Abstract
Characterizing variation in the rate of recombination across the genome is important for understanding many evolutionary processes. The landscape of recombination has been studied previously in the house mouse, Mus musculus, and it is known that the different subspecies exhibit different suites of recombination hotspots. However, it is not established whether broad-scale variation in the rate of recombination is conserved between the subspecies. In this study, we construct a fine-scale recombination map for the Eastern house mouse subspecies, M. m. castaneus, using 10 individuals sampled from its ancestral range. After inferring phase, we use LDhelmet to construct recombination maps for each autosome. We find that the spatial distribution of recombination rate is strongly positively between our castaneus map and a map constructed using inbred lines of mice derived predominantly from M. m. domesticus. We also find that levels of genetic diversity in M. m. castaneus are positively correlated with the rate of recombination, consistent with pervasive natural selection acting in the genome. Our study suggests that recombination rate variation is conserved at broad scales between M. musculus subspecies.
Introduction
In many species, rates of crossing-over are not uniformly distributed across chromosomes, and understanding this variation and its causes is important for many aspects of molecular evolution. Experiments in laboratory strains or managed populations examining the inheritance of markers through pedigrees have allowed direct estimation of rates of crossing over in different regions of the genome. Studies of this kind are impractical for many wild populations, where pedigree structures are largely unknown (but see Johnston et al. 2016). In mice, there have been multiple genetic maps published (e.g. Jensen-Seaman et al. 2004; Paigen et al. 2008; Cox et al. 2009; Liu et al. 2014), typically using the classical inbred laboratory strains, which are predominantly derived from the Western European house mouse subspecies, Mus musculus domesticus (Yang et al. 2011). Recombination rate variation in laboratory strains may not, therefore, reflect natural rates and patterns in wild mice of different subspecies. In addition, recombination rate modifiers may have become fixed in the process of laboratory strain management. On the other hand, directly estimating recombination rates in wild house mice is not feasible without both a population’s pedigree and many genotyped individuals (but see Wang et al. 2017).
To understand variation in recombination rates, patterns of linkage disequilibrium (LD) in a sample of individuals drawn from a population can be used. Coalescent-based methods have been developed that use such data to indirectly estimate recombination rates at very fine scales (Hudson 2001; Mcvean et al. 2002; Mcvean et al. 2004; Auton and Mcvean 2007; Chan et al. 2012). The recombination rates estimated in this way reflect variation in crossing over rates in populations ancestral to the extant population, and are averages between the sexes. Methods using LD have been applied to explore variation in recombination rates among mammals and other eukaryotes, and have demonstrated that recombination hotspots are associated with specific genomic features (Myers et al. 2010; Paigen and Petkov 2010; Singhal et al. 2015).
The underlying mechanisms explaining the locations of recombination events have been the focus of much research. In house mice and in most other mammals, the PRDM9 zinc-finger protein binds to specific DNA motifs, resulting in an increased probability of double-strand breaks, which can then be resolved by reciprocal crossing-over (Grey et al. 2011; Baudat et al. 2013). Accordingly, it has been shown that recombination hotspots are enriched for PRDM9 binding sites (Myers et al. 2010; Brunschwig et al. 2012). PRDM9-knockout mice still exhibit hotspots, but in dramatically different genomic regions (Brick et al. 2012). Variation in PRDM9, specifically in the exon encoding the zinc-finger array, results in different binding motifs (Baudat et al. 2010). Davies et al. (2016) generated a line of mice in which the exon encoding the portion of the PRDM9 protein specifying the DNA binding motif was replaced with the orthologous human sequence. The recombination hotspots they observed in this ‘humanized’ line of mice were enriched for the PRDM9 binding motif observed in humans.
Great ape species have different alleles of the PRDM9 gene (Schwartz et al. 2014) and relatively little hotspot sharing (Winckler et al. 2005; Stevison et al. 2015). Correlations between the broad-scale recombination landscapes of the great apes are, however, relatively strongly positive (Stevison et al. 2011; Stevison et al. 2015). This suggests that, while hotspots evolve rapidly, the overall genetic map changes more slowly. Indeed, multiple closely related species pairs with different hotspot locations show correlations between recombination rates at broad scales (Smukowski and Noor 2011), as do species that share hotspots or lack them altogether (Singhal et al. 2015; Smukowski Heil et al. 2015).
