Elise Huchard
email: ehuchard@gmail.com

Peter M Kappeler

Cornelia Kraus

The inbreeding strategy of a solitary primate, Microcebus murinus

Keywords: sex-biased dispersal, inbreeding risk, inbreeding avoidance, mate bias, heterozygosity, survival, Microcebus murinus

Inbreeding depression may be common in nature, reflecting either the failure of inbreeding avoidance strategies, or inbreeding tolerance when avoidance is costly. The combined assessment of inbreeding risk, avoidance and depression is therefore fundamental to evaluate the inbreeding strategy of a population, i.e., how individuals respond to the risk of inbreeding.

Here, we use the demographic and genetic monitoring of 10 generations of wild grey mouse lemurs (Microcebus murinus), small primates from Madagascar with overlapping generations, to examine their inbreeding strategy. Grey mouse lemurs have retained ancestral mammalian traits including solitary lifestyle, polygynandry and male-biased dispersal, and may therefore offer a representative example of the inbreeding strategy of solitary mammals. The occurrence of close kin among candidate mates was frequent in young females (~37%, most often the father) and uncommon in young males (~6%) due to male-biased dispersal.

However, close kin consistently represented a tiny fraction of candidate mates (<1%) across age and sex categories. Mating biases favouring partners with intermediate relatedness were detectable in yearling females and adult males, possibly partly caused by avoidance of daughter-father matings. Finally, inbreeding depression, assessed as the effect of heterozygosity on survival, was undetectable using a capture-mark-recapture study. Overall, these results indicate that sex-biased dispersal is a primary inbreeding avoidance mechanism at the population level, and mating biases represent an additional strategy that may mitigate residual inbreeding costs at the individual level. Combined, these mechanisms explain the rarity of inbreeding and the lack of detectable inbreeding depression in this large, genetically diverse population.

INTRODUCTION

Inbreeding depression is defined as a decline of fitness in offspring of related individuals relative to offspring of unrelated individuals [START_REF] Charlesworth | Inbreeding depression and its evolutionary consequences[END_REF]. Decreases in the fitness of inbred individuals are thought to result from a reduced reaction scope of the immune system and/or from deleterious combinations of recessive alleles in the genome due to genome-wide increased homozygosity [START_REF] Charlesworth | Inbreeding depression and its evolutionary consequences[END_REF][START_REF] Charlesworth | The genetics of inbreeding depression[END_REF]. Fitness-related traits found to be negatively affected by inbreeding include birth weight [START_REF] Coltman | Birth weight and neonatal survival of harbour seal pups are positively correlated with genetic variation measured by microsatellites[END_REF][START_REF] Coulson | Microsatellites reveal heterosis in red deer[END_REF], development [START_REF] Diehl | Multiple-locus heterozygosity, mortality, and growth in a cohort of Mytilus edulis[END_REF][START_REF] Charpentier | Life history correlates of inbreeding depression in mandrills (Mandrillus sphinx)[END_REF][START_REF] Nielsen | Inbreeding and inbreeding depression of early life traits in a cooperative mammal[END_REF], reproductive success [START_REF] Foerster | A spatial genetic structure and effects of relatedness on mate choice in a wild bird population[END_REF][START_REF] Zeh | Outbred embryos rescue inbred half-siblings in mixed-paternity broods of live-bearing females[END_REF], resistance to disease and environmental stress [START_REF] Coltman | Parasite-mediated selection against inbred Soay sheep in a free-living, island population[END_REF][START_REF] Acevedo-Whitehouse | Inbreeding: disease susceptibility in California sea lions[END_REF] and survival [START_REF] Acevedo-Whitehouse | Inbreeding: disease susceptibility in California sea lions[END_REF]. Effects are often age-dependent, with younger individuals suffering higher levels of inbreeding depression [START_REF] Stockley | Female multiple mating behaviour in the common shrew as a strategy to reduce inbreeding[END_REF][START_REF] Markert | Neutral locus heterozygosity, inbreeding, and survival in Darwin's ground finches (Geospiza fortis and G. scandens)[END_REF][START_REF] Cohas | Age-specific effect of heterozygosity on survival in alpine marmots, Marmota marmota[END_REF] although inbreeding effects on adult traits have been far less studied and could also impose a substantial cost to fitness [START_REF] Grueber | Inbreeding Depression Accumulation across Life-History Stages of the Endangered Takahe[END_REF].

Inbreeding depression may commonly occur in wild populations [START_REF] Saccheri | Inbreeding and extinction in a butterfly metapopulation[END_REF][START_REF] Keller | Inbreeding effects in wild populations[END_REF], and its implications for extinction risk have long been debated [START_REF] Lande | Genetics and demography in biological conservation[END_REF][START_REF] Caro | Ecological and genetic factors in conservation: a cautionary tale[END_REF]. It is a question of considerable significance at a time when population fragmentation and associated loss of genetic diversity may threaten the viability of many populations [START_REF] Hedrick | Inbreeding depression in conservation biology[END_REF]. Nevertheless, it remains difficult to evaluate the frequency and intensity of inbreeding depression across wild populations for several reasons. First, it is often difficult to assess patterns of parentage in large representative samples of individuals with known life-histories in natural populations. Second, studies focusing on inbreeding effects may often target small or fragmented populations. Third, a potential publication bias towards positive results might further bias the empirical record [START_REF] Chapman | A quantitative review of heterozygosity-fitness correlations in animal populations[END_REF]. Multigenerational individually-based studies of vertebrates offer a unique opportunity to generate unbiased estimates of the occurrence and fitness costs of inbreeding depression across taxa [START_REF] Kempenaers | Inbreeding and hatching failure in blue tits: are unhatched eggs infertile?[END_REF][START_REF] Keller | Inbreeding and its fitness effects in an insular population of song sparrows (Melospiza melodia)[END_REF][START_REF] Walling | Inbreeding depression in red deer calves[END_REF][START_REF] Nielsen | Inbreeding and inbreeding depression of early life traits in a cooperative mammal[END_REF][START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF].

Inbreeding depression may represent a significant evolutionary pressure even where it is undetectable. Inbreeding risk may be intrinsically low in a given population due to a combination of demographic and life history factors as in large populations with nonoverlapping generations, but it may also be actively contained by behavioural strategies of inbreeding avoidance, including sex-biased dispersal [START_REF] Greenwood | Mating systems, philopatry and dispersal in birds and mammals[END_REF][START_REF] Clutton-Brock | Female transfer and inbreeding avoidance in social mammals[END_REF][START_REF] Pusey | Inbreeding avoidance in animals[END_REF] or discrimination against related mates [START_REF] Tregenza | Genetic compatibility, mate choice and patterns of parentage: invited review[END_REF][START_REF] Kempenaers | Mate choice and genetic quality: a review of the heterozygosity theory[END_REF]. Estimating the extent of inbreeding depression is therefore insufficient to evaluate the evolutionary importance of inbreeding within and across taxa.

