunting (females often scattered by hunting dogs) and the removal of big males, homogenizing the reproductive success. The null value of ΔI shows that sexual selection is low in this population and not higher in males than in females which supports the promiscuous mating system previously described for this species [START_REF] Bergeron | Bateman gradients in a promiscuous mating system[END_REF]. Considering these results, no mate choice exists in this population. Investigating if this is true for other populations remains to be tested.

The randomness of the mating system is supported by genetic results. Analyses of relatedness and the results about individual heterozygosity also showed that mating occur randomly and there is no preference toward genetically similar or dissimilar mates. These results are contradictory to the conclusions of the study of [START_REF] Pérez-González | Heterozygosity decrease in wild boar mating system -a case of outbreeding avoidance?[END_REF] who found evidence of outbreeding avoidance in five populations of wild boars from Spain, Portugal and Hungary. They hypothesized that inbred mating may be associated with fitness benefits, but they were not able to test it. In our focus population, such benefits may not be strong enough to favor outbreeding avoidance. Moreover, high hunting pressure greatly reduce survival.

Mating opportunistically may be a best strategy than risking a reproductive failure by trying to select partner based on genetic characteristics [START_REF] Kokko | Multiple mating by females is a natural outcome of a null model of mate encounters[END_REF]. Also, the results may be different because their methodology to assess relatedness between mating partners was different. Indeed, inferring parents' relatedness from fetuses allowed them to get a higher sample size but it did not allow to measure relatedness of mating partners directly, which can influence the outcome of the result [START_REF] Van De Casteele | A comparison of microsatellitebased pairwise relatedness estimators[END_REF] We acknowledge this study has some limits. Most litters produced a given year cannot be sampled as they are produced by females that are not killed, especially big females which are protected. Thus, it is difficult to quantify the proportion of undetected fetuses produced by sampled males. We cannot know if we sampled the whole progeny of a male that may lead to an underestimation of both their mating and reproductive success. However, the results highlight random mating that would suggest that samples are representative of the overall trend in the population. The probability of having or missing fetuses sired by a male should be the same for all other males. Another limit is the sampling protocol of males. Due to budget constraints, sampling focused mainly on big males as they were supposed to be the most successful. This may also explain the lack of effect of body mass on mating success.

Model selection for mating success and reproductive success

Chapter VI

Discussion and perspectives

Overview

On the first part (Chapter IIIA), the investigation on the mating system between five populations of wild boars showed high levels of multiple paternity in all populations, clearly demonstrating the promiscuous mating system of the species in hunted populations.

Longitudinal data analyzed in the population of Châteauvillain (Chapter IIIB) showed that probability of female to engage in multiple male mating was influenced by the proportion of big males in hunting bags and body mass of dead males, but not by food resources availability. This suggests that the mating system, in this population at least, is mostly influenced by the quantity and quality of available males in the population.

Investigating the relation between the number of fathers estimated with different methods and the number of offspring of females highlighted the positive effect of the number of males contributing to a litter on the fertility of females (Chapter IVA). Increased number of males contributing to the next generation allows to maintain high levels of genetic diversity to withstand yearly bottleneck ensuing from harvesting, compared to a polygynous mating system.

No effect of the father identity was found on fetus mass (Chapter IVB) and the number of fathers did not influence phenotypic diversity within litter previously reported in wild boar. This confirms that variation of mass of fetuses in a litter is due to different allocation of female resources rather than a paternal effect.

Finally, reproductive success of both males and females increased with the number of mating partners (Chapter V). However, neither male body mass or genetic characteristics influenced their reproductive success showing that mating is random and bigger males do not sire more offspring.

Parentage studies

Since the development of molecular makers, they were widely used to study very different topics in ecology and evolution. These topics include, but not only, speciation, hybridization, migration and sexual selection. At the beginning, only low resolution markers were known, mostly protein based marker like allozyme [START_REF] Hubby | A molecular approach to the study of genic heterozygosity in natural populations. I. The number of alleles at different loci in Drosophila pseudoobscura[END_REF]. Parentage analyses were developed later because they require a higher discriminant power. The discovery of PCR in 1983 [START_REF] Mullis | Specific enzymatic amplification of DNA in vitro: The polymerase chain reaction. Mysterud, A. 2000. The relationship between ecological segregation and sexual body size dimorphism in large herbivores[END_REF]) and the characterization of microsatellites in 1984 [START_REF] Jeffreys | Hypervariable minisatelite regions in human DNA[END_REF] made possible reliable genetic identification. From there and up to now, microsatellites became markers of choice in forensic science and paternity studies [START_REF] Jones | Methods of parentage analysis in natural populations[END_REF].

Moreover, nowadays a lot of software are available for parentage analysis depending on the question investigated and data sampling. Most of them are described in Jones et al. (2010).

For my PhD, I used four different technics of paternity analysis each having its advantages and disadvantages. Here are some feedbacks of my experience about the different methods, they may not be adapted for analysis with significantly higher sample size or number of loci (Table VI 1). The simplest was to calculate the number of paternal allele (NPA). I performed the analysis using R software (R Core Team 2017), which is very quickly executed. New samples can be analyzed very easily by slightly adapting the code. However, this method only allows to have a proxy of the number of fathers in a litter. GERUD [START_REF] Jones | GERUD 2.0: a computer program for the reconstruction of parental genotypes from half-sib progeny arrays with known or unknown parents[END_REF] estimates the minimum number of genotypes (in our cases fathers, as mother-offspring relations were known) necessary to explain the genotypes of a litter. Simulations confirmed that it tends to underestimate the real number of fathers. However, technical limits worth to be mentioned for this software. Indeed, the analysis is time consuming for several reasons. The whole dataset needs to be partitioned in a lot of smaller ones. To avoid computational problems, we only included five loci (the most polymorphic) in the analysis out of twelve. Then, the software takes as an input only one mother-litter array and each of them must be analyzed separately (with repeated selection of parameters), giving an individual output. Also, as allele frequencies are required, analyses need to be performed again when new genotypes of adults are included, in order to be the most accurate and up to date possible. Thus, all mother-litter arrays must be analyzed individually again with the new allele frequencies to remains consistent over the different sampling years. The software itself is not hard to use but the analysis can be laborious. CERVUS [START_REF] Kalinowski | Revising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment[END_REF]) allows to assign parents (in my case fathers) from sampled individuals (males) to offspring. It is often the favored method for parentage identification (Jones et al. 2010). However, it is especially efficient when most of possible breeders are sampled as it assigns a father among sampled males only. Thus, no father is assigned if no sampled males fit its criteria leading to litters with missing data (incomplete resolution of the fathers of the litter) which do not allows to find the number of mating partners of females. As for GERUD, the use of the software requires few interventions of the user but to a lesser extent, as all fathers and offspring can be put in two arrays (one for each) and it makes fewer outputs.

Finally, COLONY [START_REF] Jones | COLONY: A program for parentage and sibship inference from multilocus genotype data[END_REF] was used because like CERVUS, it can assign fathers from sampled males and like GERUD, it makes genotypes reconstitution when no sampled males is identified as father. This means we can estimate the number of father for every litters included in the analysis. However, it was not used for Chapter IA because permutation analysis was not possible to test the positive link between litter size and number of father later reported in Chapter V (no configuration showed a number of offspring higher or equal than the number of fathers). The computational time can be long however computing facilities in the lab allowed to perform a lot of analyses simultaneously. This allowed me to perform analyses with different parameters, especially changing the proportion of sampled males which is a determinant parameters in paternity analysis (Jones et al. 2010).

Multi-sites studies

Working with the French Hunting and Wildlife Agency (ONCFS) allowed me to have access to exceptional data from five different populations of wild boars. Studies based on multiple sites are essential to infer general conclusions on species characteristics. This is especially true when investigating parameters depending on social factors, such as reproduction mechanisms. Population characteristics often have high impact on these processes for variety of taxa [START_REF] Schoen | Intraspecific variation in population gene diversity and effective population size correlates with the mating system in plants[END_REF][START_REF] Griffith | Extra pair paternity in birds: A review of interspecific variation and adaptive function[END_REF][START_REF] Maher | Intraspecific variation in space use, group size, and mating systems of caviomorph rodents[END_REF], although I did not record any variation between populations in our study. It is noteworthy my results are obtained from descriptive analyses, as I was not able to include fine scale information for all populations. More in depth investigations should be realized by including parameters similar to the study in Châteauvillain (Chapter IIIB: resource availability; mating date). Also, conclusions would be greatly improved by obtaining information of the structure of each population. Except in Châteauvillain where Capture-Mark-Recapture protocol is performed for many years, other populations are not as intensively monitored. Such intensive population monitoring requires a lot of field work and to invest time and money to capture and tag wild boars. This explains why it was not possible to collect so much information in every populations. However, obtaining information of the population structure before rutting (and hunting) would be very interesting.

In particular, estimating the number of reproductive males (separating big males from medium size males) and females before hunting and linking them with the hunting bag records would allow to get temporal estimations of which individuals remain in the populations. Thus, parameters such as the operational sex-ratio and the proportion of big males could be inferred to measure the intra-sexual competition between males. In large and open population like Châteauvillain, such intense monitoring may be difficult. Indeed, it is already heavily monitored and increasing catch rate would be problematic. Data from such long-term monitoring are priceless (around forty years now!) and such program should not be forsaken. However, if achievable, leading intense monitoring in closed population like Belval with smaller number of individuals could be very interesting. Indeed, small closed populations have already proven helpful to shade light on interesting mechanisms in ungulates, including reproductive processes.

For instance, Soay sheeps (Ovis aries) from the Hirta island, with a similar surface to Belval, are subject to many studies. In this population, where promiscuous mating system was observed, males mating success and reproductive success were investigated regarding morphological measures such as body mass, horn length and testes size and evidence of sperm depletion in male were reported [START_REF] Preston | Dominant rams lose out by sperm depletion[END_REF][START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF]. It is noteworthy that this population

Chapter VI Discussion and perspectives 123 is intact from human intervention for many year, contrary to Belval where wild boars are supplementary fed. Similarly, the island of Vega hosts a population of around 25 moose individuals (Alces alces) allowing very precise studies as 100% of animal are radio-collared.

Moreover, experimental tests were realized by manipulating population structure by removing older males to mimic selective hunting, for example [START_REF] Saether | Offspring sex ratio in moose Alces alces in relation to paternal age: an experiment[END_REF]. This is only possible in small and isolated populations. Of course, observations in closed populations like Belval should be confirmed with observations in free-ranging ones, as they do not necessarily reflect natural processes.

Life history traits: where does wild boar fit?

Belonging to ungulates, wild boar is often compared with other species such as red deer (Cervus elaphus), as they co-occurs in the same areas, or bighorn sheep (Ovis canadensis),

widely studied for hunting consequences, in studies of behavior and life history traits (Mysterud 2000; [START_REF] Scillitani | Do intensive drive hunts affect wild boar (Sus scrofa) spatial behaviour in Italy? Some evidences and management implications[END_REF]Frantz et al. 2012;[START_REF] Prévot | Comparing red deer (Cervus elaphus L .) and wild boar (Sus scrofa L .) dispersal patterns in southern Belgium[END_REF][START_REF] Gamelon | Do age-specific survival patterns of wild boar fit current evolutionary theories of senescence ?[END_REF].

Also, due to their overabundance and agroforest damages ensuing, it can also be compared to white-tailed deer (Odocoileus virginianus), which is a problematic species in North-America [START_REF] Russell | Effects of white-tailed deer (Odocoileus virginianus) on plants, plant populations and communities: a review[END_REF][START_REF] Rutberg | Effects of immunocontraception on a suburban population of white-tailed deer Odocoileus virginianus[END_REF][START_REF] Gortázar | Disease risks and overabundance of game species[END_REF][START_REF] Barrios-Garcia | Impact of wild boar (Sus scrofa) in its introduced and native range: a review[END_REF].

These comparisons make sense regarding several traits and phylogeny (Figure II 1, Price et al. 2005). However, other traits highly deviate from other ungulates including diet [START_REF] Schley | Diet of wild boar Sus scrofa in Western Europe, with particular reference to consumption of agricultural crops[END_REF], litter size [START_REF] Servanty | Litter size and fetal sex ratio adjustment in a highly polytocous species: the wild boar[END_REF], juvenile survival [START_REF] Jezierski | Longevity and mortality rate in a population of wild boar[END_REF], and senescence [START_REF] Gamelon | Do age-specific survival patterns of wild boar fit current evolutionary theories of senescence ?[END_REF]. These traits are closer to far different species. In late 70 's, Jezierski (1977) already pointed out striking similarities between wild boar and European hare (Lepus europaeus) concerning juvenile survival patterns and reproduction of young individuals.

However, he noticed that female wild boars reproduce when they reach two years of age while female hares can reproduce in the end of their first year. It is noteworthy that reproduction in wild boar females in their first year of age occurs, associated with heavy hunting mortality, which gives support to the comparison with hare [START_REF] Gamelon | High hunting pressure selects for earlier birth date : wild boar as a case study[END_REF][START_REF] Focardi | Survival of wild boars in a variable environment: unexpected life-history variation in an unusual ungulate[END_REF] confirmed, once again, Jezierski's comparison by reporting low ratio of weight at independence to adult weight, contrary to most ungulates, and closer to species in the fast end of the lifehistory continuum. They also point out that mammals with comparable litter size and body mass are mostly found in carnivores, for example gray wolf (Canis lupus), arguing that such reproductive outputs are made possible by their diet. Indeed, except suids, no ungulate produce litter larger than three offspring but in the same time, most ungulates are strictly herbivore.

Finally, wild boar exhibit traits of species from the slow part of the slow-fast continuum [START_REF] Gaillard | An analysis of demographic tactics in birds and mammals[END_REF](Gaillard et al. , 2000b)).

Regarding its mating system, due to the big litter size, the wild boar is hardly comparable to other ungulates in term of multiple-male mating. However, promiscuous mating system has already been reported in Soay sheep (Ovis aries), with reports of females mating with up to ten different males during 47 mating event in one day based on behavioral observations [START_REF] Grubb | Male reproductive success in a promiscuous mammal: behavioural estimates compared with genetic paternity[END_REF]Jewell 1973, cited in Coltman et al. 1999). It is noteworthy that such observations are possible in this population because it lives in a deserterd island. Habitat and nocturnal behavior of most of other ungulate species does not allow to record this kind of behavior. Moreover, for ungulates, number of offspring per litter does not allow to measure such intense multiple-male mating of females. In my study (Chapter III), the highest number of sire reported was seven which probably underestimates the number of mating partners of the females. However, estimating number of mating is not possible as most of them occur at night and in the forest.

Thus, the estimation from the number of fathers contributing to a litter makes inevitably the wild boar close to other mammals with similare litter sizes, mostly rodents like squirrels or marmots [START_REF] Martin | Environmental, social, morphological, and behavioral constraints on opportunistic multiple paternity[END_REF][START_REF] Wells | Determinants of multiple paternity in a fluctuating population of ground squirrels[END_REF]. To confirm the mating strategy, identifying (with genetic or behavioral study) which males reproduce in an hunted population would be interesting. Just like with Soay sheep, different males strategies would probably co-occurs with big males defending groups of females and smaller males using sneaker strategy by remaining near the females and trying to get access whenever it is possible for them.

