Conserved Genetic Architecture Underlying Individual Recombination Rate Variation in a Wild Population of Soay Sheep (Ovis aries)

Meiotic recombination breaks down linkage disequilibrium (LD) and forms new haplotypes, meaning that it is an important driver of diversity in eukaryotic genomes. Understanding the causes of variation in recombination rate is important in interpreting and predicting evolutionary phenomena and in understanding the potential of a population to respond to selection. However, despite attention in model systems, there remains little data on how recombination rate varies at the individual level in natural populations. Here we used extensive pedigree and high-density SNP information in a wild population of Soay sheep (Ovis aries) to investigate the genetic architecture of individual autosomal recombination rates. Individual rates were high relative to other mammal systems and were higher in males than in females (autosomal map lengths of 3748 and 2860 cM, respectively). The heritability of autosomal recombination rate was low but significant in both sexes (h2 = 0.16 and 0.12 in females and males, respectively). In females, 46.7% of the heritable variation was explained by a subtelomeric region on chromosome 6; a genome-wide association study showed the strongest associations at locus RNF212, with further associations observed at a nearby ∼374-kb region of complete LD containing three additional candidate loci, CPLX1, GAK, and PCGF3. A second region on chromosome 7 containing REC8 and RNF212B explained 26.2% of the heritable variation in recombination rate in both sexes. Comparative analyses with 40 other sheep breeds showed that haplotypes associated with recombination rates are both old and globally distributed. Both regions have been implicated in rate variation in mice, cattle, and humans, suggesting a common genetic architecture of recombination rate variation in mammals.

M EIOTIC recombination is a fundamental feature of sexual reproduction in nearly all multicellular organisms. In many species, it ensures the proper segregation of homologous chromosomes during meiosis, avoiding deleterious outcomes such as aneuploidy (Hassold and Hunt 2001;Fledel-Alon et al. 2009). It is also an important driver of diversity because it rearranges existing allelic variation to create novel haplotypes. It can prevent the accumulation of deleterious mutations by uncoupling them from linked beneficial alleles (Muller 1964;Crow and Kimura 1965) and can lead to an increase in genetic variance for fitness, allowing populations to respond to selection at a faster rate (McPhee and Robertson 1970;Felsenstein 1974;Charlesworth and Barton 1996;Burt 2000): this is particularly true for small populations under strong selection, where beneficial and deleterious alleles are more likely to be linked (Hill-Robertson interference), and their relative selective costs and benefits are likely to be stronger (Hill and Robertson 1966;Otto and Barton 2001). However, recombination may be associated with fitness costs; higher rates of crossing over may increase deleterious mutations and chromosomal rearrangements (Inoue and Lupski likely to vary within different contexts, leading to an expectation of variation in recombination rates within and between populations (Barton 1998;Burt 2000;Otto and Lenormand 2002).
Recent studies of model mammal systems have shown that recombination rates vary at an individual level and that a significant proportion of variance is driven by heritable genetic effects (Kong et al. 2004;Dumont et al. 2009;Sandor et al. 2012). In cattle, humans, and mice, the heritability of recombination rate is 0.22, 0. 08-0.30, and 0.46, respectively, and genome-wide association studies (GWASs) have repeatedly attributed some heritable variation to specific genetic variants, including ring finger protein 212 (RNF212), complexin 1 (CPLX1), meiotic recombination protein REC8 (REC8), and PR domain zinc finger protein 9 (PRDM9), among others (Kong et al. 2008(Kong et al. , 2014Baudat et al. 2010;Sandor et al. 2012;Ma et al. 2015). Most of these loci appear to influence crossover frequency, may have sex-specific or sexually antagonistic effects on recombination rate (e.g., RNF212 and CPLX1 in humans and cattle) (Kong et al. 2014;Ma et al. 2015), and may be dosage dependent (e.g., RNF212 in mice) (Reynolds et al. 2013). The locus PRDM9 is associated with the positioning and proportion of crossovers that occur in mammalian recombination hotspots (i.e., regions of the genome with particularly high recombination rates) (Baudat et al. 2010;Ma et al. 2015), although this locus is not functional in some mammal species, such as canids (Auton et al. 2013). These studies suggest that recombination rate has a relatively oligogenic architecture and therefore has the potential to respond rapidly to selection over relatively short evolutionary timescales. Such studies in model systems have provided key insights into the causes of recombination rate variation. However, with the exception of humans, studies have been limited to systems that are likely to have been subject to strong artificial selection in their recent history, a process that will favor alleles that increase recombination rate to overcome Hill-Robertson interference (Hill and Robertson 1966;Otto and Barton 2001). Some experimental systems show increased recombination rates after strong selection on unrelated characters (Otto and Lenormand 2002), and recombination rates are higher in domesticated plants and animals than in their progenitors (Burt and Bell 1987;Ross-Ibarra 2004; but see Muñoz-Fuentes et al. 2015). Therefore, artificial selection may result in different genetic architectures than exist in natural populations. Studies examining recombination rates in wild populations will allow dissection of genetic and environmental drivers of recombination rate to determine whether it is underpinned by similar or different genetic architectures and ultimately will allow examination of the association between recombination rate and individual fitness, enabling understanding of how this trait evolves in natural systems.
Here we examine the genetic architecture of recombination rate variation in a wild mammal population. The Soay sheep (Ovis aries) is a Neolithic breed of domestic sheep that has lived unmanaged on the St. Kilda archipelago in Scotland since the Bronze Age ( Clutton-Brock et al. 2004). In this study, we integrate genomic and pedigree information to characterize autosomal crossover positions in more than 3000 gametes in individuals from both sexes. Our objectives were as follows: (1) to determine the relative importance of common environment and other individual effects to recombination rates (e.g., age, sex, and inbreeding coefficients), (2) to determine whether individual recombination rates were heritable, (3) to identify specific genetic variants associated with recombination rate variation, and (4) to determine whether the genetic architecture of recombination rate variation is similar to that observed in other mammal species.

Study population and pedigree
Soay sheep living within the Village Bay area of the Island of Hirta (57°49'N, 8°34'W) have been studied on an individual basis since 1985 ( Clutton-Brock et al. 2004). All sheep are ear tagged at first capture (including 95% of lambs born within the study area), and DNA samples for genetic analysis are routinely obtained from ear punches and/or blood sampling. All animal work was carried out according to UK Home Office procedures and was licensed under the UK Animals (Scientific Procedures) Act of 1986 (license no. PPL60/4211). A Soay sheep pedigree has been constructed using 315 SNPs in low linkage disequilibrium (LD) and includes 5516 individuals with 4531 maternal and 4158 paternal links (Bérénos et al. 2014).