In addition, some studies indicate that animals sometimes show no inbreeding avoidance or even preferentially mate with relatives, suggesting that inbreeding is not universally detrimental and that 'inbreeding strategies' may differ across individuals, populations and species, according to the relative costs and benefits of inbreeding and of inbreeding avoidance [START_REF] Bateson | Sexual imprinting and optimal outbreeding[END_REF][START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF]. Avoiding mating with kin may sometimes be more costly than having inbred offspring. Moreover, kin selection theory suggests that inbreeding may be adaptive under specific circumstances, by increasing the relatedness between parents and offspring [START_REF] Bateson | Sexual imprinting and optimal outbreeding[END_REF][START_REF] Waser | When should animals tolerate inbreeding?[END_REF][START_REF] Kokko | When not to avoid inbreeding[END_REF][START_REF] Puurtinen | Mate choice for optimal (k)inbreeding[END_REF][START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF]. Overall, the current state of the field suggests that our theoretical understanding of animal inbreeding strategies remains limited and calls for further empirical efforts to examine inbreeding risk, inbreeding avoidance strategies and depression in concert.

This study presents a quantitative investigation of inbreeding risk, avoidance and depression in a large population of wild primates. Grey mouse lemurs (Microcebus murinus) are small nocturnal and solitary foragers distributed along Southern and Western Madagascar [START_REF] Kappeler | Microcebus, mouse lemurs, tsidy. In: The Natural History of Madagascar[END_REF]. They are polygynandrous with no paternal care (Eberle & Kappeler, 2004a). Individuals acquire feeding independence at around 2 months of age and can reproduce for the first time at 10 months of age and then every year thereafter. Each female is sexually receptive for one to two nights per year, and may mate with up to seven different males during those nights, while up to 14 candidate males have been observed around a receptive female (Eberle & Kappeler, 2004a). Mortality rates of grey mouse lemurs are high, especially in the first year of life [START_REF] Kraus | The costs of risky male behavior: sex differences in seasonal survival in a small sexually monomorphic primate[END_REF] but some individuals survive 6 to 10 years (unpublished observation), which generates a potential overlap between reproductive periods of parents and offspring and may create inbreeding risk. Natal dispersal is strongly male-biased [START_REF] Schliehe-Diecks | Walk the line -natal dispersal movements in gray mouse lemurs[END_REF] and secondary dispersal, where individuals disperse repeatedly, is low [START_REF] Radespiel | Sociogenetic structure in a free-living nocturnal primate population: sex-specific differences in the grey mouse lemur (Microcebus murinus)[END_REF][START_REF] Eberle | Mouse lemurs in space and time: a test of the socioecological model[END_REF][START_REF] Kappeler | Microcebus, mouse lemurs, tsidy. In: The Natural History of Madagascar[END_REF][START_REF] Fredsted | Microsatellite analyses reveal fine-scale genetic structure in gray mouse lemurs (Microcebus murinus)[END_REF] so that fathers often live close to their philopatric daughters and individual variation in relatedness levels is locally high, creating ample opportunities for inbreeding avoidance or tolerance [START_REF] Radespiel | Sociogenetic structure in a free-living nocturnal primate population: sex-specific differences in the grey mouse lemur (Microcebus murinus)[END_REF][START_REF] Fredsted | Microgeographic heterogeneity in spatial distribution and mtDNA variability of gray mouse lemurs (Microcebus murinus, Primates: Cheirogaleidae)[END_REF][START_REF] Fredsted | Microsatellite analyses reveal fine-scale genetic structure in gray mouse lemurs (Microcebus murinus)[END_REF].

Two previous studies have detected mate choice for dissimilar partners at immune genes of the Major Histocompatibility Complex (MHC) in females of this population [START_REF] Schwensow | Compatibility counts: MHC-associated mate choice in a wild promiscuous primate[END_REF][START_REF] Huchard | MHC-disassortative mate choice and inbreeding avoidance in a solitary primate[END_REF], but avoidance of mating with kin was only detected by one of these studies, where mated pairs were less related than random pairs. This study, however, only adopted a female perspective and did not document the extent of inbreeding risk and depression across age and sex categories [START_REF] Huchard | MHC-disassortative mate choice and inbreeding avoidance in a solitary primate[END_REF]. Here, we extend these studies and combine a 10-generation dataset of a capture-mark-recapture (CMR) study with genetic data to provide an integrative analysis of inbreeding risk and its evolutionary consequences in a natural primate population by estimating, for both the philopatric sex (females) and the dispersing sex (males) in adults and in yearlings, the extent of (1) inbreeding risk, (2) inbreeding avoidance via mating biases between actual mates and random members of the mating pool (although observing such a bias does not inform us on the choosy sex, as choice by one sex will generate a detectable mating bias in the other sex), and (3) inbreeding depression by quantifying the survival cost of inbreeding.

METHODS

Study population and trapping procedures

The study population is located within a 12,500 ha forestry concession of the Centre National de Formation, d'Etude et de Recherche en Environnement et Foresterie (C.N.F.F.R.E.F.) in Kirindy Forest [START_REF] Kappeler | A 15-year perspective on the social organization and life history of sifaka in Kirindy Forest[END_REF]. Since 1994, DNA samples and population parameters have been collected during monthly captures using about 160 traps at a time in an area of about 9 ha within a 60 ha grid system. Additional captures in surrounding areas were conducted once or twice a year and covered an area of about 18 ha. For trapping, Sherman live traps were baited with small pieces of banana and positioned near trail intersections at dusk on three consecutive nights. Captured animals were collected at dawn and marked with subdermal transponders if captured for the first time, and otherwise simply weighed and handled according to published protocols [START_REF] Eberle | Mouse lemurs in space and time: a test of the socioecological model[END_REF]. Data on 1,298 individuals were available for analyses between 2000 and 2010.

Microsatellite DNA analyses

DNA was isolated from ear biopsies, using the QIAGEN QIAamp Tissue Kit for DNA Purification (Qiagen) [START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF]. DNA amplification and sequencing are described in Supporting Information, Appendix S1. A total of 1073 to 1278 individuals were typed for each locus, with an average of 21.5 alleles per locus.

Parentage analyses and calculation of relatedness estimates and heterozygosity

Parentage analyses for determination of true parents and their spatial distribution were based on a likelihood analysis using CERVUS 3 [START_REF] Kalinowski | Revising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment[END_REF] and COLONY v 2.0.1.9 [START_REF] Jones | COLONY: a program for parentage and sibship inference from multilocus genotype data[END_REF] and are fully described in the Supporting Information, Appendix S2.

Relatedness estimates were calculated with the software COANCESTRY v 1.0.0.0 [START_REF] Wang | Coancestry: a program for simulating, estimating and analysing relatedness and inbreeding coefficients[END_REF] for all individuals captured between 1999 and 2010, based on the triadic individual by descent (IBD) 'TrioML' index [START_REF] Wang | Triadic IBD coefficients and applications to estimating pairwise relatedness[END_REF], which uses the genotypes of a triad of individuals in estimating pairwise relatedness (r). To estimate individual genome-wide heterozygosity, we calculated the homozygosity by loci (HL) index of [START_REF] Aparicio | What should we weigh to estimate heterozygosity, alleles or loci?[END_REF], which has been found to perform better than two other estimators of heterozygosity, internal relatedness (IR) [START_REF] Amos | The influence of parental relatedness on reproductive success[END_REF] or uncorrected homozygosity (HO, [START_REF] Aparicio | What should we weigh to estimate heterozygosity, alleles or loci?[END_REF]. Unless otherwise stated, all analyses were run in R 3.0.2 (R Development Core Team 2013).

Assignment of candidate mates

A list of candidate mates was established for each individual and for each mating season in our sample (thereafter referred to as a "mating season") following [START_REF] Huchard | MHC-disassortative mate choice and inbreeding avoidance in a solitary primate[END_REF].

