Guillaume Martinez
email: gmartinez@chu-grenoble.fr

Cécile Garcia
email: cecile.garcia@mnhn.fr

Sexual selection and sperm diversity in primates AUTHORS

Keywords: sexual selection, sperm competition, semen evaluation, testes, sperm allocation, trade-off

Many aspects of primate sperm physiology and reproductive behavior have been influenced by sexual selection, especially in taxa exposed to sperm competition where females mate with multiple partners. Primate sperm diversity reflects therefore the evolutionary divergences of the different primate species and the impact of a combination of variables exerting selection pressures on sperm form, function, and competition. Thereby, mating systems, life cycle or ecological variables are some of the important factors driving sperm diversity and explaining variation in terms of sperm morphology, parameters or male sexual characters. Here, we address primate sperm diversity through a compilation of all data available in the literature concerning primate sperm parameters and relationships between them. We then review the most important variables, e.g. seasonality, social constraints or trade-off between investments in precopulatory and postcopulatory sexual traits, which can influence primate sperm diversity and discuss also their relevance to our understanding of human reproduction.

INTRODUCTION

Mammalian spermatozoa are motile, highly differentiated and oriented haploid cells with a specific size, shape and axes of symmetry. They are composed of a head and a flagellum and of various subcellular structures adapted to the physiological processes that are essential for the reproduction of the species (capacitation, acrosomal reaction, gametic fusion). Basic head structure is a haploid nucleus containing a highly compacted chromatin, with very little cytoplasm and covered at the apical pole by the acrosome, a large secretion vesicle derived from the Golgi apparatus. The flagellum ensures cell mobility and is divided into three parts: an intermediate piece surrounded by a mitochondria sheath, a large main piece and a short terminal piece. This base structure is preserved in all mammals with specificities for some taxa such as the head sickle shape in rodents.

Primates are an order within placental mammals that includes more than 500 species.

While primate sperm displays a considerable uniformity, there are still some variations between species in terms of sperm morphology and overall sperm parameters. This primate sperm diversity reflects the evolutionary divergences of the different taxa and is the result of a combination of variables exerting selection pressures on them, such as mating system variables, life cycle characteristics or ecological variables.

The first part of this review will describe primate sperm diversity through a compilation of all data available in the literature. The second part will be devoted to the most important mechanisms and factors influencing sperm form, function, and competition across primates.

About primate form and sh-ape

Sperm morphometry

The action of centripetal forces on spermatozoa evolution has considerably reduced morphological variations between the different species and created an overall mammalian morphometric uniformity (1980 Gould). Sperm global shape is well preserved among primates, but some interspecies variations are still observed, mainly regarding spermatozoa length. We compiled species-specific primate sperm morphometric data of 76 primates (table 1). Across all species analyzed, mean±SE total sperm length is 70.69±10 µM with a ratio of 2.4 between the shortest and longest representatives Lepilemur mustelinus (52 µM) and Ateles paniscus (124.61 µM). With a 56.15 µM total length, Homo sapiens is below average and also the shortest representative of Hominidae family, more than 15% less than Pongo pygmaeus. Head length ranged from 2.8 to 9.0 µM with a mean of 5.83±0.84 µM, accounting for 8.2 % of total sperm length. Midpiece length ranged from 3.56 to 20.7 µM with a mean of 10.07±2.13 µM, accounting for 14.3 % of total sperm length. Tail length ranged from 17.3 to 83.5 µM with a mean of 55.14±10.10 µM, accounting for 77.9 % of total sperm length. Human sperm are again under average among primates, especially regarding the midpiece length.

Sperm length is the result of a complex set of evolutionary pressures such as the female reproductive tract [START_REF] Higginson | Female reproductive tract form drives the evolution of complex sperm morphology[END_REF], metabolic requirements of sperm [START_REF] Gomendio | Why mammalian lineages respond differently to sexual selection: metabolic rate constrains the evolution of sperm size[END_REF] or sperm competition which can exert a positive [START_REF] Fitzpatrick | Female promiscuity promotes the evolution of faster sperm in cichlid fishes[END_REF] or negative [START_REF] Stockley | Sperm competition in fishes: the evolution of testis size and ejaculate characteristics[END_REF] influence (see below in 2.1). In human, having long spermatozoa appears to be an advantage as the overall lengths of sperm components and their degree of variability within an ejaculate have been positively associated with sperm concentration and motility (2013 Mossman), which are significant fertility determinants.

Regarding the head, human sperm is similar to the chimpanzee shape (ellipticity=1.61 and elongation=0.23). However, the pleiomorphic nature of human ejaculate allows us to identify two populations similar to those observed in other great apes, albeit with smaller volumes. The first is similar to orangutans sperm with a large paddle-shaped head and thinner in the vertical dimension (ellipticity=1.40 and elongation=0.17). The second is similar to gorilla, with a shape intermediate to the previous two (ellipticity=1.38 and elongation=0.16).

Sperm parameters

We compiled literature data on sperm parameters from 43 primate species. Summarized in table 2, these data support the known high heterogeneity of primate ejaculates, both at the inter-and intra-species levels.

Collection method

Masturbation

Masturbation is the natural and best collection method to obtain ejaculates truly representative of testicular function. In human, semen analyses are therefore carried out on samples obtained by masturbation under specific disinfection and abstinence protocols. While the aseptic conditions of the human clinic are clearly not reproducible for other primates, it is still possible to obtain great ape masturbation samples from Gorilla (1997Pope, 2005O'brien, 2008 Nascimento), Pan (1988Marson, 1993Gould, 1995Young, 1998Younis, 2004Kuehl, 2005Agca, 2008Nascimento, 2018 Yu) and Pongo (1995 Joslin), with higher total sperm counts and fewer abnormal forms than samples obtained via electrostimulation methods (1989Schaffer, 1995Gould, 1995Young, 1996 Gould). Semen collection can be manual as part of specific training or assisted via artificial vaginas.

As male masturbation is the most frequent sexual behavior observed after copulation (2003Thomsen, 2005Frearson, 2012 Dixson) for primate species, another method consists in collecting the products of punctual masturbation on the ground (in Macaca (2014Thomsen), Papio (1969Kraemer) and Chlorocebus (1999 Hiyaoka)). This noninvasive collection method allows some precious semen analysis (2004Dejucq-Rainsford, 2006Thomsen, 2012 Inoue), but soil contamination prevents us from accurately assessing the quality and fertilizing potential of the male. Another pitfall associated with these samplings is the potential difficulty of quickly collecting the material prior its consumption by the male (personal observations).

Epididymal extraction

Samples obtained by epididymal extraction are numerous and are mainly collected opportunistically following castrations [START_REF] Gupta | Seasonal variations in daily sperm production rate of rhesus and bonnet monkeys[END_REF] or in post-mortem contexts (2001Kusunoki, 2005Anderson, 2008 Dong). Analysis of sperm from the tail of the epididymis allows to acquire some data on sperm morphometry or production but is not representative of an individual's ejaculate and fertility potential.

