Patterns of MHC- dependent sexual selection in a free- living population of sheep

The MHC is one of the most polymorphic gene clusters in vertebrates and play an essential role in adaptive immunity. Apart from pathogen- mediated selection, sexual selection can also contribute to the maintenance of MHC diversity. MHC- dependent sexual selection could occur via several mechanisms but at present there is no consen-sus as to which of these mechanisms are involved and their importance. Previous studies have often suffered from limited genetic and behavioural data and small sample size, and were rarely able to examine all the mechanisms together, determine whether signatures of MHC- based non- random mating are independent of genomic effects or differentiate whether MHC- dependent sexual selection takes place at the pre- or post- copulatory stage. In this study, we use Monte Carlo simulation to investigate evidence for non- random MHC- dependent mating patterns by all three mechanisms in a free- living population of Soay sheep. Using 1710 sheep diplotyped at the MHC class IIa region and genome- wide SNPs, together with field observations of consorts, we found sexual selection against a particular haplotype in males at the pre- copulatory stage and sexual selection against female MHC heterozygosity during the rut. We also found MHC- dependent disassortative mating at the post- copulatory stage, along with strong evidence of inbreeding avoidance at both stages. However, results from generalized linear mixed models suggest that the pattern of MHC- dependent disassortative mating could be a by- product of inbreeding avoidance. Our results therefore suggest that while multiple apparent mechanisms of non- random mating with respect to the MHC may occur, some of them have alternative explanations.