Individuals were considered as candidate mates if they fulfilled the following three criteria: (1) they were present in captures immediately preceding or following the mating season (there are no captures during the mating season, in order to avoid potential disruption of mating patterns) to ensure that only live animals were included in the analysis; (2) the average distance between home range centres of partners is lower than the maximum distance recorded between the two parents of an offspring using long-term parentage data from this population (females: perimeter=319m; males: perimeter=336m, see [START_REF] Huchard | MHC-disassortative mate choice and inbreeding avoidance in a solitary primate[END_REF]).;

(3) they ranged within the core study area where the demographic monitoring has been regular and continuous throughout the study period. A total of 56 females and 81 males that were found to be part of a parent-offspring triad between 2000 and 2010 were included in the analyses.

Estimating inbreeding risk

To estimate inbreeding risk, we used parentage analyses and pedigree data to determine whether first order relatives (parent-offspring and full siblings) were present within pools of candidate mates. Inbreeding risk was quantified by its occurrence and intensity and compared between males and females and between yearlings and adults. The occurrence of inbreeding risk was computed as the presence/absence of at least one first order relative in each mating season. To test for possible sex and age differences in the occurrence of inbreeding risk, we ran a binomial generalized linear mixed model (GLMM) (response variable: presence/absence of at least one first order relative during a mating season) including the fixed effects sex, age and their interaction and the crossed random effects year and individual identity, to control for the non-independence of observations from a same individual or from a same year. Then, we computed the intensity of inbreeding risk by calculating, for each mating season, the proportion of first order relatives among the candidate mates. We evaluated age and sex effects on the intensity of inbreeding through a second binomial GLMM with the same structure of fixed and random effects as the occurrence model (response variable: number of first order relatives/number of candidates in a given season).

Model selection was based on AIC or one of its appropriate variants (here QAICc which adjusts for small sample sizes and the presence of overdispersion, [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF] using the dredge function from the MuMIn package [START_REF] Barton | Multi-Model Inference[END_REF] in R 3.0.2. We interpreted model selection results based on AICc differences (Δi) and normalised Akaike weights (wi) as described by [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF]. We further computed estimates of fixed effects for the top models.

Investigating inbreeding avoidance

To test whether relatedness among mates is minimized, we compared the mean observed relatedness values of the parents in our long-term dataset to a distribution of the mean relatedness values of randomly matched partners generated under the null hypothesis of random mating. We further compared the mean-corrected variance (assessed by the coefficient of variation) in the relatedness of true versus randomly assigned parents for two reasons. First, if some individuals avoid inbreeding whereas others preferentially inbreed, mean observed relatedness could match null expectation but with an increased variance [START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF]. Second, if individuals avoid mates that are either too closely or too distantly related, thereby optimizing rather than minimizing relatedness to their mates, mean observed relatedness could match null expectation but with a decreased variance. The coefficient of variation ('CV', standard deviation divided by the mean) was used as a measure of variance to ensure that results would be statistically independent from results obtained on the mean. The correlation between mean and variance of parental relatedness was positive and high in all four samples (yearling females, adult females, yearling males and adult males) with Pearson's r values comprised between 0.70 and 0.80 (df=19998 and p<10 -15 in all four cases), while there was no correlation between mean relatedness and the coefficient of variation in relatedness (Pearson's r was comprised between -0.09 and -0.03 in all four cases).

Finally, we tested whether individuals may choose partners with high heterozygosity, which may occur if these partners are more competitive than, or preferred over, less heterozygous individuals. They could be preferred if choosing a heterozygous partner brings direct benefits (such as a decreased risk of infection by sexually transmitted diseases) or indirect benefits (such as the transmission of rarer -and therefore more heterozygous -genotypes to offspring) [START_REF] Fromhage | Evolution of mate choice for genome-wide heterozygosity[END_REF][START_REF] Kempenaers | Mate choice and genetic quality: a review of the heterozygosity theory[END_REF].

The distribution of the mean and coefficient of variation of relatedness between random partners to an individual was generated by randomly matching each individual 20,000 times to one mate of their pool of candidate mates for a given mating season. P-values were computed in two ways, due to the difficulties, and the resulting lack of consensus, regarding the calculation of two-sided p-values in the case of asymmetrical distributions (e.g., [START_REF] Gibbons | P-values: interpretation and methodology[END_REF][START_REF] Kulinskaya | On two-sided p-values for non-symmetric distributions[END_REF], as well as to facilitate future meta-analytic approaches: first, a one-tailed p-value was computed as the proportion of cases displaying a lower (for mean and variance of relatedness) or greater (for mean heterozygosity) than the observed value.

Second, an exact two-tailed p-value was computed as the proportion of cases displaying a greater value than the observed value for successful partners plus the proportion of cases displaying a lower value than the symmetrical (relative to the simulated mean) of the observed value. Results are presented using both one-and two-tailed p-values, and interpreted based on the two-tailed p-value, in order to be conservative, and consistent with other analyses presented in this study. Note that more than one individual could be chosen per mating season since mouse lemurs commonly give birth to mixed-paternity litters [START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF] and that some individuals appeared repeatedly in the dataset, which is inevitable in a system where both home ranges and generations are overlapping. We further tested whether individuals choose partners that have higher heterozygosity than randomly matched individuals following the same procedure.

We ran these simulation tests for datasets of adults and yearlings in both females and males (Table 1). We specifically compared patterns occurring in adults and yearlings to test whether the strength of mate selectivity may reflect variation in inbreeding risk across individuals belonging to different sex and age classes.

Heterozygosity and survival

To determine whether heterozygosity affected survival probabilities, we used a two-step approach (similar to [START_REF] Cohas | Age-specific effect of heterozygosity on survival in alpine marmots, Marmota marmota[END_REF]. We first modelled survival and recapture probabilities using capture-mark-recapture models [START_REF] Lebreton | Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies[END_REF]. We selected the most parsimonious model out of a candidate set of models using AIC [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF].

In the second step, we added heterozygosity as an individual covariate to this basic model to test specific hypotheses regarding survival consequences of variation in heterozygosity using likelihood-ratio tests (LRT).

Capture-mark-recapture data

To model survival probabilities, we used CMR data from 1999 to 2011. We did not include data from before 1999 because too few animals from these cohorts were genotyped. As described in [START_REF] Kraus | The costs of risky male behavior: sex differences in seasonal survival in a small sexually monomorphic primate[END_REF], we estimated seasonal survival using data from the main trapping season at the onset of the austral winter (April/May) and the secondary trapping session at the onset of summer (end of the dry season), before the mating season starts in October. We could not use the summer trapping season from 2004, since it was conducted too late. Hence, we created a dummy trapping season ("10 October") and fixed its recapture probabilities at 0. The complete data set included 481 animals (294 males, 187 females) for which we have heterozygosity estimates and which were caught a total of 1031 times.

Modelling survival probabilities

We used the Cormack-Jolly-Seber model for open populations (CJS: [START_REF] Cormack | Estimates of survival from the sighting of marked animals[END_REF][START_REF] Jolly | Explicit estimates from capture-recapture data with both death and immigration-stochastic model[END_REF][START_REF] Seber | A note on the multiple-recapture census[END_REF] implemented in the program MARK [START_REF] White | Program MARK: survival estimation from populations of marked animals[END_REF] to statistically model survival (ϕ) and recapture probabilities (p). As for GLMMs, model selection was based on AIC or one of its appropriate variants (here QAICc which adjusts for small sample sizes and the presence of overdispersion [START_REF] Burnham | Model selection and multimodel inference: a practical information-theoretic approach[END_REF].