Electro-stimulation

Electro-stimulation (ES) is the most widely used method for primate semen collection (1968Ackerman, 1978Gould, 1980Platz, 1983Bader, 2002Aslam, 2003Amboka, 2007Vidal, 2009 Da Silva, 2016Oliveira, 2016Swanson, 2017Sampaio, 2018Devilliers, 2019 Arakaki) including Human (1996 Nehra). Using rectal probe or penis electrodes, ES has many practical and logistical advantages (no training required, programmable in time, sleeping individuals), but this approach has also several drawbacks.

Indeed, ES is restricted to facilities with a laboratory because of the devices needed for basic (incubator, centrifuge) or advanced sperm analysis (CASA device) and the monitoring period required at the end of the experiment due to the invasive nature of the method. Beyond the dangers associated with the capture and immobilization of an adult male in the wild, this induces a high level of stress to the subject but also to the group as a whole (2014 Thomsen), with possible negative repercussions at reintroduction time. In order to obtain consistency in physiological response, specific protocols have to be establish for each species regarding both anesthetic and stimulation phase (1990Durrant, 1996 Morrell). Anesthesia presents significant health risks for the animals and limits the sampling frequency, whereas the stimulation phase requires trained technicians, with rectal probe placement being essential to obtain ejaculation and avoid burns. Even with robust protocols, some studies indicate that ejaculates obtained by ES tend to contain more immature sperm (1992Matsubayashi, 1996Morrell, 2014 Thomsen) and more coagulum formation (1986Wildt, 1989 Schaffer) than those obtained by masturbation.

It should be noted that urethral massage is a good complement to electro-ejaculation techniques to recover residual semen and increase the volume of the sample.

Finally, ES appears to be best suited for larger primates and safer alternative methods (vaginal washing and penile vibrostimulation; see below for further details) have been developed for smaller species for which ES may be unsuitable or unsuccessful (1996Morrell, 2000[START_REF] Kuederling | Non-invasive collection of ejaculates from the common marmoset (Callithrix jacchus) using penile vibrostimulation[END_REF].

Vaginal washing

Vaginal washing (VW) consists of retrieving a male's ejaculate by washing a female's vagina quickly after a successful coitus. This method has been developed in small primates, such as marmosets (1996[START_REF] Kuederling | Collection of semen from marmoset monkeys (Callithrix jacchus) for experimental use by vaginal washing[END_REF]Morrell, 1997[START_REF] Morrell | Artificial insemination in Callithrix jacchus using fresh or cryopreserved sperm[END_REF]Morrell, 2004 Schneiders) and macaques (1973 Cho), for which sedation is not required to obtain the sample. Although VW allows the collection of natural ejaculates for assisted reproduction techniques (1996Kuderling, 1996Morrell, 1997[START_REF] Morrell | Artificial insemination in Callithrix jacchus using fresh or cryopreserved sperm[END_REF], it is less efficient for sperm parameters analysis as the sample is contaminated by secretions and some of it is lost in the female genital tract (1996Kuderling, 1996 Morrell). VW protocols are time-consuming to set up and carry out, and have to be species-specific (2004 Schneiders). The VW is therefore effective but limited to specific applications in small species at this time.

Penile vibrostimulation

This procedure provides ejaculate through normal ejaculation via application of vibration to the penis of a restrained individual. Although there is no need to sedate the animal, it must be trained to the restriction chair. This method proved its worth in marmosets (2000 Kuederling, 2005Hernandez-Lopez, 2005Valtonen, 2012Valle, 2016Swanson, 2018 Arakaki), macaques (2000 Kholkute) and saïmiris (1997Yeoman, 1998 Yeoman).

The main benefit of this procedure is, as with masturbation, the production of a natural ejaculate that displays a higher number of motile and total sperm versus electrostimulation (1995Young, 1997Yeoman, 1998 Yeoman). The main concern is that this protocol is obviously challenging to implement for great apes, but recent studies (2018 Arakaki) pointed out that, with species-specific adaptations, this technique could be very promising.

In conclusion, from a practical point of view, inter-species constraints do not allow to propose an optimal method consensus and each collection must be considered on a caseby-case basis according to the species and to the context. From a biological point of view, ejaculates obtained through natural ejaculation (masturbation and vibrostimulation) proved their superiority and should be favored when possible.

Sperm motility

The average primate has about two-thirds motile sperm in an ejaculate, a proportion that logically correlates with vitality (measured as the percentage of intact membrane sperm). It is challenging to interpret motility data because of the very high variability in the percentage of motile sperm with ejaculates ranging from almost fully motile to fully immobile present in all families.

The heterogeneity of motility data comes in part from the inherent limitations of data collection protocols (discussed in section 1.3), but mostly from the existence of sperm subpopulations in mammalian ejaculates [START_REF] Holt | Concepts in sperm heterogeneity, sperm selection and sperm competition as biological foundations for laboratory tests of semen quality[END_REF]. Many studies concluded that variations among these sub-populations have functional relevance with identified associations to fertility or post-freezing survival outcomes (2001Thurston, 2006Martinez, 2008Muino, 2009Ortega-Ferrusola, 2010Dorado, 2013Ramon, 2014Beracochea, 2015Yaniz, 2016 Santaloria).

Although the development of computer-assisted sperm analysis (CASA) systems has made it possible to bring more accuracy and depth to mobility studies, the majority of the observations compiled here have been carried out manually by technicians, as these systems are rarely used outside of human medicine. Among CASA parameters, average straight-line velocity is recognized as a main factor in fertility (1999Birkhead, 2005 Malo) and have previously been correlated with total sperm length (2009Lupold, 2009Gomez Montoto, 2011 Tourmente) and relative testes mass in mammals ( 2011Tourmente). However, in light of the limited data available for mobility parameters in the literature (table 3), it is not yet established whether these results can be reproducible for primates alone.

Nevertheless, we can observe that human has a curvilinear velocity, a proxy for the effective sperm velocity, lower than that of other primates. This confirms conclusions of previous studies (2011 Maree) showing that sperm from polygynandrous primate species swims faster than human one. Motility percentages for Homo and Gorilla taxa are lower than those of Pan and Pongo, which suggests that sperm from polygynandrous primates swim faster than sperm from species less exposed to sperm competition in general. It is also plausible that the mobility alterations in Homo and Gorilla are only the result of the pleiotropism present in the ejaculate of these taxa, abnormal forms sperm producing lower velocities than normal form sperm. Again, the limited number of studies using CASA does not allow us to reach a robust conclusion.

Other issues would also benefit from more CASA studies, for example, we still do not know if larger sperm swim faster when there is a higher risk of sperm competition in some primate species like demonstrated in rodents (2011 Montoto).