SNP data set
A total of 5805 Soay sheep were genotyped at 51,135 SNPs on the Ovine SNP50 BeadChip using an Illumina Bead Array genotyping platform (Illumina, San Diego) (Kijas et al. 2009). Quality control on SNP data was carried out using the check. marker function in GenABEL v1. 8-0 (Aulchenko et al. 2007) implemented in R v3.1.1 with the following thresholds: SNP minor allele frequency (MAF) . 0.01, individual SNP locus genotyping success . 0.95, individual sheep genotyping success . 0.99, and identity by state (IBS) with another individual , 0.90. Heterozygous genotypes at nonpseudoautosomal X-linked SNPs within males were scored as missing, accounting for 0.022% of genotypes. The genomic inbreeding coefficient [measure b F III in Yang et al. (2011), hereafter b F] was calculated for each sheep in the software GCTA v1.24.3 (Yang et al. 2011) using information for all SNP loci passing quality control.

Estimation of autosomal meiotic crossover count
Subpedigree construction: To allow unbiased phasing of the SNP data, a standardized pedigree approach was used to identify crossovers that had occurred within the gametes transferred from a focal individual to its offspring; hereafter, focal individual (FID) refers to the sheep in which meiosis took place. For each FID-offspring combination in the Soay sheep pedigree, a subpedigree was constructed to include both parents of the FID ("Father" and "Mother") and the other parent of the "Offspring" ("Mate"), where all five individuals had been genotyped (Figure 1). This subpedigree structure allowed phasing of SNPs within the FID and thus identification of autosomal crossover events in the gamete transferred from the FID to the offspring (Figure 1). Subpedigrees were discarded from the analysis if they included the same individual twice (e.g., father-daughter matings; N = 13).
Linkage map construction and chromosome phasing: All analyses in this section were conducted using the software CRI-MAP v2.504a (Green et al. 1990). First, Mendelian incompatibilities in each subpedigree were identified using the prepare function; incompatible genotypes were removed from all affected individuals, and subpedigrees containing parent-offspring relationships with more than 0.1% mismatching loci were discarded. Second, sex-specific and sexaveraged linkage map positions (in Kosambi centimorgans) were obtained using the map function, where SNPs were ordered relative to their estimated positions on the sheep genome assembly Oar_v3.1 (GenBank assembly ID GCA_000298735.1) (Jiang et al. 2014). SNP loci with a map distance of .3 cM to each adjacent marker (10 cM for the X chromosome, including the pseudoautosomal regions) were assumed to be incorrectly mapped and were removed from the analysis, with the map function rerun until all map distances were below this threshold; in total, 76 SNPs were assumed to be incorrectly mapped (these SNP IDs are included in archived data; see the section Data availability). Third, the chrompic function was used to identify informative SNPs (i.e., those for which the grandparent of origin of the allele could be determined) on chromosomes transmitted from the FID to its offspring; crossovers were deemed to have occurred where there was a switch in the grandparental origin of a SNP allele (Figure 1).
Quality control and crossover estimation in autosomes: Errors in determining the grandparental origin of alleles can lead to false calling of double crossovers (i.e., two adjacent crossovers occurring on the same chromatid) and, in turn, an overestimation of recombination rate. To reduce the likelihood of calling false crossover events, runs of grandparental origin consisting of a single allele (i.e., resulting in a double crossover either side of a single SNP) were recoded as missing (N = 973 of 38,592 double crossovers) (Supplemental Material, Figure S1). In the remaining cases of double crossovers, the base pair distances between immediately adjacent SNPs spanning a double crossover were calculated (hereafter span distance) ( Figure S1). Informative SNPs that occurred within double-crossover segments with a log 10 span distance ,2.5 SD from the mean log 10 span distance (equivalent to 9.7 Mb) also were recoded as missing (N = 503 of 37,619 double crossovers) ( Figure S1). The autosomal crossover count (ACC), the number of informative SNPs, and the informative length of the genome (i.e., the total distance between the first and last informative SNPs for all chromosomes) then were calculated for each FID. A simulation study was conducted to ensure that our approach accurately characterized ACC and reduced phasing errors. Autosomal meiotic crossovers were simulated given an identical pedigree structure and population allele frequencies (N simulations = 100) (see File S1 for detailed methods and results). Our approach was highly accurate in identifying the true ACC per simulation across all individuals and per individual across all simulations (adjusted R 2 . 0.99) but indicated that accuracy was compromised in individuals with high values of b F. This is likely to be an artifact of long runs of homozygosity as a result of inbreeding, which may prevent detection of double crossovers or crossovers in subtelomeric regions. To ensure accurate individual estimates of ACC, gametes with a correlation of adjusted R 2 # 0.95 between simulated and detected crossovers in the simulation analysis were removed from the study (N = 8) (File S1).