We first assessed the goodness-of-fit of global models using the median-ĉ approach implemented in the program MARK. The variance inflation factor ĉ was estimated to be slightly above 1 (ĉ=1.09), indicating a low level of extra-binomial variance. We still adjusted model selection statistics (QAICc, QDeviance) accordingly. For the basic seasonal survival model we considered the factors sex (s), age (a) and time (t). To evaluate state-determined effects of heterozygosity and to account for high mortality in the first year of life [START_REF] Kraus | The costs of risky male behavior: sex differences in seasonal survival in a small sexually monomorphic primate[END_REF], age was represented by three classes: juveniles (juv, 3-9 months old, i.e., first winter), yearlings (yrl: 10-16 months old, i.e., first summer, first breeding season) and adults (ad: > 16 months old). Our candidate model set was partly based on a priori knowledge from an earlier study on seasonal survival of the same mouse lemur population which included the years 1995 to 2005 [START_REF] Kraus | The costs of risky male behavior: sex differences in seasonal survival in a small sexually monomorphic primate[END_REF]. As our global model (GM), we used ϕ W (a*s+t) ϕ S (a*s+t) p W (a*s+t) p S (a*s+t) (W: winter, S: summer, *: interactive effect, +: additive effect). This analysis uses CMR data from 1999-2011 and hence only partially overlaps with the data set from the earlier study. Moreover, strong population fluctuations were observed between 2005 and 2011 (with, e.g., a mean of 23 individuals captured across capture sessions in 2005, and of 56.5 in 2008). Therefore we did not simply use the top model from that analysis for further inference, but included candidate models incorporating model terms that received some support in the confidence set of models established in that analysis (all models with a relative likelihood >0.05, [START_REF] Kraus | The costs of risky male behavior: sex differences in seasonal survival in a small sexually monomorphic primate[END_REF]. All candidate models for winter survival included an age effect, because natal male dispersal in the Kirindy population takes place between April and September [START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF]. With the CJS-model we cannot separate emigration and mortality, and hence estimates for juvenile males represent so-called "apparent survival" probabilities. We do know that female dispersal and/or secondary male dispersal are at most very rare events in this population [START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF]) and thus, we feel confident that estimates for these sex-age-classes closely estimate "true survival" probabilities. Hence, our candidate models for winter and summer recapture probabilities, as well as for summer survival included a*s+t (GM), a+s+t, a+t, s+t and t. For winter survival we used a*s+t, a*s, juv(s)ad(.) and a.

In order to limit the total number of models, we selected the most parsimonious model for each major model part (i.e., survival winter, survival summer, recapture summer, recapture winter) against the global model for the remaining model parts. We then built our basic survival and recapture model by combining the selected models for each part.

Effects of heterozygosity

To test for an association between heterozygosity levels and survival, we added our heterozygosity estimate (HL) as an individual covariate to the most parsimonious model for survival and recapture probabilities (the basic model). Because the basic model and those incorporating heterozygosity effects are nested, we compared these models using likelihood ratio tests (LRTs, a=0.05). Our LRTs aimed to address 3 specific hypotheses. (1) We tested for an overall effect of heterozygosity on mouse lemur survival. We excluded juvenile males from the heterozygosity effect, because for these we cannot distinguish between survival and emigration (see above). ( 2) Based on the idea that heterozygosity effects can be age-specific [START_REF] Cohas | Age-specific effect of heterozygosity on survival in alpine marmots, Marmota marmota[END_REF], we added the heterozygosity effect only for juvenile females (i.e., first winter survival). (3) To evaluate the hypothesis that heterozygosity effects are exacerbated under harsher conditions [START_REF] Kempenaers | Mate choice and genetic quality: a review of the heterozygosity theory[END_REF], we added the heterozygosity effect only to summer survival, and, respectively, only to male summer survival, because survival was found to be substantially lower in summer and even more so in males, probably reflecting the costs of intrasexual competition over reproduction (see also [START_REF] Kraus | The costs of risky male behavior: sex differences in seasonal survival in a small sexually monomorphic primate[END_REF]. Because heterozygosity estimates were rather high, we always tested for a linear and for a quadratic effect. Linear effects were expected to show improved survival chances with increasing heterozygosity. Quadratic effects would represent an optimal heterozygosity level between inbreeding and outbreeding depression. None of the effects tested were statistically significant; therefore we did not correct p values for multiple testing.

RESULTS

Inbreeding risk

Inbreeding risk was moderate in males and females. First, our estimates of the number of candidate mates per female were high, ranging from 23 to 69 males (Table 1; mean=49).

Similarly, the number of candidate mates per male ranged from 17 to 79 females (Table 1; mean = 51). For females, there were 21% of mating seasons (19 of 90) during which a father (n=13), a son (n=4) or both (n=2) were present as potential mates. For males, there were 16% of mating seasons (19 of 116) for which first order relatives were present in the mating pool.

In five cases, two first order relatives were present (four times two daughters and once the mother and a daughter). In the remaining 14 mating seasons, a mother (n=6), a daughter (n=7) or a full-sister (n=1) of the male was present. Within individuals, the presence of a 1 st order relative in the mating pool was usually observed in one and maximum two mating seasons, with one exception: one female coexisted with her father for seven years.

Sex and age classes differed with respect to the occurrence and intensity of inbreeding risk, as the best models included a sex by age interaction for both the occurrence and the intensity models of inbreeding risk (Tables 2 &3, Fig 1). For females, the occurrence and intensity were both higher for yearlings than for adults, with more than a third of young females having at least one close kin in their mating pool. For males, the occurrence and intensity of inbreeding risk increased with age. While occurrence reached comparable levels for adult males and females, the average intensity of inbreeding risk was approximately twice as high for adult males as for adult females. However, intensity remained low in both sexes and at all ages, since first order relatives constituted only a tiny fraction of the candidate mate sets (mean±SD, young females: 0.93±1.39%, young males: 0.18±0.62%, adult females: 0.39±0.99%, adult males: 0.70±1.44%).

Inbreeding avoidance

In the present 10-generation data set, no case of breeding between first order relatives could be detected. The closest proven case of reproduction between individuals with a known common ancestor in this population was a coupling of aunt and nephew (inbreeding coefficient (f) ≈ 0.125). For other true parents displaying a relatively high coefficient of relatedness (TrioML > 0.20), we were not able to detect any close family relationships through the pedigree data.

For adults of both sexes, average relatedness (mean TrioML) of true parents tended to be lower than simulated averages (Table 4, Fig. 2). The results for yearlings showed no significant deviation from random mate choice in both females and males (Table 4, Fig. 2). A shift towards lower values of relatedness to mates was observed in the random distribution for yearling males compared to both adult males and yearling females (Fig. 2), probably as a consequence of the change in their genetic environment following natal dispersal.

For both yearling females and adult males, the observed coefficient of variation of relatedness estimates for true parents was significantly lower than expected under random mating (Table 4,Fig 3). Finally, there was no departure from random expectations concerning the mean heterozygosity of chosen mates.