Sperm morphology

In human reproductive medicine, the criteria for defining normal-form sperm (NFS) have been established by averaging the observed characteristics of the sperm population that reach the oocyte (2010 Cooper). Morphological analyses of assisted reproduction centers are mostly based on the World Health Organization guidelines on semen analysis, which use very strict analysis criteria and a pathological cutoff established at 4% NFS. Based on these criteria, the species presenting the lowest and highest rates of NFS are from the Hominidae family with 23.75% and 98.5% NFS for Gorilla gorilla and Pongo pygmaeus respectively. Of all 43 primate species studied, the spermatozoa from the ejaculate of Human and Gorilla spp. are the only ones characterized by an extreme pleiomorphism with 23.75% and 32.22% NFS respectively. These two species also exhibit more variation in size and shape within a single ejaculate than some species between them. The pleiomorphic nature of sperm found in both species does not seem to affect their fertility, whereas when abnormal forms are found in other species, they are associated with infertility or occur outside the reproduction period (1983[START_REF] Gould | Semen characteristics of the adult male chimpanzee (Pan troglodytes)[END_REF]Seier, 2002Hernandez-Lopez, 2016 Pina-Aguilar). Again, these sub-populations could present functional relevance and play a key role in fertility. However, the relationship between sperm morphology and fertility is still debated and results are controversial (for review, see 2016 Garcia-Vasquez). These very low NFS rates could be explained by the lack of pressure from sperm competition. Indeed, it has been shown in other taxa that an absence of sperm competition leads to increases of abnormal sperm form in the naked mole-rat (2011 van der Horst) and of morphological variability in insects (2011 Fitzpatrick). Since gorillas and humans are considered polygynous or mildly polygynous species (2005 Marlowe), they are not supposed to be exposed to high sperm competition pressure and they may therefore allocate their resources to other parameters (see below for further details).

It is to note that the New World monkey Callithrix penicillata is also described with a low NFS (30,17%) but this species should not be considered as pleiomorphic, as this affirmation is based on a single study (2018 Arakaki) of four animals collected during the rainy season and the Callithrix genus is known for its large range of NFS (range 25% to 91.9% NFS in Callithrix jacchus according to data from 127 individuals among 9 studies: 1991 Cui, 1996Cui, 1996Morrell, 1997Morrell, 2004Schneiders, 2009Da silva, 2014Valle, 2016Swanson, 2018 Arakaki).

Testes mass

Martinez 12

Total testes mass of 71 primate species are compiled in table 4 and illustrate primate diversity, with a ratio of 400 between the lightest and heaviest representatives Cebuella pygmaea (0.16 g per testis) and Pan paniscus (67.6 g per testis). With an average of 21.54±2.85 g per testicle, and despite a high body weight, human testicular mass is similar to that of most Macaca species (mean Macaca: 25.23±5.44 g) and inferior to Papio species (mean Papio: 34.38±7.16 g) and some Atelidae (Ateles paniscus: 32.12 g, Brachyteles arachnoides: 39.18 gone data point per species). Among Hominidae, humans have heavier testicles than gorillas (12.84g ±1.24 g) and orang-utans (17.65±1.2 g), but much lighter ones than Pan species.

When this mass is adjusted to body weight (figure 1), human appears to have relatively small testicles and to be closer to polygynous species like Gorilla than to polygynandrous species Pan, despite a closer common ancestor. Overall, we find that polygynandrous primates have bigger relative testes mass than those found in other mating systems, confirming results of previous studies (2016 Parker, 2018 Dixson) on the relationships between relative testes sizes and mating systems (see section 2.1. for discussion).

Limitations

While based on numerous independent sources, it should be kept in mind that all data on primate sperm should be interpreted in regard to the main sources of possible variation due to subspecies, populations, individuals, time collection and technical differences. Indeed, variations are reported at the subspecies level (2009 Steinberg), but also between populations of identical taxa but of different geographical locations ( 2014Valle). Many environmental factors, such as season [START_REF] Gupta | Seasonal variations in daily sperm production rate of rhesus and bonnet monkeys[END_REF]2002 Muehlenbein;2002 Hernandez-Lopez;2008 Hernandez-Lopez;[START_REF] Cerda-Molina | Seasonality of LH, testosterone and sperm parameters in spider monkey males (Ateles geoffroyi)[END_REF] and toxic exposition (2007 Hung;2011 Falzone;[START_REF] Nyachieo | Short-term effects of high-dose khat on sperm parameters and reproductive hormonal levels in olive baboons (Papio anubis)[END_REF], may also play a role, as well as individual factors, such as age [START_REF] Sloter | Quantitative effects of male age on sperm motion[END_REF], sexual maturity [START_REF] Marson | Cellular and biochemical characteristics of semen obtained from pubertal chimpanzees by masturbation[END_REF], abstinence time (1989Marson, 2017 Alipour) and current health status. At a technical level, there is no universal standard method for the analysis of primate sperm parameters ( 2010Auger). Variations may therefore be due to the use of different procedures ( 2005Hernandez-Lopez), such as the sperm recovery method (1995 Young;1998 Yeoman;2000 Kuederling;2004 Schneiders)

Factors of sperm diversity

Here, we will review some of the most important variables (e.g. mating-system variables, life-history traits, ecological variables) influencing sperm form, function, and competition across primates.

Mating systems

Sperm characteristics in group-living animals, such as primates, will depend on the relative numbers of males and females mating with each other in a given social unit or population i.e. on mating systems. Four types of mating systems are commonly found among primates (2012 Dixson): monogamy (one male -one female), polygyny (one malemultifemale, also often called harem systems), polyandry (one femalemultimale, mostly in cooperatively breeding primates) and polygynandry (i.e. multimale-multifemale, MMMF). Concerning polygyny, the extent and exclusiveness of Martinez 14

this mating system will be affected by the distribution of mating opportunities in space and time (dispersion of females and synchronicity of their fertile periods; see further details on seasonality), in interaction with female behavior, i.e. the ability to monopolize them (see below for further details on sexual monopolization and coercion). The strength of intra-sexual selection in male primates, via sperm competition, correlates with the mating system, with higher levels of selection in MMMF systems (such as macaques, baboons and chimpanzees) and then bigger relative testes size (i.e. greater investment in sperm production) and mass (figure 1) than in monogamous (e.g., owl monkeys and gibbons) or polygynous (e.g., proboscis monkeys, gorillas and geladas) mating systems (2016Parker, 2018 Dixson). Sperm competition does seem to be the primary agent of testes size evolution in primates with large testes being adaptive under conditions where females mate with multiple partners during their fertile period (because they usually contain a greater volume of seminiferous tissue). Testes size in humans occupy an intermediate position between gorillas and chimpanzees (2014 van der Horst & Maree). As suggested by [START_REF] Dixson | Copulatory and Postcopulatory Sexual Selection in Primates[END_REF], this relatively small testes size does not seem to provide evidence for a significant role of sperm competition during human evolution.