Assessing variation in the recombination landscape
Broad-scale recombination rate: Relationships between chromosome length and linkage map length and male and female linkage map lengths were analyzed using linear regressions in R v3.1.1. The relationship between chromosome length and chromosomal recombination rate (defined as cM length/Mb length) was modeled using a multiplicative inverse (1/x) regression in R v3.1.1.
Fine-scale recombination rate: The probability of crossing over was calculated in 1-Mb windows across the genome using information from the male and female linkage maps, with each bin containing a mean of 15.6 SNPs (SD = 4.04). Briefly, the probability of crossing over within a bin was the sum of all recombination fractions r in that bin; in cases where an r value spanned a bin boundary, it was recalculated as r 3 N boundary =N adjSNP , where N boundary is the number of bases to the bin boundary, and N adjSNP is the number of bases to the closest SNP within the adjacent bin. Figure 1 Diagram of the subpedigree structure used to infer crossover events. Rectangle pairs next to each individual represent chromatids, with black and gray shading indicating chromosome or chromosome sections of FID paternal and FID maternal origin, respectively. White shading indicates chromatids for which the origin of SNPs cannot be determined. Crossovers in the gamete transferred from the focal individual (FID) to its offspring (indicated by the gray arrow) can be distinguished at the points where the origin of alleles flips from FID paternal to FID maternal and vice versa.
Variation in crossover probability relative to proximity to telomeric regions on each chromosome arm was examined using general linear models with a Gaussian error structure. The response variable was crossover probability per bin; the fitted covariates were as follows: distance to the nearest telomere, defined as the best fit of either a linear (x), multiplicative inverse (1/x), quadratic (x 2 + x), cubic (x 3 + x 2 + x), or log term (log 10 x); sex, fitted as a main effect and as an interaction term with distance to the nearest telomere; number of SNPs within the bin; and GC content of the bin (percent, obtained using a sequence from Oar_v3.1) (Jiang et al. 2014). The best model was identified using Akaike's information criterion (Akaike 1974). An additional model was tested using the ratio of male-to-female crossover probability as the response variable, with the same fixed-effect structure (omitting sex). In both models, the distance to the nearest telomere was limited to 60 Mb, equivalent to half the length of the largest acrocentric chromosome (chromosome 4). Initial models also included a term indicating whether a centromere was present or absent on the 60-Mb region, but this term was not significant in either model.
Factors affecting autosomal recombination rate, including heritability and cross-sex genetic correlations ACC was modeled as a trait of the FID. Phenotypic variance in ACC was partitioned using a restricted maximum-likelihood (REML) animal model (Henderson 1975) implemented in ASReml-R (Butler et al. 2009) in R v3.1.1. To determine the proportion of phenotypic variance attributed to additive genetic effects (i.e., narrow-sense heritability h 2 , hereafter heritability), a genomic relatedness matrix (GRM) at all autosomal markers was constructed for all genotyped individuals using GCTA v1.24.3 (Yang et al. 2011). The GRM was adjusted using the argument 2grm-adj 0, which assumes that frequency spectra of genotyped and causal loci are similar; matrices with and without adjustment were highly correlated (R 2 . 0.997), and variance components estimated from models with and without adjustment were highly similar, suggesting that adjusting for sampling error in this way did not introduce bias. Matrices were not pruned to remove related individuals (i.e., the 2grm-cutoff option was not used) because there is substantial relatedness within this population, and models included common environment and parental effects, controlling for some consequences of shared environment among relatives (see below). Trait variance was analyzed first with the following univariate model: where y is a vector of the ACC per transferred gamete; X is an incidence matrix relating individual measures to a vector of fixed effects; b, Z 1 , and Z r are incidence matrices relating individual measures with additive genetic effects and random effects, respectively; a and u r are vectors of additive genetic effects from the GRM and additional random effects, respectively; and e is a vector of residual effects. The herita-bility h 2 was calculated as the ratio of the additive genetic variance to the sum of the variance estimated for all random effects. Model structures were initially tested with a number of fixed effects, including sex, b F, and FID age at the time of meiosis; random effects tested included individual identity to account for repeated measures within the same FID (sometimes referred to as the permanent environment effect), maternal and paternal identity, and common environment effects of FID birth year and offspring birth year. The significance of fixed effects was determined using a Wald test, whereas the significance of random effects was calculated using likelihood-ratio tests (LRTs) between models with and without the focal random effect. Only sex and additive genetic effects were significant in any model, but b F and individual identity were retained in all models to account for potential underestimation of ACC and the effects of pseudoreplication, respectively.
To investigate whether the additive genetic variation underlying male and female ACC was associated with sexspecific variation in ACC, bivariate models were run. The additive genetic correlation r A was determined using the CORGH error-structure function in ASReml-R (correlation with heterogeneous variances) with r A set to be unconstrained; models fitted sex-specific inbreeding coefficients and individual identity effects. To test whether the genetic correlation was significantly different from 0 and 1, the unconstrained model was compared to models with r A fixed at a value of 0 or 0.999. Differences in additive genetic variance in males and females were tested by constraining both to be equal values using the CORGV errorstructure function in ASReml-R. Models then were compared using LRTs with 1 degree of freedom.
Genetic architecture of autosomal crossover count Genome-wide association study of variants controlling ACC: Genome-wide association studies (GWASs) of autosomal recombination rates under different scenarios were conducted using ASReml-R (Butler et al. 2009) in R v3.1.1, fitting individual animal models for each SNP locus using the same model structure as earlier. SNP genotypes were fitted as a fixed effect with two or three levels. The GRM was replaced with a relatedness matrix based on pedigree information to speed up computation; the pedigree and genomic relatedness matrices have been shown to be highly correlated (Bérénos et al. 2014). Sex-specific models also were run. Association statistics were corrected for any population stratification not captured by the animal model by dividing them by the genomic control parameter l (Devlin et al. 1999) when l . 1, which was calculated as the median Wald test x 2 2 divided by the median x 2 2 expected from a null distribution. The significance threshold after multiple testing was determined using a LD-based method (outlined in Moskvina and Schmidt 2008) using a sliding window of 50 SNPs; the effective number of tests in the GWAS analysis was 22,273.61, meaning that the significance threshold for P after multiple testing at a = 0.05 was 2.245 3 10 26 . Although sex chromosome recombination rate was not included in the analysis, all GWASs included the X chromosome and SNP markers of unknown position (N = 314). The proportion of phenotypic variance attributed to a given SNP was calculated using the following equation (Falconer and Mackay 1996): where p and q are the frequencies of alleles A and B at the SNP locus, a is half the difference in the effect sizes estimated for the genotypes AA and BB, and d is the difference between a and the effect size estimated for genotype AB when fitted as a fixed effect in an animal model. The proportion of heritable variation attributed to the SNP was calculated as the ratio of V SNP to the sum of V SNP and the additive genetic variance estimated from a model excluding the SNP as a fixed effect. Standard errors of V SNP were estimated using a delta method approach. Gene annotations in significant regions were obtained from Ensembl (gene build ID Oar_v3.1.79) (Cunningham et al. 2014). The position of a strong candidate locus, RNF212, is not annotated on Oar_v3.1, but sequence alignment indicated that it is positioned at the subtelomere of chromosome 6 (see File S2).
Genome partitioning of genetic variance (regional heritability analysis) Although a powerful tool to detect regions of the genome underlying heritable traits, the single-locus approach of GWAS has reduced power to detect rare variants and variants with small effect sizes (Yang et al. 2011;Nagamine et al. 2012). One solution to this is to use a regional heritability approach that incorporates the effects of multiple haplotypes and determines the proportion of phenotypic variance explained by defined regions of the genome. The contribution of specific genomic regions to trait variation was determined by partitioning the additive genetic variance across all autosomes as follows (Nagamine et al. 2012): where v is the vector of additive genetic effects explained by autosomal genomic region i, and nv is the vector of the additive genetic effects explained by all remaining autosomal markers outside region i. Regional heritabilities were determined by constructing GRMs for regions of i of increasing resolution (whole-chromosome partitioning, sliding windows of 150, 50, and 20 SNPs corresponding to regions of 9.41 6 1.42, 3.12 6 0.60, and 1.21 Mb mean 6 0.32 SD length, respectively) and fitting them in models with an additional GRM of all autosomal markers not present in region i (sliding windows overlapped by half their length, i.e., 75, 25, and 10 SNPs, respectively). GRMs were constructed in the software GCTA v1.24.3 and were adjusted using the 2grmadj 0 argument (see earlier) (Yang et al. 2011). Adjusted and unadjusted matrices were highly correlated, but unadjusted matrices had higher incidences of negative pivots at the regional level. In cases where both models with adjusted and unadjusted matrices were used, there was little variation in estimated variance components, again suggesting that estimates were unbiased. The significance of additive genetic variance attributed to a genomic region i was tested by comparing models with and without the Z 1 v i term using a LRT; in cases where the heritability estimate was zero (i.e., estimated as "boundary" by ASReml), significant model comparison tests were disregarded. A Bonferroni approach was used to account for multiple testing across the genome by taking the number of tests and dividing by 2 to account for overlap of the sliding windows (because each genomic region was modeled twice).
Accounting for cis and trans genetic variants associated with recombination rate: In the preceding analyses, we wished to separate potential associations with ACC due to cis effects (i.e., genetic variants that are in LD with polymorphic recombination hotspots) from those due to trans effects (i.e., genetic variants in LD with genetic variants that affect recombination rate globally). By using the total ACC within a gamete, we incorporated both cis and trans effects into a single measure. To examine trans effects only, we determined associations between each SNP and ACC minus crossovers that had occurred on the chromosome on which the SNP occurred; e.g., for a SNP on chromosome 1, association was examined with ACC summed across chromosomes 2-26. We found that in this case, examining trans variation (ACC minus focal chromosome) obtained similar results to cis and trans variation (ACC) for both regional heritability and genome-wide association analyses, leading to the same biological conclusions.
LD and imputation of genotypes in significant regions: A reference population of 189 sheep was selected and genotyped at 606,066 SNP loci on the Ovine Infinium HD SNP BeadChip for imputation of genotypes into individuals typed on the 50K chip. Briefly, the reference population was selected iteratively to maximize P m i¼1 p i using the equation where p is a vector of the proportion of genetic variation in the population captured by m selected animals, A m is the corresponding subset of a pedigree relationship matrix, and c is a vector of the mean relationship of the m selected animals [as outlined in Pausch et al. (2013) and Goddard and Hayes (2009)]. This approach should capture the maximum amount of genetic variation within the main population for the number of individuals in the reference population. SNP loci were retained if call rate . 0.95 and MAF . 0.01, and individuals were retained if more than 95% of loci were genotyped. LD between loci was calculated using Spearman's rank correlations (r 2 ) in the 188 individuals passing quality control.
Genotypes from the high-density SNP chip were imputed to individuals typed on the SNP50 chip in the chromosome 6 region significantly associated with ACC using pedigree information in the software MaCH v1.0.16 (Li et al. 2010). This region contained 10 SNPs from the Ovine SNP50 BeadChip and 116 additional independent SNPs on the high-density SNP chip. Because the software requires both parents to be known for each individual, cases where only one parent was known were scored as both parents missing. Genotypes were accepted when the dosage probability was between 0 and 0.25, 0.75 and 1.25, or 1.75 and 2 (for alternate homozygote, heterozygote, and homozygote, respectively). The accuracy of genotyping at each locus was tested using 10-fold cross-validation within the reference population: genotypes were imputed for 10% of individuals randomly sampled from the reference population using genotype data for the remaining 90%; this crossvalidation was repeated 1000 times to compare imputed genotypes with true genotypes. Cross-validation showed a relationship between number of missing genotypes and number of mismatching genotypes within individuals; therefore, individuals with ,0.99 imputed genotypes scored were removed from the analysis. Loci with ,0.95 of individuals typed also were discarded. Imputation accuracy was calculated for all loci as the proportion of imputed genotypes matching their true genotypes; all remaining loci had imputation accuracies .0.95.