Heterozygosity and survival

The most parsimonious survival model selected from the set of candidate models was the same as in the earlier study (covering the years 1995-2005), and parameter estimates were similar, suggesting that the survival patterns found are quite representative for this population (Table 1; [START_REF] Kraus | The costs of risky male behavior: sex differences in seasonal survival in a small sexually monomorphic primate[END_REF]. There was little model selection uncertainty in choosing the most parsimonious model for recapture probabilities and summer survival: an additive effect of sex to temporal variation was strongly supported for each of these model parts (p W : w+(s+t)=0.93, p S : w+(s+t)=0.87, ϕ S : w+(s+t)=0.75). Summer survival probabilities varied between 0.38 and 0.84 among years with female survival exceeding male survival (geometric means ϕ S females=0.61±0.09SE, 95%CIs=[0.40; 0.77], ϕ S males=0.55±0.10SE, 95%CIs=[0.35; 0.73], all probabilities are given on a semi-annual time-scale). In contrast, winter survival was rather constant over the years (w+(no t)=0.99), and higher than summer survival, with juveniles surviving less well than adults (ϕ W ad males=ϕ W ad females=0.88±0.04SE, 95%CIs=[0.77; 0.94], ϕ W juv females=0.75±0.08SE, 95%CIs=[0.56; 0.87], ϕ W juv males=0.52±0.06SE, 95%CIs=[0.41; 0.62]). We cannot currently estimate how much of the difference between juvenile male and female survival is due to male natal dispersal. Despite important variation in heterozygosity in our sample (n=525, range: 0.00-0.60, mean±SD=0.18±0.10), we did not find any statistical evidence for a linear or quadratic effect of heterozygosity on overall (excluding juvenile males), juvenile female, summer, or male summer survival (Table 6).

DISCUSSION

We used a ten-generation dataset to investigate the extent of inbreeding risk in a solitary and polygynandrous mammal, the grey mouse lemur. The home range of one male typically encompasses the home ranges of several females [START_REF] Eberle | Mouse lemurs in space and time: a test of the socioecological model[END_REF][START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF], Eberle & Kappeler, 2004a), a social system that is close to the ancestral mammalian state and remains widespread in extant mammals [START_REF] Lukas | The evolution of social monogamy in mammals[END_REF].

Inbreeding risk was generally low and primarily resulted from reproductive overlap between generations, where the reproductive lifespan of one sex exceeded the developmental period of the other sex. Its variation across ages and sexes was directly shaped by a combination of life-history traits including age at first breeding, reproductive longevity and sex-biased natal dispersal. Across age and sex categories, the relatively frequent occurrence of close kin in the mating pool was always diluted by the large size of the mating pool, with each individual having about 20 to 70 candidate mates. Female grey mouse lemurs reach sexual maturity at around 9 months and frequently have at least one first order relative among candidate mates during their first breeding season, usually their father and occasionally a brother. Inbreeding risk decreases as a function of female age, reflecting the progressive disappearance of females' fathers. It was lowest for young males, who have just dispersed into unfamiliar areas, and subsequently increased as a function of male age and reproductive success, reflecting the presence of one or more daughters in the surrounding area.

Male-biased dispersal therefore appears as the primary inbreeding avoidance mechanism in grey mouse lemurs. Whereas male-biased dispersal is the ancestral condition in mammals [START_REF] Lukas | Group structure, kinship, inbreeding risk and habitual female dispersal in plural-breeding mammals[END_REF] and remains considerably more frequent than female-biased dispersal across extant species [START_REF] Greenwood | Mating systems, philopatry and dispersal in birds and mammals[END_REF][START_REF] Pusey | Sex-biased dispersal and inbreeding avoidance in birds and mammals[END_REF][START_REF] Clutton-Brock | Female transfer and inbreeding avoidance in social mammals[END_REF][START_REF] Clutton-Brock | The evolution of social philopatry and dispersal in female mammals[END_REF], comparative analyses indicate that female dispersal has evolved in some group-living species where females start to breed while their father is still reproductively active in their natal group [START_REF] Clutton-Brock | Female transfer and inbreeding avoidance in social mammals[END_REF][START_REF] Lukas | Group structure, kinship, inbreeding risk and habitual female dispersal in plural-breeding mammals[END_REF]. This suggests that sex-biased dispersal may have primarily evolved in response to inbreeding risk, rather than under the influence of other selective pressures like kin competition or the distribution of food resources. Under this scenario, it may appear unclear why males, rather than females, disperse in grey mouse lemurs. Unlike many solitary mammals where females are intolerant of other females, grey mouse lemur females forage solitarily but rest and breed communally with female kin [START_REF] Radespiel | Sociogenetic structure in a free-living nocturnal primate population: sex-specific differences in the grey mouse lemur (Microcebus murinus)[END_REF][START_REF] Eberle | Mouse lemurs in space and time: a test of the socioecological model[END_REF][START_REF] Eberle | Family insurance: kin selection and cooperative breeding in a solitary primate (Microcebus murinus)[END_REF]) so they may derive direct benefits from social philopatry, like many groupliving mammals [START_REF] Clutton-Brock | The evolution of social philopatry and dispersal in female mammals[END_REF]. In such conditions, females may only disperse when unrelated mates are unavailable, for example if their father holds the dominant breeding status and monopolizes most reproduction in their group by the time they reach sexual maturity, as in chimpanzees or gorillas [START_REF] Clutton-Brock | The evolution of social philopatry and dispersal in female mammals[END_REF]. In contrast, male grey mouse lemurs cannot monopolize females and sperm competition prevails over contest competition (Eberle & Kappeler, 2004a[START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF], Huchard et al., 2012). In addition, our results indicate that young females have access to a large pool of unrelated candidate mates on top of their relative(s), explaining why the intensity of selective pressures favouring female dispersal may remain moderate.

Individuals that face residual inbreeding risk despite natal male-biased dispersal may have developed additional inbreeding avoidance strategies, like secondary dispersal or avoidance of mating with kin. Secondary dispersal may occasionally occur when male grey mouse lemurs have many closely related females in their vicinity [START_REF] Radespiel | Patterns and dynamics of sex-biased dispersal in a nocturnal primate, the grey mouse lemur, Microcebus murinus[END_REF], though it appears rare as no incidents have ever been recorded in this 10-year study population (unpublished observation). Mating biases appear more common, and are detectable in young females and adult males, who select mates with a narrower relatedness range than random partners. Adult females and males also show a marginally non-significant trend for mating with partners who are less related than random partners. Regarding the coefficient of variation of mate relatedness, significant results in young females and adult males may reflect the fact that these two age-sex categories face, respectively, a higher prevalence and intensity of inbreeding risk than other age-sex categories, and greater variation in the relatedness coefficients of candidate mates may confer more power to the analyses. However, it is important to realize that our analyses cannot identify the choosing sex: if one sex chooses partners with a low relatedness, or with a narrower range of relatedness, this preference will influence the results of the randomization analyses for both sexes. As a result, these mating biases may reflect the avoidance of daughter-father matings, the kin relationship that is most represented in individual mating pools, due to active discrimination by either young females or adult males. In addition, failure to detect significant mating biases for partners with low relatedness may also reflect methodological issues, and specifically the fact that mating patterns are inferred from patterns of parentage. It is possible that inbreeding depression may be more severe on early life traits [START_REF] Stockley | Female multiple mating behaviour in the common shrew as a strategy to reduce inbreeding[END_REF][START_REF] Markert | Neutral locus heterozygosity, inbreeding, and survival in Darwin's ground finches (Geospiza fortis and G. scandens)[END_REF][START_REF] Cohas | Age-specific effect of heterozygosity on survival in alpine marmots, Marmota marmota[END_REF][START_REF] Nielsen | Inbreeding and inbreeding depression of early life traits in a cooperative mammal[END_REF] and compromise the survival of inbred juveniles, resulting in their non-detectability by our sampling design, which only traps and marks recruited individuals.