Besides testes size, some other traits have been under positive selection, via sperm competition (and/or cryptic female choice, see below), in polygynandrous primates (and more generally polygynandrous mammals): faster rates of spermatogenesis, greater capacity to sustain high sperm counts, copulatory plug formation, etc… ( 2018 2005) (with the exception of the common marmoset). Sperm kinematic parameters (swimming characteristics) might also be related to mating systems, with sperm from MMMF primate species swimming faster and with greater force than sperm from polygynous primate species [START_REF] Nascimento | The use of optical tweezers to study sperm competition and motility in primates[END_REF]. Nevertheless, as discussed previously (section 1.2.3.), these findings have to be taken with caution because the sample size was small and semen samples from each species were prepared using different methods. Semen quality parameters, such as the percentage of normal sperm in the ejaculate, are also related to the levels of sperm competition experienced by the different species (figure 2). The high incidence of pleiomorphism in Human and Gorilla, associated with the striking similarities between other sperm traits (e.g. ejaculate volume, sperm concentration and motility, table 2), support the view of a very low risk of sperm competition in humans compared to other primates (2018 Dixson). Finally, there is also evidence that male copulation frequencies and frequencies of ejaculation (ejaculatory mounts and masturbation) are significantly higher in MMMF systems than in polygynous and monogamous systems, including humans (1995 Dixson) whose reproductive system does not seem to be adapted to sustain high sperm counts during periods of high sexual activity. Such findings can be interpreted as indicating that "masturbation is more likely to occur in multimale-multifemale primate groups because males possess neuroendocrine specialization for greater sexual arousal and performance in such mating systems" (2004 Dixson). However, the question of why there are so frequent masturbations in some primate species remains unresolved. One hypothesis is that regular masturbation would have a positive physiological effect on the general quality of spermatogenesis.

Interplay between pre-and post-copulatory selection

Male secondary sexual characters are traits that bias mating success because their expression influences the outcome of male-male contests over access to females (weapons) or renders males more attractive to females (ornaments). There are evidence that weapons (e.g. canines) and ornaments (e.g. the red chest patches of geladas (Theropithecus gelada), the red face and genital sex skin in mandrills (Mandrillus sphinx) and Japanese macaques (Macaca fuscata), the hair capes of hamadryas baboons (Papio hamadryas), the cheek flanges of orangutans (Pongo spp.), enlarged noses of proboscis monkeys (Nasalis larvatus), the beards of men, etc. (see 2012 Dixson)) evolved under pre-copulatory sexual selection. When these attributes do not contribute to have a better access to mates, sexual selection will be on the ability to find and reach the fertile females (mobility, sensory abilities) and/or to fertilize her. Thereby, when females have multiple mating partners, as it is the case in many groups of primates, sexual selection will continue after mating in the form of sperm competition [START_REF] Parga | wbprim0223 Parker GA. Sperm competition and its evolutionary consequences in the insects[END_REF] and through cryptic post-copulatory female choice (1996 Eberhard), i.e. females selecting sperm with particular characteristics (see section 2.4.). Theoretical models of sperm competition predict a trade-off between expenditure on the acquisition of mates (pre-mating sexual selection) and expenditure on post-copulatory traits (testes size, sperm number and quality) that promote fertilization success (post-mating sexual selection), i.e. an increased expenditure on testes and sperm should be associated with a decreased expenditure on the weapons and ornaments (2010 Parker and Pizzari).

Numerous comparative analyses have investigated the evolutionary associations between weapons and testes in a wide range of taxa (see [START_REF] Simmons | Evolutionary Trade-Off between Secondary Sexual Traits and Ejaculates[END_REF] for a review). In general, the covariance between these sexual traits changes from positive to negative as male-male competition and female monopolization increase within animal taxa (2014[START_REF] Simmons | Evolutionary Trade-Off between Secondary Sexual Traits and Ejaculates[END_REF]. Across primates, there is an increase in sizecorrected testes mass with the number of males within breeding groups (2019 Lüpold), which is in accordance with predictions of sperm competition models (2016 Parker).

Similarly, primate species characterized by a higher female monopolization show a decreased investment in testes size [START_REF] Lüpold | Sexual ornaments but not weapons trade off against testes size in primates[END_REF]. In a previous study, [START_REF] Lüpold | Female monopolization mediates the relationship between pre-and postcopulatory sexual traits[END_REF] estimated that the proportion of species within each taxon where males monopolize females was about 20% in their primate sample (e.g. species with monogamous and multimale mating systems were classified as low monopolization while single-male mating systems were classified as high monopolization), showing that female monopolization is not very common in this Order. Given that, one should predict a general positive relationship between weapons and testes at the Order level (as shown in a comparative study of gregarious primate species by [START_REF] Lüpold | Sexual ornaments but not weapons trade off against testes size in primates[END_REF]: testes mass increases with increasing sexual dimorphism of the canines), with some taxon-specific associations depending on additional life-history, ecological and mating-system variables. For example, in polygynous species like gorillas, male body size/canines are under very intense sexual selection and greatly exaggerated, suggesting that those very costly traits will be more likely to trade off evolutionarily against investment in sperm production, which could explain their relatively small testicles compared to their body size.

Most of the studies investigating the evolutionary trade-off between pre-and postcopulatory traits have focused on the associations between weapons and testes, and very little attention has been paid to the patterns of covariation between ornaments and postcopulatory traits. At the within-species level, studies on visual sexual signaling traits, such as nose size in proboscis monkeys (2018 Koda) or face redness in mandrills ( 2001Setchell & Dixson), showed that there was a positive relationship between the strength of these ornaments and testes size. However, at the interspecific level, it has been shown that species who invested most in the acoustic ornaments (enlargement of the larynx and hyoid allowing males to broadcast low formant-frequency vocalizations) used during male pre-mating competition in the genus Alouatta (howler monkeys), had smaller testes (2015 Dunn). Moreover, a very recent comparative study in more than 100 primate species documented an evolutionary trade-off between pre-mating ornaments (e.g. fleshy swellings, skin color, hairy traits etc) and testes mass (2019 Lüpold). The authors suggested that "if male ornaments function as badges of status, with privileged mating opportunities for highly ranked males similar to female monopolization by the most successful males in contest competition, investment in male ornaments should also lower the level of sperm competition and relax selection on sperm production". Therefore, the contrasting evolutionary trajectories between weapons/testes (positive relationship) and ornaments/testes (negative relationship) reported in primates could be driven by differential selection, functional constraints or temporal patterns of metabolic investment between the different types of sexual traits (2019 Lüpold). There is a need for more research on the trade-offs between weapons/ornaments and ejaculate traits in primates (sperm number, viability, swimming speed and size; see meta-analysis by [START_REF] Mautz | Do male secondary sexual characters signal ejaculate quality? A meta-analysis[END_REF]: positive but non-significant relation between male secondary sexual characters and ejaculate quality across taxa), as most studies until now focused almost exclusively on testes size as a proxy for post-copulatory sexual selection. Similarly, studies in sensory ecology and ecophysiology that focus on the evolutionary trade-off between ejaculate expenditure and mate-searching (linked to sensory abilities and multimodal sexual communication), rather than direct male-male contest, would be a productive avenue for future research.

From the male's perspective: Mate guarding and copulatory plugs

There is considerable evidence that males have evolved behavioral adaptations, such as mate guarding, that function to prevent competitor males from gaining access to reproductively active females [START_REF] Andersson | Sexual selection[END_REF], thereby limiting the extent of sperm competition (1998 Birkhead and Møller) and increasing their chances of fertilizing the egg. Mate guarding is widespread among polygynous primates, where it has been described in detail for about 20 species of New and Old World monkeys (2012 Dixson).