selection has been assessed theoretically (Ejsmond et al., 2014) and documented in empirical studies (Kamiya et al., 2014;Winternitz et al.,. ,2013Winternitz et al.,. , , 2017)).MHC-dependent sexual section could act through both intrasexual selection via male-male competition and through intersexual selection including mate choice based on the partner's MHC constitution (additive benefits) or based on the MHC compatibility (non-additive benefits).
More specifically, MHC-dependent sexual selection could occur via three non-mutually exclusive mechanisms: selection could favour particular MHC alleles or haplotypes, MHC diversity or MHC compatibility.First, individuals with specific MHC alleles could be favoured by intrasexual or intersexual selection and such a pattern has been reported in several studies (Eizaguirre et al., 2009;Ekblom et al., 2004).Second, some studies have reported that individuals with higher diversity or heterozygosity at the MHC were favoured as partners (Cutrera et al., 2012;Landry et al., 2001;Richardson et al., 2005;Winternitz et al., 2015).Third, in terms of MHC compatibility, MHC-dependent disassortative mating has been reported, which could maximise the MHC diversity of offspring (Han et al., 2019;Hoover et al., 2018;Schwensow et al., 2008;Setchell et al., 2010).
Several studies have also demonstrated that MHC genes could be a cue for kin recognition enabling avoidance of mating with relatives through MHC-associated odours (Grob et al., 1998;Milinski, 2006;Penn, 2002).However, as excessive expression of MHC molecules could lead to depletion of the mature T-cell repertoire and elevated risk of autoimmune disease (Migalska et al., 2019), it has also been suggested that individuals may optimise rather than maximise MHC diversity (Griggio et al., 2011;Rekdal et al., 2019;Reusch et al., 2001).Fourth, some studies have found mate choice favouring MHC-similar mates and explained such patterns as local adaption to endemic pathogens (Bichet et al., 2014;Bonneaud et al., 2006;Sin et al., 2015).Finally, some studies have found no evidence of MHCdependent sexual selection and suggested it may not be a universal phenomenon (Huchard et al., 2010;Paterson & Pemberton, 1997;Sepil et al., 2015;Westerdahl, 2004;Yu et al., 2018).However, few previous studies have investigated all possible mechanisms together within the same study.A meta-analysis of MHC-dependent sexual selection in non-model species found support for female choice for MHC diversity and selection for dissimilarity when the MHC is characterized across multiple loci, but selection for particular MHC alleles was not examined (Kamiya et al., 2014).Therefore, more empirical studies are needed to draw definite conclusions about MHCdependent sexual selection.
Future studies on MHC-dependent sexual selection would ideally include advances in a number of aspects of data quality.First, accurate estimates of relatedness should be examined at the same time as MHC-dependent sexual selection.Rather than being the actual cues for sexual selection, MHC variation could be incidentally associated with signals of genome-wide relatedness.Thus, signatures of MHC-dependent disassortative mating could be a byproduct of inbreeding avoidance (Hurst et al., 2005;Sherborne et al., 2007).In the previous studies reported above (Bichet et al., 2014;Bonneaud et al., 2006;Ferrandiz-Rovira et al., 2016;Huchard et al., 2013;Setchell et al., 2010;Winternitz et al., 2015), relatedness was usually estimated from small panels of microsatellite markers rather than genome-wide SNPs, which may have been imprecise.Second, behavioural observations of mating are required to differentiate preand post-copulatory MHC-dependent sexual selection, especially since pre-and post-copulatory sexual selection on MHC genes could occur in opposite directions.For example, pre-copulatory sexual selection favouring MHC-dissimilar partners has been demonstrated in a population of salmon (Salmo salar) (Landry et al., 2001) while post-copulatory sexual selection favoured MHC-similar partners in another salmon study system (Yeates et al., 2009).However, few studies have examined whether MHC-dependent sexual selection occurs at the pre-and post-copulatory sexual selection stages using field observations of mating behaviour in the same population, except for a study of mouse lemur (Microcebus murinus) (Schwensow et al., 2008).Third, detailed knowledge about MHC haplotype structure are needed to study MHC-dependent sexual selection.MHC loci genes are usually in strong linkage disequilibrium and inherited as haplotypes such that deviation of random mating based on MHC genes may be imprecisely measured without haplotype information.
However, only a handful of studies in wild populations has managed to haplotype the MHC region (Gaigher et al., 2016;Huchard et al., 2008;Niskanen et al., 2014;Sin et al., 2014) and few studies have investigated MHC-dependent sexual selection using MHC haplotypes (Sin et al., 2015).Finally, larger sample sizes are essential in future studies to secure confident results (Hoover & Nevitt, 2016;Kamiya et al., 2014;Winternitz et al., 2017).A recent study documented the impact of sample size on error rates and effect sizes and suggested a sample size of 500 mating pairs is required for testing MHC-dependent sexual selection (Hoover & Nevitt, 2016) which was not always available in previous studies.
In this study, we used a free-living population of Soay sheep (Ovis aries) on the island of Hirta, St Kilda to investigate MHCdependent sexual selection.An individual-based study has been carried out on the population since 1985 (Clutton-Brock & Pemberton, 2004).A large number of male-female consorts has been recorded during the rut each year and a multi-generation pedigree including most study individuals has been constructed.
Previous studies have suggested intensive male-male competition and male mate choice in Soay sheep (Preston et al., 2003(Preston et al., , 2005)).
Also, selection on load and tolerance of gastrointestinal parasites has been demonstrated (Hayward et al.,. ,2011(Hayward et al.,. , , 2014)).Therefore, we assume there could be MHC-dependent sexual selection to increase an offspring's fitness to better combat parasites.However, a previous study using five MHC-linked microsatellite loci genotyped in between 887 and 1209 individuals born between 1985 and 1994 found no evidence for MHC-dependent assortative or disassortative mating in this population (Paterson & Pemberton, 1997).Recently, using genotyping-by-sequencing, a total of eight MHC class II haplotypes have been identified in the study populations and a large number of individuals alive between 1989 and 2012 have been diplotyped (Dicks et al., 2019, Dicks et al., 2020).In addition, pairwise relatedness based on genome-wide SNPs is available between most individuals.This genetic and genomic data combined with a large number of consort and parent- A large number of study area sheep alive since 1989 have been genotyped on the Illumina Ovine 50 K SNP array.Parentage was determined for each individual using a subset of 315 unlinked SNPs derived from the SNP array using the R library Sequoia (Berenos et al., 2014;Huisman, 2017).