Demography of wild boar: Do males matter?

This question was already raised in a paper from [START_REF] Rankin | Do males matter? The role of males in population dynamics[END_REF] in a general context approach. They explain how effect of the change of the proportion of males depends on species-specific characteristics. Also, using simple models, they show how female fertilization probability can be reduced when proportions of males are very low. At the very least, removal of males in population subject to density-dependence can increase resource availability for females by reducing intraspecific competition [START_REF] Clutton-Brock | Sex differences in emigration and mortality affect optimal management of deer populations[END_REF]. This may lead to direct increase of density as reproduction of females is improved. Subsequently, increase of proportion of males can decrease fitness of females. Less directly, high proportion of males can impair female fitness with sexual aggression and harassment during rutting period [START_REF] Réale | Female-biased mortality induced by male sexual harassment in a feral sheep population[END_REF]. On the other hand, decreasing proportion of males in the population can impact density.

In population with high rates of removal of males, in most extreme cases, sperm limitation can occur leading to decreased fertility of females [START_REF] Milner-Gulland | Reproductive collapse in saiga antelope harems[END_REF]. Also, in some species high turn-over of males induce increased infanticide as male would kill female offspring to induce a new estrus [START_REF] Whitman | Sustainable trophy hunting of African lions[END_REF]. Altogether and as concluded by [START_REF] Rankin | Do males matter? The role of males in population dynamics[END_REF], the effect of males on population demography is not as trivial as it seemed [START_REF] Caswell | Matrix population models[END_REF] and demographic models including males should be considered.

My results (Chapter IV) support this statement. The number of partners of a female has a positive impact on its fertility. This suggest that the number of males available for mating (present in the population and able to access females without competitor) can influence wild boar demography. However, further studies need to be realized to measure the real effect of males. [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF] developed a body weight-structured model to estimate growth rate of wild boar populations. They showed that body weight was a better structuring factor for this species, and an easier information to collect than age which is usually used in demographic models [START_REF] Caswell | Matrix population models[END_REF]. Indeed, this model mainly includes sex and weight of wild boar shot a given year. Implementing this model with a parameter allowing the fecundity of females to vary in response to the relative proportion of small and big males (the ratio 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑚𝑎𝑙𝑙 𝑚𝑎𝑙𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑒 𝑚𝑎𝑙𝑒𝑠 for example so that fertility increases when the opportunity for females monopolization decreases) could allow to measure how multiple paternity can impact wild boar demography. Such results would greatly complement studies focusing on quantifying how males can impact demography. However, it is worth mentioning that such studies are interesting from a fundamental research point of view to shade light on processes on population demography, but management applications are rather limited especially in a species like the wild boar.

First of all, the increased fecundity of females observed with their number of mating partners is significant but would hardly justify management strategies. Indeed, protecting big males would reduce multiple-male mating opportunity (and multiple paternity rates), but small males will probably still use sneaker strategy. Encouraging small males culling could be a solution but the hunting effort required would be very important to observe a reduction of female fertility. Moreover, the reduction of fertility observed would be disappointing regarding invested efforts. [START_REF] Gamelon | Making use of harvest information to examine alternative management scenarios: a body weight-structured model for wild boar[END_REF] showed that slight increase of hunting effort on big females could have a great impact on wild boar demography as they are the one with the highest reproductive outputs. The cost benefits ratio of this strategy is thus better due to its simplicity and efficiency.

The second pitfalls for management applications concerning wild boars, independently of the method proposed, is the reluctancy of hunters to change their habits. In the seventies, big females where protected to increase wild boar populations because in that time, wild boars were rarer [START_REF] Servanty | Dynamique d'une population chassée de sangliers (Sus scrofa scrofa) en milieu forestier[END_REF]. This way of thinking remains up to now even of populations are high and still increasing. For example, in the population of Châteauvillain, big females (> 50kg) are still protected and forfeits must be paid by the transgressor, and the amount is proportional to the weight of the female killed. When big females are not protected, it is not rare to hear hunters complain when one of them killed pregnant females, near the end of the hunting season when fetuses are easy to observe: "Thanks to you, we just lost six wild boars for the next hunting season!" if the dead females was pregnant with six fetuses (conversation I heard during field work). If hunters are aware of the problems associated with the demographic explosion of the wild boar, they are also worried about the sustainability of their practice and want to guarantee the results of the next hunting season. Indeed, [START_REF] Keuling | Regulating wild boar populations is "somebody else's problem"! -Human dimension in wild boar management[END_REF] elegantly showed the gap between their perception of wild boar management at local scale and at large scale. In their survey, most hunters agreed that populations of wild boars should be reduced, however a smaller proportion agreed measures should take place in their own hunting ground. Authors' conclusion was hunters consider that regulation of wild boar population is "somebody else's problem". Such studies highlight the importance of the social part of management strategies, especially for species like wild boar which inevitably forces people from very different contexts to interact, as already mentioned in the introduction. The problematic part is that each stakeholder has its own aims, making discussion complicated and often with pointless conclusions. Indeed, managers want to reduce populations to respond to both agricultural and societal concerns about the demographic explosion. Hunters want abundant game species to get a return on investment on their hunting license and they feel pressured to increase hunting pressure by manager. Due to the will to practice their activity in their own terms, the society often gets a bad image of hunters, especially with over-mediated cases of deviant behavior from hunters such as the killing of Cecil the lion [START_REF] Nelson | Emotions and the ethics of consequence in conservation decisions: lessons from Cecil the lion[END_REF].

Conclusion

In five hunted populations of wild boars, we found high levels of multiple paternity highlighting a promiscuous mating system of the species in such context. Moreover, from longitudinal analyses, we observed variations of mating system in response to hunting pressure showing the high plasticity of the wild boar to face environmental changes. Promiscuity is known to promote the transmission of genetic variability from one generation to the other by increasing the number of males that contribute to reproduction. These traits allow this already very plastic species to maintain a high adaptive potential. Moreover, wild boar females have high reproductive outputs, and we recorded an increase of fecundity with the number of mating partners. To my knowledge, it is the first time that the mating system is shown to increase the population demography in this species. The wild boar displays life history traits associated to invasive species including high fecundity, broad diet and high adaptability explaining the increasing population trends currently observed. The high population dynamic of the species can also be influenced by other factors that can impact the fecundity of the species. For example, changes in agricultural practices provide high quantity of food that can influence reproduction.

Also, hybridization is a major evolutive force because it can induce great evolutionary changes in a very short time scale in a species. For the wild boar, hybridization with domestic pig was already suggested as a factor explaining its demography. Indeed, domestic pig is the product of intense artificial selection to improve growth rate and female fecundity to increase productivity.

Hybridization between the two subspecies can introduce pig selected genes in wild boar populations and increase fecundity of hybrids and their descendants when introgression occurs (invasion of the genome of a species by another one's genome). Investigating if the individual level of introgression and fecundity are linked remains to be studied. However, finding discriminant genetic markers is difficult due to the low differentiation between pig and wild boar. New genetic markers and/or methods need to be developed to investigate such topic (see Appendices A and B).

Introduction

Hybridization is defined as interbreeding between individuals from two genetically different populations regardless of their phylogeny (sensu [START_REF] Rhymer | Extinction by hybridization and introgression[END_REF]. These populations are often considered as evolutionary significant units (ESUs, Ryder, 1986).

Hybridization has the potential to induce great changes on fitness in ESUs in short evolutionary timescales (Barrett and Schluter, 2008;[START_REF] Feulner | Introgression and the fate of domesticated genes in a wild mammal population[END_REF]. The impact of hybridization is particularly strong when it is linked to human activities. Indeed, ESUs separated by geographical barriers and exposed to different selective pressures may be brought in contact by anthropogenic factors such as habitat fragmentation or loss, or exotic species introduction.

Moreover, high hybridization rates may be maintained by significant gene flux through perpetual releases of domestic or captive-raised individuals [START_REF] Huxel | Rapid displacement of native species by invasive species: effects of hybridization[END_REF][START_REF] Laikre | Compromising genetic diversity in the wild: unmonitored large-scale release of plants and animals[END_REF].

As these anthropogenic driven hybridizations do not occur naturally, they are usually considered a threat to the genetic integrity of the ESUs. They can lead to loss of genetic diversity, genetic adaptations through introgression and, in more extreme cases, to a complete change in the genetic structure of the ESU [START_REF] Rhymer | Extinction by hybridization and introgression[END_REF][START_REF] Allendorf | The problems with hybrids: setting conservation guidelines[END_REF][START_REF] Laikre | Compromising genetic diversity in the wild: unmonitored large-scale release of plants and animals[END_REF].

Understanding the consequences of hybridization on fitness and on the genetic characteristics of the ESU is therefore of prime interest in population ecology and population genetic studies, and also in population management. Game species such as the wild boar (Sus scrofa scrofa) have often been the topic of such discussions due to the problematic demographic increase shown by the species in the past decades [START_REF] Massei | Wild boar populations up, numbers of hunters down? A review of trends and implications for Europe[END_REF]. In addition, wild boar managers have formulated hypotheses on the putative role of hybridization in this demographic increase (Fulgione et al., 2016). Indeed, wild boar can produce fertile offspring with the pig (Sus scrofa domesticus), its domestic counterpart. The pig was, and still is, heavily selected to improve production characteristics such as growth rate and fertility [START_REF] Rauw | Undesirable side effects of selection for high production efficiency in farm animals: a review[END_REF][START_REF] Skewes | Carcass and meat quality traits of wild boar (Sus scrofa s. L.) with 2n = 36 karyotype compared to those of phenotypically similar crossbreeds (2n = 37 and 2n = 38) raised under the same farming conditions 1. Carcass quantity and meat dressing[END_REF] putting wild boar at risk of being introgressed by domestic genes enhancing productivity (Fulgione et al., 2016). Moreover, the wild boar was subject to restocking practices that used, in part, individuals raised in farms; it is now well-known that breeders often crossed captive wild boars with pigs to increase litter size and growth rate [START_REF] Goulding | Possible genetic sources of free-living wild boar (Sus scrofa) in southern England[END_REF][START_REF] Canu | Are captive wild boar more introgressed than free-ranging wild boar? Two case studies in Italy[END_REF]. Hybridization between the wild boar and the domestic pig also raises methodological questions on the detection of hybrids for both legislation purposes (for example, hybrids are forbidden in wild boar farms in France) and evolutionary biology studies. Due to historical and recent gene flux between both sub-species [START_REF] Scandura | Genetic diversity in the European wild boar Sus scrofa: phylogeography, population structure and wild x domestic hybridization[END_REF][START_REF] Goedbloed | Reintroductions and genetic introgression from domestic pigs have shaped the genetic population structure of Northwest European wild boar[END_REF], molecular diagnostic tools to reliably identify hybrids are sorely lacking. Thus, measuring individual introgression rate, defined as the invasion of the genetic material of an ESU (here an individual) by another ESU [START_REF] Mallet | Hybridization as an invasion of the genome[END_REF], remains difficult.

Initially, the only method for detecting hybridization was based on individual karyotype, as the pig has 38 chromosomes while wild boar has only 36 in Europe [START_REF] Scandura | Genetic diversity in the European wild boar Sus scrofa: phylogeography, population structure and wild x domestic hybridization[END_REF].

However this method is not very reliable, as 50% of F2 hybrids may display 36 chromosomes [START_REF] Mcfee | Variation in chromosome number among European wild pigs[END_REF] despite having half of the genome from the pig. Later, numerous sets of molecular markers were developed to study hybridization in wild boar. They have been proven

efficient in detecting some past hybridization events [START_REF] Scandura | Ancient vs. recent processes as factors shaping the genetic variation of the European wild boar: are the effects of the last glaciation still detectable?[END_REF][START_REF] Goedbloed | Reintroductions and genetic introgression from domestic pigs have shaped the genetic population structure of Northwest European wild boar[END_REF][START_REF] Canu | Are captive wild boar more introgressed than free-ranging wild boar? Two case studies in Italy[END_REF] but not in inferring hybridization rates in wild boar populations or individual rates of admixture. For example, Asian pig mitochondrial DNA (mtDNA) haplotype appeared in European pig breeds when species were crossed to improve European pig breeds [START_REF] Giuffra | The origin of the domestic pig: independent domestication and subsequent introgression[END_REF]. The presence of Asian pig mtDNA in European wild boar clearly proves past hybridization events (Fang et al., 2006;[START_REF] Scandura | Ancient vs. recent processes as factors shaping the genetic variation of the European wild boar: are the effects of the last glaciation still detectable?[END_REF] but it only shows hybridization with domestic pigs that bear the Asian mtDNA, and it is not transmitted by male hybrids. To circumvent this pitfall, male specific markers were also investigated on the Ychromosome [START_REF] Iacolina | Novel Y-chromosome short tandem repeats in Sus scrofa and their variation in European wild boar and domestic pig populations[END_REF]. A non sex-specific gene coding for a protein involved in coat color, melanocortin-1 receptor (MC1R), was also used to detect hybridization in wild boar, as some allelic forms are specific to the domestic pig [START_REF] Canu | Lack of polymorphism at the MC1R wild-type allele and evidence of domestic allele introgression across European wild boar populations[END_REF]. Finally, more neutral markers such as SNPs (Single Nucleotide Polymorphism) and microsatellites have also been used, as in numerous taxa, without giving hybrid identification beyond any doubt for wild boar [START_REF] Scandura | Ancient vs. recent processes as factors shaping the genetic variation of the European wild boar: are the effects of the last glaciation still detectable?[END_REF][START_REF] Scandura | Genetic diversity in the European wild boar Sus scrofa: phylogeography, population structure and wild x domestic hybridization[END_REF]Frantz et al., 2012;[START_REF] Goedbloed | Reintroductions and genetic introgression from domestic pigs have shaped the genetic population structure of Northwest European wild boar[END_REF][START_REF] Canu | Are captive wild boar more introgressed than free-ranging wild boar? Two case studies in Italy[END_REF].

Therefore, the identification of hybrids, estimation of the population hybridization rate and the level of individual introgressions are still a major concern in both wild boar management and evolutionary biology. Comparing different sets of molecular markers in terms of their reliability in detecting hybrids and their levels of introgression is a first step toward a better understanding of the wild boar/domestic pig hybridization complex and its consequences in evolutionary biology. Such a comparison must rely on a simulated dataset but would also benefit from the inclusion of real hybrid individuals in data analysis. Despite increasing interest in the wild boar-domestic pig hybridization complex, to our knowledge no study including individuals of known hybrid origin has been carried out. Obtaining such individuals would require experimental crosses, which are difficult to carry out due to legislation and costly husbandry. However, individuals with a hybrid phenotype (i.e. displaying phenotypic characters of both wild boar and domestic pig) can be found in natural populations. Including such individuals in analysis is important to quantify the ability of markers to detect hybridization and validate genetic tools only if they are able to detect it. This kind of approach has already proved efficient for other hybridization complexes (see Godinho et al., 2011 for wolf×dog;Nussberger et al., 2013 for wildcat×dometic cat).