Mate choice for partners with intermediate relatedness suggests that young females and adult males may optimize, rather than maximize genetic dissimilarity to their partners by avoiding partners that are too closely or too distantly related. Such result may reflect the spatial genetic structure of the population if young females and adult males (1) tend to avoid mating with closely related partners, and (2) have lower chances to mate with distantly related partners (compared to partners with intermediate relatedness) because mating probability and relatedness between candidate mates both decrease as spatial distance between them increases, under a scenario of isolation by distance. In the first case, variance may be more sensitive than mean to a scenario of avoidance of mating with close kin. Under such scenario, mate choice will only erase the most extreme points of the distribution of relatedness among actual partners compared to random partners, which may impact the variance of this distribution more than its mean. Consequently, future studies should integrate variancebased analyses in their design more systematically. In the second case, although assignment of candidate mates partially took into account their spatial proximity by including only individuals that were less distant than the maximal distance recorded between actual parents in our dataset, our analyses did not control for the residual effect of variable spatial distance within this range. Alternatively, mates with intermediate relatedness may balance the costs of inbreeding and the benefits of increasing the representation of genes identical by descent in future generations [START_REF] Parker | Sexual selection and sexual conflict. In: Sexual selection and reproductive competition in insects[END_REF][START_REF] Puurtinen | Mate choice for optimal (k)inbreeding[END_REF][START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF]. Theory predicts that levels of inbreeding that maximize inclusive fitness are low and compatible with a wide range of realistic inbreeding depression strengths, as well as with mate choice for intermediately related individuals [START_REF] Puurtinen | Mate choice for optimal (k)inbreeding[END_REF], as observed in a number of vertebrates [START_REF] Pusey | Inbreeding avoidance in animals[END_REF][START_REF] Reusch | Female sticklebacks count alleles in a strategy of sexual selection explaining MHC polymorphism[END_REF][START_REF] Mays | Female choice for genetic complementarity in birds: a review[END_REF][START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF]. Mating strategies observed in our population are therefore in agreement with theoretical expectations in large outbred populations. Although preferences for intermediate relatedness have not been previously reported in wild primates, they may be under-detected as studies often test for differences in mean relatedness between actual and random mates, without testing for differences in relatedness variance [START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF].

Selecting mates based on their relatedness coefficients requires efficient kin discrimination mechanisms. While familiarity may mediate kin recognition among maternal kin, it is less clear how fathers can avoid mating with their daughters in species where both sexes mate with multiple partners and where paternity certainty is therefore low [START_REF] Widdig | Paternal kin discrimination: the evidence and likely mechanisms[END_REF] as in grey mouse lemurs [START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF], Eberle & Kappeler, 2004a). Previous work in this population shows that individuals choose MHC-dissimilar partners [START_REF] Schwensow | Compatibility counts: MHC-associated mate choice in a wild promiscuous primate[END_REF][START_REF] Huchard | MHC-disassortative mate choice and inbreeding avoidance in a solitary primate[END_REF] and suggests that kin discrimination may rely on odour cues influenced by MHC genes in this nocturnal species characterized by an acute sense of smell [START_REF] Schilling | Olfactory communication in Prosimians[END_REF][START_REF] Schilling | Chemical signals and reproductive capacity in a male prosimian primate, Microcebus murinus[END_REF]. Additionally, a recent experiment shows that females can detect relatedness in vocalizations of unfamiliar individuals, suggesting that acoustic cues may also play an important role in kin discrimination [START_REF] Kessler | Paternal kin recognition in the high frequency/ultrasonic range in a solitary foraging mammal[END_REF].

Beside active mate discrimination, mate selection may also occur post-copulation via cryptic female choice. Whereas males show an impressive enlargement of testes size and roam extensively in search of mating opportunities during the breeding season [START_REF] Eberle | Mouse lemurs in space and time: a test of the socioecological model[END_REF][START_REF] Eberle | Sperm competition and optimal timing of matings in Microcebus murinus[END_REF], females actively seek multiple mates during their short period of sexual receptivity, suggesting that they benefit from such a strategy (Eberle & Kappeler, 2004a, Huchard et al., 2012). Experimental studies in both invertebrates and vertebrates, including mammals, have shown that mating with multiple males may represent an efficient strategy to avoid inbreeding [START_REF] Tregenza | Polyandrous females avoid costs of inbreeding[END_REF][START_REF] Simmons | Postcopulatory inbreeding avoidance by female crickets only revealed by molecular markers[END_REF][START_REF] Zeh | Outbred embryos rescue inbred half-siblings in mixed-paternity broods of live-bearing females[END_REF][START_REF] Firman | Polyandry facilitates postcopulatory inbreeding avoidance in house mice[END_REF], thereby offering a potential mechanism for the mating biases reported in grey mouse lemurs.

No mating biases, or even trends, were detected in young males. Several possibilities may explain this age effect. Young males have just left their natal area [START_REF] Schliehe-Diecks | Walk the line -natal dispersal movements in gray mouse lemurs[END_REF] and as a result appear to have no close relatives in their mating pool. The variance of relatedness to their potential mates may consequently be too weak to detect a signal of inbreeding avoidance or they may not need to be discriminative. Moreover, young males struggle to access mates when competing with older and heavier males [START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF] and the costs of inbreeding avoidance may exceed the costs of inbreeding for them.

Overall, these results indicate that several inbreeding strategies co-occur within a single population and may reflect individual variation in the relative benefits and costs of inbreeding and inbreeding avoidance [START_REF] Szulkin | Inbreeding avoidance, tolerance or preference in animals[END_REF].

Finally, we could not detect a positive effect of heterozygosity on mating success and on survival probability, despite a reasonable individual variance in heterozygosity and, in the case of survival analyses, irrespective of whether we considered state-dependant (age) or environmental influences (season) which are supposed to alter the magnitude of genomewide heterozygosity effects on fitness [START_REF] Balloux | Does heterozygosity estimate inbreeding in real populations?[END_REF][START_REF] Brouwer | Heterozygosity-fitness correlations in a bottlenecked island species: a case study on the Seychelles warbler[END_REF][START_REF] Kempenaers | Mate choice and genetic quality: a review of the heterozygosity theory[END_REF][START_REF] Cohas | Age-specific effect of heterozygosity on survival in alpine marmots, Marmota marmota[END_REF]. This lack of effect may first reflect methodological caveats, such as the use of indices of heterozygosity based on a limited number of microsatellites which may poorly reflect overall genome-wide diversity [START_REF] Chapman | A quantitative review of heterozygosity-fitness correlations in animal populations[END_REF][START_REF] Szulkin | Heterozygosity-fitness correlations: a time for reappraisal[END_REF], but see Forstmeier et al., 2012). However, the incomplete nature of our pedigree precluded the use of pedigree-based measures. Second, inbreeding depression may be particularly acute in early life [START_REF] Stockley | Female multiple mating behaviour in the common shrew as a strategy to reduce inbreeding[END_REF][START_REF] Markert | Neutral locus heterozygosity, inbreeding, and survival in Darwin's ground finches (Geospiza fortis and G. scandens)[END_REF][START_REF] Cohas | Age-specific effect of heterozygosity on survival in alpine marmots, Marmota marmota[END_REF][START_REF] Nielsen | Inbreeding and inbreeding depression of early life traits in a cooperative mammal[END_REF] and it is possible that inbred individuals may often die before being captured and marked, or that inbreeding depression may only be detectable on developmental traits which were not examined here. Finally, even if the genetic load responsible for inbreeding depression may be substantial in the population, our results may simply reflect the scarcity of inbred individuals in the population. The high genetic diversity of our study population indicates that it is of sufficient size and density to ensure healthy pools of largely unrelated candidate mates and fully operational inbreeding avoidance strategies. We also did not find any support for an optimal heterozygosity level balancing potential costs of inbreeding and outbreeding depression, but recent models suggest that levels of inbreeding selected under this scenario are low [START_REF] Puurtinen | Mate choice for optimal (k)inbreeding[END_REF], which may explain why they were undetectable.