| Rut behavioural data
Soay sheep have a promiscuous mating system with intensive malemale competition as well as male mate choice (Preston et al., 2003(Preston et al., , 2005)).The onset of the rut in early November is marked by increasing male aggression as males roam and search for oestrous females across the study area.Males compete to gain access to oestrous females and the winner defends and mates with the female repeatedly over several hours in a so-called 'consort'.However, only large and mature males with big horns can defend a female for long.Younger, smaller males and those with scurred horns constantly search for oestrous females, chase them and get quick matings if they can.
Matings are mostly between males and females aged one year or older, but some male lambs aged seven months obtain matings and some female lambs give birth at the age of one (Table S1).Throughout the rut the study area is continually monitored for consorts throughout each day, with consorts defined as being a close spatial relationship between a male and female with frequent male courtship and defence of a receptive female (Clutton-Brock & Pemberton, 2004).

| Molecular data
The molecular data used in this study included MHC class II diplotypes and pairwise genomic relatedness.We used a two-step haplotyping method involving characterisation of the MHC haplotypes The individual inbreeding coefficients and the pairwise genomic relatedness between all individuals were calculated using GCTA (Yang et al., 2011) and DISSECT respectively (Canela-Xandri et al., 2015) based on 37 K polymorphic SNPs from the Ovine 50 K SNP array (Illumina).The X chromosome and chromosome 20 where the MHC genes are located were excluded when calculating the pairwise genomic relatedness.

| Assortative mating analysis
We performed Monte-Carlo simulations to examine whether there were MHC-dependent or relatedness-dependent mating patterns in Soay sheep.
We first selected all females and males older than one year which were diplotyped at the MHC and genotyped on the SNP chip into a "primary mating pool".We focused on mating between adult sheep because relatively few offspring have a juvenile parent (that is, a male lamb for a father and/or a female lamb for a mother; Table S1) and including the large number of non-reproductive male and female lambs present each breeding season could have biased the simulations.We excluded individuals whose birth year was unknown, as they do not live mainly in our study area and we had no information about when they start to be involved in mating.For the few individuals with no recorded death year, death year was estimated from the last-seen year recorded in the census data or the last year they sired or gave birth to offspring.A total of 889 females and 821 males were included in the primary mating pool dataset and each of them is recorded once per year they were alive (Table S1).
Second, we extracted all the consorts between any male and female in the primary mating pool dataset as the "consort dataset".
Multiple observations of the same pair together on the same day were counted as one consort observation.
Third, we assembled an "observed parentage dataset" comprising all mother-father-offspring trios in which the offspring birth year was known and the parents were successfully diplotyped at the MHC and genotyped on the SNP chip.To be consistent between the primary mating pool and observed parentage dataset, we excluded trios in which either of the parents was a lamb or an adult not included in primary mating pool, such that all parents could be sampled from the primary mating pool.In total, 2068 trios were included in the observed parentage dataset (Table S2).Twins and triplets were not common in our dataset comprising less than a quarter of all individuals born.Twins are usually half-sibs with different fathers, coming from different mating events (Table S3).Thus, we treated each offspring as an independent data point.Finally, the null model of random mating (adjusted random mating model) was defined for simulation.
For each year, we first randomly assigned a male or a female living in the same year from the primary mating pool to replace each known mother and father in the observed parentage dataset and then adjusted the record of the sampled sheep based on the annual breeding success (number of offspring produced each year) of the replaced sheep to produce an "adjusted mating pool".Then, each offspring in the observed parentage dataset was randomly assigned a father and mother in the year before its birth year without replacement from the adjusted mating pool.Annual breeding success in the simulated results was the same as the observed parentage dataset, while lifetime breeding success differed slightly from the observed parentage dataset with the mean of lifetime breeding success lower in the simulated data than that from the observed parentage dataset (Figure S1).The model was simulated for 10000 iterations in R v.3.5.2 using a custom script (R Core Team, 2013).
Previous studies have suggested accounting for spatial distance when designing null models of random mating (Huchard et al., 2013;Sepil et al., 2015).However, during the rut, male sheep rove around the entire study area to search for oestrous females such that there is little evidence of spatially-restricted mating patterns (Clutton-Brock & Pemberton, 2004).Therefore, we did not account for spatial distance in our null models.
After simulation, we summarised the results of all the iterations using various indices in response to the questions we proposed: 1) The frequency of each haplotype in simulated mothers and fathers.
2) The ratio of homozygote: heterozygote in simulated mothers and fathers.3) The average number of shared MHC haplotypes between simulated parents and the proportion of simulated parents sharing 0, 1 and 2 haplotypes.4) To account for MHC functional variation, the pairwise divergence of MHC haplotypes between each simulated parent pair, which has been found to be associated with fitness and parasite resistance (Lenz et al., 2013;Pierini & Lenz, 2018;Wakeland et al., 1990), was first measured by the proportion of the amino acid sequence that differed between them (p-distance) (Henikoff, 1996).
We then defined two indices AAdist and distmax as the mean and maximum MHC divergence between the 4 possible haplotype combinations of each simulated parent pair respectively.Finally, the mean of AAdist and distmax were calculated.5) The mean and median of genomic relatedness between simulated parents.These indices were also calculated for the real data using the "consort dataset" and "observed parentage dataset".Specifically, the first two indices were measured in mated females and males (consort dataset) or in mothers and fathers (observed parentage dataset) while the last three indices were measured between consort pairs or between genetic parents.For each index, statistical significance