In this study, we compared the efficiency of two sets of molecular markers, 20 SNPs and 12 microsatellites, to detect hybridization and quantify the level of introgression of the pig genome in wild boars. The 20 SNPs were specifically developed for the study of wild boar hybridization [START_REF] Beugin | A set of 20 multiplexed Single Nucleotide Polymorphism (SNP) markers specifically selected for the identification of the wild boar (Sus scrofa scrofa) and the domestic pig (Sus scrofa domesticus)[END_REF] while the microsatellites were commonly used in genetic population studies including paternity analysis (Gayet et al., 2016). The genotypes of 270 wild boars and 57 pigs from commercial breeds defined the parental populations for both sets of markers. We conducted simulation analysis to assess the efficiency of both types of molecular markers to detect hybrids of different generations including F1 hybrids and backcrosses. We also added 139 individuals collected in wild populations of wild boars showing phenotypic evidence of pig introgression in order to verify the ability of both sets of markers to detect hybridization and quantify the level of introgression on real genotypes. This allowed us to be sure that hybrids detected in the wild boar population were not artefacts of the genetic analysis.

Material and Methods

Sample collection

Two hundred and seventy wild boars, i.e. with a typical wild boar phenotype, were sampled from the population located in the Châteauvillain-Arc-en-Barrois forest (48°02′N; 4°55′E, France) for five hunting seasons (2007)(2008)(2009)(2010)(2011). In addition, 57 domestic pigs were sampled from commercial butchery meat as described in [START_REF] Beugin | A set of 20 multiplexed Single Nucleotide Polymorphism (SNP) markers specifically selected for the identification of the wild boar (Sus scrofa scrofa) and the domestic pig (Sus scrofa domesticus)[END_REF]. A national sampling campaign was carried out by the ONCFS (French hunting and wildlife agency) for two years: hunters were asked to collect samples from wild boars showing evidence of hybridization with domestic pig (called thereafter phenotypically anomalous wild boars, abbreviated PAWs). We asked hunters to report criteria justifying sampling of a PAW. The criteria were part of a list of phenotypic evidence of hybridization with domestic pig described by [START_REF] Pinet | L'élevage du sanglier de race pure[END_REF] see Supplementary Material, Table S1). A total of 139 samples of PAWs were obtained from all parts of France (Supplementary Material, Figure S1). PAWs were grouped according to the number of phenotypic characteristics from the pig that they displayed and that were realized from K=1 to K=9. The program STRUCTURE HARVESTER [START_REF] Earl | STRUCTURE HARVESTER: a website and program for visualizing STRUCTURE output and implementing the Evanno method[END_REF] was then used to estimate the most likely number of clusters K that fit the data with the method described by [START_REF] Evanno | Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study[END_REF]. The results of the 20 runs were averaged using CLUMPP [START_REF] Jakobsson | CLUMPP: a cluster matching and permutation program for dealing with label switching and multimodality in analysis of population structure[END_REF] to get averaged qik values for each individual.

The second method used NEWHYBRIDS software [START_REF] Anderson | A model-based method for identifying species hybrids using multilocus genetic data[END_REF] ). The analysis was carried out with 20 independent runs of 20,000 iterations of burn-in and followed by 500,000 iterations of MCMC. As the origin of the pigs is known, we used the parameter z to specify they belong to the genotype class of pig but all other parameters were set as default. The 20 runs were then averaged.

Simulation analysis

These Bayesian approaches do not permit statistical assessment of the efficiency of loci to detect hybridization. Simulations have been made to overcome this problem [START_REF] Vähä | Efficiency of model-based Bayesian methods for detecting hybrid individuals under different hybridization scenarios and with different numbers of loci[END_REF]. For both sets of markers, all pigs showing a qi-Pig (individual probability to belong to pig group) equal to or higher than 0.99 with STRUCTURE (34 with SNPs and 36 with microsatellites) were used to create the reference population of pure pig. Subsequently, the same number of wild boars was kept to create the reference population of pure wild boars (they all had a qi-WB higher than 0.996 whether it was with SNPs or microsatellites). We used the function hybridize from adegenet to create 100 individuals of each of the 10 genotype classes described above. A total of 20 datasets of 1000 individuals each containing the 10 different hybrid genotypic classes were simulated for SNPs and for microsatellites. They were analyzed with STRUCTURE and NEWHYBRIDS with the same parameters used for real datasets. These simulations allowed us to obtain threshold values of assignment to the different hybrid classes for individuals whether datasets were real or simulated.

For each marker in STRUCTURE, thresholds were determined based on simulated datasets results to create a decision rule to assign a real individual to one of the parental or hybrid groups.

For clarity, we only considered probabilities of assignation to the wild boar group (i.e. qi-WB, acknowledging for K=2, qi-Pig = 1-qi-WB). The threshold of assignment to the wild boar group (qWB-WB-95%) was calculated as the qi-WB value obtained by 95% of simulated wild boars. Thus, a real individual with a qi-WB higher than qWB-WB-95% would be considered a true wild boar.

Symmetrically, a threshold of assignment for the pig group (qPig-WB-95%) was also calculated using qi-WB values obtained for simulated pigs. Real individuals obtaining qi-WB below qPig-WB-95% would be assigned to pigs but those with qi-WB between qWB-WB-95% and qPig-WB-95% would be considered hybrid. To go further and estimate individual introgression level, threshold values were also calculated for assignment to the eight hybrid genotypic groups. However STRUCTURE only gives assignment to parental populations, so we calculated an upper and a lower threshold for each genotypic (qH-WB-97.5% and qH-WB-2.5% respectively, H indicating the hybrid genotypic class considered), containing 95% of simulated individuals' qi-WB values of the given genotypic group. The genotypic class of a real individual can be assessed using these thresholds. Firstly, we compare the qi-WB obtained by a given real individual to qWB-WB-95%. If qi-WB > qWB-WB-95%, the individual is considered a wild boar, otherwise a hybrid (or assigned to pig if qi-WB < qPig-WB-95%). To identify the hybrid class, the qi-WB must be between the qH-WB-97.5% and qH-WB-2.5% of the H hybrid genotypic class, and out of all the others. Then the individual can be considered a hybrid of the H class. For each marker, the medians of obtained qi-WB values per genotypic class were compared to expected qi-WB values (considering qPig-WB=0, qWB-WB=1, qF1-WB=0.5, qF2-WB=0.5, qBackcross.Pig-WB=0.25, qBackcross.WB-WB=0.75, qBackcross.WB×WB-WB=0.875…etc.) using chi-squared tests.

For each marker in NEWHYBRIDS, 10 thresholds (one for each of the 10 genotype classes described above) were calculated to get a decision rule to assign an individual to one of the 10 genotype classes. Each threshold was calculated, based on the results obtained for each of the 10 simulated genotype classes, considering the probability of assignment to the right group obtained by 95% of simulated individuals of the group (for example, the probability of assignment to the F1 group obtained by simulated F1). Thus, a real individual was considered to belong to a genotypic group if its individual probability of assignment to this group was higher than the threshold of this group and below all other nine thresholds. For example, an individual was considered to be F1 if the assignment to the F1 group was higher than the threshold value of F1 group and assignments to other genotypic groups were below corresponding threshold values.

The results of the simulation allowed us to evaluate the accuracy (the ratio of the number of individuals correctly assigned to the group and the number of all individuals assigned to the group) per genotypic group, for both sets of markers and for each method, as described in [START_REF] Vähä | Efficiency of model-based Bayesian methods for detecting hybrid individuals under different hybridization scenarios and with different numbers of loci[END_REF] as the efficiency (proportion of individuals of a genotypic group correctly Table 1: Information for SNP loci for wild boar (Wb) and pig hybridization analysis. The name, the FST between wild boar and pig and the informativeness index (I_n) are given for each locus.

For each population, the number of individuals genotyped (n), the frequency of the major allele (F) and the expected heterozygosity at the locus (He) are provided. PAWs were excluded from the analysis. The marker name, the FST between wild boar and pig, the informativeness index (I_n), and the total number of alleles (N) are given for each locus. For each population, the number of individuals genotyped (n), the allelic richness (Ar), the number of private alleles (Np), the frequency of the most frequent allele (F) and the expected heterozygosity at the locus (He) are provided. PAWs were excluded from the analysis. Overall accuracies were similar between SNPs and microsatellites (χ² = 0.588, df = 9, p-value = 0.999, Supplementary Material, Table S2). The threshold values of assignment to the wild boar population calculated using simulated wild boar results were estimated at qWB-WB-95% = 0.931 with SNPs and 0.924 with microsatellites. Symmetrically, thresholds were estimated for assignment to the pig group qPig-WB-95% = 0.110 and 0.111 with SNPs and microsatellites respectively (Figure 1). Other hybrid genotypic groups displayed ranges of qi-WB values that strongly overlapped each other (Supplementary Material, Figure S2). These hybrid genotypic groups were poorly differentiated one from another because many individuals were assigned to several groups. Thus accuracy was very low for hybrid and introgressed groups with a maximum of 42.5% with SNPs and 34.7% with microsatellites (Supplementary Material, Table S2). This means less than 50% of individuals assigned to a group are really from this group. So threshold values (qH-WB-97.5% and qH-WB-2.5%) were not reported for these groups. Moreover, some backcrosses with wild boar obtained qi-WB values higher than the thresholds qWB-WB-95% for both sets of markers. This means they would be wrongly assigned to the wild boar groups (explaining the accuracy of 89.9% with SNPs and 83.4% for microsatellites) and that wild boar detected by this method are in fact a mixture of pure individuals and backcrosses of different generations. However, backcrosses with pig were always separated from the wild boar genetic cluster. To summarize, individuals with qi-WB values above qWB-WB-95% will be assigned to the wild boar parental population. Real individuals with qi-WB values below qWB-WB-95% values cannot be considered as individuals from the wild boar group. They will be identified as hybrids. However their hybrid class cannot be categorized due to overlapping ranges of values of different hybrid genotypic groups and the low accuracy of detection. Individuals with a high proportion of the genome from one of the parental populations (especially Bc.WB×WB and Bc.P×P) may not be identified as hybrids and would be assigned to this parental population.

On real genotypes, 1.92% of wild boars obtained qi-WB values below the qWB-WB-95% threshold value with both SNPs and microsatellites (Table 3). PAWs from the sampling campaign also showed qi-WB values below the qWB-WB-95% threshold. This was the case for 31% and 42.9% out of 42 PAW0, and for 35.1% and 37.2% out of the 94 PAW+, for SNPs and microsatellites respectively. The proportion of individuals showing qi-WB below qWB-WB-95% increased with the number of criteria for both sets of markers because 27.2% and 30.9% out of the 87 PAW1 and 75% and 62.5% out of the 8 PAW2 were detected as hybrids, with SNPs and microsatellites respectively. All PAW3 and PAW4 obtained qi-WB values below qWB-WB-95%.

Overall, 23.4% of PAW+ were identified as hybrids with both sets of markers (Table 3).

NEWHYBRIDS results with real and simulated data

With both sets of markers, the pigs were well separated from the wild boars using NEWHYBRIDS (Figure 2 a andc).

With both SNPs and microsatellites, simulation analysis results showed pigs, wild boars and F1 were globally well identified (Figure 2 b and d) as they were assigned to their right group with high probabilities, despite some individuals obtaining low probabilities of right assignment (down to 0 for F1). Thus, proportions of correct assignment were high especially compared to other genotypic classes. Threshold values were calculated using probabilities of assignment above which 95% of simulated individuals were assigned to their right genotypic group. No difference in overall accuracy was found between SNPs and microsatellites (χ² = 1.98, df = 9, p-value = 0.992). Accuracies for pigs, wild boars and F1 were the highest for both set of markers (Supplementary Material, Table S3). Exact assignment occurred mainly for wild boar and F1 with both SNPs (more than 91% of accuracy) and microsatellites (more than 73% of accuracy). Further introgression levels were assigned to their right genotypic group with lower values of probabilities, thus with less accuracy. Indeed, some genotypic groups obtained a high proportion of individuals with a probability of 0 to be assigned to the right group (Figure 2 b and d for the F2 hybrid class, Supplementary Material, Figure S4) giving 95% threshold values close to 0. Only threshold values of assignment for pigs, wild boars and F1 were considered for further analysis for both sets of markers due to low accuracies for other genotypic groups. These thresholds were always higher with SNPs than with microsatellites.

Probabilities of assignment above which 95% of simulated wild boars were assigned were 0.773 and 0.707 for SNPs and microsatellites respectively. These 95% threshold values of assignment to pig were 0.786 with SNPs and 0.731 with microsatellites. Threshold of assignment to F1 were 0.578 with SNPs and 0.289 with microsatellites.

On real genotypes, proportions of wild boars that displayed probabilities of assignment below the wild boar threshold was 6.13% with SNPs and 5.75% with microsatellites (Figure 2a

Discussion Marker description and informativeness

The comparison between SNP and microsatellite sets showed higher differentiation indexes for SNPs. This is consistent with the design of the set of SNPs since they were especially developed for the study of hybridization [START_REF] Beugin | A set of 20 multiplexed Single Nucleotide Polymorphism (SNP) markers specifically selected for the identification of the wild boar (Sus scrofa scrofa) and the domestic pig (Sus scrofa domesticus)[END_REF]. In addition, the SNPs were located in coding regions which may have been under selection in pigs [START_REF] Beugin | A set of 20 multiplexed Single Nucleotide Polymorphism (SNP) markers specifically selected for the identification of the wild boar (Sus scrofa scrofa) and the domestic pig (Sus scrofa domesticus)[END_REF] increasing differentiation indexes between pigs and wild boars. Private alleles occurred in domestic pigs (although less than in [START_REF] Beugin | A set of 20 multiplexed Single Nucleotide Polymorphism (SNP) markers specifically selected for the identification of the wild boar (Sus scrofa scrofa) and the domestic pig (Sus scrofa domesticus)[END_REF])) but they were not fixed. For microsatellites, some alleles were also private to the pig parental group. Finding these private alleles in wild boar may reveal hybridization as finding Asian mtDNA in a wild boar proves that hybridization occurred in the wild boar lineage (Fang et al., 2006;[START_REF] Scandura | Ancient vs. recent processes as factors shaping the genetic variation of the European wild boar: are the effects of the last glaciation still detectable?[END_REF]. However, these pig private alleles cannot be considered diagnostic since they are not fixed in the pig parental group. Even if FST indexes differed between sets of markers, the informativeness indexes did not, highlighting that both sets of markers may perform equally well in detecting hybridization. This last point was confirmed by the simulated data analysis results and fits previous studies that showed that fewer microsatellite loci are required than SNPs to obtain a given amount of information [START_REF] Rosenberg | Informativeness of genetic markers for inference of ancestry[END_REF][START_REF] Liu | Comparison of single-nucleotide polymorphisms and microsatellites in inference of population structure[END_REF].

