High-Resolution Sex-Specific Linkage Maps of the Mouse Reveal Polarized Distribution of Crossovers in Male Germline

Abstract

Since the publication of the first comprehensive linkage map for the laboratory mouse, the architecture of recombination as a basic biological process has become amenable to investigation in mammalian model organisms. Here we take advantage of high-density genotyping and the unique pedigree structure of the incipient Collaborative Cross to investigate the roles of sex and genetic background in mammalian recombination. Our results confirm the observation that map length is longer when measured through female meiosis than through male meiosis, but we find that this difference is modified by genotype at loci on both the X chromosome and the autosomes. In addition, we report a striking concentration of crossovers in the distal ends of autosomes in male meiosis that is absent in female meiosis. The presence of this pattern in both single- and double-recombinant chromosomes, combined with the absence of a corresponding asymmetry in the distribution of double-strand breaks, indicates a regulated sequence of events specific to male meiosis that is anchored by chromosome ends. This pattern is consistent with the timing of chromosome pairing and evolutionary constraints on male recombination. Finally, we identify large regions of reduced crossover frequency that together encompass 5% of the genome. Many of these “cold regions” are enriched for segmental duplications, suggesting an inverse local correlation between recombination rate and mutation rate for large copy number variants.

RECOMBINATION is a basic biological process that is shared among most sexually reproducing organisms (Morgan 1911; Gerton and Hawley 2005). It plays a key role in genome stability by ensuring the fidelity of chromosome segregation during meiosis (Sears et al. 1992; Hassold and Hunt 2001) and contributes to other processes such as DNA repair (Howard-Flanders and Theriot 1966; Niedzwiedz et al. 2004; Krejci et al. 2012). At the population level, recombination is an important generator of genetic diversity (Feldman et al. 1996; Otto and Lenormand 2002). Abnormal recombination is associated with increased aneuploidy and decreased fitness of offspring and has been associated with several human diseases (Warren et al. 1987; Hassold and Hunt 2001; Kong et al. 2004). Recombination can be exploited experimentally to map loci associated with biological traits: indeed, the construction of linkage maps is among the oldest activities in genetics (Sturtevant 1913). Finally, the recombination machinery can be co-opted for genetic engineering of many organisms (Smithies et al. 1985; Court et al. 2002).

In mammals, many factors—including sex, taxon, and genetics—are known to affect the global, as opposed to local, rate of recombination. The total number of events per meiosis and the recombination rate per unit sequence length vary widely among mammals but are strongly correlated with the fundamental number (number of chromosome arms) present in the karyotype of each species (Pardo-Manuel De Villena and Sapienza 2001). Although the molecular process of recombination can result in either a noncrossover or a crossover event, to date the study of recombination in mammals has been limited almost exclusively to crossovers, which are more readily detected. Previous studies have shown that, as a general rule, the number of crossovers observed in autosomes is higher in female meiosis than in male meiosis and thus the linkage map is longer in the gametes of females (Dunn and Bennett 1967; Broman et al. 1998; Kong et al. 2002; Cox et al. 2009). These same studies demonstrated that the genomic distribution of crossovers between female and male meiosis is significantly different: uniform in females, but subtelomerically enhanced and pericentromerically suppressed in males. Crossover interference (Petkov et al. 2007) and sex-specific patterns of hotspot usage (Paigen et al. 2008; Kong et al. 2010) have been advanced as candidate explanations for these phenomena. Recently, based on evidence from flowering plants, a population genetics basis for the evolution of sex differences in recombination rates—differences in gametic selection between males and females—has been proposed (Lenormand and Dutheil 2005). Despite these advances the presence and causes of sex differences in the overall rate and spatial distribution of recombination remain the object of study and controversy.

Recent studies indicate that recombination rate also varies between closely related species and subspecies and that alleles responsible for these effects may in fact be segregating within species (Dumont et al. 2009; Murdoch et al. 2010; Dumont and Payseur 2011; Auton et al. 2012). In particular, crossover frequency in male mice is known to vary across different inbred strains (Koehler et al. 2002) and these differences have been exploited to map genetic loci affecting recombination rates in F₂ intercrosses (Murdoch et al. 2010; Dumont and Payseur 2011). Finally, mutations at several genes are known to lead to pathological changes in recombination (Niedzwiedz et al. 2004; Liebe et al. 2006).