CONCLUSION

We simultaneously investigated the occurrence and intensity of inbreeding risk (via parentage and pedigree analyses), of inbreeding avoidance (via mating biases), and of inbreeding depression (via the survival costs of heterozygosity) in a large natural population of grey mouse lemurs. Grey mouse lemurs have retained a number of ancestral mammalian traits including a solitary lifestyle, a promiscuous mating system and male-biased dispersal [START_REF] Lukas | Group structure, kinship, inbreeding risk and habitual female dispersal in plural-breeding mammals[END_REF][START_REF] Lukas | The evolution of social monogamy in mammals[END_REF] and may therefore offer a classic example of the inbreeding strategy prevailing in large populations of solitary mammals.

Inbreeding risk was low, and its variation across ages and sexes suggests that male-biased dispersal is a primary inbreeding avoidance mechanism at the population level. Mating biases favouring partners with intermediate relatedness were detectable in yearling females and in adult males, the two age-classes that face the highest prevalence and intensity of inbreeding risk, respectively, suggesting that mate choice may represent a facultative secondary strategy of inbreeding avoidance that mitigates residual inbreeding risk at the individual level. The effect of genome-wide heterozygosity on survival was undetectable using a ten-generation survival analysis, suggesting that inbreeding avoidance strategies were efficient in this large, open and genetically-diverse population.

Table 1. Composition of datasets for mating bias permutation tests. The number of mating seasons lists the number of individual-seasons: 42 adult females have been present in the dataset for one to six years each, resulting in a total of 67 mating seasons (there is one mating season per year). The number of choice events differs from the number of mating seasons because both females and males may sire offspring with multiple partners in any given season (most females only have one litter per year but mixed-paternity litters are common (Eberle & Kappeler, 2004a[START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF]). The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7).

Sex

Age *Threshold deviation between true and random pairs required for reaching statistical significance for each parameter examined given the power of our analyses.

We followed procedures described in [START_REF] Huchard | MHC, mate choice and heterozygote advantage in a wild social primate[END_REF], obtaining percentage differences by dividing the 95% CI threshold by the mean of the simulated distribution.

Figure 1 .

 1 Figure 1. Sex differences in inbreeding risk. (a) Occurrence of inbreeding risk, scored as the

Figure S2 .

 S2 Figure S2. Coefficient of variation in relatedness between true parents compared to the

Table 2 .

 2 Model selection statistics for age and sex effects on the occurrence and intensity of inbreeding risk. Model notation: I for the intercept, + for an additive effect, * for an interaction. The degrees of freedom (df), the loglikelihood (LogLik), Akaike's Information Criterion (AICc), the difference between the AIC of the top model and the model considered (Δi) and Akaike weights are given for each model.

		class	No. of mating seasons [no. of individuals]	No. of choice events [no. of chosen individuals]	Mean no. of candidate mates per individual during one mating season [range]
		Adult	67 [42]	91 [59]	50 [23-69]
	Female	Yearling	23 [23]	30 [25]	47 [23-69]
		Adult	69 [44]	109 [55]	69 [17-79]
	Male
		Yearling	47 [47]	61 [45]	50 [25-79]

Table 3 .

 3 Estimates and standard error (SE) of the Generalized Linear Mixed Models (GLMMs) investigating age and sex effects on the occurrence and intensity of inbreeding risk. Occurrence was scored as the presence/absence of at least one first order relative in the pool of candidate mates, while intensity was scored as the proportion of first order relatives in the pool of candidate mates. Random factors included individual identity crossed with year. The 95% confidence intervals were computed for the two top models -see Table2.

	Fixed effect	Estimate	SE
	Inbreeding risk -Occurrence
	Intercept	-2.61	0.76
	Age class (adult vs. yearling) 1	1.83	0.87
	Sex 2	0.75	0.66
	Age class: Sex	-3.55	1.26
	Inbreeding risk -Intensity
	Intercept	6.36	0.50
	Age class (adult vs. yearling) 1	-0.72	0.49
	Sex 2	-1.13	0.59
	Age class: Sex	2.34	0.83

Table 4 .

 4 Summary table of the randomization tests of mating biases.

	Age-sex class	Observed value Simulated value [95%CI]	One-sided p-value	Two-sided p-value	Minimum deviation (%)*
		Choice for partners with low relatedness: results on mean relatedness
	Adult females	0.053	0.071 [0.052-0.089]	0.029	0.071	26.39
	Yearling females	0.079	0.076 [0.039-0.112]	0.605	0.840	48.16
	Adult males	0.059	0.076 [0.057-0.095]	0.039	0.089	24.89
	Yearling males	0.063	0.060 [0.041-0.079]	0.646	0.730	30.92
		Choice

for partners with intermediate relatedness: results on the CV of relatedness

	Adult females	1.179	1.305 [1.017-1.605]	0.202	0.395	22.21
	Yearling females	0.827	1.349 [0.863-1.833]	0.004	0.033	35.95
	Adult males	0.987	1.380 [1.110-1.650]	<0.001	0.004	19.57
	Yearling males	1.275	1.260 [0.966-1.555]	0.576	0.926	23.51
		Choice

for partners with high heterozygosity: results on mean heterozygosity

	Adult females	0.197	0.182 [0.161-0.202]	0.070	0.137	11.39
	Yearling females	0.191	0.181 [0.146-0.216]	0.292	0.585	19.59
	Adult males	0.179	0.169 [0.148-0.190]	0.162	0.318	12.16
	Yearling males	0.191	0.170 [0.142-0.198]	0.075	0.147	16.5

Table 5 .

 5 Model selection statistics for recapture probabilities in (a) winter (p W ) and (b) summer (p S ), and for apparent survival probabilities in (c) winter (ϕ W ) and (d) summer (ϕ S ) nested in the most general model for the remaining components (a*s+t). Factors considered are age (a; juv: juveniles, ad: adults), sex (s) and year (t). Model notation: (.) constant, * interaction, + additive effect (parallel lines on a logit-scale). The number of estimable parameters (K), The Quasi-likelihood adjusted deviance (QDEV), Akaike's Information Criterion (QAICc), the difference between the minimum QAICc of the top model and the model considered (Δi) and Akaike weights (wi) are given for each model.