Given the costs associated with mate guarding (e.g. reduction in foraging time, [START_REF] Alberts | Mate guarding constrains foraging activity of male baboons[END_REF]physiological costs, Girard-Buttoz et al. 2014), one should expect that males would invest in mate guarding if the reproductive benefits outweigh the costs associated with this activity. However, the extent to which male primates may adjust their relative use of mate guarding compared to the opposite tactic, which is the engagement in sperm competition through an increased expenditure on the ejaculate, remains largely unexplored. In one of the rare studies examining the relationship between mate guarding and ejaculate quality, [START_REF] Leivers | Sperm competition in humans: mate guarding behavior negatively correlates with ejaculate quality[END_REF] showed that men who performed more mate guarding behaviors produced lower quality ejaculates, with a lower concentration of sperm, a lower percentage of motile sperm and sperm that swam slowly and erratically.

Concerning male non-human primates, there is a paucity of empirical data on the costs of this behavior and its effectiveness does not seem to be absolute but rather dependent on its timing relative to the moment of ovulation. Moreover, whether a correlation between mate guarding and ejaculate quality exists in non-human primates remains to be investigated.

Another adaptation for the avoidance of sperm competition and an increase in male fertilization success is the use of coagulated ejaculate that forms sperm plugs (also called copulatory plugs). These copulatory plugs are found in many species of primates, but especially in those having polygynandrous mating systems (e.g., ring-tailed lemurs, muriquis, chimpanzees;2002 Dixson and Anderson). Two main hypotheses have been proposed to explain the evolution of pronounced sperm plugs in polygynandrous primate species: it promotes the passage of highly motile sperm through the cervix (2008 Hernandez-Lopez), buffers pH, and raises the temperature of the vagina which improve sperm survival in the vagina and its transcervical transport; it obstructs semen deposition and sperm transport by a second male. This second hypothesis seems less supported by the empirical data, and even if plugs tend to close the entry to the female's genital tract, they do not prevent her from subsequently mating with other males in primates (2017 Parga). Indeed, several studies have shown that penile morphology, such as spines, found in different primate species may facilitate the removal or displacement of coagulated semen and plugs deposited by previous matings, and hence reduce potential sperm competition (1993Hershkovitz, 2003 Parga). Moreover, males and females (see section 2.4. below) can also manually and/or orally remove these plugs, with semen ingestion being also reported (Garcia, personal observations in olive baboons and Japanese macaques).

Female choice & sexual conflict (sexual coercion)

Whenever polyandrous matings occur, sperm competition will inevitably arise, setting up selection on males (quantity and quality of sperm that improve their chances to fertilize the ova) but also on females to select sperm with particular characteristics and circumvent male control of reproduction (i.e. cryptic post-copulatory female choice; 1996 Eberhard). There will be also antagonistic selection on males and females due to sexual conflict.

Post-copulatory female choice is expected to occur more often in species in which females have little direct control over choice of mating partners or in which female mate choice is especially costly. This is particularly the case in species characterized by a high level of sexual dimorphism, and/or in species in which males are aggressive towards females in the context of mating (e.g. chimpanzees, pigtailed macaques, etc). In cases of sexual conflict, some traits that benefit males oppose with the female's interests and vice versa. For example, some conflicts can emerge in species where penile morphology might damage the female's genital structures during intromission (e.g. spines in galagos). They can also occur in species where females show prominent sexual swellings (e.g. chimpanzees, baboonsserving to attract multiple partners and Martinez 22 encourage the likelihood of mating and sperm competition; 2012 Dixson) that could influence the distance that males must cover during mating and sperm transport, and then increase the chances of being fertilized by males with longer penises. This conflict can also take the form of sexual coercion (review by [START_REF] Smuts | Male Aggression and Sexual Coercion of Females in Nonhuman Primates and Other Mammals: Evidence and Theoretical Implications[END_REF][START_REF] Smuts | Male Aggression and Sexual Coercion of Females in Nonhuman Primates and Other Mammals: Evidence and Theoretical Implications[END_REF][START_REF] Muller | Sexual coercion by male chimpanzees shows that female choice may be more apparent than real[END_REF] with direct (females are compelled to copulate more frequently with their aggressors) and indirect coercion (females are prevented from mating with other males).

Until recently, post-copulatory female choice had received little attention in the primate literature, especially because of practical difficulties of conducting such experiments in this Order, and more generally in mammals. There is therefore little evidence for differential fertilization chances of sperm of different males once inside the female reproductive tract. Nevertheless, there is ample reason to consider that, as in a number of insects and birds, there are anatomical, physiological and behavioral adaptations for post-copulatory female choice in primates. Here are a few examples of indirect evidence of possible cryptic female choice in primates.

At the anatomical level, after their deposition in the vagina during ejaculation, spermatozoa have to cross numerous barriers, such as the cervix or the uterotubal junction, before reaching the oviduct. There is a huge filtering in the number of spermatozoa from the vagina to the oviduct, with only about 200 being found in the human oviduct whereas 280 million sperm were initially released (2018 Dixson).

Moreover, it seems that elongated oviducts may serve to "test" the relative fitness of gametes from rival males and thus represent a mechanism of cryptic female choice in mammals, with longer and more convoluted oviducts being associated with higher relative testes size and sperm midpiece volumes [START_REF] Anderson | Mammalian sperm and oviducts are sexually selected: evidence for co-evolution[END_REF]. There are unfortunately not enough data on the anatomy of these potential physical barriers in non-human primates to assess the differential effects of the female's anatomical structures as selective filters upon sperm transport and then fertilization success and a lot more comparative studies are needed in this area of research.

At the physiological level, [START_REF] Hernandez-Lopez | [END_REF] have shown that there is a buffering effect of seminal fluid on vaginal pH in the spider monkey, which increased sperm motility in the vagina. Even if these results did not provide a distinct proof of female cryptic choice in this species, they still suggest that sperm selection could start as early as the vagina, with females relying on cues provided by the seminal coagulum in favoring or opposing sperm migration.

At the behavioral level, it has been suggested that female copulation calls (i.e. auditory signal occurring after mating) in Old World monkeys and apes are a form of postcopulatory female choice that encourages post-copulatory mate guarding by preferred males and minimize the probability of sperm competition by non-preferred males ( 2005Maestripieri & Roney). By calling after copulation with certain males, females express their preferences for these males and their sperm; whereas by not calling after copulation with other males, they do not encourage mate guarding by these males, which leaves the possibility that other males will mate with them and engage in sperm competition. Another behavioral mechanism that could be used to choose among different males is the active manipulation of their ejaculates. It has been shown that in chickens, females can expel the sperm from matings with low-ranking roosters immediately after insemination (cited in van Schaik 2016). Nevertheless, so far, we still do not know whether primate female's behavior might actively bias the fate of spermatozoa originating from different males, and if so, how.

Therefore, the question of how the primate female's reproductive system preferentially receives and influences processes associated with sperm transport, storage and viability remains to be investigated in more details.