Traditionally recombination has been studied in large pedigrees, using small numbers of informative markers. The first comprehensive linkage map of the laboratory mouse was developed in 1992 by genotyping hundreds of microsatellite markers in an interspecific backcross (Dietrich et al. 1992), work that was crucial to the success of the Mouse Genome Project (Waterston et al. 2002). Since then several linkage maps have been reported that have used larger experimental populations and taken advantage of denser single-nucleotide polymorphism (SNP) genotyping arrays (Shifman et al. 2006; Cox et al. 2009). Increasingly fine-grained linkage maps are an important technical resource for the research community, enabling the development of more sophisticated genetic mapping methods and the explosive growth of complex-traits analysis in the laboratory mouse (Flint and Mackay 2009; Flint and Eskin 2012). In addition, such maps provide a window into fundamental processes of transmission genetics.

The development of very dense genotyping arrays and the concurrent genotyping of large numbers of unrelated human individuals opened the door to the development of high-resolution genetic maps based on linkage disequilibrium (LD) (McVean et al. 2004; Myers et al. 2005). This type of analysis has been recently extended to mouse (Brunschwig et al. 2012). However, in contrast to human studies that use unrelated individuals, work in mouse has been limited to laboratory strains for which the presence of population structure and introgression between clades makes the interpretation of the data challenging (Yang et al. 2011; Collaborative Cross Consortium 2012). New mouse populations, in particular the highly randomized and fully traceable Collaborative Cross population, aim to mitigate these concerns (Churchill et al. 2004).

Even more recently the power of next-generation sequencing technologies has been applied to identify and characterize thousands of recombination hotspots by mapping meiotic double-strand breaks (DSBs) in male germ cells (Smagulova et al. 2011; Brick et al. 2012). These new approaches have focused attention on hotspots, short discrete regions of the genome with recombination frequencies that are significantly above the genome-wide average. This led to the identification of Prdm9 (and its human homolog PRDM9) as the key trans-regulator of meiotic hotspot activity in mice and humans, respectively (Myers et al. 2010; Parvanov et al. 2010). The fact that PRDM9 is a histone 3 lysine 4 trimethyltransferase that plays a role in epigenetic modification in the germline and that there are multiple alleles in both humans and mouse with different functional characteristics has resulted in the publication of a large body of literature in only a few years (Berg et al. 2010; Hinch et al. 2011; Brick et al. 2012; Hussin et al. 2013).

Despite the accomplishments of the LD and DSB approaches to study recombination, these methods are unsuited for the characterization of sex effects: LD represents a sex average and sequencing protocols to map DSBs have been implemented only for male germ cells. In addition, these approaches cannot determine the number of crossovers within a single chromosome in a given meiosis. As we demonstrate, these limitations obscure the important properties of mammalian meiosis.

Here we applied new high-density genotyping technology to the highly informative pedigree structure of the incipient Collaborative Cross (CC) to investigate the roles of sex and genetic background in mammalian recombination. The CC is a multiparental recombinant inbred population derived from eight founder inbred Mus musculus strains that collectively span 90% of the segregating variation in laboratory mice (Churchill et al. 2004; Roberts et al. 2007; Chesler et al. 2008; Collaborative Cross Consortium 2012). Each CC line is independently derived through three generations of outbreeding followed by multiple generations of inbreeding. The unique pedigree structure of this population during the first four generations (referenced hereafter as G₀, G₁, G₂, and G₂:F₁) allows us to observe up to eight informative meioses by genotyping a single G₂:F₁ sibling pair: each crossover observed in a G₂:F₁ individual can be assigned with certainty to a specific meiosis (Figure 1). Due to randomization in the order of matings across breeding “funnels,” these meioses have balanced contributions from each of the eight founder inbred strains through both female and male germlines. We genotyped 237 G₂:F₁ sib pairs from independent CC lines, using the Mouse Diversity Array platform (Yang et al. 2009), which allowed us to map each individual crossover to a genome interval of 35 kbp on average. This level of resolution is similar to what can be attained in LD and DSB methods while retaining the ability to determine the detailed composition of individual meioses, against a randomized and extremely diverse genetic background, capturing variants known to influence global recombination rate.

Figure 1.