Haplotype sharing of associated regions with domesticated breeds
A recent study has shown that Soay sheep are likely to have experienced an introgression event with a more modern breed (the Old Scottish Shortwool, or Dunface, breed, now extinct) approximately 150 years ago (Feulner et al. 2013). Therefore, we wished to determine whether alleles at the most highly associated imputed SNP, oar3_OAR6_116402578 (see Results), had recently introgressed into the population by examining haplotype sharing (HS) between Soay sheep and Boreray sheep, a cross between Dunface and Scottish Blackface sheep. We used data from the OvineSNP50 BeadChip for Soays and a further 2709 individuals from 73 different sheep breeds [provided by the International Sheep Genomics Consortium (ISGC)] Feulner et al. 2013) (Table  S1). In both the Soay and non-Soay data sets of the Ovine SNP50 BeadChip, we extracted 58 SNPs corresponding to 4 Mb of the subtelomeric region on chromosome 6 and phased them using Beagle v4.0 (Browning and Browning 2007). We identified core haplotypes of six SNP loci that tagged different alleles at oar3_OAR6_116402578. The length of HS between the core Soay haplotypes and the non-Soay breeds then was calculated as follows: for each core haplotype i and each sheep breed j, any haplotypes containing i were extracted, and the distance from i to the first mismatching SNP downstream of i was recorded. This was repeated for all pairwise comparisons of Soay and non-Soay haplotypes to determine a mean and SD of HS between i and breed j.

Data availability
The Supplemental Material contains information on additional analyses conducted and is referenced within the text. Table S1 contains the sex-averaged and sex-specific linkage map positions and genomic positions of SNP loci. Table S3,  Table S4, and Table S5 contain full detailed results and effect sizes of the regional heritability, genome-wide association, and imputed association studies, respectively. A Dryad repos-itory (doi: 10.5061/dryad.pf4b7) contains genomic data after quality control measures, pedigree information and subpedigree structures, autosomal GRMs, population-wide crossover probabilities, and individual recombination rate results. All scripts used for the analysis are provided at https://github. com/susjoh/GENETICS_2015_185553.

Broad-scale variation in recombination landscape
We used information from 3330 subpedigrees and data from 39,104 genome-wide SNPs typed on the Ovine SNP50 Bead-Chip (Kijas et al. 2009) to identify 98,420 meiotic crossovers in gametes transferred from 813 unique focal individuals to 3330 offspring; this included 2134 offspring from 586 unique females and 1196 offspring from 227 unique males. A linkage map of all 26 autosomes had a sex-averaged length of 3304 cM and sex-specific lengths of 3748 and 2860 cM in males and females, respectively, indicating strong male-biased recombination rates in this population (male-female linkage map lengths = 1.31) ( Figure S2 and Table S2). There was a linear relationship between the length of autosomes in megabases and linkage map lengths (adjusted R 2 = 0.991, P , 0.001; Figure 2A). Chromosomewide recombination rates (cM/Mb) were higher in smaller autosomes (fitted as a multiplicative inverse function; adjusted R 2 = 0.616, P , 0.001; Figure 2B), indicative of obligate crossing over. The degree of sex differences in recombination rate based on autosome length in centimorgans (i.e., differences in male and female recombination rates) was consistent across all autosomes (adjusted R 2 = 0.980, P , 0.001; Figure 2C).

Fine-scale variation in recombination landscape
Finer-scale probabilities of crossing over were calculated for 1-Mb windows across the genome for each sex using recombination fractions from their respective linkage maps. Crossover probability varied relative to proximity to telomeric regions, with a significant interaction between sex and distance to the nearest telomere fitted as a cubic polynomial function ( Figure 3A). Males had significantly higher probabilities of crossing over than females between distances of 0-18.11 Mb from the nearest telomere ( Figure 3B and Table S3). Increased crossover probabilities were associated with higher GC content (general linear model, P , 0.001; Table S3). Investigation of the relative distances between crossovers (in cases where two or more crossovers were observed on a single chromatid) indicated that there may be crossover interference within this population, with a median distance between double crossovers of 48 Mb ( Figure S1).