It has been suggested that a population ancestral to the M. musculus species complex began to split into the present day subspecies around 500,000 years ago (Geraldes et al. 2008). In this time, functionally distinct alleles of the PRDM9 gene and different suites of hotspots have evolved in the subspecies (Smagulova et al. 2016). In addition, between members of the M. musculus subspecies complex, there is also variation in recombination rates at relatively broad scales for multiple regions of the genome (Dumont et al. 2011), and there is genetic variation in recombination rate is polymorphic between M. m. domesticus individuals (Wang et al. 2017). Brunschwig et al. (2012) analyzed single nucleotide polymorphism (SNP) data for classical laboratory strains of mice, and used an LD-based approach to estimate the sex-averaged recombination landscape for the 19 mouse autosomes. The recombination rate map they constructed is similar to a genetic map generated using crosses by Cox et al. (2009). Both studies were conducted using the classical inbred lines (whose ancestry is largely M. m. domesticus), and their estimated recombination rate landscapes may therefore reflect that of M. m. domesticus more than other members of the M. musculus species complex.
In this study, we construct a recombination map for the house mouse subspecies M. m. castaneus. We used the genome sequences of 10 wild-caught individuals of M. m. castaneus from the species’ expected ancestral range, originally reported by Halligan et al. (2013). In our analysis, we first phased SNPs and estimated rates of error in phasing. Secondly, we simulated data to assess the power of estimating recombination rates based on 10 individuals and the extent by which phase errors lead to biased estimates of the rate of recombination. Finally, using an LD-based approach, we inferred a sex-averaged map of recombination rates and compared this to previously published genetic maps for M. musculus. We show that variation in recombination rates in M. m. castaneus is very similar to rate variation estimated in the classical inbred strains. This suggests that, at broad scales, recombination rates have been relatively highly conserved since the subspecies began to diverge.
Materials and Methods
Polymorphism data for Mus musculus castaneus
We analyzed the genomes of 10 wild-caught M. m. castaneus individuals sequenced by Halligan et al. (2013). Samples were from North-West India, a region that is believed to be within the ancestral range of the house mouse. Mice from this region have among the highest levels of genetic diversity among the M. musculus subspecies (Baines and Harr 2007). In addition, the individuals sequenced represent a single population cluster and showed little evidence for substantial inbreeding (Halligan et al. 2010). Halligan et al. (2013) sequenced individual genomes to high coverage using multiple libraries of Illumina paired-end reads, which were mapped to the mm9 reference genome using BWA (Li and Durbin 2009). Mean coverage was >20x and the proportion of the genome with >10x coverage was more than 80% for all individuals sampled (Halligan et al. 2013). Variants were called with the Samtools mpileup function (Li et al. 2009) using an allele frequency spectrum (AFS) prior. The AFS was obtained by iteratively calling variants until the spectrum converged. After the first iteration, all SNPs at frequencies >0.5 were swapped into the mm9 genome to construct a reference genome for M. m. castaneus, which was used for subsequent variant calling (for further details see Halligan et al. 2013). The variant call format files generated by Halligan et al. (2013) were used in this study. In addition, alignments of Mus famulus and Rattus norvegicus to the mm9 genome, also generated by Halligan et al. (2013), were used as outgroups.
For the purposes of estimating recombination rates, variable sites were filtered on the basis of several conditions: Insertion/deletion polymorphisms were excluded, because the method used to phase variants (seebelow) cannot process these sites. We also excluded sites with more than two alleles and those that failed the Samtools Hardy-Weinberg equilibrium test (p < 0.002).
Inferring phase and estimating switch error rates
LDhelmet estimates recombination rates from a sample of phased chromosomes or haplotypes drawn from a population. To estimate haplotypes, heterozygous SNPs called in M. m. castaneus were phased using read-aware phasing in ShapeIt2 (Delaneau et al. 2013). ShapeIt2 uses sequencing reads that span multiple heterozygous variants, phase-informative reads (PIRs), and LD to phase variants at the level of whole chromosomes. Incorrectly phased heterozygous SNPs, termed switch errors, may upwardly bias estimates of the recombination rate, because they appear identical to legitimate crossing over events. To assess the impact of incorrect phasing on our recombination rate inferences, we quantified the switch error rate as follows. The population sample of M. m. castaneus comprised of seven females and three males. The X-chromosome variants in males therefore represent perfectly phased haplotypes. We merged the BAM alignments of short reads for the X-chromosome of the three males (samples H12, H28 and H34 from Halligan et al. (2013)) to make three datasets of pseudo-females, which are female-like, but in which the true haplotypes are known (H12+H28 = H40; H12+H34 = H46; H28 + H34 = H62). We then jointly re-called variants in the seven female samples plus the three pseudo-females using an identical pipeline as used by Halligan et al. (2013), as outlined above, using the same AFS prior.