Pedigree structure of G₂:F₁ sibling pairs (representative funnel). Mice were bred in 237 funnels uniquely defined by the ordering of founder strains in the parental (G₀) generation, as illustrated. This design balances the contribution of each of the eight founder strains through both the maternal and the paternal lineage. Using funnel order and genotypes for both members of a sib pair, it is possible to assign crossover events inferred in members of the sib pair to one of eight meioses occurring in the germline of a specific ancestor: in the G₁ generation, maternal grandmother (MGM), maternal grandfather (MGP), paternal grandmother (PGM), or paternal grandfather (PGP); or in the G₂ generation, mother (Mf, Mm) or father (Pf, Pm), with independent G₂ meioses contributing to each sib pair. The method additionally distinguishes shared from singleton events.

The overall conclusions of our study provide insights into the cellular and molecular mechanisms of recombination, provide new hypotheses on its evolution, and have practical consequences for the design and interpretation of mapping experiments in the laboratory mouse.

Materials and Methods

Mouse breeding

The G₂:F₁ population used in this study was bred at Oak Ridge National Laboratory (ORNL) beginning in 2005 as described in detail previously (Chesler et al. 2008; Collaborative Cross Consortium 2012). Briefly, eight founder strains—five classical inbred strains (A/J, C57BL/6J, 129S1/SvImJ, NOD/ShiLtJ, and NZO/HILtJ) and three wild-derived strains (CAST/EiJ, PWK/PhJ, and WSB/EiJ)—were intercrossed in the G₀ generation to generate G₁ hybrids (Figure 1). These G₁ progeny were intercrossed to create the four-way G₂ generation. Finally, mice from the G₂ generation were crossed to generate the eight-way progeny, known as the G₂:F₁. We refer to such a series of matings as a funnel. A funnel can be uniquely identified by the order of matings in the G₀ generation. Each breeding funnel constitutes a unique and independent mosaic of the eight founder genomes (Collaborative Cross Consortium 2012). Under this breeding scheme, the genetic contribution of each of the eight founder strains to each line is expected to be equivalent. The present work considers sibling pairs (each consisting of one female and one male animal) from the G₂:F₁ generation of 237 breeding funnels, for a total of 474 animals.

Two additional independent populations (to which we refer herein as the “intercrosses”) were generated at the University of North Carolina at Chapel Hill (UNC) by performing intersubspecific crosses between FVB/NJ females and either (PWK/PhJ × CAST/EiJ)F₁ or (WSB/EiJ × PWK/PhJ)F₁ males. Subsets of 96 offspring from a larger total progeny from each cross were selected for this study. Throughout the article the dam is listed first and the sire last in all crosses.

G₂:F₁ and intercross mice were treated in accordance with the recommendations of the Institutional Animal Care and Use Committee of ORNL and UNC, respectively.

DNA preparation and genotyping

DNA from G₂:F₁ mice was isolated at UNC according to a protocol for isolation of high-molecular-weight DNA using proteinase K and phenol (Sambrook and Russell 2006) and genotyped using the high-density Mouse Diversity Array (Yang et al. 2009) at the Jackson Laboratory. DNA samples from intercross progeny were isolated at UNC and genotyped using the MegaMUGA platform (Neogen/Geneseek, Lincoln, NE), a new 77,000-probe array based on the Illumina Infinium platform (Rogala et al. 2014).

Haplotype reconstruction and inference of crossovers

We reconstructed founder contributions to the genomes of progeny, using microarray genotypes and pedigree information, and inferred crossovers as transitions between founder haplotypes. Crossovers are represented as intervals that span the physical genome between the nearest pair of markers that unambiguously flank the inferred event. G₂:F₁ and intercross progeny were analyzed separately; tables of all crossovers identified in both populations are included in Supporting Information, File S1 and File S2, respectively.