Seasonality & Climatological factors

Reproductive activity of many primates is more or less seasonal, resulting in an increased frequency of matings during a relatively short period, which may select for increased sperm production, compared to year-round breeders [START_REF] Short | Sexual selection and the descent of man[END_REF]. In this case, we might expect a decrease in optimal ejaculate size as sperm production rates increase.

Indeed, this sperm depletion could be promoted by oestrus synchronization, which reduces the male-bias in the operational sex ratio (i.e. the ratio of the number of fertile adult males to the number of potentially fertile females in a group at a given time; definition in van Schaik 2016) during the breeding season and forces males to mate at a higher rates than if oestrus was not synchronous (2011 Stockley and Bro-Jørgensen).

Different studies have reported a negative relationship between the ratio of oestrous females to males and conception rates in both geladas and hamadryas baboons (1983Dunbar & Sharman, 1994 Zinner). Similar findings suggested some sperm limitation in gorillas (i.e. a species where males can only sustain relatively low mating rates, 1979 Short), with females receiving fewer copulations when other females were simultaneously in oestrus (1990 Watts).

Climatological factors have been invoked as causes of seasonal variation in the frequency of intercourse within human populations and could have a direct influence on human reproductive physiology and thereby on human fecundity. One of the main factors most often raised to explain these relations is temperature. Indeed, the process of spermatogenesis in primates, and mammals in general, is temperature-sensitive and optimized at temperatures slightly below the core body temperature. This temperature sensitivity has been a selective force in primate evolution resulting in external testes (cited in Ellison et al. 2015) and leads to ask whether high ambient temperatures, such as the ones encountered by most tropical non-human primates or humans living in hottest environmental places, could compromise male fecundity by affecting sperm quality and/or quantity. Most studies relating heat and damage to spermatogenesis focused on general seasonal variation in sperm concentration and total sperm count (e.g. with summer values being much lower than the ones found during winter times; in [START_REF] Durairajanayagam | Causes, effects and molecular mechanisms of testicular heat stress[END_REF] or used experimental approaches with inducedhyperthermia to evaluate whether different frequencies of heat exposure caused different degrees of damage to spermatogenesis [START_REF] Rao | Effect of transient scrotal hyperthermia on sperm parameters, seminal plasma biochemical markers, and oxidative stress in men[END_REF] reversible decrease in sperm concentration and motility with transient scrotal hyperthermia). However, to our knowledge, studies examining the effects of living in very hot environments on human spermatogenesis and the resultant spermatozoa are lacking. There is also a scarcity of data in non-human primates, with one study showing that high temperatures could reduce 80% of the original sperm count in cynomolgus monkeys [START_REF] Liu | Control of spermatogenesis in primate and prospect of male contraception[END_REF]. Therefore, clear evidence of a relationship between high ambient temperature and defects in male reproductive physiology in wild populations of primates is lacking and would deserve more attention.

Social constraints

Optimal sperm investment within species and within animal populations is expected to vary predictably with respect to male roles in the society, as defined within theoretical models known as sperm competition games [START_REF] Parker | Sperm competition and ejaculate economics[END_REF]. Sperm competition theory predicts that males should progressively invest more resources in their germline as their mating costs increase. When access to fertile females is determined by social dominance (e.g. dominant males being more likely to ejaculate at an optimal time relative to ovulation, i.e. a favored role), allocation trade-off hypothesis (soma vs. germline) predicts that semen characteristics and within-male variance in sperm design should be affected by the social environment, with subordinate males (i.e. the disfavored phenotype) investing more in ejaculate expenditure (1990Parker, 1998 Parker). Many studies have investigated the effects of social environment and social status on ejaculate characteristics in birds and some mammals, with some conflicting results regarding the theoretical predictions of sperm competition (e. sparrows compared to subordinate ones). There are much less information on the influence of social status on non-human primate sperm features and sperm competition; even though there has been a considerable literature on the effects of social constraints on male mating and reproductive success in different primate species (1991Cowlishaw & Dunbar, 2004van Noordwijk & van Schaik, 2005 Setchell) and a few papers on the relationships between social rank and testicular physiology (e.g. smaller relative testes in subordinate males than in dominant ones in mandrills or sifakas; 1992Wickings, 2009 Lewis). This is even truer in human populations with very few studies venturing out on this touchy topic and showing solid results. For example, [START_REF] Latif | Semen quality associated with subsequent hospitalizations -Can the effect be explained by socio-economic status and lifestyle factors?[END_REF] suggested that semen quality was not explained by socio-economic status, but due to the limited sample size and the fact that participants did not represent the general population (i.e. they were referred for infertility assessment), these results need to be further confirmed in future studies. There are therefore avenues for further research on the role of social status on fertilization outcomes in human and in a range of primate species.

Besides social status, there are some other social constraints than could have an influence on sperm competition and sperm features. For example, an increased population density might reduce the efficiency of male-male contests in securing females and increase its cumulative costs, thus leading to scramble competition ( 2013Parker). In marine invertebrates, it has been shown that males experimentally allocated to high-density groups, where sperm competition is more likely, produced longer and more motile sperm that swam for longer periods of time than did males in low-density treatment groups [START_REF] Crean | Gamete plasticity in a broadcast spawning marine invertebrate[END_REF]. Another study in amphibians also showed that across geographically isolated populations of chorusing frogs, the density of males in choruses was positively associated with testes mass and sperm production (2010 Dziminski). However, whether this pattern of covariation is also found in primate species and if there is a phenotypic plasticity in male allocation to ejaculates in response to fluctuating male densities remain to be investigated.

Androgens and sperm competition

Testosterone drives the process of male genital development, supports sperm production (2004Weinbauer, 2012 Dixson) and has a wide range of effects that plausibly function to support male competitive behavior, for example the development and maintenance of the armaments and ornaments that males employ in mating competition. The "Challenge hypothesis", first developed from studies in birds [START_REF] Wingfield | The "challenge hypothesis": Theoretical implications for patterns of testosterone secretion, mating systems, and breeding strategies[END_REF], states that the temporal patterns of circulating testosterone are closely associated with aggressive mating competition (2017 Muller). Observations from a range of wild primates support this hypothesis, which is also highly relevant for understanding social interactions in humans [START_REF] Wingfield | The challenge hypothesis: Where it began and relevance to humans[END_REF]. Mean levels of testosterone in MMMF primate species are higher than in uni-male mating systems and there is a positive correlation between testosterone levels and relative testes sizes (indicative of multiple partner matings by females and sperm competition among males) for the Order Primates, as a whole [START_REF] Whitten | Evolutionary endocrinology of the cercopithecoids[END_REF]2004 Dixson). [START_REF] Muller | Sexual coercion by male chimpanzees shows that female choice may be more apparent than real[END_REF] reviewed the relationship between testosterone and mating effort in primates, with specific emphasis on the ways in which testosterone promotes male-male competition: "in both seasonally and non-seasonally breeding species, males increase testosterone production primarily when competing for fertile females. In species where males compete to maintain long-term access to females, testosterone increases when males are threatened with losing access to females […].