| Generalized linear mixed models
We used generalized linear mixed models to differentiate MHC and genomic effects on non-random mating.We drew up a matrix of all pairwise combinations of males and females in the primary mating pool in a given year.For each pair, we then recorded their consort and breeding success (0/1) based on the real data from consort dataset and observed parentage dataset respectively, with 0 meaning no successful consort or offspring observed and 1 meaning consort or offspring observed.Then, we investigated consort and breeding success as response in separate binomial regressions.In each model, year and sire ID were fitted as random effects while genome-wide heterozygosity of each mother and father measured as inbreeding coefficient, MHC heterozygosity of each mother and father, genomic relatedness and the number of shared MHC haplotypes between each pair were fitted simultaneously as fixed effects.The model was run in R v.3.5.2 using R package lme4.

| Haplotype frequency tests
The frequency of haplotype C in both consort males and fathers was significantly lower than expected under the null model, even after Bonferroni correction.In addition, the frequency of haplotype G in both consort males and fathers and the frequency of haplotype H in fathers tended to be higher than expected but these results were not significant after Bonferroni correction (Figure 1).
We did not find any significant deviation of haplotype frequency in either consort females or mothers relative to random mating.The frequency of haplotype F and H in consort females tended to be lower and higher respectively.In addition, the frequency of haplotypes A and G in mothers tended to be lower and higher respectively.
However, none of these patterns was significant after Bonferroni correction (Figure S2).

| Diplotype-based tests
Regarding individual MHC heterozygosity, we found that the ratio of homozygote to heterozygote in consort females was significantly higher than expected under the null model.However, the ratio in mothers was in line with expectation under the null model (Figure 2a).We found the average number of shared haplotypes between parents was significantly lower compared with the null expectation, but this pattern was not observed in consort dataset (Figure 2c).In addition, the proportion of parents sharing 0 haplotype was significantly higher than in the simulated results while the proportion of parents sharing 1 haplotype was significantly lower than the simulated results (Figure 2d-f).However, MHC divergence measured as amino acid sequence differences between parents was in line with expectation of random mating (Figure 2g and h).