Collaborative Cross G₂:F₁ population:

Haplotype reconstruction and localization of crossovers for CC funnels were performed with GAIN (Liu et al. 2010), a hidden Markov model-based software that incorporates the CC pedigree structure in an efficient implementation of the Lander–Green algorithm (Lander and Green 1987) to obtain fully phased, highly accurate haplotype mosaics. Analysis was performed independently on each funnel but jointly on the siblings from the same funnel: crossovers are not shared across funnels but G₂:F₁ siblings from the same funnel can share crossovers from the G₁ generation, and the joint analysis can help to resolve ambiguity with respect to haplotype segment boundaries. Note that GAIN enforces all constraints imposed by the pedigree. For example, two of the strongest constraints (see Figure 1) are (1) for any G₂:F₁ mouse, the two alleles at any marker must come from different halves of the funnel, and (2) two siblings cannot inherit different alleles from one quarter-funnel at any marker. If the input data contain errors (in either genotype calls or funnel order), GAIN will infer many more crossovers than predicted to satisfy these constraints. This provides an effective indicator to identify and correct (or remove) incorrectly labeled funnels and poorly performing markers.

For each funnel, GAIN takes the funnel order, the genotypes of the eight founder strains, and genotypes of the G₂:F₁ sibling mice as input. It infers founder ancestry probabilities at each marker by building a descent model and evaluating the probability of crossover between adjacent markers, given the genotypes and a transition penalty. Founder ancestry at each marker is defined as the probability that each of $\left(\begin{array}{c}8\\ 2\end{array}\right)=28$ possible pairs of founders (e.g., C57BL/6J and CAST/EiJ) are the two founders from which the two alleles at that marker are inherited. With such information, haplotype segments and crossovers can be obtained by tracing the maximum a posteriori ancestry probability along chromosomes, using the forward–backward algorithm as in the Lander–Green procedure. Each crossover is described by (1) proximal and distal boundaries where the probability of the most likely founder ancestry falls below a threshold, (2) proximal and distal founder ancestry on the recombining chromosome segment, and (3) the specific meiosis in the breeding funnel [maternal grandmother (MGM), maternal grandfather (MGP), paternal grandmother (PGM), paternal grandfather (PGP), mother (Mf, Mm), or father (Pf, Pm)] to which it is ascribed. The crossover interval inferred (from proximal to distal boundary) is expected to contain the crossover event with high probability. Note that there are regions where multiple founder ancestries have similar probabilities due to sparsity of markers, low genotyping quality, or similarity of DNA sequence among multiple founders (e.g., due to identity-by-descent); in such cases, crossovers can be localized only to long intervals.

Before performing haplotype reconstruction, high-quality markers were identified by examining completeness (genotypes called in ≥99% of samples) and concordance of genotypes called in G₂:F₁ siblings, G₀ founder mice, and G₁ samples from previous studies, using the Mouse Diversity Array (Yang et al. 2009). A total of 121,504 markers (representing 15–25% of markers on each chromosome) were retained in the high-quality group (File S3) and used for initial haplotype inference. The resulting crossover intervals were refined using the remaining 549,595 mid- to low-quality markers by examining the consistency of the additional markers with their expected genotypes within and around the uncertainty limits of each crossover. On average, this reduced the width of the crossover intervals by approximately half.

Intercross population:

Owing to the simplicity of the intercross pedigrees, haplotype reconstruction in the intercross population is nearly trivial. The problem reduces to identifying markers that are segregating between two paternal strains and then clustering them into haplotype blocks in a manner that minimizes the total number of crossovers. The algorithm used to reconstruct haplotypes from MegaMUGA genotype calls is described in File S7. It produces consistent results across a broad range of parameter choices and is insensitive to genotyping errors and noncrossover products.

Construction of genetic maps and estimation of local crossover density

Cumulative genetic maps for the CC funnels were computed directly from the interval representation of crossovers by integration across each chromosome to account for uncertainty in localization of crossovers. Maps were obtained separately for female and male meiosis and as a sex-averaged map. Genetic maps were computed from different subsets of the data, including separate maps for G₁ and G₂, and for genotype classes at specific loci including the Prdm9 locus on chromosome 17. Maps were computed for each strain based on the haplotypes involved in junction formation. Cumulative maps were normalized to centimorgan units as

$$\text{cM}=100\left(\frac{\text{count}\hspace{0.17em}\text{of}\hspace{0.17em}\text{crossovers}}{\text{count}\hspace{0.17em}\text{of}\hspace{0.17em}\text{meioses}\times \text{count}\hspace{0.17em}\text{of}\hspace{0.17em}\text{funnels}}\right)$$ (1)

and density estimates were obtained using a sliding window at variable widths. An R script to reproduce these analyses accompanies this article.