Simulated parental individuals identified and separated from F1 hybrids

Wild boars and pigs used to create simulated datasets had high assignment value to their respective groups. However, individuals of parental populations simulated using these individuals were assigned to their respective group with lower probabilities with both sets of markers with STRUCTURE. As for NEWHYBRIDS, some simulated parental individuals obtained very low assignment probabilities to their groups. These results can be explained by the sensitivity of both STRUCTURE and NEWHYBRIDS to the proportion of hybrids in the datasets [START_REF] Vähä | Efficiency of model-based Bayesian methods for detecting hybrid individuals under different hybridization scenarios and with different numbers of loci[END_REF], as proportions of hybrids in the simulated datasets are higher than those in the real ones. Moreover, the population sampling size can also influence the results [START_REF] Puechmaille | The program structure does not reliably recover the correct population structure when sampling is uneven: Subsampling and new estimators alleviate the problem[END_REF] and simulated data sets did not have the same characteristics as the real ones (more individuals, higher proportions of hybrids compared to parental individuals). Real individuals from parental populations obtained initially high assignment for their genotypic group while simulated individuals from parental population got lower values when analyzed in the simulated datasets. So the threshold values tended to be lower than expected and, for a real individual to be excluded from the wild boar genotypic group, the qi-WB needs to be low. With STRUCTURE, we considered qWB-WB-95% and qPig-WB-95% thresholds were conservative for the identification of hybrids (hybrid origin is sure for an individual assigned to hybrids, i.e. qi-WB < qWB-WB-95%) and relaxed for the parental population (some hybrids may be assigned to wild boar, i.e. qi-WB > qWB-WB-95%). Similarly, with NEWHYBRIDS, as some simulated individuals from parental population obtained low assignment probabilities, thresholds are low compared to what could be expected. Thresholds are once again relaxed for identification of individuals from parental populations. However, accuracy for parental group assignments was high with both SNPs and microsatellites and with both methods. This proves that despite the low threshold values compared to what could be expected, these thresholds are reliable and meaningful. In the STRUCTURE analysis, ranges of qi-WB values for F1 hybrids did not overlap parental qi-WB ranges. However, ranges of qi-WB values for F1 hybrids strongly overlapped all other genotypic class qi-WB ranges with both sets of markers. Thus, STRUCTURE can identify hybrids but not estimate the introgression level, and both types of markers performed equally well. [START_REF] Vähä | Efficiency of model-based Bayesian methods for detecting hybrid individuals under different hybridization scenarios and with different numbers of loci[END_REF] showed that 24 microsatellite loci for a FST of 0.12 are required to distinguish F1 from parental population with STRUCTURE. With half this number of loci and a similar median value of FST, our set of microsatellite markers allowed F1 differentiation from parental populations, suggesting the efficiency might also depend on loci used. NEWHYBRIDS performed slightly better because assignment probabilities for the F1 group were better with both SNP and microsatellites. Moreover, accuracy for F1 was high with both sets of markers. This suggests that F1 could be identified with confidence using NEWHYBRIDS. Overall, assignments to parental groups are reliable with both SNPs and microsatellites and the two methods, and so are assignments to F1 with NEWHYBRIDS with both sets of markers.

On the difficulty of quantifying individual introgression level beyond F1

Simulation results showed that genotypic groups other than parental and F1 groups were identified with low accuracies, independently of the marker and the method. Indeed, more than 50% of individuals assigned to any of these groups were wrongly assigned. With NEWHYBRIDS, assignment probabilities to the right group were low for individuals from these groups with both sets of markers, and high proportions of individuals obtained a probability of 0 to be assigned correctly. This led to very low threshold values, which were not reliable. With STRUCTURE, the genotypic group was impossible to infer since ranges of qi-WB values obtained for simulated hybrid groups (including F1) strongly overlapped each other. This led threshold values to be close to one another. Even if by default 95% of individuals were assigned to their right genotypic class, high proportions were also significantly assigned to other genotypic groups. As genotypic groups could not be distinguished, thresholds were not reliable. With both sets of markers and both methods, some backcrosses were even assigned to the closest parental population. This can be explained firstly by the high proportion of the parental population genome in the most introgressed genotypic groups (in theory, 87.5% of pig and wild boar genome for, respectively, Bc.P×P and Bc.Wb×Wb). Secondly, the relaxed thresholds for the parental population, allowing more assignment mistakes in parental populations than in hybrids, may cause some hybrids to be wrongly assigned to parental groups. It is noteworthy that backcrosses with pig (Bc.P, Bc.P×P or Bc.P×F1) never overlapped the range of values of wild boar even though the wild boar identification is relaxed. However, these kinds of individuals should be rare and may only occur where pigs are kept in outdoor enclosures, which is a rare practice except in a few regions [START_REF] Canu | Are captive wild boar more introgressed than free-ranging wild boar? Two case studies in Italy[END_REF]. In the wild, the most likely crosses are backcrosses with wild boars (Bc.Wb, Bc.Wb×Wb or Bc.Wb×F1). Thus these genotypic groups are the most important to detect, but simulations showed they may not be identified. To distinguish the purebred population from F1 and backcrosses, [START_REF] Vähä | Efficiency of model-based Bayesian methods for detecting hybrid individuals under different hybridization scenarios and with different numbers of loci[END_REF] suggested the use of 48 microsatellite loci with a FST value of 0.21. Our microsatellite set is thus not powerful enough to do that. Our simulation analyses results can be compared to the study realized by [START_REF] Godinho | Genetic evidence for multiple events of hybridization between wolves and domestic dogs in the Iberian Peninsula[END_REF] on wolf and dog hybridization, since they used same Bayesian approaches. Their STRUCTURE study showed high identification efficiency for the parental population, distinction between parental from F1 and from F2 and a decrease of identification for more introgressed individuals. With NEWHYBRIDS, overall they obtained better identification rates of parental groups up to the first generation backcrosses. This is mainly due to the fact that they investigated for simple backcrosses with parental population. As assignment probabilities sum to 1 for each individual, decreasing the number of possible assigned clusters tends to increase assignment probabilities in each cluster. However, this strategy does not enable the detection of more introgressed individuals, nor does it estimate how more introgressed levels are assigned in this framework.

On the detection of hybrids in real populations

Using thresholds obtained by simulation analyses, between 30% and 50% of PAW0 were excluded from the wild boar group. This suggests that they were not sampled by mistake by hunters as high proportions proved to be hybrid individuals (similar proportions to PAW1).

Depending on the marker and the analysis, between 35.1% and 43.6% of PAW+ (i.e. 33 and 41 out of 94), obtained assignment below threshold for wild boar. The proportion of PAW+ identified as hybrid was clearly dependent on the number of criteria indicating hybridization.

For both sets of markers, the proportions increased from PAW1 to PAW2, to finally reach 100% of hybrids detected for PWA3 and PAW4 (Table 4). Indeed, the probability of expressing phenotypic traits should increase with the proportion of pig genome in the individuals, which decrease with the time elapsed since the hybridization event. Both types of markers performed again equally well in identifying PAWs as hybrids (Table 4) even if they did not recognize some individuals. This can be explained by different selective pressures on microsatellites and

Faculté

  Techniques des Activités Physiques et Sportives Observatoire des Sciences de l'Univers de Lyon Polytech Lyon Ecole Supérieure de Chimie Physique Electronique Institut Universitaire de Technologie de Lyon 1 Ecole Supérieure du Professorat et de l'Education Institut de Science Financière et d'Assurances Directeur : M. F. DE MARCHI Directeur : M. le Professeur F. THEVENARD Directeur : Mme C. FELIX Directeur : M. Hassan HAMMOURI Directeur : M. le Professeur S. AKKOUCHE Directeur : M. le Professeur G. TOMANOV Directeur : M. le Professeur H. BEN HADID Directeur : M. le Professeur J-C PLENET Directeur : M. Y. VANPOULLE Directeur : M. B. GUIDERDONI Directeur : M. le Professeur E. PERRIN Directeur : M. G. PIGNAULT Directeur : M. le Professeur C. VITON Directeur : M. le Professeur A. MOUGNIOTTE Directeur : M. N. LEBOISNE Modification of the structure of wild boar populations by hunting and influence on reproductive processes Thibault GAYET A thesis presented for the degree of

Figure I 1

 1 Figure I 1 Means and variances of fitness of polygamous, promiscuous and monogamous males. .... 6 Figure I 2 Evolution of wild boar hunting bags from selected European countries (from Massei et al. 2015). ................................................................................................................................................. 11 Figure II 1 Supertree representing the phylogenic classification of cetartiodactyl from Price et al. (2005) ................................................................................................................................................. 17

Figure II 2 Figure V 1 Figure V 3 Figure V 4

 2134 Figure II 2 Worldwide distribution of Sus scrofa (wild boar and feral pigs). .................................... 18 Figure II 3 Proportions of food items in wild boar diet from various habitats. ................................. 20 Figure II 4 Location and representation of the forest of Châteauvillain-Arc-en-Barrois. The red line represents the national forest where hunting takes place. .................................................................. 22 Figure II 5 Number of wild boars killed annually and surface of the study areas for each populations of wild boars....................................................................................................................................... 23 Figure II 6 Location and representation of the study areas. ............................................................... 24 Figure III 1 Number of wild boars killed per 100ha in the five populations of wild boars. .............. 35 Figure III 2 Frequency of the number of fathers found in a litter with varying proportions of fathers sampled. ............................................................................................................................................. 37 Figure III 3 Weight of reproductive males killed at hunting each year in Chambord, Châteauvillain, Chizé and La Petite Pierre. ................................................................................................................. 40 Figure III 5 Evolution of the proportion of forest fruits and corn in wild boar stomach contents..... 56 Figure IV 1 Distribution of the estimation of number of sires per litter. ........................................... 73 Figure IV 2 Effect of the number of sires per litter on litter size and premutation tests. .................. 74 Figure IV 3 Number of sampled offspring per father and number of litters with 1 to 6 fathers observed. ....................................................................................................................................................... 92 Figure IV 4 Path model with the best fit showing how factors influence the within-litter variation in fetus mass. .......................................................................................................................................... 94 Figure IV S5 Thirteen different competing path models explaining within-litter variation in fetus mass. ................................................................................................................................................... 98 Figure IV S6 Assessment of the convergence of the linear mixed-effect model. ............................ 102 Figure V 1 Distribution of the estimated number of mating partners and number of offspring produced for males and females. ..................................................................................................................... 110 Figure V 2 Bateman's gradients for males and females. ................................................................. 110 Figure V 3 Annual mating success and reproductive success of males. .......................................... 111 Figure V 4 Comparison of the relatedness expected under random mating choice and from realized mating............................................................................................................................................... 111 Figure V S5 Dressed body mass of males sampled for paternity analysis from the population of Châteauvillain. ................................................................................................................................. 114

Figure I 2

 2 Figure I 2 Evolution of wild boar hunting bags from selected European countries (from Massei et al. 2015).

Figure II 1

 1 Figure II 1 Supertree representing the phylogenic classification of cetartiodactyl from[START_REF] Price | A complete phylogeny of the whales, dolphins and even-toed hoofed mammals (Cetartiodactyla)[END_REF]

Figure II 2

 2 Figure II 2 Worldwide distribution of Sus scrofa (wild boar and feral pigs). The species native range demarked in black and introduced range in gray. Gray circles indicate the islands where S. scrofa have been introduced. (?) denotes occurrence but unknown distribution (from Barrios-Garcia and Ballari (2012)).

Figure II 4

 4 Figure II 4 Location and representation of the forest of Châteauvillain-Arc-en-Barrois. The red line represents the national forest where hunting takes place.

Figure II 5

 5 Figure II 5 Number of wild boars killed annually and surface of the study areas for each populations of wild boars.

inFigure II 6

 6 Figure II 6 Location and representation of the study areas: a) National Reserve de La Petite Pierre, b) Domaine National de Chambord, c) Réserve Biologique Intégrale de Chizé and d) Domaine de Belval.

  were realized in the five wild boar populations of Belval, Chambord, Châteauvillain, Chizé and La Petite Pierre (described in Chapter II). The number of animals killed in a given year was recorded and reported to the hunting area to estimate a number of individuals killed per unit of space (Figure III 1), which is a proxy of hunting pressure. Belval and Chambord have the highest number of individuals killed per 100ha, while Chizé and La Petite Pierre have the lowest values. Châteauvillain is between the two groups (Figure III 1).The mean litter size ranged from 4.92 in Chambord to 7.12 in Belval with intermediate values for the three other populations (TableIII 1).

Figure III 1

 1 Figure III 1 Number of wild boars killed per 100ha (median ± SD) for five wild boar populations (nyear-Belval=4, nyear-Chambord=3, nyear-Châteauvillain=9, nyear-Chizé=2, nyear-La Petite Pierre=5). A and B symbolize significant difference between groups (Kruskal-Wallis test: χ² = 19.057, df = 4, pvalue < 0.001).

Figure III 2

 2 Figure III 2 Frequency of the number of fathers (sampled or inferred by COLONY) found in a litter for the five populations of wild boars analyzed with COLONY using different values for the proportion of fathers sampled varying from 0 to 100, increasing from left to right (also indicated by the color). The red bar highlights the value selected for analysis (50%).

Figure III 3

 3 Figure III 3 Weight of reproductive males killed at hunting each year from the four wild boar populations of a) Chambord, b) Châteauvillain, c) Chizé and d) La Petite Pierre. Sample size are given by the red values below each plot. The width shows the density of points. The white points show the median, the thick black vertical lines the central quartiles and the fine vertical lines 1.5 the inter-quartile space. Red crosses show the threshold of 80% of the weight of the heaviest male killed a given year.

  Figure III 2). Multiple paternity rates across seasons were high and do not varies between population (Figure III 4b, Kruskal-Wallis test: χ² = 1.043, df = 4, p-value = 0.90). High inter-annual variations were observed especially in population with low sample sizes (Belval and Chizé).

Figure

  Figure III 4 a) Number of fathers per litter and b) multiple paternity rates (median across seasons ± SD) obtained from the analysis with COLONY in five populations of wild boars (nlitter-Belval=17, nlitter-Chambord=170, nlitter-Châteauvillain =228, nlitter-Chizé=14, nlitter-La Petite Pierre=82). In the first figure, the width shows the density of points. The white points show the median, the thick black vertical lines the central quartiles and the fine vertical lines 1.5 the inter-quartile space.

  Jehlé who allowed us to work on Châteauvillain population. We also thank the Domaine National de Chambord which allowed us to work on Chambord population, the François Sommer foundation and E. Richard who supervised data collection and supported data analysis in Belval and Chambord. We are thankful to all members of the ONCFS involved in data collection the different study sites and to D. Pierrard for genetic sampling in Belval. This work was supported by the French National Hunting and Wildlife Agency (ONCFS) and by the University of Lyon. ONCFS contributes also by supporting TG, providing his Ph.D. fellowship. COLONY analyses were performed, using the computing facilities of the CC LBBE/PRABI.

Figure III 5

 5 Figure III 5 Evolution of the proportion of forest fruits (FF, brown) and corn (C, yellow) in wild boar stomach content killed by hunting over the study period. Months are represented by their number (10 for October, 11 November). The grey background separates hunting seasons.