| Genome-wide relatedness tests
We found mean and median genomic relatedness between consort pairs and between parents were significantly lower than expected under the null model (Figure 3).

| Generalized linear mixed models
We found a negative association between consort success and female MHC heterozygosity and positive associations between both consort and breeding success and male genome-wide heterozygosity measured as inbreeding coefficients.We found a negative association between both consort and breeding success and genomic relatedness, but no association between consort and breeding success and number of shared MHC haplotypes (Table 1).

| DISCUSS ION
In this study, we investigated MHC-dependent sexual selection in a free-living sheep population using Monte Carlo simulations.
By comparing the result of simulated and real data, we examined whether there is deviation from random mating depending on MHC variation.We found haplotype C was disfavoured in comparison with random expectation in both consort males and fathers.We F I G U R E 1 Results of MHC haplotype frequency tests in fathers following Monte Carlo simulation.Histograms represent the result of simulations with dotted black lines representing the critical p-values after Bonferroni correction.The red and blue dashed blue lines show the observed MHC haplotype frequency in the consort and observed parentage dataset respectively.Males carrying Haplotype C are rarer than expected in both the consort and parentage dataset found no evidence that MHC heterozygotes were favoured in either sex.Instead, we found MHC homozygote females were overrepresented in consort pairs but this pattern was not observed in actual mothers.We found the average number of shared MHC haplotypes between parents was lower compared with null expectation, but this pattern was not observed in the consort dataset.In addition, the proportion of parent pairs sharing no haplotype was higher and that of parent pairs sharing one haplotype was lower than expected under random mating.Finally, we found evidence of inbreeding avoidance, as the mean and median pairwise genomic relatedness in the consort and observed parentage datasets were significantly lower than expected under random mating.When In our study, sexual selection on a specific MHC haplotype (C) was probably due to differences in male competitive ability, since the frequency of C was rarer than expected, not only in male parents but also in consort males.Few previous studies have reported specific MHC variants being favoured or disfavoured during mating as the high polymorphism of MHC genes requires a large sample size to detect sexual selection on specific MHC variants (Eizaguirre et al., 2009).In this study, our finding for haplotype C in male parents was consistent with a negative association between MHC haplotype C and male breeding success found in a recent study on MHC-fitness associations (Huang et al., 2020).The fact that haplotype C males are also less often observed in consort than expected indicates that the effect of haplotype C is expressed at the pre-copulatory rather than post-copulatory stage.
Our finding that females observed in consorts are more homozygous than expected, an effect which is opposite to expectation, is not found in the observed parentage data and is independent of genomewide heterozygosity, is puzzling and requires explanation.One hypothesis is that MHC-homozygous females are less likely to conceive in a given oestrus cycle and therefore return to oestrus 14 days later.This in turn would enrich our consort data set for such females.Alternatively, if homozygous females are less attractive in some way, perhaps they are less likely to be in long, stable consorts and instead experience multiple short consorts, which would again enrich the consort data set for homozygous females.These possibilities require further investigation within our dataset but are beyond the scope of this paper.
At first sight, our results also suggest that there is sexual selection based on MHC compatibility, but our tests suggest this effect is not independent of an inbreeding avoidance effect.In a population with limited dispersal and severe inbreeding depression, inbreeding avoidance through kin recognition could arise to reduce the cost of inbreeding (Duthie & Reid, 2016;Pusey & Wolf, 1996;Szulkin et al., 2013).Previous studies have proposed MHC variation could be used as a cue for inbreeding avoidance and MHC-associated odour variation has been reported in a wide range of taxa including fish (Milinski et al., 2005;Olsen et al., 1998), reptiles (Olsson et al., 2003), birds (Leclaire et al., 2017) and mammals (Roberts et al., 2008;Wedekind & Furi, 1997;Wedekind et al., 1995;Yamazaki et al., 2000).However, if MHC haplotype sharing is associated with relatedness, as we have shown in Soay sheep, MHC-disassortative mating could be a byproduct of inbreeding avoidance.Few studies have been able to test this hypothesis, however a study of grey mouse lemur revealed both inbreeding avoidance and MHC-dependent disassortative mating, and suggested that observed deviations from random mating at the MHC are driven by the functionally important MHC gene DRB rather than resulting passively from inbreeding avoidance.In that study, MHC-dependent disassortative mating was detected at the DRB locus only for amino acid sequence and functional similarity rather than number of shared MHC alleles (Huchard et al., 2013).