	Rank Model i	K	QDEV	QAICc	Δi	wi
	(a) Recapture probabilities in winter p W depend on:
	s+t	58	1743.22	1866.45	0	0.65
	a+s+t	59	1743.21	1868.70	2.25	0.21
	a*s+t	60	1743.19	1870.94	4.49	0.07
	a+t	58	1748.51	1871.75	5.30	0.05
	t	57	1752.36	1873.34	6.89	0.02
	(b) Recapture probabilities in summer p S depend on:
	s+t	58	1745.10	1868.33	0	0.43
	a+s+t	59	1743.36	1868.86	0.53	0.33
	a*s+t	60	1743.19	1870.94	2.61	0.12
	t	57	1751.01	1872.00	3.67	0.07
	a+t	58	1749.43	1872.66	4.33	0.05
	(c) Survival probabilities in winter  W depend on:
	juv(s)ad(.)	48	1762.84	1863.76	0	0.39
	a+s	48	1763.20	1864.12	0.36	0.33
	a	47	1767.17	1865.89	2.13	0.14
	a*s	49	1762.77	1865.92	2.16	0.13
	a*s+t	60	1743.19	1870.94	7.18	0.01
	(d) Survival probabilities in summer  S depend on
	s+t	58	1743.45	1866.68	0	0.50
	t	57	1747.67	1868.65	1.97	0.19
	a+s+t	59	1743.19	1868.68	2.00	0.19
	a+t	58	1747.60	1870.84	4.16	0.06
	a*s+t	60	1743.19	1870.94	4.26	0.06

Table 6 .

 6 Likelihood ratio tests (adjusted for ĉ =1.09) of heterozygosity (HL) effects on survival. Models incorporating the heterozygosity effect (general models) were tested against the reduced basic model (ϕ W (juv(s)ad(.) ϕ S (s+t) p W (s+t) p S (s+t). Shown are the effects tested, and the survival model term added in the general survival model as well as the test statistic (χ²), degrees of freedom (d.f.) and the p value of the LRT.

	Hypothesis tested	general survival model term	χ²	d.f.	p
	linear overall* effect of HL on survival	ϕ all (HL)	1.05	1	0.30
	quadratic overall* effect of HL on survival	ϕ all (HL+HL²)	1.62	2	0.45
	linear effect of HL on juvenile female survival	ϕ W, juvF (HL)	0.51	1	0.48
	quadratic effect of HL on juvenile female survival	ϕ W, juvF (HL+HL²)	2.06	2	0.36
	linear effect of HL on summer survival	ϕ S (HL)	1.26	1	0.26
	quadratic effect of HL on summer survival	ϕ S (HL+HL²)	1.90	2	0.39
	linear effect of HL on male summer survival	ϕ S, M (HL)	1.17	1	0.28
	quadratic effect of HL on male summer survival	ϕ S, M (HL+HL²)	1.17	2	0.56

Reference category: adult

Reference category: female.

ACKNOWLEDGEMENTS

We acknowledge the authorization of this study by the Commission Tripartite and the CAFF of the Direction des Eaux et Forêts, the C.N.F.E.R.E.F. All research reported here is in compliance with animal care regulations and applicable national laws of Germany and Madagascar. The appropriate Animal Use and Care committees of Germany (Bundesministerium für Naturschutz, BfN) and Madagascar (Ministère de l'Environnement et des Eaux et Forêts, MINEEF) approved all research protocols. The CRCESP, DPZ and DFG provided financial support. We thank Dr. Rodin Rasoloarison, Léonard Razafimanantsoa, Tiana Andrianjanahary, Bruno Tsiveramana, Remy de Ampataka and the Equipe Kirindy for support and assistance in the field.

Supporting information

The inbreeding strategy of a solitary primate, Microcebus murinus Huchard, Elise 1,* Schliehe-Diecks, Susanne 2, 3,* Kappeler, Peter M. 2, 3 Kraus, Cornelia 2, 3 1 Institute of Evolutionary Sciences, University of Montpellier, France (CNRS UMR5554, IRD, EPHE)

2 Behavioral Ecology Sociobiology Unit, German Primate Center, Kellnerweg 4, 37077 Göttingen, Germany 3 Department of Sociobiology/Anthropology, Georg-August-University of Göttingen, Kellnerweg 6, 37077 Göttingen, Germany *These two authors contributed equally.

Appendix S1: DNA amplification and sequencing.

Twelve polymorphic microsatellites with an average number of 22 alleles ((Table S1) were used for analyses: Mm06, MmF3, Pvc 9.2, Pvc a1 [START_REF] Wimmer | The genetic population structure of the gray mouse lemur (Microcebus murinus)[END_REF] as well as 33104, Mm22, Mm39, Mm40, Mm42, Mm43b, Mm51, Mm60 [START_REF] Hapke | Isolation of new microsatellite markers and application in four species of mouse lemurs (Microcebus sp.)[END_REF]. PCR reactions had a total volume of 30μl and contained 1U Biotherm TM Taq DNA Polymerase, 3μl 10x Reaction Buffer provided by Genecraft, 4.8 mM (NH4)2 SO4, 20.1 mM Tris-HCl (pH 8.8), 5pmM MgCl2, 0.003% Tween 20, 0.3 pmol of each primer, 0.16 mmol dNTPs, 1.3 mg/ml bovine serum albumin, 0.06 mg Triton and about 10 ng of template DNA. The PCR program used for each primer pair is described in Table S2. PCR products were processed via capillary electrophoresis (ABI 3730 XL) and subsequently analyzed in ABI GeneMapper v4.0TM.

Appendix S2: Genetic determination of parentage

We ran the parentage analysis including all sampled females and males present in the population at the time of conception of a given offspring and who were sexually mature, so that each was considered as a potential mother and father, respectively, for each offspring.

Likelihood-based paternity analysis was carried out using two different software packages: Cervus 3.0 [START_REF] Kalinowski | Revising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment[END_REF]) and COLONY (Wang 2004). A candidate parent was considered assigned when it was identified as the most likely parent by both analyses.

Cervus calculates paternity likelihood ratios and generates a statistic, Δ, defined as the difference in the positive log likelihood ratios between the two most probable candidate parents. The statistical significance of Δ was determined at a confidence level of 95%. The likelihood analysis in CERVUS 3 was based on simulations to estimate the resolving power of all loci and critical values necessary to assess the reliability of the parentage analysis (100,000 runs, 94 candidate parents, assumptions: sampling rate=0.95; average loci typing rate=0.85; error rate=0.05; one close relative of the true parent among the other candidate parents, combined non-exclusion probability (first parent) = 3.7*10 -6 ). Sampling rate was based on behavioural observations in the study population (Eberle & Kappeler, 2004a[START_REF] Eberle | The number of choice events therefore corresponds to the number of offspring produced. The number of chosen individuals is the total number of opposite-sex partners that have produced offspring: adult females have produced a total of 91 offspring, and 59 individual males have produced at least one offspring (and a maximum of 7). Sex Age class No. of mating seasons [no. of individuals] No. of choice events [no. of chosen individuals] Mean no[END_REF]. In order to assess locus-specific genotyping error rates, we duplicated ca. 10% of our sample using independent amplification and sequencing (n=95 individuals). These gave a mean genotyping error rate across loci (combining allelic drop-out with other errors) of 5 %.

COLONY implements a maximum-likelihood method that assigns offspring into full-sib families nested within half-sib families and assigns candidate parents to the sib families, using the offspring and candidate parent genotypes. COLONY calculates family likelihood and searches for the best sibship configuration (with the maximum likelihood) through an iterative process, using a simulated annealing algorithm. Both software packages account for incomplete sampling and typing errors, and COLONY further infers parental genotypes for reconstructed sibships and detects mutations and typing errors at each locus. Locus-specific error rates calculated using repeated independent amplification and typing of the same individual for a given locus (see above) were used in the analysis. Where necessary, the same specifications were used in the COLONY analysis (e.g. the proportions of mothers and fathers sampled).