Figure

  Figure III 6 a) Yearly number of wild boars killed by hunting, b) Dressed body weight of reproductive males wild boars killed by hunting according to the year. The horizontal blue line represent the 80% threshold mass obtained from historical analysis of adult wild boar males since 1982. The width shows the density of points. The white points show the median, the thick black vertical lines the central quartiles and the fine vertical lines 1.5 the inter-quartile space. c) Yearly proportion of males killed by hunting with a dressed body mass above the historical 80% threshold of the weight of adult males since 1982 (Prop). d) Yearly median weight of reproductive males killed by hunting (Medw).

  Albeit, CERVUS failed to identify any father for 23.75% of the litters (i.e. 38 out of 160). The number of sires NC ranged from one to five for the litters with at least one father identified (mean NC = 1.78 sires per litter ± 0.86 SD, nlitter = 122, Figure IV 1a). The results obtained with GERUD were very similar. The minimum number of sires NG ranged from one to four (mean NG = 1.69 sires per litter ± 0.63 SD, nlitter = 160, Figure IV 1b). Using the maximal number of paternal alleles' approach, NPA ranged from one to four (mean NPA = 2.34 sires per litter ± 0.72 SD, nlitter = 160, Figure IV 1c). The multiple paternity rate obtained with GERUD (MPRG = 0.606, n = 160) was higher than with CERVUS (MPRC = 0.438, n = 16 fully resolved litters). With the last approach, the multiple paternity rate was the lowest (MPRNPA = 0.338, n = 160).

Figure IV 1

 1 Figure IV 1 Distribution of the estimation of the minimum number of sires per litter using a) CERVUS (NC, nlitters = 122); and b) GERUD (NG, nlitters = 160) and c) the maximal number of paternal alleles per litter (NPA, nlitters = 160).

Figure IV 2

 2 Figure IV 2 Effect of the number of sires per litter estimated by a) the maximal number of paternal alleles (NPA) and b) GERUD (NG), on the litter size (nlitters = 160). Circles, whose colour indicates the number of litters, correspond to observations, and squares (± standard error) correspond to predicted litter sizes. Note that predicted values were obtained assuming a mother body mass (BMm), and a number of alleles A equal to the mean observed values (i.e. 50.24kg, and 21.35, respectively).Distribution of the values of the coefficient associated to c) NPA and d) NG, obtained from 10,000 random permutations of the dataset. The dashed lines correspond to the observed averaged values of the coefficients (NPA = 0.112 and NG = 0.132). Note that p(NPA permuted > NPA observed) = 0.002 with 10,000 values of NPA permuted and p(NG permuted > NG observed) < 0.001 with 10,000 values of NG permuted.

  on data collected between 1999 and 2001 in the same population. The expected heterozygosity remains constant through time according to the four common loci (He 1999-2001 = 0.518 versus He 2007-2012 = 0.548) while the average allelic richness is higher (A 1999-2001 = 7.75 versus Ar 2007-2012 = 9.64 from 1,000 subsamplings of 488 individuals). Thus, both allelic number and expected heterozygosity showed no decrease over time despite the fact they are separated by at least twice the length of the generation time of the population and six hunting seasons. Such findings highlight that this heavily hunted population does not display any evidence of genetic loss over time on the studied loci.

  distribution. Including maternal identity and sex as fixed effects allowed us correcting offspring mass for factors (female body mass and condition, gestation stage, year and litter size) inducing among-litter variation in body mass as well as the sex effect on offspring mass. The remaining part of the variance in offspring mass thus only results from paternal effects and residual variation. We calculated the paternal effect as the ratio of the variance in offspring mass due to father identity, divided by the total variance: the father identity, and σ Residuals 2 is the residual variance. Half-sibs in different litters, i.e. from the same father but different mothers, may have different body mass simply because they were sampled at different gestation stages. Using mother identity as fixed factor does not entirely account for this effect because mass does not increase linearly during gestation. Neglecting such non-linear growth may artificially increase the residual variance and

  Figure IV 3 (a) Number of sampled offspring per father for the 235 identified fathers in the wild boar population of Châteauvillain-Arc-en-Barrois, France; (b) Number of litters with 1 to 6 fathers observed, for the 116 litters included in the study. Note that fathers may be sampled in the population and identified from tissue samples or not sampled and assessed by COLONY.

  increase of litter size(Figure IV 4). Looking more specifically at the relationship between the number of fathers per litter and CV of fetus mass, the full model we tested (model 8, seeTable IV S6 and Supplementary Material FigureIV S5) confirmed no effect of multiple paternity on within-litter variation (effect size ± SE = 0.003 ±0.10).

Figure

  Figure IV S5 Thirteen different competing path models (see table1) have been tested. The selected path model (model 1, table1) is shown in figure2. The other 12 path models, exploring how mother body mass (BM) and number of fathers per litter (F) influence the within-litter variation in fetus mass (CV) through litter size (LS), timing of mating (Timing) and mean fetus length (Length) in the wild boar population of Châteauvillain-Arc-en-Barrois, France, are shown below.

  1a) while females mated with one to six males (median = 2 ± 1.25 SD, Figure V 1b). Males produced 1 to 23 offspring (median = 3 ± 3.41 SD for sampled males and median = 2 ± 2.94 SD for inferred males, Figure V 1c) while females had 2 to 10 fetuses (median = 5 ± 1.67 SD for inferred males, Figure V 1d). Most males (67%) produced offspring the same year as they were killed (Figure V S5). Only three males produced offspring over more than one year (maximum of two years, Table V S1).The opportunity for sexual selection was similar for females (Ifemales = 0.29) than for males (Imales = 0.29). The Bateman's gradient was significantly positive for both females (y = 0.29x + 4.50, r² =0.04, p = 0.001, FigureV2) and males (y = 2.35x -0.18, r² =0.37, p < 0.001, FigureV2). However, the number of females they mated with and the number of offspring sired were not influenced by male individual heterozygosity or body mass (Figure V 3, see also Table V S2).

Figure V 1

 1 Figure V 1 Distribution of the estimated number of mating partners for a) males (nmales = 365) and b) females (nfemales = 226) obtained from COLONY and number of offspring produced for c) males (estimated with COLONY) and d) females (nfetus = 1179). For males, the light grey parts represent the proportion of fathers from sampled males and dark grey parts the proportions of males inferred by COLONY.

Figure V 2

 2 Figure V 2 Bateman's gradients for males (blue, nmales = 365) and females (red, nfemales = 226) wild boar of the population of Châteauvillain (2007-2015). The intensity of the color of the points reflect the number of observations (nfetus = 1179 for both sex, see also Figure V 1c and d). Shading represents 95% confidence intervals.

Figure V 3

 3 Figure V 3 Annual mating success and reproductive success according to the dressed body weight of wild boar males of the population of Châteauvillain that sired at least one offspring in litters of females sampled at hunting (nfathers = 85). The intensity of the color of the points shows the density of observation.

Figure V 4

 4 Figure V 4 Comparison of the relatedness from Queller and Goodnight expected under random mating choice (red boxplots, n= 26994) and from realized mating (with sampled fathers only, black boxplots, n=131) of female wild boars from the population of Châteauvillain. Comparisons were realized for each mating pairs to possible matings calculating 97.5 and 2.5 percentile. Red crosses symbolize mating pairs obtaining pairwise relatedness values above the rQ&G-possible-97.5 value. Blue crosses symbolize mating pairs obtaining pairwise relatedness values below the rQ&G-possible-2.5 value. Note that the value above rQ&G-possible-97.5 or below rQ&G-possible-2.5 are not necessarily extreme values as the comparison depends of relatedness of the mating pair relative to all possible mating pairs and all are pooled in the graph.

Table II 1

 II Repartition of the 16 suzerbspecies in 4 groups of Sus scrofa according to IUCN[START_REF] Oliver | Sus scrofa. IUCN Red List Threat[END_REF]. .................................................................................................................................. 17 Table II 2 Yearly number of individuals sampled for the five populations of wild boar. ................. 26 Table II 3 Microsatellite markers information used for paternity study. ........................................... 27 Table II 4 Genetic characteristics of populations ............................................................................... 28 Table II 5 Repartition of sampled and genotyped individuals in the five populations of wild boars.29 Table III 1 Number of litters, offspring and males included in paternity analyses with colony for the five populations of wild boars. ........................................................................................................... 38 Table III 2 Model results for the effect of hunting on the probability of occurrence of multiple paternity and the number of fathers in a litter for four populations and three populations (once Châteauvillain removed) .................................................................................................................... 42 Table III S3 Model selection or the effect of hunting on the probability of occurrence of multiple paternity and the number of fathers in a litter .................................................................................... 46

Table III 4

 III Model results for the effect of hunting on the probability of occurrence of multiple paternity and the number of fathers in the population of Châteauvillain........................................... 58

Table

III S5

Model selection for the effect of hunting on the probability of occurrence of multiple paternity and the number of fathers in a litter in the population of Châteauvillain. .......................... 62 Table III S6 Model results for the effect of ressources availability on the probability of occurrence of multiple paternity and the number of fathers in Châteauvillain. ........................................................ 64 Table IV 1 Model results for factors influencing litter size including number of fathers estimated with NPA and GERUD .............................................................................................................................. 75 Table IV 2 List of the eight papers including the present study dealing with multiple paternity in Sus scrofa populations (on 25 September 2015). ..................................................................................... 76 Table IV S3 Characteristics of the genetic markers used for paternity study. ................................... 82 Table IV S4 Model selection for the analysis of the effect of number of sires on litter size using maximal number of paternal alleles as a proxy.................................................................................. 84

Table IV S5

 IV Model selection for the effect of number of sires estimated by GERUD on the litter size. ....................................................................................................................................................... 84 Table IV S6 Model fit of the 13 competing path models exploring the relationship between different factors and within-litter variation in fetus mass (CV)........................................................................ 93 Table IV S7 Characteristics of the genetic markers used for paternity study. ................................... 97 Table IV S8 Assessment of the convergence of the linear mixed-effect model. ............................. 103 Table V S1 Distribution of identified fathers separated by year of sampling and year when they produced offspring. .......................................................................................................................... 114 Table V S2 Model selection for mating success and reproductive success. .................................... 115

	Chapter I
	Introduction
	Laura Touzot

Table VI 1 Description of positive and negative sides of four parentage methods used for paternity analysis in wild boars concerning their use and results obtained. ................................................... 121

Table II 1 Repartition of the 16 subspecies in 4 groups of Sus scrofa according to IUCN (Oliver and Leus 2008) Group Western Indian Eastern Indonesian

 II

  Oak and beech are the main tree items in the forest clump. The climate is between continental and oceanic like Châteauvillain and La Petite Pierre. The number of wild boar killed reaches 90 individuals each year.

	forest.
	La Petite Pierre, Chambord, Chizé, Belval
	Four other sites were also included in the study. The forest of the National Reserve of La
	Petite Pierre is a 2,800ha open forest located in North-East of France (48°5′N, 7°E, Figure II
	6a). Like the previous study site, the climate is continental, with oceanic influences but the
	forest clump composition is different. The main tree species are silver fir (Abies alba), douglas-
	fir (Pseudotsuga douglasii), Norway spruce (Picea abies) and European beech (Fagus
	sylvatica). Nearly 150 wild boars are killed each year (Figure II 5). The forest of the Domaine
	National de Chambord is a 5,440ha forest located in central France (47°36′N, 1°31′E, Figure II
	6b). It is enclosed in a 32-km-long stone wall. The climate is mild humid temperate
	characterized by moderately warm summers and no dry season. The forest is mainly composed
	of oaks (Quercus spp) and pines (Pinus spp). Chambord shows the highest number of wild boar
	killed each year with around 950 individuals shot (Figure II 5). Considering its size and that the
	population is closed, it is the population with the highest density of wild boars. The Réserve
	Biologique Intégrale of Chizé is a 2,614ha fenced forest located in Western France (46°50′N,
	0°25′W, Figure II 6c). The climate is oceanic with Mediterranean influences, characterized by
	mild winters and hot summers with frequent summer droughts (average temperatures of 6°C in
	January and 20°C in August). Oak and beech are the two main tree items in the forest. Like in
	La Petite Pierre, around 150 individuals are killed each year (Figure II 5). Finally, the forest of
	Belval is located in North-East of France (49°3'N, 5°E, Figure II 6d) is a 650ha enclosed private

Table II 2

 II Yearly number of individuals sampled for the five populations of wild boar.

	Sampling year	Châteauvillain	La Petite Pierre	Chambord	Chizé	Belval
	2007	254
	2008	90
	2009	421	83
	2010	292	65
	2011	596	220	407	118
	2012	285	120	136	23	40
	2013	201	140		1	78
	2014	279	233	584	131	70
	2015	261		499		30
	2016	378

Table II 5

 II Repartition of sampled and genotyped individuals for the five wild boar populations. 'Other' represent non-reproductive females included in allele frequency analyses.

			Class	Châteauvillain	La Petite Pierre	Chambord	Chizé Belval
			Mother		38
	2007		Fetus Male		182 34
			Other
	2008		Male Mother Fetus		49 7 34	Chapter IIIA
			Other
			Mother		52			11
	2009		Fetus Male		280 89			64 2
			Other					5
			Mother		30			5
	2010		Fetus Male		142 118			30 23
			Other					6
			Mother		36			23	43		11
	2011		Fetus Male		192 213			124 38	223 86		76 26
			Other		154			34	49		4
			Mother		10			3			2
	2012		Fetus Male		39 133			10 33			15	7 21
			Other		102			74			8	10
	2013	N	Mother Fetus Male	1385	17 105 77	Chambord 458	Chizé 20 115 111 4	La Petite Pierre 315	1	4 Belval 96 33 22
		A	12.08 ± 8.07 Other	1	8.5 ± 6.2		7.5 ± 5.37 2	8.08 ± 5.82		6.17 ± 4.11 19
		Ar	8.6 ± 5.33 Mother	32	6.76 ± 4.52	7.28 ± 5.11 29	7.18 ± 5.02 85		13	6.17 ± 4.11 8
	2014	Ho He	0.59 ± 0.24 0.61 ± 0.25 Fetus Male Other	178 63 2	0.56 ± 0.23 0.58 ± 0.24	0.63 ± 0.22 0.64 ± 0.23 200 3	0.58 ± 0.29 0.58 ± 0.29 454		81 24 13	0.61 ± 0.3 57 4 0.6 ± 0.27
		Fis	0.03 ± 0.04 Mother	32	0.03 ± 0.06	0.02 ± 0.06	-0.01 ± 0.06 56		0.01 ± 0.1 3
	HW PID 2015	NS 6.9×10 -11 Fetus Male	150 60	NS 8.1×10 -10		NS 6.8×10 -11	NS 2.1×10 -10 236 137		NS 1.6×10 -10 24 3
	PIDsib	1.5×10 -04 Other Mother		2.5×10 -04		9.6×10 -05	2.1×10 -04 2		1.6×10 -04
	2016		Fetus Male		36
			Other

Investigating factors influencing multiple paternity rates Laura Touzot

Table III 1

 III Number of litters (mothers), offspring and males included in paternity analyses with COLONY for the five populations of wild boars and the different years used for the analyses. Mean litter size (± SD) are also reported.