And when male status is linked to mating success, and dependent on aggression, highranking males normally maintain higher testosterone levels than subordinates, particularly when dominance hierarchies are unstable". Low testosterone levels of subordinate males have also been reported in other mammal species, with some extreme cases in which the investment in ejaculate and reproductive capabilities of subordinates could even be suppressed in the presence of dominant individuals (cited in 2012 Lemaître et al.). Regarding the correlation between testosterone levels and semen characteristics, [START_REF] Burger | Ejaculate characteristics depend on social environment in the horse (Equus caballus)[END_REF] found that blood testosterone levels in horses were positively correlated with both the mean sperm number (after exposure to mares but not after exposure to stallions) and curvilinear sperm velocity (after exposure to stallions), suggesting that testosterone levels during exposure to a mare can be an indicator for a stallion's willingness to invest into costly semen production. However, to our knowledge, such studies examining the links between testosterone levels and sperm features in non-human primates are currently lacking and this topic needs further attention.

CONCLUDING REMARKS AND FUTURE DIRECTIONS

This review has discussed the different selection pressures involved in the evolution of primate sperm diversity. We considered especially how sexual selection (pre-and postcopulatory), acting via mating competition, sperm competition and cryptic female choice, has influenced the evolution of primate reproductive systems and sperm parameters. Cryptic female choice is still poorly studied in mammals and in primates in particular, and this topic deserves more attention. More detailed investigation is also required to determine the evolutionary trade-off between ejaculate expenditure and mate-searching across a broad range of primate taxa. Further studies are also needed to determine how social conditions explain variation in sperm morphology and parameters.

In conclusion, further research in this field offers much exciting potential to advance our current understanding of primate reproductive system evolution. Figure 2. Relationships between total sperm length, abnormal morphology and mating system of 66 primate species. Total sperm length is presented according to the species mating system (A) and percentage of sperm with normal morphology is presented according to the mean total sperm length of the species (B) or mating system (C). Each dot refers to a single species with data presented as mean if several sources. Black

  or sample conditions (fresh, washed, frozen, contaminated; 1986 Katz). For example, despite the existence of WHO recommendations in humans, many different stains are still used such as, Haematoxylin/Eosin, Shorr,Papanicolaou, Bryan-Leishman, DiffQuik, Quickdip, Harris-schorr and SpermBlue (2009 van der horst, 2010 Cooper, 2010 Maree), which could explain in part the reported variations

  Dixson).Indeed, increased levels of sperm competition are expected to result in increased sperm numbers (increased semen volume and sperm concentration; 1990Parker, 2012 Montoto, 2013 Lupold), increased sperm length (figure2), and a higher percentage of sperm with normal morphology (figure2), progressive motility, and viability (2009Pitnick). For instance, ejaculate size should increase with the incidence of rapid female polyandry (i.e. the rate of mating relative to the duration of sperm survival in the female reproductive tract), such as in polygynandrous species compared to monogamous species with extra-pair matings and slower female polyandry (2016 van Schaik). Sperm length has also been linked to the intensity of sperm competition, with males producing longer (and faster swimming) sperm in species with promiscuous females, which are probably adaptations to reach the ova first[START_REF] Gomendio | Sperm competition influences sperm size in mammals[END_REF]. Other morphological parameters, such as the size of sperm midpiece (indicator of mitochondrial loading and thus motility), are larger in primate species whose females mate polyandrously and males have larger testes in relation to body weight (2004Dixson & Anderson, 2011 Maree), with human sperm having smaller midpiece volumes than any of the 40 primate species measured byAnderson et al. (

  g. 2007 Cornwallis & Birkhead and 2007 Pizzari et al.: ejaculates of lower quality and reduced swimming speeds of sperm in socially dominant male fowls, who experience reduced levels of sperm competition; 2009 Kruczek & Styrna: higher motility of sperm in dominant bank voles; 2012 Lemaître et al.: dominant male bank voles invest more sperm per ejaculate than subordinates; 2015 Burger et al.: higher sperm numbers and velocity in stallions exposed to other stallions than exposed to mares; 2017 Rojas Mora et al.: ejaculates with higher levels of within-ejaculate variation in sperm design in dominant house

Figure 1 .

 1 Figure 1. Relative testes mass to body mass for 71 primate species displayed by family

  Martinez 56 horizontal line is the mean of each mating system. *Gorilla gorilla and **Callithrix penicillata.

	Cercopithecus wolfi	5.0	4.0	-	-	52.4	1.25	0.11	-	-	-	-	-	68.00	73.00
	Chlorocebus aethiops	5.8	3.3	14.0	13.3	44.0	1.60	0.23	0.86	161.9	11.40	52.26	2.87	65.10	77.32
	Erythrocebus patas	7.7	-	-	-	63.2	-	-	-	-	13.55	-	-	69.90	89.50
	Lophocebus albigena	5.8	-	-	-	37.2	-	-	-	-	11.10	-	-	17.30	-
	Lophocebus aterrimus	5.2	3.8	15.2	16.6	53.4	1.36	0.15	0.90	256.6	8.51	4.54	-	-	-
	Macaca arctoides	5.9	3.4	-	-	52.5	1.64	0.24			10.52	61.46	-	64.10	77.61
	Macaca fascicularis	5.7	3.7	15.0	16.7	58.7	1.54	0.21	0.93	296.9	11.15	57.04	-	58.60	77.97
	Macaca mulatta	5.3	3.3	15.9	17.1	51.7	1.71	0.26	0.85	280.5	11.19	57.88	2.97	62.58	75.86
	Macaca nemestrina	7.4	-	-	-	48.7	-	-	-	-	13.50	-	-	69.25	90.40
	Macaca radiata	5.5	-	-	-	-	-	-	-	-	10.50	50.00	-	75.00	-
	Macaca silenus	5.7	3.2	-	-	49.7	1.50	0.20	-	-	10.83	-	-	29.93	60.04
	Macaca sinica	-	-	-	-	-	-	-	-	-	-	-	-	-	69.10
	Macaca sylvanus	5.5	-	-	-	49.5	-	-	-	-	12.80	-	-	62.10	-
	Macaca thibetana	6.0	3.5	-	-	64.9	1.72	0.26	-	-	11.98	-	-	62.01	79.96
	Mandrillus leucophaeus	4.5	3.0	-	-	31.3	1.33	0.14	-	-	12.10	-	-	36.30	70.00
	Mandrillus sphinx	6.1	4.1	-	-	64.4	1.40	0.17	-	-	11.63	55.80	-	51.65	69.63
	Papio anubis	4.8	3.1	-	-	45.3	1.56	0.22	-	-	8.40	-	-	67.48	75.30
	Papio cynocephalus	4.7	3.9	-	-	47.7	1.23	0.10	-	-	10.02	58.03	3.50	64.07	75.40
	Papio hamadryas	6.5	-	-	-	47.2	-	-	-	-	12.70	-	-	58.00	-
	Papio ursinus	5.6	3.5	15.4	16.3	56.3	1.60	0.23	0.86	248.2	9.97	58.02	3.37	70.92	76.49
	Piliocolobus badius	-	-	-	-	-	-	-	-	-	-	-	-	-	84.00
	Pygathrix nemaeus	4.3	-	-	-	44.7	-	-	-	-	11.50	-	-	23.50	-
	Theropithecus gelada	6.8	-	-	-	61.9	-	-	-	-	12.20	-	-	68.80	87.30
	Trachypithecus cristatus	6.0	3.0	-	-	56.5	2.00	0.33	-	-	11.00	-	-	42.00	59.00
	Trachypithecus francoisi	5.0	3.0	-	-	39.3	1.67	0.25	-	-	10.00	-	-	45.00	60.00
	Mean Cercopithecidae	5.6	3.4	15.1	16.0	49.4	1.6	0.2	0.9	248.8	12.3	50.6	3.2	53.7	74.5

Acknowledgments:

We would like to sincerely thank Charlotte Guyot and Marlène Gandula for their assistance in bibliography recovery and their exceptional work in general. We are also grateful to Pr. Charles Coutton for his proofreading of English spelling.