Pooled analysis of spatial distribution of crossovers across autosomes

To analyze the distribution of crossovers along all autosomes jointly, distinct crossovers on autosomes identified in the G₂:F₁ population and all autosomal crossoverss in the intercross population were analyzed together. Event positions were normalized against the length of the chromosome on which they occurred such that the normalized position of all events fell on the interval [0, 1]. For the purposes of this analysis, crossovers, inferred as intervals, were converted to points (at the midpoint between the proximal and the distal boundary): after normalization against chromosome length, event positions can be directly compared but interval widths are no longer meaningful. Kernel density estimates of crossover frequency with respect to normalized chromosomal position were obtained with the KernSmooth package (Wand and Jones 1995) for the R language (R Core Team 2012: http://www.r-project.org/), using a Gaussian kernel with bandwidth selected according to the direct plug-in method (Wand and Jones 1995). Confidence intervals about the density estimate were obtained by repeating the kernel-fitting procedure on 10,000 bootstrap samples of the crossovers, taking the 2.5th and 97.5th percentiles at each point at which the original kernel was evaluated.

Sex differences in spatial distribution of crossovers were analyzed in two ways. First, we conducted a formal test of the hypothesis that the distribution of events along chromosomes is uniform in single-recombinant meiotic products. Events on single-recombinant chromosomes in each sex (which can be identified with certainty only at the G₂ generation) were compared to a uniform distribution by the Kolmogorov–Smirnov test, stratified by chromosome, and the resulting P-values were adjusted by the method of Benjamini and Hochberg to control the false-discovery rate. Second, we used quantile regression to test for sex differences in location at quantiles along the spatial distribution of crossovers. The following model was fitted for each chromosome,

$$y_q=\beta +{\beta }_{\text{male}}+\epsilon ,$$ (2)

where y_q is the physical position corresponding to the (100 × q)th percentile of the spatial distribution of crossovers. In this model β_male gives the displacement of the male vs. the female distribution at the given quantile, such that values of β_male > 0 indicate a distally biased distribution in males.

The distribution of crossovers in males was compared to the distribution of recombination hotspots identified through high-resolution analysis of DSBs in Smagulova et al. (2011; Brick et al. 2012), using a simulation approach. For each chromosome, n DSBs (where n is the number of crossovers observed in the G₂:F₁ population) were sampled at random with replacement with probability proportional to hotspot strength. The distribution of DSBs and crossovers was compared by a Kolmogorov–Smirnov test. For each chromosome, a simulation P-value was obtained by taking the median P-value across 1000 random samples of DSBs. Simulation P-values for each chromosome were adjusted by the method of Benjamini and Hochberg to control the rate of false discovery.

Detection of cold regions

We initially identified cold regions, using a one-dimensional dynamic programming algorithm to identify regions with ≥10-fold reduction in frequency of crossovers via a generic scoring scheme (Karlin and Altschul 1990). Briefly, we first compute local crossover density ρ_i at a grid of points i = 0, … , n along a chromosome. Those densities are converted to initial scores e_i as

$$e_i=\lambda \left(1-\theta \right)+{\rho }_i\log \theta ,$$ (3)

where λ is the mean crossover density across the chromosome and θ is a prespecified enrichment threshold (and here, θ = 0.1). Then a forward pass is made over the scores to compute the dynamic-programming scores E_i,

$$E_{i+1}=\text{max}\left\{0,E_i+e_{i+1}\right\},$$ (4)

with the score at the first grid point initialized to zero (e₀ ≡ 0). Regions of interest are finally identified by performing a traceback on the E_i.

The dynamic programming method allows us to identify regions of reduced recombination without resorting to a fixed-width sliding window and can identify regions of any size. We applied the algorithm to male and female recombination separately and took the union of the results, which overlapped extensively. We retained only those regions of length >500 kbp and refined the boundaries of individual regions by manual inspection of their flanking crossovers.