				Populations
	Year	Class	Châteauvillain	La Petite Pierre	Chizé	Chambord	Belval
		Litters	32
	2007	Offspring	154
		♂	141
		Litters	7
	2008	Offspring	34
		♂	233
		Litters	47	10
	2009	Offspring	263	56
		♂	307	103
		Litters	28	4
	2010	Offspring	134	23
		♂	355	101
		Litters	34	21	10	42
	2011	Offspring	184	115	71	218
		♂	417	78	66	223
		Litters	8	1			2
	2012	Offspring	34	3			7
		♂	273	40			50
		Litters	16	17			4
	2013	Offspring	99	98			33
		♂	161	7			29
		Litters	27	29	4	77	8
	2014	Offspring	144	192	20	408	57
		♂	120	3	24	137	7
		Litters	29			51	3
	2015	Offspring	133			210	24
		♂	89			137	3
	Overall	Litter size	5.17 ± 1.67	5.94 ± 1.53	6.5 ± 1.56	4.92 ± 1.63	7.12 ± 2

Table III 2

 III Estimates, standard errors, z statistics, and P values of parameters linked with the probability of occurrence of multiple paternity (a.) and the number of fathers (c.) in a litter for four populations and without Châteauvillain (b) and (d) from full averaged model. Values for the proportion of males killed with a dressed weigh above the annual threshold (Prop) and the difference between the median of dressed weigh of males killed and the annual threshold (Diff), the number of wild boars killed per surface unit (Nha), the mother body mass (BMm) and the litter size (LS) were obtained from averaged model strongly supported by the data. Châteauvillain was removed from (b.) and (d.). Significant parameters are in bold (nlitter-Chambord=166, nlitter-Châteauvillain =226, nlitter-Chizé=14, nlitter-La Petite Pierre=65).

	a.			b.
	Parameter Estimate SE	z-test statistic	P-value Parameter Estimate SE	z-test statistic	P-value
	Intercept 0.728 0.145	-	-	Intercept 0.651 0.135	-	-
	Prop 0.374 0.177	2.108	0.035
	Diff 0.556 0.344	1.611	0.107
	BMm 0.033 0.076	0.431	0.666
	Nha 0.020 0.065	0.305	0.760
	c.			d.
	Parameter Estimate SE	z-test statistic	P-value Parameter Estimate SE	z-test statistic	P-value
	Intercept 0.826 0.033	-	-	Intercept 0.819 0.043	-	-
	LS 0.113 0.032	3.493	<0.001	LS 0.113 0.045	2.493	0.013
	Prop 0.040 0.058	0.691	0.490	Diff 0.005 0.022	0.226	0.821
	Diff 0.058 0.071	0.812	0.417	BMm 0.003 0.021	0.154	0.877
	Nha 0.008 0.024	0.345	0.730	Nha 0.003 0.020	0.130	0.897
	BMm -0.003 0.016	0.174	0.862

  D BMm Prop Nha Medw # parameter Log Likelihood AICc ΔAICc AICc weight Table III S6 Estimates, standard errors, z statistics, and P values of parameters linked with the probability of occurrence of multiple paternity (a.) and the number of fathers (b.) in a litter. Values for the Julian date of mating (D), the proportion of males killed with a dressed weigh above the historical threshold (Prop) and the proportion of forest fruits in stomach content (FF), the number of wild boar killed per surface unit (Nha), the mother body mass (BMm) and the litter size (LS) were obtained from averaged models strongly supported by the data. Significant parameters are in bold (nlitters = 149).

	b. X	X						X		4	-232.77	473.82 10.88	0.00
	X Intercept D LS BMm Prop Nha Medw # parameter Log Likelihood AICc ΔAICc AICc weight X X X X X 7 -229.52 473.84 10.89 0.00 X X X 4 -227.33 462.94 0.00 X X X X 5 -232.13 474.68 11.73 0.00 0.12 X X X X X 6 -225.57 463.73 0.78 X X X X 5 -232.15 474.71 11.77 0.00 0.08 X X X X 5 -226.76 463.93 0.99 X X X X 5 -232.25 474.91 11.97 0.00 0.07 X X X X 5 -226.83 464.08 1.14 0.07 X X X X X 6 -231.43 475.45 12.51 0.00
	X				X					3	-229.05	464.26 1.31	0.06
	X		X X	X					5	-227.21	464.84 1.89	0.04
	X X 2. Model results including food resources X X X 5 X X 4	-227.28 -228.44	464.97 2.03 465.15 2.21	0.04 0.04
	X	X X		X	X		X		7	-225.19	465.17 2.23	0.04
	X		X X	X			X		6	-226.59	465.76 2.82	0.03
	X	X X X	X			X		7	-225.51	465.82 2.87	0.03
	X	X			X			X		5	-227.72	465.87 2.92	0.03
	X	X X		X	X				6	-226.66	465.90 2.96	0.03
	X	X			X					4	-228.82	465.92 2.97	0.03
	X X	X	X	X	X X	X	X	X	6	6	-80.96 -226.67	174.51 0.00 465.93 2.98	0.23 0.03
	X X X X X X X X X X X X X X	X X X X X X X X X X X X X X a. X X Parameter X X X X X X X X X X X X X X X X X Intercept X X X X D	X Estimate X X X X X X X X 0.831 X X 0.561	7 5 6 4 5 5 0.238 6 4 4 5 6 SE 6 5 8 0.242	-80.15 -226.74 -83.14 -228.91 -82.08 -84.26 -228.92 -228.16 -227.16 z-test statistic 175.08 0.58 466.06 3.12 176.69 2.19 466.10 3.16 176.75 2.24 176.81 2.30 466.13 3.18 466.74 3.80 466.92 3.97 P-value -83.29 177.00 2.49 -83.32 177.06 2.55 -227.23 467.05 4.11 -228.39 467.20 4.26 ---225.16 467.34 4.40 2.297 0.022	0.02 0.17 0.02 0.08 0.07 0.02 0.02 0.02 0.07 0.06 0.06 0.01 0.01 0.01
	X X X X X X X	X X X X X X X X X X X X X	X Prop X X X X Nha X FF	X X	X 0.829 X X -0.196 0.255	6 0.294 5 5 4 6 7 0.240 5 0.300	-82.59 -228.50 2.802 -84.27 -85.37 -227.48 -226.44 0.810 -228.65 0.845	177.77 3.26 467.43 4.48 0.005 178.96 4.45 179.03 4.52 467.55 4.60 467.67 4.73 0.418 467.73 4.78 0.398	0.01 0.04 0.02 0.02 0.01 0.01 0.01
	X X		X	X	BMm		0.118	3 0.197 3	-86.51 -230.85 0.596	179.19 4.68 467.87 4.93 0.551	0.02 0.01
	X X X X X	X X X X X X X X X b.	X X X	X X			4 4	5 7 4	-85.52 -228.78 -85.77 -226.64 -230.06	179.32 4.82 467.99 5.04 179.81 5.31 468.08 5.14 468.40 5.45	0.01 0.02 0.02 0.01 0.01
	X X	X X		X Parameter X	X Estimate X	3	7 SE	-86.88 -226.94 z-test statistic 179.93 5.42 468.67 5.73 P-value	0.01 0.01
	X X X X X	X	X X	X X X X Intercept X X X X Prop	X X X	X 0.770 X 0.194	5 5 0.057 6 6 4 0.060	-84.91 -85.12 -228.12 -228.30 --230.47 3.230	180.24 5.73 180.67 6.16 468.83 5.88 469.20 6.25 -469.22 6.28 0.001	0.01 0.01 0.01 0.01 0.00
	X X X X X X X	X X X X X X X X X X	X D FF BMm	X	X X 0.027 X 0.017 -0.004	4 4 6 0.055 5 4 4 0.049 2 0.024	-86.22 -86.28 -84.21 -229.60 -230.82 0.491 -230.82 0.355 -233.18 0.152	180.71 6.21 180.84 6.33 181.00 6.50 469.62 6.67 469.92 6.98 0.624 469.93 6.98 0.722 470.43 7.49 0.879	0.01 0.01 0.00 0.00 0.00 0.01 0.00
	X X X X	X X X X X X X X	X LS		X X 0.091 X	5 5 0.065 5 5	-85.50 -85.72 -230.06 -230.06 1.397	181.43 6.92 181.86 7.35 470.54 7.59 470.54 7.59 0.162	0.01 0.01 0.00 0.00
	X X X X X	X	X X X X X	X	X X X	X X	X	4 6	5 5 3	-86.86 -230.45 -84.77 -230.47 -232.65	182.01 7.50 471.32 8.38 182.12 7.61 471.37 8.42 471.46 8.52	0.00 0.01 0.00 0.00 0.00
	X X	X X X	X		X	X	X	5	6	-86.07 -229.52	182.55 8.04 471.64 8.70	0.00 0.00
	X X X X X	X X X X X	X	X			2 3	3 3 6	-89.40 -232.78 -88.48 -232.79 -229.60	182.89 8.38 471.72 8.78 183.13 8.62 471.74 8.80 471.79 8.84	0.00 0.00 0.00 0.00 0.00
	X X		X X X				X	3	5	-88.71 -230.80	183.59 9.08 472.01 9.07	0.00 0.00
	X X X X X	X X	X	X	X	X	X	X	4 3	3 4 4	-87.77 -233.13 -89.27 -232.13 -232.18	183.82 9.31 472.43 9.49 184.70 10.19 472.55 9.60 472.64 9.70	0.00 0.00 0.00 0.00 0.00
	X X	X X X	X		X	X	4	6	-88.46 -230.06	185.21 10.70 472.71 9.76	0.00 0.00
	X X X X X	X	X X X X X X	X	X X X	X X	X	4 5	4 5 6	-88.56 -232.25 -87.75 -231.48 -230.45	185.39 10.89 472.77 9.82 185.92 11.41 473.37 10.43 473.50 10.55	0.00 0.00 0.00 0.00 0.00
	X					X		X		4	-232.65	473.57 10.63	0.00
	X			X				X		4	-232.73	473.74 10.80	0.00

Table IV 2

 IV List of the eight papers including the present study dealing with multiple paternity in Sus scrofa populations (on 25 September 2015). The subspecies (S.s.d. for S.s.domesticus corresponds to feral pig populations, S.s.s for S.s.scrofa), the sample size, the number of microsatellite loci (Nloci), the mean number of alleles (A), the mean allelic richness (Ar, obtained from 1,000 random subsamplings of our dataset corresponding to the sample size of the study cited), the mean observed heterozygosity (Ho), the mean expected heterozygosity (He), the mean number of litters (Nlitter), the mean litter size (LS), the multiple paternity rate (MPR) with the number of litters showing multiple paternity in brackets, information about harvesting pressure found in the study and the reference of the study (with information about population´s location when required) are provided. Values in brackets show the range of the values when available. Bold values for A, Ar, Ho and He show values higher than the ones obtained in the present study. Bold values for MPR show values higher than the mean value of our three methods (i.e. 46%).

				a)
				Parameter Estimate Standard error z-test statistic p value
				Intercept 0.475		0.222		2.14	-
	Subspe cies	Sam ple size	Nlo ci	A	A 0.017 BMm 0.010 Ar Ho	He	0.007 0.002 Nlit ters LS	MPR	2.30 4.34 Harvesting pressure 0.02 <0.001 in the study information	Study (Population)
					NPA 0.112		0.047		A population 'sampling 2.36 0.02 rate' of 70% was
	S.s.d	354 14	b) 8.14 Parameter Estimate Standard error z-test statistic p value [4-17] 9.96 [2-25] 0.575 [0.367-0.756] 0.68 [0.504-0.833] 11 assumed on the basis of 5.64 * [3-very similar trapping 10] published estimates of 0% from studies that used (0) feral pig capture rates	Hampton et al. (2004)
											methods to those used in
					Intercept	0.852		0.153		5.57 Prior to our study, this this study. -
					BMm	0.011		0.002		4.63 region was subjected to <0.001 at least two years of
	S.s.d	55	13	4.62 [2-6]	7.55 [1-20]	NG 0.663 [0.333-0.889]	0.132 0.641 [0.5-0.822]	0.054 21 No data	48% (10)	2.44 intensive feral pig 0.015 (sodium aerial baiting with 1080 control, mainly through	Spencer et al. (2005)
											monofluoroacetate)
											baits.
	2 5 Our results show that the average number of alleles per locus and heterozygosity were Delgado-Acevedo et 50% al. (2010) (1) (Brooks) Discussion Delgado-Acevedo et 40% al. (2010) (2) (Cameron) high and moderate, respectively, in this wild boar population, despite intensive hunting. The 2 Delgado-Acevedo et 0% al. (2010) (0) (Coryell)
	rates of multiple paternity varied between 0.338 and 0.606 depending on the approach used for estimating the number of sires. Regardless of the method used, we found larger litter sizes with increasing number of sires. a 409 12 8.3 [4-12] 10.1 2 [2-25] 0.595 [0.294-0.78] 0.68 [0.39-0.838] Feral pig were trapped, harvested or removed by 8 Delgado-Acevedo et 13% al. (2010) (1) (Dimmit) 5.4* * [2-aerial and ground shooting as part of damage-control 1 Delgado-Acevedo et 0% al. (2010) (0) (Hidalgo) 11] management activities and sport hunting. 1 Delgado-Acevedo et 100% al. (2010) (1) (Kerr)
									11	27% (3)		Delgado-Acevedo et al. (2010) (Kleberg)
									16	38% (6)		Delgado-Acevedo et al. (2010) (McMullen)
									18	39% (7)		Delgado-Acevedo et al. (2010) (San Patricio)
												(Continued)

Subspec ies Samp le size Nlo ci A Ar Ho He Nlitte rs LS MPR Harvesting pressure information in the study Study (Population)

											The hunting pressure is
											high and so is the number
	S.s.s	9	7	4.14 [3-6]	4.63 [1-13]	0.603 [0.339 -0.731]	0.576 [0.443-0.707]	9	5.56* ** [5-7]	11% (1)	of wild boars taken per From this study: 9.49 ± 100ha of shooting area (Fernandez-Llario et al. 2003)	Delgado et al. (2008)
											8.65/100 ha, n=17 hunt,
											mean ± SD)
											40% probability of being
	S.s.s	488	12	6.58 [2-16]	10.3 2 [2-25]	0.518 [0-0.83]	0.552 [0.21-0.87]	21	4.05 [2-6]	10% (2)	et al. 2009 shot up to 70% for males from Toigo et al. 2008 5.21⁄100 ha (±2.66, range: 0.64 -9.27) from Servanty	Poteaux et (2009) (Population of the al. study)
		49		6.21 [3-14]	7.42 [1-20]	0.718 [0.444 -1]	0.698 [0.396-0.901]	5	5.8	40% (2)	No information	Costa et al. (2012) (Hungary)
	S.s.s	72	14	5.07 [3-10]	7.95 [2-21]	0.542 [0.268 -0.861]	0.552 [0.259-0.776]	5	6.2	20% (1)	No information	Costa et al. (2012) (Portugal)
		46		5.5 [4-12]	7.3 [1-20]	0.647 [0.364 -0.909]	0.646 [0.411-0.906]	5	4.8	40% (2)	No information	Costa et al. (2012) (Spain)
	S.s.s	181 188 74 260	14	9.64 [5-24]	10.7 6 [2-25]	0.548 [0.451 -0.833] ** 0.658 [0.451 -0.833] ** 0.634 [0.451 -0.833] ** 0.683 [0.451 -	0.553 [0.412-0.837]** 0.632 [0.412-0.837]** 0.632 [0.412-0.837]** 0.692 [0.412-	27 35 13 35	4.3 3.9 3.5 5.9	Different estimate s not directly compara ble with ours (MPR defined as number of sires per sow)	Past experience with the study areas suggests a sampling intensity between 10-20%	Pérez-González et al. (2014) (Spain Western Iberian Peninsula) Pérez-González et al. (2014) (Spain Azagala) Pérez-González et al. (2014) (Spain Santa Amalia) Pérez-González et al. (2014)
						0.833]	0.837]**					(Hungary)
						**
										MPRG =	40% probability of being
	S.s.s	1054 12	11.2 5 [2-25]	-	0.590 [0.107 -0.845]	0.602 [0.125-0.891]	160	5.1 [1-10]	61% MPRNPA MPRC = 44%	shot up to 70% for males 0.64 -9.27) from Servanty from Toigo et al. 2008 5.21⁄100 ha (±2.66, range:	Present study
										= 34%	et al. 2009
	*only litters with three or more piglets/fetuses were analyzed
	** no data per population available
	***only litters with five or more fetuses were selected

Table IV S3

 IV Number of alleles A, observed Ho and expected He heterozygosity, Hardy-Weinberg equilibrium (NS: equilibrium; *: non-equilibrium) and estimated frequency of null alleles for each locus as provided by CERVUS for adult wild boars (n = 1054 genotypes). Fluorescent dyes used for the resolution of the PCR amplified products and their expected size have been added.