Switch error rates in Shapeit2 are sensitive both to coverage and quality (per genotype and per variant) (Delaneau et al. 2013). We explored the effects of different filter parameters on the switch error rates produced by ShapeIt2 using the X-chromosomes of the pseudo-females. We filtered SNPs based on combinations of variant and genotype quality scores (QUAL and GQ, respectively) and on an individual’s sequencing depth (DP) (Table S1). For the individual-specific statistics (DP and GQ), if a single individual failed a particular filter, then that SNP was not included in further analyses. By comparing the known X-chromosome haplotypes and those inferred by ShapeIt2, we calculated switch error rates as the ratio of incorrectly resolved heterozygous SNPs to the total number of heterozygous SNPs for each pseudo-female individual. We used these results to choose filter parameters to apply to the autosomal data that generated a low switch error rate in ShapeIt2, while maintaining a high number of heterozygous SNPs. We obtained 20 phased haplotypes for each of the 19 mouse autosomes. With these, we estimated the recombination rate landscape for M. m. castaneus.
Estimating recombination maps and validation of the approach
LDhelmet (v1.7;Chan et al. 2012) generates a sex-averaged map of recombination rates from a sample of haplotypes that are assumed to be drawn from a randomly mating population. Briefly, LDhelmet examines patterns of LD in a sample of phased chromosomal regions and uses a composite likelihood approach to infer recombination rates that are best supported between adjacent SNPs. LDhelmet appears to perform well for species with large effective population size (Ne) and has been shown to be robust to the effects of selective sweeps, which may be prevalent and reduce diversity in and around functional elements of the M. m. castaneus genome (Halligan et al. 2013). However, the analyses conducted by Chan et al. (2012), in which the software was tested, were performed with a larger number of haplotypes than we have in our sample. To assess whether our smaller sample size gives reliable recombination maps, we validated and parameterized LDhelmet using simulated datasets.
A key parameter in LDhelmet is the block penalty, which determines the extent by which likelihood is penalized by spatial variation in the recombination rate, such that a high block penalty results in a smoother recombination map. We performed simulations to determine the block penalty that leads to the most accurate estimates of the recombination rate in chromosomes that have levels of diversity and base content similar to M. m. castaneus. Chromosomes with constant values of ρ (4Ner) ranging from 2 × 10-6 to 2 × 101 were simulated in SLiM v1.8 (Messer 2013). For each value of ρ, 0.5Mbp of neutrally evolving sequence was simulated for populations of N = 1,000 diploid individuals. Mutation rates in the simulations were set using the compound parameter θ = 4Ne μ, where μ is the per-base, per-generation mutation rate. The mutation and recombination rates of the simulations were scaled to θ/4Ν and ρ/4N, respectively. θ was set to 0.01 for all simulations, as this is close to the genome-wide average for our data, based on pairwise differences. Simulations were run for 10,000 generations to achieve equilibrium levels of polymorphism, at which time 10 diploid individuals were sampled from the population. Each simulation was repeated 20 times, resulting in 10Mbp of sequence for each value of ρ. The SLiM output files were converted to sequence data, suitable for analysis by LDhelmet, using a custom Python script that incorporated the mutation rate matrix estimated for non-CpG prone sites in M. m. castaneus (see below). We inferred recombination rates from the simulated data in windows of 4,400 SNPs with a 200 SNP overlap between windows, following (Chan et al. 2012). We analyzed the simulated data using LDhelmet with block penalties of 10, 25, 50 and 100. The default parameters of LDhelmet are tuned to analyze Drosophila melanogaster data (Chan et al. 2012). Since the D. melanogaster population studied by Chan et al. (2012) has comparable levels of genetic diversity to M. m. castaneus we used the defaults for all other parameters, other than the block penalty and estimate of θ.
Errors in phase inference, discussed above, may bias our estimates of the recombination rate, since they appear to break apart patterns of LD. We assessed the impact of these errors on recombination rate inference by incorporating them into the simulated data at a rate estimated from the pseudo-female individuals. For each of the 10 individuals drawn from the simulated populations, switch errors were randomly introduced at heterozygous positions at the rate estimated using the chosen SNP filter set (see Results). We then inferred the recombination rates, as above, for the simulated population using these error-prone data. We assessed the effect of switch errors on recombination rate inference by comparing estimates based on the simulated data both with and without switch errors. It is worth noting that there is the potential for switch errors to undo crossing-over events, reducing inferred recombination rates, if they affect heterozygous SNPs that are breakpoints of recombinant regions.
Recombination rate estimation for M. m. castaneus
We used LDhelmet (Chan et al. 2012), to estimate recombination rates for each of the M. m. castaneus autosomes. It is well established that autosomal recombination rates differ between the sexes in M musculus (Cox et al. 2009; Liu et al. 2014). A drawback of LD-based approaches is that they give sex-averaged recombination rates.