Genomic analysis of cold regions

To capture the most up to date sequence information in all these analyses we used the newest mouse assembly, GRCm38, released by the Genome Reference Consortium in January 2012. Having obtained a list of candidate cold regions, we first determined the fraction of no calls (N’s) in the reference genome sequence for a given interval and excluded those with >10% no calls. We then determined the following for each region: (1) the number and identity of crossovers in the region in the G₂:F₁ population; (2) the recombination rate in the population reported in Cox et al. (2009); (3) the DSB density in C57BL/6J, 9R, 13R, and (9R × 13R)F₁ males based on the data reported in Brick et al. (2012); (4) whether the region overlaps a “recombination desert” reported in (C57BL/10.S × C57BL/10.F)F₁ mice by Smagulova et al. (2011); (5) the number of crossovers in the 192 intercross progeny of (PWK × CAST)F₁ and (WSB × PWK)F₁ males; (6) the fraction of C+G base composition in the reference genome sequence; (7) the fraction of the region’s sequence spanned by segmental duplications (of length >20 kbp); (8) the number of genes in the cold region; and finally (9) the number of structural variants reported in the region in the 18 strains sequenced by Yalcin et al. (2011).

Analysis of structural variation in cold regions

Segmental duplications were identified using dotplots generated by the software Gepard (Krumsiek et al. 2007). For each cold region, we compared the sequence in the region against itself to identify local segmental duplications (tandem or inverted) of length >20 kbp and computed the duplication rate as the fraction of the region spanned by such duplications. In determining the genome-wide segmental duplication rate, we used a sliding window of 1 Mbp with 500-kbp overlap between adjacent windows and calculated the average duplication rate across all windows.

To explore the relationship between segmental duplication, coldness for recombination, and structural variation we examined probe intensities for 62 representatives of the G₀ founders genotyped using the MegaMUGA platform. Each probe on this platform yields two intensity values per sample (x and y), locating samples in a two-dimensional intensity space that is partitioned into three discrete clusters (a homozygous cluster along each of the x- and y-axes and a heterozygous cluster along a 45° line drawn from the origin) for genotype calling. For a well-behaved SNP probe, the sum intensity (x + y) of all samples is approximately equal independent of genotype. Violations of this criterion provide evidence in support of structural variation. To capture the totality of information contained in probe intensities to provide evidence for structural variation between inbred strains, we performed principal components analysis (PCA) on the n × p matrix P of probe intensities for n = 62 individuals and p probes in each cold region to yield a new matrix P′ containing the projection of M onto the subspace defined by the p principal components. Pairwise Minkowski distances (a generalization of the Euclidian distance metric) between samples were computed on M′, and an unrooted neighbor-joining tree was constructed from the resulting n × n distance matrix, using the R package ape (http://ape-package.ird.fr/). We repeated the analysis using pairwise intensities (and thus an n × 2p data matrix).

Because off-target variation in or near the probe sequence may influence hybridization efficiency (Didion et al. 2012), such that samples more genetically distant from the reference used to design the array have systematically lower probe intensities, we restricted this analysis to the five closely related classical inbred strains (A/J, C57BL/6J, 129S1/SvImJ, NOD/ShiLtJ, and NZO/H1LtJ).

Results

Overview of the mapping population and recombination map

The genotypes of 237 G₂:F₁ sibling pairs were combined with the funnel information (see Materials and Methods) to infer fully phased founder haplotypes for each chromosome (Figure 1). Note that each G₂:F₁ female is the product of six meioses and her male sib is also the product of six meioses with four meioses shared between them. The four shared meioses (denoted as MGM, MGP, PGM, and PGP in Figure 1) occur at the G₁ generation. The four unique meoises (Mf, Mm, Pf, and Pm in Figure 1) occur at the G₂ generation. Crossovers are identified as transitions between founder haplotypes. Given the structure of the pedigrees, every crossover can be unambiguously assigned to one of the eight meioses, since at any given locus, any pair of founder haplotypes can be paired only in one of these eight meioses. Therefore, the identification and analysis of crossovers relies on knowledge of the order of the founder strains in the G₀ generation.

The breeding scheme ensures equal and balanced contribution of each of the eight founder strains in the autosomes and equal representation of male and female meioses. Genotyping of both male and female offspring allows the study of recombination on the X chromosome while retaining the ability to test whether the distribution of the observed crossovers is influenced by sex of the offspring analyzed.