	Locus A	Ho	He	HW	F(Null)	Dye	Expected size
	CGA 25	0.845	0.891	*	0.026	Fam	250-320
	SO005 23	0.832	0.891	NS	0.034	Ned	200-280
	SW2496 16	0.836	0.826	NS	-0.007	Ned	180-230
	SO068 15	0.562	0.573	NS	0.010	Hex	210-260
	SW2021 11	0.748	0.744	NS	-0.004	Hex	100-130
	SW240 8	0.662	0.681	NS	0.015	Ned	90-150
	SO228 8	0.638	0.653	NS	0.012	Hex	220-250
	SW122 8	0.432	0.427	NS	-0.007	Fam	110-120
	SW24 7	0.708	0.703	NS	-0.003	Hex	96-120
	SW936 6	0.529	0.516	NS	-0.011	Fam	80-120
	SO355 6	0.107	0.125	*	0.068	Fam	240-280
	SO215 2	0.186	0.193	NS	0.019	Fam	135-169

Table V S2

 V Model selection to test the effect on (a.) the yearly number of offspring produced and (b.) the number of female mating partners of the individual heterozygosity index (Ho) and the dressed body mass (BM) for the male wild boars from the population of Châteauvillain, France (nmales = 85).

	a.
	Intercept Ho	BM df logLik AICc delta weight
	1.162	2 -87.59 179.32 0	0.434
	0.837	0.004 3 -86.92 180.14 0.82 0.289
	1.312 -0.153	3 -87.46 181.21 1.89 0.169
	0.982 -0.145 0.004 4 -86.80 182.11 2.78 0.108
	b.
	Intercept Ho	BM df logLik AICc delta weight
	0.092	0.003 3 -48.68 103.67 0	0.368
	0.356	2 -49.76 103.68 0.01 0.367
	0.289 0.068	3 -49.70 105.70 2.03 0.133
	0.018 0.074 0.003 4 -48.61 105.72 2.05 0.132

Table VI 1

 VI Description of positive and negative sides of four parentage methods used for paternity analysis in wild boars concerning their use and results obtained.

		NPA µ	GERUD	CERVUS	COLONY
	Estimation of
	the number of	Proxy	Yes	Yes	Yes
	fathers
	Father
	identification (from sampled	No	No	Yes	Yes
	males)
	Number of loci restriction	No	Yes	No	No
	Father genotype
	reconstruction (non-sampled	No	Yes	No	Yes
	males)
					Slow
	Analysis speed	Fast	Fast	Fast	(but parallelization
					possible)*
	Automating analysis possible	Yes (R code easily adapted)	No (lot of user's manipulations required)	Yes (Run from command line)	Yes (Run from command line)
	Input format	Flexible (User's choice)	Not easy	Easy	Adaptable template with the software
	Output format	Flexible (User's choice)	One array per litter	One array per analysis	Many arrays per analysis
	Linux version available	Not required*	No	Not required*	Yes*
	µ Number of paternal alleles
	*only from my own judgement considering the data I had to work with. For COLONY, Linux
	version allowed quick parallelized calculations on the computing facilities of the CC
	LBBE/PRABI.

Table 2 :

 2 Information for microsatellite loci for wild boar (Wb) and pig hybridization analysis.

	Locus	FST	I_n n_Wb F Wb He_Wb n_Pig F Pig He_Pig
	SNP56 0.96 0.55	261	0.99	0.03	50	0.95	0.10
	SNP46 0.93 0.54	261	0.97	0.06	49	0.96	0.08
	SNP43 0.92 0.55	261	0.96	0.08	50	0.98	0.04
	SNP53 0.83 0.39	261	0.94	0.12	50	0.88	0.21
	SNP15 0.81 0.27	261	0.99	0.02	50	0.63	0.47
	SNP48 0.76 0.34	261	0.90	0.18	50	0.87	0.23
	SNP4	0.72 0.21	205	1	0	47	0.51	0.50
	SNP12 0.70 0.20	261	0.98	0.05	50	0.56	0.49
	SNP52 0.64 0.34	261	0.77	0.35	50	0.97	0.06
	SNP23 0.58 0.13	259	0.98	0.03	50	0.60	0.48
	SNP41 0.56 0.12	245	1	0	50	0.70	0.42
	SNP50 0.55 0.26	261	0.73	0.39	50	0.93	0.13
	SNP27 0.54 0.11	259	0.99	0.02	50	0.67	0.44
	SNP55 0.50 0.17	261	0.82	0.30	50	0.75	0.38
	SNP57 0.47 0.18	248	0.74	0.39	50	0.84	0.27
	SNP2	0.45 0.08	237	1	0	50	0.78	0.34
	SNP54 0.44 0.15	261	0.77	0.36	50	0.77	0.35
	SNP39 0.44 0.08	253	1	0	50	0.79	0.33
	SNP28 0.24 0.04	249	0.98	0.03	50	0.83	0.28
	SNP33 0.19 0.04	255	0.92	0.15	50	0.70	0.42

  values ranged from 0.855 to 0.972 for wild boars and from 0.023 to 0.207 for pigs with SNPs. For microsatellites, qi-WB values ranged from 0.829 to 0.969 for wild boars and from 0.029 to 0.237 for pigs with SNPs. These ranges were also separate from F1's (from 0.282 to 0.790 with microsatellites and from 0.320 to 0.687 with SNPs, Figure1, b and d). Assignment threshold values were calculated to evaluate the significance of qik values obtained on real data.

	Locus	FST	I_n N	N Wb	Ar Wb	Np Wb	F Wb	He Wb	N Pig	Ar Pig	Np Pig	F Pig	He Pig
	SO355	0.50 0.22 8 250 2.83	0	0.95 0.1	50	7.12	4	0.39 0.73
	SO068	0.38 0.48 14 243 8.92	4	0.63 0.55 48	8.87	2	0.53 0.67
	SW936	0.31 0.30 9 261 4.84	0	0.69 0.48 50	8.37	3	0.38 0.76
	SW122	0.26 0.21 7 259 4.61	0	0.73 0.45 49	6.26	2	0.35 0.76
	SW24	0.17 0.40 9 255 5.28	2	0.42 0.7	43	6.88	3	0.31 0.81
	SW240	0.17 0.36 10 259 6.39	3	0.49 0.65 50	6.99	3	0.24 0.81
	SW2496 0.09 0.32 16 250 9.99	7	0.24 0.83 44	8.65	2	0.28 0.83
	SO228	0.07 0.16 10 259 3.78	2	0.43 0.65 50	7.51	4	0.39 0.77
	CGA	0.07 0.34 19 245 14.25	8	0.16 0.9	44 10.13 1	0.22 0.86
	SO005	0.07 0.32 24 233 14.33 10 0.18 0.88 48 12.57 2	0.18 0.88
	SW2021 0.05 0.25 16 257 9.01	4	0.38 0.75 50 10.99 6	0.28 0.85
	SO215	0.05 0.08 5 260	2	1	0.91 0.17 50	3.61	3	0.86 0.25

WB

Table 3 :

 3 Number of common individuals between two analyses (STRUCTURE and NEWHYBRIDS)and/or two markers (SNPs and microsatellites) with assignment probabilities to the wild boar group lower than the threshold values for wild boars (bold values, n = 261) and PAW+ (i.e. phenotypic anomalous wild boars with at least one trait associated with hybridization recorded by the hunters, normal values, n = 94). The diagonal shows the number of individuals with assignment probabilities to the wild boar group lower than the threshold values in each analysis and for each marker.

Table 4 :

 4 Proportions of real wild boars (n=261) and phenotypically anomalous wild boars (PAWx, x indicating the number of criteria reported by hunters, and n0=42, n1=81, n2=8, n3=4 and n4=1) identified as hybrids 0 to 4 times with STRUCTURE and NEWHYBRIDS analysis with a) SNPs, b) microsatellites, c) all analyses combined

Acknowledgments

First, I want to warmly thank the members of my PhD defense jury for evaluating my work to make it (and me) better. Many thanks to Albano Beja-Perreira and Dustin Penn for agreeing to review my manuscript and to Emmanuelle Gilot-Fromont and Nirmala Seon-Massin for accepting to be present for the defense.

Acknowledgment

We thank all those who helped collect harvested wild boars, the ONF (Office National des Forêts), and F. Jehlé who allowed us to work in the study area. This work was supported by the French National Hunting and Wildlife Agency (ONCFS) and by the University of Lyon.

ONCFS contributes also by supporting TG, providing his Ph.D. fellowship. COLONY analyses were performed, using the computing facilities of the CC LBBE/PRABI.

Acknowledgment

We are grateful to all those who helped collect harvested wild boars and to the ONF, and to F. Jehlé who allowed us to work in the study area. We thank Diane Gonzalez for the preliminary analysis of the first years' data. We thank J-M. Gaillard and J. O'Brien for their helpful comments which markedly improved our paper and C. Carter for the proofreading. This work was supported by the French National Hunting and Wildlife Agency (ONCFS), by the University of Lyon and by the Research Council of Norway through its Centres of Excellence funding scheme, project number 223257.

Acknowledgments

We are grateful to all those who helped collect harvested wild boars, especially P. Van den Bulck, to the ONF, and to F. Jehlé, who allowed us to work in the study area. We thank Réseau Ongulés Sauvages for the organization of the national sampling campaign of phenotypically anomalous wild boars. This work was supported by the French national hunting and wildlife agency (ONCFS) and by the University of Lyon. ONCFS contributes also by supporting T.

Gayet with a PhD fellowship.

My PhD grant was fund by the French Hunting and Wildlife Agency (Office National de la Chasse et de la Faune Sauvage, ONCFS), which is a public institution. Expenses related to my PhD were financially supported by both the Laboratory of Biometry and Evolutive Biology (Laboratoire

volumes of 20l containing 10l of PCR Multiplex Master Mix (2x, QIAGEN), 0.6l of each primer (10mM) and 2l of the extraction product. PCR was conducted using a BIOBLOCK PTC 100 thermal cycler with the following program: 95°C/15 min, 30 cycles with 94°C/30 s, 57°C/1.30 min and 72°C/1 min denaturing, annealing and extension temperatures respectively, and finally 60°C/30 min. The sizes of PCR amplified products were resolved by GENOSCREEN (http://www.genoscreen.fr) using an APPLIED BIOSYSTEMS 3730xl DNA Sequencing Analyzer (Supplementary Material 1, Table IV S3). Three mother-litter pairs and two males were removed from the analysis due to the high number of missing genotypes.

Genetic and paternity analysis

CERVUS 3.0.7 [START_REF] Kalinowski | Revising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment[END_REF]) was used to compare observed (Ho) and expected (He) heterozygosity (using only adult genotypes to avoid biases from family genetic links, Supplementary Material 1, Table IV S3), to identify mother-offspring mismatches, to estimate the null allele rate and to conduct maximum likelihood paternity analyses. CERVUS compares potential sires using mismatches in the fetus-mother-male trio and likelihood ratio scores. Males were considered to be a fetus's genetic sire when there was no father-offspring mismatch, when the fetus-mother-male trio had a positive likelihood of detection (LOD) and when a LOD higher than the 80% critical likelihood ratio (determined by simulations (Supplementary Material 2)). Putative sires for fetuses sampled in a given hunting season i were composed of all males sampled during the hunting season i, all yearlings and adult males sampled in the hunting season i+1, and adult males sampled in the hunting season i+2. Overall, the numbers of putative sires were 141, 233, 307, 346, 332 and 122 for the six hunting seasons (2007)(2008)(2009)(2010)(2011)(2012), respectively. The number of sires per litter NC, estimated with CERVUS, was recorded as the number of identified fathers.

To circumvent CERVUS failures to identify sires for all fetuses within a litter, GERUD 2.0 [START_REF] Jones | GERUD 2.0: a computer program for the reconstruction of parental genotypes from half-sib progeny arrays with known or unknown parents[END_REF] was also used to provide a second measure of the minimum number of males contributing to each litter NG. Using known maternal genotypes, GERUD calculates the minimum number of fathers contributing to a given litter by subtracting the known maternal alleles from fetus genotypes, simulating all possible paternal genotypes, and determining the combinations of the remaining alleles that yield the fewest possible sires [START_REF] Jones | GERUD 2.0: a computer program for the reconstruction of parental genotypes from half-sib progeny arrays with known or unknown parents[END_REF]. The error rate was estimated by simulations using GERUDsim (Supplementary Material 2). Due to computational limitations, we used for each mother-litter array only the five most polymorphic loci showing no missing data, when possible. In 87 out of 160 mother-litter arrays, the five loci

Model selection for the analysis of the effect of number of sires on litter size using maximal number of paternal alleles as a proxy

Table IV S4 Model selection to test the effect of the locus-specific observed heterozygosity Ho and observed number of alleles A, the mother dressed body mass BMm and the maximal number of paternal alleles in a litter NPA on the litter size (LS) in the wild boar (Sus scrofa) population of Châteauvillain, France. The model retained is in bold (ΔAICc<2). 'Χ' denotes that the explanatory variable was included in the model (nlitters = 160).

Supplementary Material

Model 13.

Model convergence checks

Figure IV S6 Assessment of the convergence of the linear mixed-effect model linking individual fetus mass (log-transformed) as response variable, to fetus sex and mother identity as explanatory variables and father identity as a random effect through (a) visual inspection. Note that because many mother identities were included in the analysis, only the convergence diagnostics for the intercept, sex and father identity are shown.