In contrast, when studied in terms of MHC divergence measured as amino acid sequence differences between parents in Soay sheep, our results were in line with the expectation from random mating (Figure 2g and h).In Soay sheep, inbreeding depression has been documented repeatedly using different approaches (Coltman et al., 1999;Overall et al., 2005;Berenos et al., 2016, Stoffel et al., 2020), so it is possible the sheep have evolved inbreeding avoidance.Using genomic relatedness calculated from a large number of SNPs, we demonstrated genomic inbreeding avoidance in Soays at the precopulatory stage for the first time.When tested in the same model, MHC haplotype sharing was not significant.We therefore cannot claim that the apparent disassortative mating based on haplotype sharing is anything but a correlated effect of inbreeding avoidance.
Our results differ from a previous study in Soay sheep (Paterson & Pemberton, 1997) which found no evidence for MHC-dependent assortative or disassortative mating.In the current study, we found evidence of MHC-dependent disassortative mating, at the postcopulatory stage which carried through to the parentage stage, based on the number of shared MHC haplotypes.Reasons for this difference include the fact our data consisted of MHC class II haplotypes rather than MHC-linked microsatellite markers, and these two approaches do not have a perfect read through.Also, our sample sizes are very much larger and our methodology (Monte Carlo simulation) is different from the previous study which used a likelihood-based approach.
By using a large number of consort observations, we were able to differentiate MHC-dependent sexual selection at the pre-and postcopulatory stages.In this area, field observations were first used in a study of mouse lemur which demonstrated post-copulatary MHCdependent disassortative mating (Schwensow et al., 2008).Here, we used both the consort and the observed parentage datasets to examine MHC-dependent sexual selection.We found sexual selection against a specific MHC haplotype at pre-copulatory stage and sexual selection favouring MHC compatibility at the postcopulatory stage.Interestingly, we found that the ratio of homozygote:heterozygote was significantly higher in consort females than the simulated results but this pattern were not observed in mothers.
These results indicate the value of using field observations to differentiate pre-and post-copulatory sexual selection.
In this study, we examined whether there was MHC-dependent age records enabled us to test MHC-dependent sexual selection more thoroughly than before using Monte Carlo simulations.We aimed to test for specific mechanisms of MHC-dependent sexual selection by asking the following questions: 1) Are individuals carrying specific MHC haplotypes favoured during mating?2) Are MHC-heterozygote individuals favoured during mating?3) Is there MHC-dependent disassortative or assortative mating?4) If there is disassortative mating, is it based on haplotype divergence? 5) Is there inbreeding preference or avoidance?6) If any signature of non-random mating is detected, does it occur at the pre-or postcopulatory stage?7) If there is any signature of MHC-based mating, is this signature independent of genome-wide heterozygosity or relatedness? 2 | ME THODS 2.1 | Study population and data collection An unmanaged population of Soay sheep has resided unmanaged on the island of Hirta, St Kilda since 1932 when they were introduced there from the nearby island of Soay.From 1985, a longitudinal individual-based study has been conducted on the sheep resident in the Village Bay area of Hirta.Nearly all individual Soay sheep living in the study area have been followed from birth, through all breeding attempts, to death.Lambs born as singletons, twins or (rarely) triplets are ear tagged shortly after birth in April or May, sampled for genetic analysis and weighed.Any missed lambs or immigrant adults are captured, tagged and sampled in an August catch up or in the rut in November.The population is regularly censused throughout the year with individual locations recorded (Clutton-Brock & Pemberton, 2004).
present and then Kompetitive Allele-specific PCR (KASP) genotyping to impute haplotypes of individuals that lived in the study area between 1989 and 2012.First, seven expressed loci (DRB1, DQA1, DQA2, DQA2-like, DQB1, DQB2 and DQB2-like) within the MHC class IIa region were characterized in 118 Soay sheep using genotyping-by-sequencing which identified eight haplotypes named A to H (Dicks et al., 2019).Second, a panel of 13 SNPs located in the MHC class IIa region haplotypes including 11 SNPs from the Ovine Infinium high density SNP array (Illumina) and two other SNPs located within DQA1 gene were selected to impute eight haplotypes using Kompetitive Allele-specific PCR (KASP) in 5951 Soay sheep(Dicks, Pemberton et al. 2020).After genotyping quality control and pedigree checking, 5349 individuals were successfully diplotyped.