We used both M. famulus and R. norvegicus as outgroups to assign ancestral alleles to polymorphic sites. LDhelmet incorporates both the mutation matrix and a prior probability on the ancestral allele at each variable position as parameters in the model. We obtained these parameters as follows. For non-CpG prone polymorphic sites, if the outgroups shared the same allele, we assigned that allele as ancestral and these sites were then used to populate the mutation matrix, following Chan et al. (2012). This approach ignores the possibility of both back mutation and homoplasy. To account for this uncertainty, LDhelmet incorporates a prior probability on the ancestral base. Following Singhal et al. (2015), at resolvable sites (i.e. when both outgroups agreed), the ancestral base was given a prior probability of 0.91, with 0.03 assigned to each of the three remaining bases. This was done to provide high confidence in the ancestral allele, but to also include the possibility of ancestral allele misinference. At unresolved sites (i.e., if the outgroup alleles did not agree or there were alignment gaps in either outgroup), we used the stationary distribution of allele frequencies from the mutation rate matrix as the prior (Table S2).
We analyzed a total of 43,366,235 SNPs in LDhelmet to construct recombination maps for each of the M. m. castaneus autosomes. Following Chan et al. (2012), windows of 4,400 SNPs, overlapping by 200 SNPs on either side, were analysed. We ran LDhelmet with a block penalty of 100 for a total of 1,000,000 iterations, discarding the first 100,000 as burn-in. The block penalty value was chosen to obtain a conservatively estimated recombination map, on the basis of the simulation analysis. We analyzed all sites that passed the filters chosen using the pseudo-female phasing regardless of CpG status; note that excluding CpG-prone sites removes ~50% of the available data and thus would substantially reduce the power to infer recombination rates. We assumed θ = 0.01, the approximate genome-wide level of neutral diversity in M. m. castaneus, and included ancestral allele priors and the mutation rate matrix for non-CpG sites as parameters in the model. Following the analyses, we removed overlapping SNPs and concatenated SNP windows to obtain recombination maps for whole chromosomes.
It is worthwhile noting that our map was constructed with genotype calls made using the mm9 version of the mouse reference genome. This version was released in 2007 and there have been subsequent versions released since then. However, previously published genetic maps for M. musculus were constructed using mm9, so we used that reference to make comparisons (see below).
Comparison to previously published maps
The recombination rate map inferred for M. m. castaneus was compared with two previously published genetic maps for M. musculus. The first map was generated by analyzing the inheritance patterns of markers in crosses between inbred lines (Cox et al. 2009)(downloaded from http://cgd.jax.org/mousemapconverter/). Hereafter, this map shall be referred to as the Cox map. The second map was generated by Brunschwig et al. (2012), by analyzing SNPs in a large number of inbred mouse lines using LDhat (Auton and Mcvean 2007), the software upon which LDhelmet is based (available at http://www.genetics.org/content/early/2012/05/04/genetics.112.141036). Hereafter, this map shall be referred to as the Brunschwig map. Both maps were generated using classical strains of laboratory mice, which are predominantly of M. m. domesticus origin (Yang et al. 2011). Both the Brunschwig and Cox maps were constructed using far fewer markers than the present study, ~250,000 and ~10,000 SNPs, respectively.
Recombination rates in the Brunschwig map and our castaneus map were inferred in terms of the population recombination rate (ρ = 4Ner), units that are not directly convertible to centimorgans (cM), but were converted to cM/Mb for comparison purposes using frequency weighted means, as follows. Both LDhat and LDhelmet give estimates of ρ (per Kbp and bp, respectively) between pairs of adjacent SNPs. To account for differences in the physical distance between adjacent SNPs when calculating cumulative ρ, we used the number of bases between a pair of SNPs to weight that pair’s contribution to the sum. By setting the total map distance for each chromosome to be equal to those found by Cox et al. (2009), we scaled the cumulative ρ at each analyzed SNP position to cM values.
At the level of whole chromosomes, we compared mean recombination rates from the castaneus map with several previously published maps. The frequency-weighted mean recombination rates (in terms of ρ) for each of the autosomes from the castaneus and Brunschwig maps were compared with the cM/Mb values obtained by Cox et al. (2009) as well as independent estimates of the per chromosome recombination rates from Jensen-Seaman et al. (2004). Pearson correlations were calculated for each comparison. Population structure in the inbred line data analyzed by Brunschwig et al. (2012) may have elevated LD, thus downwardly biasing estimates of ρ. To investigate this, we divided the frequency-weighted mean recombination rates per chromosome from the castaneus and Brunschwig maps by the rates given in Cox et al. (2009) to obtain estimates of effective population size.