Chapter V

Characteristics of reproductive males

Laura Touzot

Supplementary Material Abstract: Hybridization between wild and domestic species or subspecies is widespread in vertebrates, but may be difficult to detect, especially when subspecies remain genetically close despite strong anthropic selection in the domestic counterpart. Developing molecular tools to enable efficient identification of hybrids is crucial for a better understanding of both evolutionary and conservation consequences of hybridization in the wild. Here we compared the efficiency of a set of 20 SNPs (Single Nucleotide Polymorphism) with a set of 12 microsatellites to detect hybridization between wild boars (Sus scrofa scrofa) and domestic pigs (S. s. domesticus). The accuracy of the two sets of molecular markers in detecting hybrid individuals was investigated with two different standard Bayesian analyses on simulated genotypes. Parental and hybrid individual detection was also performed on the real genotypes of 270 wild boars, 57 pigs and 139 phenotypically anomalous wild boars (PAWs). Both simulation and real genotype analyses showed similar capacity of both sets of markers to detect hybridization. Overall, first generation hybrids were the only hybrids detected well. In the PAWs sample, various proportions of molecular hybrids (up to 100%) were detected, depending on the marker and the method used. In addition, the probability of being detected as a hybrid increased with the number of domestic pig traits borne by PAWs. We concluded that despite the different characteristics of the sets of markers, they performed equally well in detecting hybridization. Choice of the molecular marker should thus be based on the economic costs of each type of marker.

Dressed body mass of sampled males

Mating and sampling year for identified fathers

Keywords: Bayesian analysis, Hybridization, Introgression; Microsatellite; Single nucleotide polymorphism; Sus scrofa. Gayet T., L. Say, E. Baubet, S. Brandt and S. Devillard. SNPs or Microsatellites? Assessing the reliability of different molecular markers to study hybridization between wild boar and domestic pig (Sus scrofa). In prep hunters reported: no information (we assumed missing information was due to a careless mistake, nPAW0=43), one criterion (nPAW1=83), two criteria (nPAW2=8), three criteria (nPAW3=4) and four criteria (nPAW4=1). Hereafter, PAWx is used to identify individuals with 'x' pig phenotypic reported by hunters (PAW+ indicates PAWs with one or more criteria).

Molecular analysis

All tissue samples were stored in alcohol in an individual hermetic straight container of 25ml and then were genotyped for 12 microsatellite and 20 SNP loci. The protocol of extraction, amplification and genotyping for SNPs is detailed elsewhere [START_REF] Beugin | A set of 20 multiplexed Single Nucleotide Polymorphism (SNP) markers specifically selected for the identification of the wild boar (Sus scrofa scrofa) and the domestic pig (Sus scrofa domesticus)[END_REF]. For microsatellite loci, the procedure has already been described in Gayet et al. (2016).

Genetic analysis

All analyses were carried out only with individuals that had more than 50% of the genotypes obtained for both microsatellites and SNPs. A total of 447 individuals were included in analyses: 261 wild boars, 50 domestic pigs and 136 PAWs. A qualitative analysis of markers was first conducted with R 3.3.3 software (R Core Team, 2017) using adegenet 2.0.1 [START_REF] Jombart | adegenet: a R package for the multivariate analysis of genetic markers[END_REF] and diveRsity 1.9.90 [START_REF] Keenan | diveRsity: An R package for the estimation and exploration of population genetics parameters and their associated errors[END_REF]. For each SNP and microsatellite locus, the differentiation index between pigs and wild boars (FST), informativeness of ancestry index as described in [START_REF] Rosenberg | Informativeness of genetic markers for inference of ancestry[END_REF], expected heterozygosity (He) and allelic frequency of the most common allele (F) for pigs and wild boars were calculated. For microsatellite loci, the total number of allele (N), the allelic richness (Ar) and the number of private alleles were estimated in each population. Values obtained for pigs and wild boars were compared using Wilcoxon tests.

Two Bayesian statistics-based software programs were used to investigate hybridization patterns between wild boars and pigs with both sets of markers. The first was the clustering method STRUCTURE 2.3.4 [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF]. It was used to infer the most probable number of parental groups (K), and also to assign each individual to one (or several) of the K parental groups with defined probabilities (qik). All analyses were carried out with 20,000 iterations of burn-in followed by 500,000 iterations of MCMC (Markov chain Monte Carlo). According to the documentation, the parameter λ (index of correlation of allele frequencies) was first estimated for K=1 and set to 0.6877 for microsatellites and to 0.7823 for SNPs in further analyses. Other parameters were set as follows: admixture model, correlated allele frequencies among populations without including population information and other parameters were set as their default value. Using these parameters for SNPs and microsatellites, 20 independent runs assigned to the genotypic group) is already set at 95%. The accuracy of the sets of markers for each analysis were compared using chi-squared tests. Thresholds obtained made it possible to classify PAWs in parental or hybrid groups with both methods and to verify the ability of both sets to detect them as hybrids.

Results

Markers description

SNP data analysis showed that an allele is present in four loci in the wild boar population (frequency of 1) but they were also present in more than 50% of the pigs (Table 1). The genetic diversity measured as the expected heterozygosity was significantly higher in the domestic population than in the wild one (Wilcoxon test: W=77.5, p < 0.01, Table 1). With microsatellites, both allelic richness and expected heterozygosity were the same between pigs and wild boars (Wilcoxon test: W = 57, p = 0.41 and W = 42, p = 0.08 respectively; Table 2). Some alleles were specific to each population (present in one but not in the other) but none of these specific alleles were fixed in any population. Differentiation indexes were higher with SNPs than with microsatellites. The FST ranged from 0.19 to 0.96 with a median of 0.57 for SNPs (Table 1) versus a median value of 0.13 for microsatellites ranging from 0.05 to 0.50 (Table 2) (Wilcoxon test: W = 12, p < 0.01). However, the informativeness indexes were not significantly different (Wilcoxon test: W = 155, p = 0.18), with SNPs showing a median of 0.19 versus 0.31 for microsatellites (Table 1 and2).

STRUCTURE results with real and simulated data

Using the method described by [START_REF] Evanno | Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study[END_REF] based on STRUCTURE analyses, the most likely number of genetic groups was K = 2 for both sets of markers. Wild boars are separated from domestic pigs (Figure 1, a andc). The horizontal lines represent the threshold values determined as the value 95th percentile of assignment values to the wild boar group obtained by simulated wild boar and pig (qWB-WB-95% = 0.931 and qPig-WB-95% = 0.111 with SNPs and qWB-WB-95% = 0.924 and qPig-WB-95% = 0.111 with microsatellites for wild boar and pig respectively). Simulated datasets analysis gave information about the range of qi-WB values that may be obtained for the different genotypic classes (Supplementary Material, Figure S2). Results were similar between SNPs and microsatellites with lower ranges of qi-WB values for parental populations (pigs and wild boars) than for other genotypic groups. In both cases, the median of qi-WB values obtained for each genotypic group was similar to expected values (χ² = 3.23, df = 9, p-value = 0.95 for SNPs and χ² = 3.26, df = 9, p-value = 0.95 for microsatellites). The ranges obtained by wild boar and pig were separate from each other for both sets of markers. The qi-and 2c). Considering the 42 PAW0, 38.1% and 50% obtained assignment to wild boar below the threshold, with SNPs and microsatellites respectively. Focusing on PAW+, 43.6% of the 94 showed no significant assignment to wild boar group with both SNPs and microsatellites. These proportions increased with the number of criteria for both sets of markers as 35.8% and 38.7% of PAW1, 87.5% and 62.5% of PAW2 and 100% of PAW3 and PAW4 were not assigned to the wild boar group with SNPs and microsatellites respectively (Supplementary Material, Figure S5). Overall, 25 PAW+ were identified as hybrids with both sets of markers (Table 3).

No individual was assigned to the F1 genotypic group (Supplementary Material, Figure S3) significantly suggesting that individuals detected as hybrids have deeper introgression levels. Assignment probabilities to the pig, wild boar (Wb), F1 and F2 genotypic groups obtained by pig, wild boar, F1 and F2 individuals (n = 2000 for each class) simulated with b) SNPs and d) microsatellites. The width shows the density of points. The white points show the median, the thick black vertical lines the central quartiles and the fine vertical lines 1.5 the inter-quartile space.

The horizontal lines represent the threshold values determined as the value 95 th percentile of values obtained by simulated wild boar and pigs (0.773 and 0.786 with SNPs and 0.707 and 0.731 with microsatellites for wild boar and pigs respectively).

(Colored figures are available in the Supplementary Material, Figure S3) SNPs. Indeed, SNPs were chosen in coding genome region [START_REF] Beugin | A set of 20 multiplexed Single Nucleotide Polymorphism (SNP) markers specifically selected for the identification of the wild boar (Sus scrofa scrofa) and the domestic pig (Sus scrofa domesticus)[END_REF] increasing the probability to be expressed and counter-selected in the wild [START_REF] Frantz | Genetic evidence for introgression between domestic pigs and wild boars (Sus scrofa) in Belgium and Luxembourg: a comparative approach with multiple marker systems[END_REF][START_REF] Battocchio | How much does it cost to look like a pig in a wild boar group?[END_REF], while microsatellites are considered more neutral. Overall, 23.4% of PAW+ were assigned to hybrids in all analyses proving the ability of our sets of markers to detect hybridization (Table 3). As no individual was significantly assigned to the F1 group with NEWHYBRIDS, their levels of introgression were not assessed.

So far, with simulation analysis we showed both sets of markers were able to identify parental individuals with high accuracy. Thus hybrid individuals are recognized as such when excluded from parental groups, but individual introgression rates cannot be assessed. Analysis of genotypes of PAWs showed high proportions of individuals assigned to hybrid groups with both SNPs and microsatellites, proving them reliable in identifying hybrids in real datasets. As no set outperformed the other, we used both to estimate hybridization rates for a wild boar population. Between 1.9% and 7.3% of 261 wild boars were identified as hybrids, depending on the marker and the method. As none was assigned to the F1 group with NEWHYBRIDS, the introgression level was not considered. Only one real wild boar was identified by all four analyses giving confidence about the fact that hybridization events happened in the past in this population (Table 3). The proportion of hybrids in our population is consistent with other studies on free-ranging populations of wild boars in Europe, which ranged from around 2% to 10% [START_REF] Scandura | Ancient vs. recent processes as factors shaping the genetic variation of the European wild boar: are the effects of the last glaciation still detectable?[END_REF][START_REF] Scandura | Genetic diversity in the European wild boar Sus scrofa: phylogeography, population structure and wild x domestic hybridization[END_REF][START_REF] Koutsogiannouli | Detection of hybrids between wild boars (Sus scrofa scrofa) and domestic pigs (Sus scrofa f. domestica) in Greece, using the PCR-RFLP method on melanocortin-1 receptor (MC1R) mutations[END_REF][START_REF] Frantz | Genetic evidence for introgression between domestic pigs and wild boars (Sus scrofa) in Belgium and Luxembourg: a comparative approach with multiple marker systems[END_REF][START_REF] Goedbloed | Reintroductions and genetic introgression from domestic pigs have shaped the genetic population structure of Northwest European wild boar[END_REF][START_REF] Canu | Are captive wild boar more introgressed than free-ranging wild boar? Two case studies in Italy[END_REF][START_REF] Canu | Lack of polymorphism at the MC1R wild-type allele and evidence of domestic allele introgression across European wild boar populations[END_REF]. Some individuals, PAWs or wild boars, were identified as hybrids by some analyses but not all of them. Apart from the different information provided by markers, this can be explained, on the one hand because they may have been wrongly identified as wild boar in one or several cases since we were conservative in identifying hybrids.

On the other hand, we chose the threshold as the 95 th percentile of simulated value, thus some wild boar may also be falsely assigned as hybrids for one or several analyses, but not for the others.

The detection of PAWs as hybrids, associated with simulation analyses, made it possible to prove both the efficiency and the reliability of our markers to detect hybridization. Both sets of markers were equally efficient in detecting hybridization because none outperformed the other whether with simulated or real data. However none of them is able to identify individual levels of introgression after F1 hybrids. More studies are thus required to estimate individual introgression rates. Next generation sequencing methods such as RADSeq may be promising tools to investigate the whole genome scale for new sets of markers. Powerful diagnostic markers could help study fine-scale hybridization to understand the impact of hybridization on wild boar life history traits like Fulgione et al. (2016), to improve management practices when choosing pure population sources for restocking and to improve legislation to detect fraud.

Nevertheless both sets can measure introgression rates at the population scale. For future studies, it may be worthwhile to consider the cost benefits ratio of different sets depending on the question investigated. SNP genotyping is cheaper than microsatellite genotyping, but microsatellites enable investigation of other population genetic questions. We hope these results provide researchers and managers with guidelines in the use of genetic tools to investigate hybridization issues and new insights in the design of sets of markers for genetic studies.

Supplementary Material (SM)

SM1 Figure S1 Origin of sampled phenotypic anomalous wild boars (PAWs) included in the analysis.

SM2 Table S1 Classification based on morphological characteristics from Pinet (2002) to select reproductive wild boars in farm, used in this study to count the number of phenotypic characteristics from the pig displayed by PAWs SM3 Figure S2 Assignment probabilities to the wild boar group inferred by STRUCTURE analysis obtained by the 10 genotype classes (n=2000 for each class) performed on simulated datasets a) with SNPs and c) with microsatellites.

SM4 Table S2 Significant assignments of individuals from each of the 10 simulated genotypic groups (2000 individuals per group) given by STRUCTURE with a) SNPs and b) microsatellites. SM8 Table S3 Significant assignments of individuals from each of the 10 simulated genotypic groups (2000 individuals per group) given by newhybrids with a) SNPs and b) microsatellites.

Supplementary Material 1

Supplementary Material 2

Table S1: Classification based on morphological characteristics from Pinet (2002) to select reproductive wild boars in farm, used in this study to count the number of phenotypic characteristics from the pig displayed by PAWs

Supplementary Material 4

Table S2 Significant assignments of individuals from each of the 10 simulated genotypic groups (2000 individuals per group) given by STRUCTURE with a) SNPs and b) microsatellites. Wb stands for wild boar, P for pig, Bc for backcross and × shows a cross between flanking genotypic groups. Accuracies of the identification of each genotypic groups calculated with the method described by [START_REF] Vähä | Efficiency of model-based Bayesian methods for detecting hybrid individuals under different hybridization scenarios and with different numbers of loci[END_REF] are also given. Note that the sums in row are not equal to 2000 as individuals might have assignment probabilities to the different genotypic groups higher than corresponding thresholds for several genotypic classes leading thus for these individuals to be assigned in several groups.

Supplementary Material 8

Table S3 Significant assignments of individuals from each of the 10 simulated genotypic groups (2000 individuals per group) given by newhybrids with a) SNPs and b) microsatellites. Wb stands for wild boar, P for pig, Bc for backcross and × shows a cross between flanking genotypic groups. Accuracies of the identification of each genotypic groups calculated with the method described by [START_REF] Vähä | Efficiency of model-based Bayesian methods for detecting hybrid individuals under different hybridization scenarios and with different numbers of loci[END_REF] are also given. Note that the sums in row are not equal to 2000 as individuals might have assignment probabilities to the different genotypic groups higher than corresponding thresholds for several genotypic classes leading thus for these individuals to be assigned in several groups.