(
p value) was determined by comparing the index in the real data with the 2.5% and 97.5% tails of the distribution of the index in the simulated results.To account for multiple testing, we applied a Bonferroni correction to the eight haplotype frequency tests across two sexes, and significant results were determined based on the refined critical p-value (p = 0.0015625).Once significant results were identified, we determined whether the distortion occurred at the pre-or post-copulatory stage based on the following logic.1) If indices in the consort dataset and observed parentage dataset both deviate from expectations of random mating, this is evidence of pre-copulatory selection.2) If indices in the consort dataset and observed parentage dataset both deviate from expectations of random mating but in opposite directions, or only indices in the consort dataset deviated, this is evidence of both pre-and post-copulatory selection acting in different directions.3) If only indices in the observed parentage dataset deviate from expectations of random mating, this is evidence of post-copulatory selection.4) If indices in the consort dataset and observed parentage dataset were both in line with expectations of random mating, this suggests no evidence of sexual selection.

F
Results of MHC diplotype-based tests following Monte Carlo simulation.Histograms represent the result of simulations, with dotted lines representing the 2.5% and 97.5% tails of the distributions.The red and blue dashed blue lines show observed values for the indices in the consort and observed parentage datasets respectively.Homozygote females are commoner than expected in the consort but not the parentage dataset and parents share fewer haplotypes than expected F I G U R E 3 Results of tests of pairwise genomic relatedness following Monte Carlo simulation.Histograms represent the result of simulations, with dotted lines representing the 2.5% and 97.5% tails of the distributions.The red and blue dashed blue lines show observed values for genomic relatedness in the consort and observed parentage dataset respectively.Partners are less related than expected in both the consort and the parentage datasets fitting MHC and genomic effects in the same model of consort or parentage, we could not demonstrate an independent effect of disassortative mating based on MHC haplotype sharing, but we found the deviation towards MHC homozygote females in the consort data was independent of genome-wide heterozygosity.
sexual selection in a population of free-living Soay sheep.Benefiting from intermediate MHC polymorphism, high quality genetic and genomic information, intensive field observations and large sample size, we have demonstrated sexual selection based on a specific MHC haplotype at the pre-copulatory stage and MHC compatibility at the postcopulatory stage occurs simultaneously.We have also demonstrated sexual selection against female MHC heterozygosity in dependent of genome-wide heterozygosity during the rut.Finally, we report inbreeding avoidance in this population for the first time and find that we cannot show an independent effect of disassortative mating based on the MHC.Our results suggest that multiple mechanisms of MHCdependent sexual selection could act simultaneously in Soay sheep and that it is necessary to have an exhaustive examination of all possible mechanisms when investigating MHC-dependent sexual selection.

TA B L E 1
Results of generalized linear mixed model testing associations between consort/breeding success and MHC/genomic heterozygosity and relatedness Significant effects and standard errors are marked with asterisk (* p<0.05, **p<0.01)and shown in brackets respectively.