We identified 25,038 crossovers in the 474 individual G₂:F₁ mice (Table 1). Of these, 18,948 events are observed only once and 3,045 crossovers are shared by both siblings in the pair (i.e., were observed exactly twice). Therefore, we have identified 21,993 distinct crossovers in our population, 21,368 on the autosomes and 625 on the X chromosome. Because a crossover in generation G₁ can be observed only if it is transmitted to at least one G₂:F₁ individual (which occurs with probability 3/4) while all G₂ events are observable, the effective number of observed autosomal meioses per funnel is $(3/4)\left(4\hspace{0.17em}\text{meioses}\right)+1\left(4\hspace{0.17em}\text{meioses}\right)=7$ and the thus the sex-averaged autosomal map length is 1288 cM. The effective of number of meioses observed per funnel on the X chromosome is 3.5, by similar logic, giving an overall length of 75 cM.

Table 1. Crossover counts in the G₂:F₁ population.

			Autosomes			X chromosome
Sex	Meiosis	Sib	Singleton	Shared	Unique	Singleton	Shared	Unique	Total
Female	Mf	Female	3,282	NA	3,282	183	NA	183	3,465
Female	Mm	Male	3,255	NA	3,255	150	NA	150	3,405
Male	Pf	Female	2,871	NA	2,871	NA	NA	NA	2,871
Male	Pm	Male	2,783	NA	2,783	NA	NA	NA	2,783
Female	MGM	Female	826	756	1,582	35	48	83
		Male	767	756	1,523	35	48	83
		All	1,593	756	2,349	70	48	118	2,467
Male	MGP	Female	733	730	1,463	NA	NA	NA
		Male	768	730	1,498	NA	NA	NA
		All	1,501	730	2,231	NA	NA	NA	2,231
Female	PGM	Female	807	766	1,573	174	NA	174
		Male	782	766	1,548	NA	NA	NA
		All	1,589	766	2,355	174	NA	174	2,529
Male	PGP	Female	740	745	1,485	NA	NA	NA
		Male	757	745	1,502	NA	NA	NA
		All	1,497	745	2,242	NA	NA	NA	2,242
		All
Female	All	All	9,719	1,522	11,241	577	48	625	11,866
Male	All	All	8,652	1,475	10,127	NA	NA	NA	10,127
Total	All	All	18,371	2,997	21,368	577	48	625	21,993

We subjected the raw recombination data to a comprehensive quality-control pipeline to detect errors and to test expectations regarding the ratio at which different types of events should be observed according to Mendelian rules (File S7 and Table 2). In all cases the data conform closely to expectations, providing strong evidence for the integrity of both the breeding process and our methods for constructing the recombination map.

Table 2. Expectations regarding autosomal recombination in G₂:F₁ pedigrees based on Mendelian rules.

Relationship	Expected	Observed
Observed events in G1 vs. G2	3:4	0.747 (P = 0.78)
Same event type from opposite half-funnels	1:1	1.00 (P = 1.00)
Mf vs. Mm		1.02
Pf vs. Pm		1.03
MGM vs. PGM		0.975
MGP vs. PGP		0.999
Singleton vs. shared events in G1	2:1	0.673 (P = 0.17)
MGM		0.678
MGP		0.672
PGM		0.675
PGP		0.668

Except when noted otherwise, the counts to which this table refers are those in Table 1. All P-values were obtained via a χ²-test with a single degree of freedom. A more detailed discussion of these expectations is provided in File S7.

A key feature of our experiment is that crossovers are mapped with high precision. The median uncertainty interval is 34.9 kbp but the range is wide (19–25,150,032 bp) and the distribution bimodal (Figure S1). The uncertainty intervals in the right tail of the distribution are due to either the lack of SNPs in some genomic regions (Yang et al. 2009) or the lack of informative SNPs between the strains involved in particular crossovers, as a consequence of recent shared ancestry (Yang et al. 2011). All analyses of the spatial distribution of recombination account for these uncertainties (see Materials and Methods).

The resolution of our map is ∼114 kbp (8.8 crossovers per megabase pair). The spatial distribution of crossover density estimated over large windows (for example, 5 Mbp; see panel 1 in Figure S2) in the G₂:F₁ population is qualitatively similar to that of the most current mouse linkage map (Cox et al. 2009). This similarity gradually disappears as the window is narrowed, likely due to a combination of technical (density and informativeness of the marker panel) and biological (sex and strain effects) differences between these experiments (panel 2 in Figure S2). The linkage map reported by Cox et al. (2009) was based on reanalysis of pedigrees from the eight-way heterogenous stock (HS). The HS founders are classical inbred strains; these partially overlap the CC founders but do not include the wild-derived strains. The Cox map is based on 3546 informative meioses—roughly double the number of meioses in the G₂:F₁ population—but the HS animals were genotyped at only 10,202 informative markers.