Variation in individual recombination rate
Individual ACC was heritable (h 2 = 0.145, SE = 0.027), with the remainder of the phenotypic variance being explained by the residual error term (Table 1). ACC was significantly 588 S. E. Johnston et al.
higher in males than in females, with 7.376 (SE = 0.263) more crossovers observed per gamete (animal model, Z = 28.02, P Wald , 0.001). However, females had marginally higher additive genetic variance (P LRT = 0.040) and higher residual variance (P LRT = 1.11 3 10 23 ) in ACC than males (Table 1). There was no relationship between ACC and FID age, offspring sex, and the genomic inbreeding coefficient of the FID or offspring; furthermore, there was no variance in ACC explained by common environmental effects such as FID birth year, year of gamete transmission, or maternal/paternal identities of the FID (animal models, P . 0.05). A bivariate model of male and female ACC showed that the cross-sex additive genetic correlation (r A ) was 0.826 (SE = 0.260); this correlation was significantly different from 0 (P LRT = 1.14 3 10 23 ) but not different from 1 (P LRT = 0.551).
Genetic architecture of recombination rate Genome-wide association study: The most significant association between SNP genotype and ACC in both sexes was at s74824.1 in the subtelomeric region of chromosome 6 (P = 2.92 3 10 210 ; Table 2). Sex-specific GWASs indicated that this SNP was highly associated with female ACC (P = 1.07 3 10 211 ) but was not associated with male ACC (P = 0.55; Table 2 and Figure 4); the SNP had an additive effect on female ACC, with a difference of 3.37 (SE = 0.49) autosomal crossovers per gamete between homozygotes (Table 2). This SNP was the most distal typed on the chromosome from the Ovine SNP50 BeadChip at 116.7 Mb (Figure 4 and Table 2) and corresponded to a genomic region containing RNF212 and CPLX1, two loci that have previously been implicated in recombination rate variation in humans, cattle, and mice (Kong et al. 2008(Kong et al. , 2014Sandor et al. 2012;Reynolds et al. 2013;Ma et al. 2015). A further SNP on an unmapped genomic scaffold (1.8 kb; NCBI accession no. AMGL01122442.1) also was highly associated with female ACC (Figure 4). BLAST analysis indicated that the most likely genomic position of this SNP was at 113.8 Mb on chromosome 6, corresponding to the same subtelomeric region. Two further regions on chromosome 3 were associated with ACC using the GWAS approach. A single SNP, OAR3_51273010.1, was associated with ACC in males but not in females and had an approximately dominant effect on ACC (P = 1.15 3 10 26 ; Figure 4 and Table 2). This SNP was 17.8 kb from the 39 UTR of leucine-rich repeat transmembrane neuronal 4 (LRRTM4) in an otherwise gene-poor region of the genome (i.e., the next protein-coding regions are .1 Mb from this SNP in either direction). A second SNP on chromosome 3, OAR3_87207249.1, was associated with ACC in both sexes (P = 1.95 3 10 26 ; Figure 4 and Table 2). This SNP was 137 kb from the 59 end of an ortholog of WD repeat domain 61 (WDR61) and 371 kb from the 59 end of an ortholog of ribosomal protein L10 (RPL10). Full results of GWASs are provided in Table S4.
Partitioning variance by genomic region: The contribution of specific genomic regions to ACC was determined by partitioning the additive genetic variance in sliding windows (regional heritability analysis) (Table S5). There was a strong sex-specific association of ACC in females within a subtelomeric region on chromosome 6 (20-SNP sliding window) ( Figure 5B). This corresponded to a 1.46-Mb segment containing 37 protein-coding regions, including RNF212 and CPLX1. The region explained 8.02% of the phenotypic variance (SE = 3.55%) and 46.7% of the additive genetic variance in females (P LRT = 9.78 3 10 214 ) but did not contribute to phenotypic variation in males (0.312% of phenotypic variance; SE = 1.2%, P LRT = 0.82; Figure 5C and Table S5). There was an additional significant association between ACC in both sexes and a region on chromosome 7 corresponding to  Figure 5A and Table S5); this region had not shown any significant associations using the GWAS approach alone. The region explained 4.12% of phenotypic variance (SE = 2.3%) and 26.2% of the additive genetic variance in both sexes combined; however, in sex-specific models, the significant association with ACC did not remain after correction for multiple testing (Table S5). No association was observed in the regional heritability analysis with the two regions on chromosome 3 identified using the GWAS approach. Full results for the regional heritability analysis are provided in Table S5.
Accounting for cis and trans genetic variants associated with recombination rate: The results presented earlier were ACC incorporating both cis and trans effects on recombination rate. When repeated with trans effects only, all variants associated with ACC in both the GWAS and regional heritability analyses remained significant (see Materials and Methods and Table S4 and Table S5), meaning that they are likely to affect recombination rate globally (i.e., trans-acting effects) rather than being in LD with polymorphic recombination hotspots.
Genotype imputation and association analysis at the subtelomeric region of chromosome 6: Genotyping of 187 sheep at a further 122 loci in the subtelomeric region of chromosome 6 showed that this region has elevated levels of LD, with the two most significant SNPs from the 50K chip tagging a haplotype block of 374 kB (r 2 . 0.8; File S3, Figure 6, and Table S6). This block contained three candidate genes, CPLX1, cyclin-G-associated kinase (GAK), and polycomb group ring finger 3 (PCGF3), and was 177 kb away from the candidate locus RNF212 (Kong et al. 2014). SNP genotypes were imputed for all individuals typed on the 50K chip at these 122 loci, and the association analysis was repeated. The most highly associated SNP (oar3_OAR6_116402578, P = 1.83 3 10 219 ; Table 2 and Figure 6) occurred within an intronic region of an uncharacterized protein orthologous to transmembrane emp24 protein transport domain containing TMED11, 25.2 kb from the putative location of RNF212 and 13 kb from the 39 end of spondin 2 (SPON2). A bivariate animal model including an interaction term between ACC in each sex and the genotype at oar3_OAR6_116402578 confirmed that this locus had an effect on female ACC only; this effect was additive, with a difference of 4.91 (SE = 0.203) autosomal crossovers per gamete between homozygotes ( Figure 7, Table 2, and Table S6). There was no difference in ACC between the three male genotypes. Full results for univariate models at imputed SNPs are given in Table S6.

HS of associated regions with domesticated breeds
Seven core haplotypes of six SNPs in length tagged different alleles at oar3_OAR6_116402578 at the subtelomeric region of chromosome 6. Two were perfectly associated with the A allele at oar3_OAR6_116402578 (conferring reduced ACC), and five were perfectly associated with the G allele (conferring increased ACC) ( Table S8). The extent of HS between Soays and non-Soays sheep was low, and there was no evidence of long-range HS between Soays and Boreray sheep compared with other domesticated breeds ( Figure S3). This test is not definitive owing to the relatively small size of the Boreray sample (N = 20), meaning that it is possible that either allele occurs in Boreray sheep but has not been sampled. Nevertheless, low levels of HS with other breeds throughout the sample suggest that the alleles at oar3_ OAR6_116402578 have not been introduced recently to the Soay sheep population. For example, HS of core haplotypes with Boreray sheep for coat color, coat pattern (Feulner et al. 2013), and normal horn development (Johnston et al. 2013) extended to longer distances, up to 5.7, 6.4, and 2.86 Mb, respectively. In contrast, the maximum HS observed here was 0.38 Mb. A shorter haplotype may be expected because the core haplotype occurs at the end of the chromosome, so HS is only calculated downstream of the core haplotype; however, this value is much lower than half that of previously identified introgressed haplotypes (Feulner et al. 2013). The three most common haplotypes, H2, H3, and H6 (for high, high, and low ACC, respectively), are found in many other sheep breeds across the world ( Figure S3), suggesting that both high and low ACC haplotypes are ancient across sheep breeds.