At a finer scale, we compared variation in recombination rates across the autosomes in the different maps using windows. We calculated Pearson correlations between the frequency weighted-mean recombination rates (in cM/Mb) in non-overlapping windows for the castaneus, Cox and Brunschwig maps. The window size considered may affect the correlation between maps, so we calculate Pearson correlations in windows of 1Mbp to 20Mbp in size. For visual comparison of the castaneus and Cox maps, we plotted recombination rates in sliding windows of 10Mbp, offset by 1Mb.
Examining the correlation between nucleotide diversity and recombination rate
There is evidence that natural selection is pervasive in the protein-coding genes and conserved non-coding elements in the murid genome (Halligan et al. 2010; Halligan et al. 2011; Halligan et al. 2013). Directional selection acting on selected sites within exons may reduce diversity at linked neutral sites through the processes of background selection and/or selective sweeps. These processes have the largest effect in regions of low recombination, and can therefore generate positive correlations between diversity and the recombination rate, as has been observed in multiple species (Cutter and Payseur 2013). We used our castaneus map to examine the relationship between nucleotide diversity and recombination rates as follows. We obtained the coordinates of the canonical spliceforms of protein coding genes, orthologous between mouse and rat from Ensembl Biomart (Ensembl Database 67; http://www.ensembl.org/info/website/archives/index.html). We calculated the frequency-weighted mean recombination rate and the GC content for each gene. Using the approximate castaneus reference, described above, and the outgroup alignment, we obtained the locations of 4-fold degenerate synonymous sites. If a site was annotated as 4-fold in all three species considered, it was used for further analysis. We removed poor quality alignments between mouse and rat, exhibiting a spurious excess of diverged sites, where >80% of sites were missing. We also excluded five genes that were diverged at all non-CpG prone 4-fold sites, as it is likely that these also represent incorrect alignments. After filtering, there were a total of 18,171 protein-coding genes for analysis.
We examined the correlation between local recombination rates in protein coding genes with nucleotide diversity and divergence. Variation in the mutation rate across the genome may influence genome-wide analyses of nucleotide polymorphism, so we also examined the correlation between the ratio of nucleotide diversity and divergence from R. norvegicus at neutral sites and the rate of recombination. We used non-parametric Kendall rank correlations for all comparisons.
All analyses were conducted using custom Python scripts, except correlation analyses which were conducted using R (R Core Team 2016).
Results
Phasing SNPs and estimating the switch error rate
In order to infer recombination rates from our sample of individuals, we required phased SNPs. Taking advantage of the high sequencing depth of the sample, we phased SNPs using ShapeIt2, an approach that makes use of both LD and sequencing reads to resolve haplotypes. We phased each of the mouse autosomes, giving a total of 43,366,235 SNPs for estimation of recombination rates.
By constructing pseudo-female individuals, we quantified the switch error rate incurred when inferring phase from our data. After filtering of variants, ShapeIt2 achieved low switch error rates for all parameter combinations tested (Table S1). We chose a set of filters (GQ > 15, QUAL > 30) that resulted in a mean switch error rates across the three pseudo-females of 0.46% (Table S1). More stringent filtering resulted in slightly lower mean switch error rates, but also resulted in the removal of many more variants from the dataset (Table S1), thus reducing power to resolve recombination rates in downstream analyses.
Simulations to validate LDhelmet for the population sample ofM. m. castaneus
We assessed the performance of LDhelmet when applied to our dataset by simulation. In the absence of switch errors, LDhelmet accurately infers the average recombination rate down to values of ρ/bp = 2×10-4 (Figure 1). Below this value, LDhelmet overestimated the scaled recombination rate for the simulated populations (Figure 1). With switch errors incorporated into simulated data, LDhelmet accurately estimated ρ/bp in the range 2×10-3 to 2×102. When the true ρ/bp was <2×10-3, however, LDhelmet overestimated the mean recombination rate for 0.5Mbp regions (Figure 1). This behavior was consistent for all block penalties tested (Figure S1). Given that the simulations incorporated the mutation rate matrix (Table S2) and mutation rate (θ = 4Νe μ) estimated for M. m. castaneus we concluded that LDhelmet is applicable to the dataset of 10 M. m. castaneus individuals sequenced by Halligan et al. (2013).
The effect of switch errors on the mean recombination rate inferred using LDhelmet with a block penalty of 100. Each black point represents results for a window of 4,000 SNPs, with 200 SNPs overlapping between adjacent windows, using sequences simulated in SLiM for a constant value of ρ/bp. Red points are mean values. Switch errors were randomly incorporated at heterozygous SNPs with probability 0.0046. The dotted line shows the value for inferred=true.