Funding: This work was partially supported by the Centre National de la Recherche Scientifique (France), Projet International de Coopération Scientifique (grant number 7258) to C. Garcia.

Declarations of interest:

The authors have declared that no competing interests exist. All measurements are presented uncritically and as mean when multiple sources. References: Aotidae : 1938 Schultz, 1981Harcourt, 2004 Dixson ;Atelidae : 1925Hrdlicka, 1938Schultz, 1981Harcourt, 1998Parker, 2004Dixson, 2019Arakaki, 2019 Steinberg ;Callitrichidae : 1925Hrdlicka, 1981Harcourt, 1987Dixson, 1993Soini, 1999Birkhead, 2004Dixson, 2019 San Diego Zoo ;Cebidae : 1960Hill, 1972Middleton, 1981Harcourt, 1998Parker, 1999Birkhead, 2004 Dixson ;Cercopithecidae : 1938Schultz, 1941Kennard, 1960Kinsky, 1966[START_REF] Hill | Primates Comparative Anatomy and Taxonomy VIII-Cynopithecinae (Papio, Mandrillus, Theropithecus)[END_REF]Hill, 1976Amann, 1981Harcourt, 1986Amann, 1987Dixson, 1991Harcourt, 1992Wickings, 1993Bercovitch, 1998Parker, 1999Birkhead, 2000Gupta, 2004Dixson, 2019 San Diego Zoo ;Cheirogaleidae : 1964Petter-Rousseaux, 1998Parker, 2002Aslam, 2004 Dixson ;Galagidae : 1964Butler, 1987Dixson, 1998Parker, 2004 Dixson ;Hominidae : 1938Schultz, 1962Hall-Craggs, 1981Harcourt, 1986Amann, 1998Parker, 1999Birkhead, 2004Dixson, 2019 San Diego Zoo ;Hylobatidae : 1938Schultz, 1941Kennard, 1946Harrison-Matthews, 1981Harcourt, 1998Parker, 1999Birkhead, 2004 Dixson ;Indriidae : 1964 Petter-Rousseaux ;Lemuridae : 1964Petter-Rousseaux, 1977Bogart, 1993Morland, 1998Parker, 2004 Dixson ;Lorisidae : 1981Harcourt, 1967 Ramakrishna ;Pitheciidae : 1960Hill, 1995Harcourt, 2019 San Diego Zoo.

Martinez 60 number of individuals (as some authors did not give the number of individuals included in their studies, these numbers should be considered as minima). 1547

Martinez 63 Kinsky, 1981Harcourt, 1999Birkhead, 2004Dixson Colobus guereza 2.980 1987Dixson Colobus polykomos 12.200 1960Kinsky, 2004Dixson Erythrocebus patas 7.200 1991Harcourt, 1998Parker, 2004Dixson Lophocebus aterrimus 13.780 1966Hill Macaca arctoides 48.200 1981Harcourt, 1999Birkhead, 2004Dixson Macaca fascicularis 35.450 1938Schultz, 1981Harcourt, 1999Birkhead, 2004Dixson Macaca fuscata 72.300 2004Dixson Macaca mulatta 49.565 1938Schultz, 1976Amann, 1981Harcourt, 1986Amann, 1993Bercovitch, 1999Birkhead, 2000Gupta, 2004Dixson Macaca nemestrina 66.700 1938Schultz, 1981Harcourt, 1999Birkhead, 2004Dixson Macaca radiata 38.950 1938Schultz, 1981Harcourt, 2000Gupta, 2004 25.673 1962Hall-Crags, 1981Harcourt, 1999Birkhead, 2004Dixson Homo sapiens 43.080 1938Schultz, 1981Harcourt, 1986Amann, 1999Birkhead, 2004Dixson Pan paniscus 135.200 1998Parker, 2004Dixson Pan troglodytes 118.800 1938Schultz, 1999Birkhead, 2004Dixson Pongo pygmaeus 35.300 1938Schultz, 1999Birkhead, 2004


Zakariya Ghalmane

Chantal Cherifi

Hocine Cherifi

Mohammed El

Localization of hubs in complex networks with

overlapping modular structure

Localization of hubs in complex networks with overlapping modular structure

	Zakariya Ghalmane	Mohammed El Hassouni	Chantal Cherifi	Hocine Cherifi
		University Mohammed V MOROCCO	University of Lyon 2 FRANCE	University of Burgundy FRANCE
	C1	C2
	C3	C4
	Overlapping nodes

Hubs ? Problematic Evaluation measures Community detection Ego-network of overlapping nodes & List of Hubs

	University Mohammed V MOROCCO
	University of Burgundy FRANCE
		Methodology
		Proportion of hubs
		Rank-biased overlap
		Correlation
		Degree distribution
		Empirical Networks
	Small Network	Medium Network	Large Network
		Ego-
	Results Proportion of hubs	Rank-biased overlap	Degree distribution
		Correlation

Facebook network Karate network Condense Matter network

		Social network					Social network	Collaboration network
			N 34					N	4039	N 23133
			E 78					E 88234	E 93497
		Relatively high density					Small density	Very small density
		Non Assortative					Assortative	Assortative
								Neighbors of the overlapping nodes
	p = 77.6 %
	P. overlapping
	nodes: 14.7 %
				Network	RBO p=0.5 p=0.8 p=0.98
				Karate club 0.998 0.952	0.844
				Ego-facebook 0.998 0.952	0.844	Hubs
				ca-CondMat	1	0.999	0.999
	Overlapping	Hubs
	nodes
	ego-Facebook ca-CondMat Network	P. overlapping nodes (%) 3.1 2.1	Proportion of hubs (%) 59.25 79.57	ego-Facebook Network Karate club	0.985 Pearson Correlation 0.991	0.98 Spearman Correlation 0.98	Power law distribution
				ca-CondMat	0.989			0.99

Ghalmane, Z., Cherifi, C., Cherifi, H., & El Hassouni, M. (2020). Exploring Hubs and Overlapping Nodes Interactions in Modular Complex Networks. IEEE Access, 8, 79650-79683.