Discussion
In this study, we have shown that ACC is heritable in Soay sheep and that variation in female ACC is strongly influenced by a genomic region containing RNF212 and CPLX1, loci that have been implicated previously in recombination rate variation in other species. The narrow-sense heritability (h 2 ) was 0.15 across both sexes and was lower than estimates in some mammal species (h 2 = 0.22 and 0.46 in cattle and mice, respectively) (Dumont et al. 2009;Sandor et al. 2012) and similar to recent estimates in humans (0.13 and 0.08 in females and males, respectively) (Kong et al. 2014). ACC was 1.3 times higher in males, but females had a higher proportion of heritable variation than males (h 2 = 0.16 compared to h 2 = 0.12).
Here we discuss the genetic architecture of the trait in more detail, the observation of sexual dimorphism and male-biased recombination rates, and how our findings inform the broader topic of understanding the genetic architecture of recombination rates in mammals.

Genetic variants associated with individual recombination rate
Most of the variants associated with ACC in this study have been implicated previously in recombination rate variation in other mammal species, suggesting a shared genetic architecture across taxa. The strongest association was observed at locus RNF212, occurring 88.4 kb from an 374-kb block of high LD (r 2 . 0.8) containing three further candidate loci, CPLX1, GAK, and PCGF3 ( Figure 6). Both RNF212 and CPLX1 have been associated with recombination rate variation in mammals (Kong et al. 2008;Sandor et al. 2012;Reynolds et al. 2013;Ma et al. 2015), and mouse studies have established that the protein RNF212 is essential for the formation of crossover-specific complexes during meiosis and that its effect is dosage sensitive (Reynolds et al. 2013). We observed an additive effect of the RNF212 region on female recombination rate (Figure 7), suggesting that dosage dependence could be a plausible mechanism driving rate differences in Soay sheep. GAK forms part of a complex with cyclin G, a locus involved in meiotic recombination repair in Drosophila (Nagel et al. 2012), and PCGF3 forms part of a PRC1-like complex (polycomb repressive complex 1) that is involved in meiotic gene expression and the timing of meiotic prophase in female mice (Yokobayashi et al. 2013). High LD within this region meant that it was not possible to test the effects of these loci on recombination rate independently; however, the cosegregation of several loci affecting meiotic processes may merit further investigation to determine whether recombination is suppressed in this region and whether this cosegregation is of adaptive significance.
Additional genomic regions associated with recombination rate included two loci at 48.1 and 82.4 Mb on chromosome 3 (identified using GWAS) with effects on males only and both sexes, respectively, and a 1.09-Mb region of chromosome 7 affecting rates in both sexes (identified using regional heritability analysis). Although the chromosome 7 region was large and specific loci cannot be pinpointed, it contained REC8, which codes a protein required for the separation of sister chromatids and homologous chromosomes during meiosis (Parisi et al. 1999), and RNF212B, a paralogue of RNF212. The same region is also associated with recombination rate in cattle (Sandor et al. 2012). The chromosome 3 variants identified were novel to this study and occurred in relatively gene-poor regions of the genome (see earlier).
Although there are homologs of PRDM9 on chromosomes 1, 5, 18, and X, it is not currently known whether any of these copies are functional in sheep. Here we did not identify any association between recombination rate and any of these regions using either GWAS or regional heritability approaches. This may not be surprising because this locus is primarily associated with recombination hotspot usage. Nevertheless, PRDM9 has been associated with recombination rate in cattle and male humans (Kong et al. 2014;Ma et al. 2015) and is likely to be a consequence of differences in the abundance of motifs recognized by the PRDM9 protein in hotspots rather than the locus itself affecting rate. In this study, it was not possible to examine hotspot usage because crossovers could only be resolved to a median interval of 800 kb. This is unlikely to be of a scale fine enough to characterize hotspot variation because hotspots typically occur within 1-to 2-kb intervals in mammals (Paigen and Petkov 2010). Further studies would require higher densities of markers to determine crossover positions at a greater resolution and to determine the functionality and/or relative importance of PRDM9 within this system.

Sexual dimorphism in the genetic architecture of recombination rate
This study identified sexual dimorphism in the genetic architecture of recombination rate in Soay sheep. Using a classical quantitative genetics approach, the between-sex genetic correlation was not significantly different from 1, indicating that male and female recombination rate variation had a shared genetic basis-albeit with a relatively large error around this estimate. However, females had significantly higher additive genetic and residual variance in the trait in comparison with males, and GWAS and regional heritability analyses showed that the RNF212/CPLX1 region was associated with female recombination rate only. This is consistent with previous studies, where this region was associated with sexually dimorphic and sexually antagonistic variation in recombination rates in cattle and humans, respectively (Kong et al. 2014;Ma et al. 2015). Therefore, our findings suggest that variation in recombination rate has some degree of a shared and distinct genetic architecture between the sexes, which may be expected as a result of various similarities of this process of meiosis, but differences in its implementation within each sex (discussed further later). There were some differences in sample sizes between the sexes, with twice as many meioses characterized in females than in males, so it could be argued that low sample sizes in males may have had less power to identify specific loci. While possible, it is unlikely that the absence of associations between the RNF212/ CPLX1 region and male recombination rate is due to low power to detect the effect because (1) models including both sexes showed reduced, rather than increased, significance in this region, (2) bivariate models accounting for variation in RNF212 as a fixed effect supported a sexually dimorphic genetic effect with a lower degree of error than the bivariate approach (Figure 7), and (3) repeating the association analysis at the most highly associated SNP using sampled data sets of identical size in males and females found consistently higher association at this locus in females ( Figure S4).

How much phenotypic variation in recombination rate is explained?
The approaches used in this study were successful in characterizing several regions of the genome contributing to the additive genetic variance in recombination rate. The regional heritability approach demonstrated some potential for characterizing variation from multiple alleles and/or haplotypes encompassing both common and rare variants that are in LD with causal loci that were not detectable by GWAS alone (Nagamine et al. 2012). However, while some of the genetic contribution to phenotypic variance was explained by specific genomic regions, the overall heritability of recombination rate was low, and a substantial proportion of the heritable variation was of unknown architecture (i.e., "missing heritability") (Manolio et al. 2009). In females, 64% of additive genetic variance was explained by the RNF212/CLPX1 and RNF212B/REC8 regions combined, but this only accounted for 11% of the phenotypic variance (Table S9), leaving the remaining additive genetic and phenotypic variance unexplained. Our sample size is small relative to such studies in model systems, Results provided are from the Ovine SNP50 BeadChip and (below the line) the most highly associated imputed SNP from chromosome 6 (oar3_OAR6_116402578). Additional loci that were significantly associated with ACC and in strong LD with these hits are not shown; full GWAS results are provided in Table S5 and and there may have been reduced power to detect genetic variants, particularly in males, which were under-represented in the data set. However, our findings of low heritability and unexplained additive genetic variance are consistent with recent results from Icelandic humans, where despite a larger sample size (N = 15,253 males and 20,674 females) and greater marker density (N = 30.3 3 10 6 ), the fraction of phenotypic variance explained by specific loci remained small; identified variants including RNF212 and CPLX1 explained just 2.52 and 3.15% of male and female phenotypic variance, respectively, accounting for 29 and 24.8% of the additive genetic variance (Kong et al. 2014). Therefore, despite evidence of a conserved genetic architecture across mammal systems, a very large proportion of both the additive genetic and phenotypic variance remains unexplained.