Recombination rates across the M. m. castaneus autosomes
A recombination rate map for each M. m. castaneus autosome was constructed using LDhelmet. We analyzed a total of 43,366,235 phased SNPs across the 19 mouse autosomes. The frequency weighted mean value of ρ/bp for all autosomes was 0.009. This value is greater than the lower detection limit suggested by both the simulations with and without switch errors (Figure 1).
We assessed variation in whole-chromosome recombination rates between our LD-based castaneus map and direct estimates of recombination rates published in earlier studies. Comparing the mean recombination rates for whole chromosomes provides us with a baseline comparison for which we have an a priori expectation: we expect that chromosome 19, the shortest in physical length, should have the highest mean recombination rate, since at least one crossing over event is required per meiosis per chromosome in mice. This has been demonstrated in previous studies of recombination in M. musculus (Jensen-Seaman et al. 2004; Cox et al. 2009). Indeed, we find that the frequency-weighted mean recombination rate for chromosome 19 is the highest among the autosomes (Table 1). We also found that the frequency-weighted mean recombination rates for each of the autosomes were highly correlated with the direct estimates given in Jensen-Seaman et al. (2004) (Pearson correlation = 0.66, p = 0.002) and Cox et al. (2009) (Pearson correlation = 0.88, p < 0.0001), suggesting that our analysis captures real variation in recombination rates at the scale of whole chromosomes in the M. m. castaneus genome.
Summary of sex-averaged recombination rates estimated for the M. m castaneus autosomes compared with the rates from Brunschwig et al. (2012) and Cox et al. (2009). Rates for the castaneus and Brunschwig maps are presented in terms of 4Ner/bp. Estimates of Ne were obtained by assuming the recombination rates from Cox et al. (2009).
Comparison of the M. m. castaneus map to maps constructed using inbred lines
We compared the intra-chromosomal variation in recombination rates between our castaneus map and previously published maps. Figure 2 shows the variation in recombination rates across the largest and smallest autosomes in the mouse genome, chromosomes 1 and 19, respectively. It is clear that the castaneus and Cox maps are very similar (see also Figure S2 showing a comparison of all autosomes). Correlation coefficients between the maps are >0.8 for window sizes of 8Mbp and above (Figure 3). Although the overall correlation between the castaneus and Cox maps is high (Figure 3), there were several regions of the genome that substantially differ, for example in the centre of chromosome 9 (Figure S2). The Cox and castaneus maps are more similar to one another than either are to the Brunschwig map (Figure 3), presumably because the Brunschwig map was constructed with a sample of 60 inbred mouse strains. Population structure in the lines or the subspecies from which they were derived would elevate LD, resulting in downwardly-biased chromosome-wide values of ρ. This is also reflected in the Ne values estimated from the frequency-weighted average recombination rates for each chromosome. The estimates of Ne are substantially different between the castaneus and Brunschwig maps, i.e. the castaneus estimates are consistently ~500x higher (Table 1). The estimates of Ne from the castaneus map are in broad agreement with the estimates of Ne based on polymorphism data (Geraldes et al. 2008).
Comparison of the sex-averaged recombination rate inferred for chromosomes 1 and 19 of M. musculus castaneus using LDhelmet in red and those estimated from the pedigree-based study of Cox et al. (2009) in blue. Recombination rates in units of cM/Mb for the castaneus map were obtained by setting the total genetic lengths for each chromosome to the corresponding lengths from Cox et al. (2009).
Pearson correlation coefficients between the recombination map inferred for M. m. castaneus, the Brunschwig et al. (2012) map and the Cox et al. (2009) map. Correlations were calculated in non-overlapping windows of varying size across all autosomes. Confidence intervals (95%) are indicated by shading around each line.
Correlations between recombination rate and properties of protein codinggenes in M. m. castaneus
By examining the correlation between genetic diversity and recombination rate, we determined whether our map captures variation in Ne across the genome. We found that recombination rates at protein coding genes are significantly and positively correlated with levels of neutral genetic diversity (Table 2), at all sites regardless of base context and at non-CpG-prone sites only (Table 2). Divergence from the rat at 4-fold sites was also significantly and positively correlated with recombination rate when analyzing all sites. However, for non-CpG-prone sites we found a small negative correlation (Table 2). There was also a significant and positive relationship between recombination rate and a gene’s GC content (τ = 0.125, p < 2.2×10-16). The correlation between recombination rate and neutral diversity divided by divergence from the rat was both positive and significant, regardless of base context (Table 2; Figure S3). This indicates that natural selection may have a role in reducing diversity via hitchhiking and/or background selection.
Correlation coefficients between recombination rate and pairwise nucleotide diversity and divergence from the rat at 4-fold degenerate sites for protein coding genes. Non-parametric Kendall correlations were calculated for non-CpG prone sites and for all sites, regardless of base context. All coefficients shown are highly significant (p < 10-10).
Discussion
By constructing fine-scale maps of the recombination rate for the autosomes of M. m. castaneus, we have shown that there is a high degree of similarity between the recombination landscape for wild-caught mice and their laboratory counterparts. Our map captures variation in the recombination rate, similar to that observed in a more traditional linkage map, at the level of both whole chromosomes and genomic windows of varying size.
Recombination landscapes inferred using coalescent approaches, as in this study, reflect ancestral variation in recombination rates. We show that this ancestral variation is highly correlated with contemporaneous recombination rates in inbred mice of a different subspecies, suggesting that the broad-scale variation in recombination rate has not evolved dramatically since the subspecies diverged around 500,000 years ago (Geraldes et al. 2008). At a finer scale, however, Smagulova et al. (2016) showed that there is considerable variation in the locations of recombination hotspots between the M. musculus subspecies. Their findings, taken together with ours, parallel results in hominids and the great-apes, which suggest that, although the locations of recombination hotspots are strongly diverged between species, broad-scale patterns of recombination rate are relatively conserved (Lesecque et al. 2014; Stevison et al. 2015). However, there do seem to be multiple regions of the genome that distinguish M. m. castaneus and M. m. domesticus. For example, we observe peaks in recombination rate for M. m. castaneus on chromosomes 4, 5, 14 and 15 that are not present in the Cox map (Figure S2). These results are seemingly consistent with those of Dumont et al. (2011), who found that there are significant differences in genetic length between M. m. castaneus and M. m. musculus (when crossed to M. m. domesticus) in multiple regions of the genome (though a large proportion of the differences they detected were on the X-chromosome, which was not analyzed in our study). Performing a comparative analysis of recombination rates in the different subspecies of house mice, as well as sister species, using LD-based methods would help elucidate the time-scale of recombination rate evolution in wild mice.
The castaneus map constructed in this study appears to be more similar to the Cox map than the Brunschwig map (Figure 3). There are number of potential reasons for this. Firstly, we used a much larger number of markers to resolve recombination rates than Brunschwig et al. (2012), giving us more power to capture variation in the recombination rate. Secondly, it seems probable that population structure within and between the inbred and wild-derived lines studied by Brunschwig et al. (2012) could have resulted in biased estimates of the recombination rate. By dividing the mean estimated ρ/bp values (inferred using LDhelmet) for each chromosome by the corresponding recombination rate estimated from crosses (Cox et al. 2009), we showed that Ne estimates from the Brunschwig map are much lower than estimates based on our map (Table 1). This is consistent with the presence of elevated LD between the SNPs in the inbred lines analyzed by Brunschwig et al. (2012). It should be noted, however, that the estimates of Ne will be biased, as θ = 4Νe μ is a parameter in both LDhat and LDhelmet. In spite of this potential bias, the differences in Ne estimated from the Brunschwig and castaneus maps shown in Table 1 are striking, given that the ancestral effective population sizes of M. m. domesticus and M. m. castaneus are expected to be ~150,000 and ~350,000, respectively (Geraldes et al. 2008). The Brunschwig map does, however, capture true variation in recombination rates, because their map is also highly correlated with the Cox map (Pearson correlation >0.6) for all genomic windows wider than 8Mbp (Figure 3). Indeed, Brunschwig et al. (2012) showed by simulation that hotspots are detectable by analysis of inbred lines and validated their inferred hotspots against the locations of those observed in crosses among classical strains of M. m. domesticus (Smagulova et al. 2011). This suggests, that while estimates of the recombination rate in the Brunschwig et al. (2012) map may have been downwardly biased by population structure, variation in the rate and locations of hotspots were still accurately detected in their study.
We obtained an estimate of the switch error rate, taking advantage of the hemizygous sex chromosomes of males present in our sample. This allowed us to assess the extent by which switch errors affected our ability to infer recombination rates in M. m. castaneus. It should be noted, however, that our inferred switch error rate may not fully represent that of the autosomes. This is because multiple factors influence the ability to phase variants using ShapeIt2 (i.e. LD, SNP density, sample size, depth of coverage and read length) and some of these factors differ between the X-chromosome and the autosomes. Firstly, as the sex-averaged recombination rate for the X-chromosome is expected to be 3/4 that of the autosomes, it likely has elevated LD, and thus there will be higher power to infer phase. In contrast, the level of X-linked nucleotide diversity in M. m. castaneus is approximately one half that of the autosomes (Kousathanas et al. 2014), and thus there would be a higher probability of phase informative reads on the autosomes. While it is difficult to assess whether the switch error rates we estimated from the X-chromosome analysis will be the same as on the autosomes, the analysis allowed us to explore the effects of different SNP filters on the error rate.