Variation and sexual dimorphism in the recombination landscape
Males had considerably higher recombination rates than females, which was driven mainly by large differences in crossover frequencies in the subtelomeric regions between 0 and 18.11 Mb ( Figure 3); recombination was reduced in males if the centromere was present in the subtelomeric region (i.e., in autosomes 4-26, which are acrocentric) but, unlike in cattle, was still significantly higher than that in females (Ma et al. 2015) ( Figure S5). Outside the subtelomeric region, recombination rates were more similar between the sexes, with females showing slightly higher recombination rates between 18.1 and 40 Mb from the telomere ( Figure 3B). This observation of increased subtelomeric recombination in males is consistent with studies in humans, cattle, and mice (Kong et al. 2002;Shifman et al. 2006;Ma et al. 2015), although the magnitude of the difference is much greater in the Soay sheep population. Within females, the rate differences associated with different genotypes at RNF212 were most clear in regions likely to be euchromatic, whereas there was no difference in rate in regions likely to be heterochromatic, such as the subtelomeric and centromeric regions ( Figure S6 and Table S10).
Why is the recombination rate higher in males?
In placental mammals, females usually exhibit higher recombination rates than males (Lenormand and Dutheil 2005), and it has been postulated that this is a mechanism to avoid aneuploidy after long periods of meiotic arrest (Koehler et al. 1996;Morelli and Cohen 2005;Nagaoka et al. 2012). However, Soay sheep exhibited male-biased recombination rates to a greater degree than observed in any placental mammal to date The left column shows association statistics relative to genomic position; points are color-coded by chromosome. The right column shows the distribution of observed P-values against those expected from a null distribution. Association statistics were not corrected using genomic control because l was less than 1 for all GWASs (l = 0.996, 0.933, and 0.900 for plots A, B, and C, respectively). Underlying data on associations at the most highly associated SNPs, their genomic positions, and the sample sizes are given in Table S5. The significant SNP in gray at position zero in A and B occurs on an unmapped contig that is likely to correspond to the distal region of chromosome 6 (see text).
(male-female linkage map ratio = 1.31). The biological significance of this remains unclear, although a number of mechanisms have been proposed to explain variation in sex differences more generally, including haploid selection (Lenormand and Dutheil 2005), meiotic drive (Brandvain and Coop 2012), sperm competition, and sexual dimorphism and dispersal (Trivers 1988;Burt et al. 1991;Mank 2009). Nevertheless, testing these ideas has been limited by a paucity of empirical data. One possible explanation for elevated recombination in males is that Soay sheep have a highly promiscuous mating system. Males have the largest testes-to-body size ratio within ruminants ) and experience high levels of sperm competition, with dominant rams becoming sperm depleted toward the end of the annual rut (Preston et al. 2001). Increased recombination may allow more rapid sperm production through formation of meiotic bouquets (Tankimanova et al. 2004). Another argument made by Ma et al. (2015) to explain increased recombination in male cattle (male-female linkage map ratio = 1.1) is that stronger selection in males may have indirectly selected for higher recombination rates in bulls and may be a consequence of domestication (Burt and Bell 1987;Ross-Ibarra 2004). Soay sheep underwent some domestication before arriving on St. Kilda and have comparable levels of male-biased recom-bination to domestic sheep (male-female linkage map ratio = 1.19) (Maddox et al. 2001). In contrast, wild bighorn sheep (O. canadensis) have not undergone domestication and have female-biased recombination rates (male-female linkage map ratio = 0.89; divergence 2.8 million years ago) (Poissant et al. 2010). However, low marker density (N = 232 microsatellites) in the bighorn sheep study may have failed to resolve crossovers in the subtelomeric regions; furthermore, a recent study of chiasma count in wild progenitor vs. domestic mammal species found that recombination rates had not increased with domestication in sheep ( Muñoz-Fuentes et al. 2015). In addition, wild cattle and sheep may have higher levels of sperm competition than other mammal species, supporting the former argument. Regardless, more empirical studies are required to elucidate the specific drivers of sex differences in recombination rate at both a mechanistic and an interspecific level. Given our finding that the RNF212/CPLX1 region is involved in the sex differences in Soay sheep, there is a compelling case for a role for this region in driving sex differences in mammal systems over relatively short evolutionary timescales.

Examining recombination rates in the wild
A principal motivation for this study was to determine how recombination rate and its genetic architecture may vary  Table S4.
relative to model species that have undergone strong selection in their recent history. We found that the heritability of recombination rate in Soay sheep was much lower than in cattle and mice and was comparable with recent estimates in humans, which also can be considered a wild population (Kong et al. 2014). Despite these differences, variants affecting Figure 6 Associations at the subtelomeric region of chromosome 6. Local associations of female ACC with Ovine SNP50 BeadChip SNPs (black circles, middle panel) and imputed genotypes from the Ovine HD SNP BeadChip (red triangles). The top panel indicates protein-coding regions within this region, as provided by the NCBI Graphical Sequence Viewer v3.8, with genes previously implicated in recombination or meiosis given in boldface type [see introduction and Yokobayashi et al. (2013) and Kong et al. (2014)]. The dashed line in the middle panel indicates the significance threshold after multiple testing. The lower panel is a heat map of LD in this region calculated for the 188 individuals typed on the high-density SNP chip using Spearman's rank correlation r 2 created using the R library LDheatmap (Shin et al. 2006). The superimposed beige block indicates a region that is likely to be incorrectly assembled on the sheep genome assembly (Oar v3.1) based on sequence comparison with the homologous region of the cattle genome assembly (vUMD3.1) (see File S3); its position is likely to fall within the region indicated by the gray-checkered pattern to the left, leaving a large region of very high LD at the distal end of chromosome 6.
Genetic Basis of Recombination Rate recombination rate on sheep chromosomes 6 and 7 have been associated previously with recombination rates in other mammalian populations (see earlier), and only the two relatively gene-poor regions identified on chromosome 3 are novel. Furthermore, examination of haplotypes around RNF212 suggests that variation in the RNF212/CPLX1 region affecting recombination rate has been segregating for a long time in sheep. Examining variation in the wild also allowed us to quantify the effects of the individual and the environment on recombination rate; however, we found no effect of common environment (i.e., birth year and year of gamete transmission), individual age, or inbreeding on recombination rate; rather, most of the variation was attributed to residual effects. This contrasts with the observation in humans that recombination rates increase with age in females (Kong et al. 2004). Overall, our findings suggest a strong stochastic element driving recombination rates, with a small but significant heritable component that has a similar architecture to other mammal systems regardless of their selective background. The Soay sheep system is one of the most comprehensive wild data sets in terms of genomic resources and sampling density, making it one of the most suitable in terms of quantifying and analyzing recombination rate variation in the wild. A future ambition is to investigate the fitness consequences of phenotypic variation in ACC and more specifically the relationship between variants identified in this study and individual life-history variation to determine whether the maintenance of genetic variation for recombination rates is due to selection, sexually antagonistic effects, or stochastic processes.

Conclusions
In this study we have shown that recombination rates in Soay sheep are heritable and have a sexually dimorphic genetic architecture. The variants identified have been implicated in recombination rates in other mammal species, indicating a conserved genetic basis across distantly related taxa. How-ever, the proportion of phenotypic variation explained by identified variants was low; this was consistent with studies in humans and cattle, in which although genetic variants were identified, and most of both additive genetic and phenotypic variance has remained unexplained. Similar studies in both mammalian and nonmammalian wild systems may provide a broader insight into the genetic and nongenetic drivers of recombination rate variation, as well its evolution in contemporary populations. However, the question remains as to whether variation in recombination rate is adaptive or merely a by-product of other biological processes. Overall, the approaches and findings presented here provide an important foundation for studies examining the evolution of recombination rates in contemporary natural populations.

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S. E. Johnston et al. Figure S1. Histogram of the span distances (in Mb) between double crossovers on autosomal chromatids. Bar segments are color coded as double crossovers spanning a single SNP locus (blue) and those spanning more than one SNP (red). All double crossovers across a single SNP were discarded from the dataset, as they are likely to be the result of a genotyping error at that SNP. Short crossovers below a certain threshold (indicated by the solid vertical line) were also discarded (see text for rationale).   Table S8, for breeds listed in Table S1. Red and blue coloration indicates haplotypes tagging the high (G) and low (A) recombination alleles at oar3_OAR6_116402578, respectively.    Table S10.     Table S5. Full results of the regional heritability analysis of ACC for sliding window sizes of 150, 50 and 20 SNPs across all autosomes. Models were run in all sheep, and in males and females only. Type indicates whether ACC was modelled as the total number of crossovers across all autosomes ("cistrans") or the total number on all autosomes minus the number of crossovers on the focal chromosome ("trans"; see Materials and Methods). First.SNP.Pos and Last.SNP.Pos indicate the positions of the first and last SNP within the window. RestofGenome.GRM.h2 and Window.GRM.h2 are the proportions of phenotypic variance attributed to the rest of the genome and the sliding window, respectively (SE is their standard errors). ASReml.Error indicates cases where models had no errors ("none") or abnormal termination ("A.T."). Window.GRM.h2.constraint indicates cases where the estimate of heritability was positive or fixed at the boundary (i.e. not significantly different from zero). LL indicates the log likelihoods of animal models without and with the window, respectively. The χ2 and P values are from likelihood ratio tests. (.txt, 4,561 KB)

File S1 -Simulation of recombination events.
To verify the accuracy of our estimation of autosomal crossover count (ACC), we simulated meiotic crossovers within the Soay sheep pedigree using information from linkage map positions and allele frequencies, and then compared the observed and true crossover counts in simulated datasets.
Simulations were conducted using the entire Soay sheep pedigree. Each individual was assigned to an ordered cohort using the kindepth function in the package kinship2 v1.6.0 (Therneau et al. 2014) implemented in R v3.1.1. For all pedigree links where a parent was unknown (i.e. founder individuals), haplotypes were simulated for each chromosome, where each SNP allele was sampled with a probability equal to its minor allele frequency across the entire genomic dataset. In order to simulate recombination events in transmitted haplotypes, we used the following approach sequentially across each ordered cohort.
Positions of meiotic crossovers were determined by sampling the likelihood of a crossover between each pair of adjacent markers with probability r, where r was the sex-specific recombination fraction determined from the linkage map. As cross-over interference was apparent in the main analysis, positions were re-sampled in cases where two crossover events occurred within 10cM of each other. Recombinant haplotypes were constructed based on the simulated crossover positions between the two haplotypes within the parent, and one recombinant haplotype was sampled with a probability of 0.5 and transmitted to the offspring. The positions and counts of crossovers per chromosome were recorded. Each haplotype pair was then condensed into an unphased SNP genotype dataset. Missing genotypes and genotype errors were assigned to genotypes at random, with probabilities of 1×10 -3 and 1×10 -4 , respectively. An R function for this process has been archived at http://github.com/susjoh/simperSNP. Individual ACCs were then calculated in FIDs in each simulated dataset as using the same analysis outlined in the methods section "Estimation of meiotic crossovers".
Our approach was highly accurate in identifying the true simulated crossover count across all individuals (linear regression of observed counts as a function of true simulated counts, ̅ = 1.014 ± 1.51 × 10 -3 (s.d.), mean adjusted r 2 = 0.991 ± 6.7 × 10 -4 ). The per-individual correlations across all simulations were also high ( ̅ = 0.992 ± 0.013, mean adjusted r 2 = 0.99 ± 0.011). A general linear model of per individual mean adjusted r 2 was fitted, including sex and genomic inbreeding coefficient ̂ as fixed effects. Adjusted r 2 values and slopes were significantly higher in females than in males (P < 0.001, Table 1, Figure 1); This may be due to increased crossover rates in males resulting in some crossovers not being identified; the removal of single SNP runs may also have more acute effects at telomeric regions of chromosomes, where crossovers may be more likely to occur in males. Adjusted R 2 values and slopes were also negatively correlated with the genomic inbreeding coefficient ̂ (P < 0.001, Table 1, Figure 1), which may be due to an increased chance of runs of homozygous genotypes, meaning that substantial regions of the genome cannot be assigned to a particular grandparent of origin. Double crossovers occurring within such regions are therefore less likely to be identified. In both cases, slopes are lower than 1, indicating that crossover counts are consistently under-estimated, albeit to a small degree, in males and/or in more inbred individuals (Table 1).

References
Therneau T., Atkinson E., Sinnwell J., Schaid D., McDonnell S., 2014 kinship2 v1.6.0.  The locus RNF212 has not been annotated on the domestic sheep genome (Oar_v3.1). Here, we present evidence that RNF212 occurs within the region most highly associated with autosomal crossover count (ACC). Sheep sequences for RNF212 were obtained from Genbank (Accession Numbers provided in Figure 1 and aligned against the Oar_v3.1 genome sequence using BLAST v2.2.27+ using the default parameters and a word size of 15 to determine if the locus was likely to be present within this region. Matches of length < 50 bp and matching bases of < 95% were discarded .The strongest associations on the assembled genome sequence were at the sub-telomeric region of chromosome 6 identified in the main results, falling between positions 116,427,802 and 116,446,904 ( Figure 1). This positioned RNF212 between an uncharacterised protein (orthologous to Tmed11) and FGFRL1, and suggested that its lack of annotation on the domestic sheep genome is due to its occurrence across a gap in contiguous sequences ( Figure 2). Gene order in this region showed high similarity to gene orders obtained for homologous genome regions in cow (UMD3.1), dog (CanFam3.1), human (GRCh38) and mouse (GRCm38); all annotations were obtained from Ensembl build v1.79 (Cunningham et al. 2014). The alignment of RNF212 shown in Figure 5 (main text) and Figure 2 is to sequence XM_012167676.1.