By simulating the effect of switch errors on estimates of the recombination rate, we inferred the range over which ρ/bp is accurately estimated in our data. Switch errors appear identical to legitimate crossing-over events and, if they are randomly distributed along chromosomes, a specific rate of error will resemble a constant rate of crossing over. The rate of switch error will then determine a detection threshold below which recombination cannot be accurately inferred. We introduced switch errors at random into the simulation data and estimates of ρ/bp obtained from these datasets reflect this detection threshold; below 2×10-3 ρ/bp, we found that LDhelmet consistently overestimates the recombination rate in the presence of switch errors (Figure 1; Figure S1). This highlights a possible source of bias affecting LD-based recombination mapping studies using inferred haplotypes. In a recent study, Singhal et al. (2015) showed that the power to detect recombination hotspots is reduced when the recombination rate in the regions surrounding a hotspot is low. Though we did not attempt to locate recombination hotspots in this study, our findings and those of Singhal et al. (2015) both suggest that error in phase inference needs to be carefully considered before attempting to estimate recombination rates and/or recombination hotspots using LD-based approaches.
Consistent with studies in a variety of organisms, we found a positive correlation between genetic diversity at putatively neutral sites and the rate of recombination. Both unscaled nucleotide diversity and diversity divided by divergence between mouse and rat, a proxy for the mutation rate, are positively correlated with recombination (Table 2). Cai et al. (2009) found evidence suggesting that recombination may be mutagenic, though insufficient to account for the correlations they observed between recombination and diversity. The Kendall correlation between π/drat and recombination rate of 0.20 for all 4-fold sites, a value that is similar in magnitude to the corresponding value of 0.09 reported by Cai et al. (2009) in humans. The correlations we report may be downwardly biased, however, because switch errors may result in inflated recombination rates inferred for regions of the genome where the true recombination rate is low (see above). Genes that have recombination rates lower than the detection limit set by the switch error rate may be reported as having inflated ρ/bp (Figure 1; Figure S1), and this would have the effect of reducing correlation statistics. It is difficult to assess the extent of this bias, however, and in any case the correlations we observed between diversity and recombination suggest that our recombination map does indeed capture real variation in Ne across the genome. This indicates that a recombination mediated process influences levels of genetic diversity. Previously, Halligan et al. (2013) showed that there are troughs in nucleotide diversity surrounding protein coding exons in M. m. castaneus, characteristic of natural selection acting within exons reducing diversity at linked sites. Their results and ours suggest pervasive natural selection in the genome of M. m. castaneus.
In conclusion, we find that sex-averaged estimates of the ancestral recombination landscape for M. m. castaneus are highly correlated with contemporary estimates of the recombination rate estimated from crosses of M. m. domesticus (Cox et al. 2009). It has been demonstrated previously that the turnover of hotspots has led to rapid evolution of fine-scale rates of recombination in the M. musculus subspecies complex (Smagulova et al. 2016). On a broad scale, however, our results suggest that the recombination landscape is very strongly conserved between the subspecies. In addition, our estimate of the switch-error rate implies that phasing errors leads to upwardly biased estimates of the recombination rate when the true recombination rate is low. This is a source of bias that should be assessed in future studies. Finally, we showed that the variation in recombination rate is positively correlated with genetic diversity, suggesting that natural selection reduces diversity at linked sites across the M. m. castaneus genome, consistent with the findings of Halligan et al (2013).
To further our understanding of the evolution of the rate of recombination in the house mouse we need to directly compare subspecies. The comparison of our results and previously published maps indicates that there is broad-scale agreement in recombination rates between M. m. castaneus and M. m. domesticus. In this study, we have assumed that inbred lines derived from M. m. domesticus reflect natural variation in recombination rates in that sub-species, though this is not necessarily the case. Population samples like the one studied here could be used to more clearly elucidate the recombination rate maps specific to the different subspecies. A broad survey of this kind would most efficiently be generated using LD-based approaches.
Acknowledgements
We are grateful to Bettina Harr, Dan Halligan, Ben Jackson and Rory Craig for discussions and helpful comments on the manuscript. Tom Booker is supported by a BBSRC EASTBIO studentship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694212). Rob Ness was funded by the BBSRC (BB/L00237X/1).
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