Sex and strain effects on overall level of recombination

As expected, the total number of crossovers in autosomes is significantly smaller in male meiosis than in female meiosis (10,127 events and 11,241 events, respectively, Table 1; P = 2.5 × 10⁻¹⁴ by t-test, H₀: equal number of events in both sexes). Table 3 provides point estimates and 95% bootstrap confidence intervals for sex-specific map length at each generation (lack of overlap between two such intervals is asymptotically equivalent to rejection of the null hypothesis that the corresponding point estimates are equal by Student’s t-test). The sex effect on recombination is more pronounced in G₂ than in G₁. Note that the female map expands in G₂ compared to G₁ (although the effect is not statistically significant) while the male map contracts significantly between these two generations (Figure 2). The sex difference is also observed in the distribution of total number of crossovers per individual (Figure S3). A greater number of crossovers in female meiosis are observed in both the G₁ and G₂ generations (P = 0.019 and P = 1.3 × 10⁻¹⁵ by t-test, respectively; H₀: equal number of events in both sexes). Table 3 provides point estimates and 95% bootstrap confidence intervals for sex-specific map length at each generation.

Table 3. Cumulative autosomal map length in the G₂:F₁ by sex and generation.

	Generation
Sex	G1 (cM)	G2 (cM)
Female	1330 (1296, 1365)	1381 (1351, 1409)
Male	1279 (1247, 1311)	1211 (1182, 1236)

Confidence intervals were obtained from a nonparametric bootstrap procedure with 100 replicates.

Figure 2.

Sex-specific cumulative autosomal map length. Map length was computed within each generation among females (solid line) and males (dashed line). Vertical bars indicate 95% bootstrap confidence intervals.

To investigate the possible causes of these differences we determined the effect of strain in the sex-specific maps at each generation. Two previous studies have mapped a strong quantitative trait locus (QTL) controlling male map length on the X chromosome (Murdoch et al. 2010; Dumont and Payseur 2011). Both studies reported that a QTL associated with the inheritance of the CAST/EiJ chromosome X resulted in significant expansion of the male map. To confirm and extend this observation we compared the number of crossovers in the progeny of G₁ males, which are hemizygous for chromosome X and are heterozygous for exactly two founder haplotypes on the autosomes, classified according to the subspecific origin of the X chromosome (Figure 3). We observe that the M. m. castaneus (CAST/EiJ, discounting regions of intersubspecific introgression) X chromosome is associated with an expansion of the male map, the M. m. musculus (PWK/PhJ) X chromosome is associated with contraction of the male map, and the M. m. domesticus X chromosomes yield intermediate male map length. We conclude that one or more loci on the X chromosome controlling the length of the male map segregate in the CC.

Figure 3.

Effect of the X chromosome on overall recombination rate in male meiosis at G₁. Males at the G₁ generation are hemizygous for a single founder haplotype along the entire X chromosome and heterozygous for that founder haplotype everywhere else, allowing a direct test for the effect of the X chromosome against a varying genetic background. Alleles were defined on the basis of subspecific origin: CAST/EiJ, M. m. castaneus (cas); PWK/PhJ, M. m. musculus (mus); and all others, M. m. domesticus (dom), with the caveat that regions of intersubspecific introgression will be misclassified. Unique crossovers attributed to G₁ male meioses (classes MGP and PGP, Figure 1) were counted within all seven possible combinations of X chromosome haplotype and autosome diplotype (e.g., cas/dom) for the G₁ offspring of a CAST/EiJ dam and an A/J sire. Boxplots represent map lengths computed on 100 bootstrap replicates of the observed G₁ crossovers. The two boxes with dotted outlines represent predicted values for allelic combinations not observed in the G₂:F₁ population.

We additionally observed an overall effect of the autosomal genome on recombination rate that is in opposition to the effect of chromosome X. The CAST/EiJ autosomal background is associated with a contraction of the male map while the PWK/PhJ autosomal background is associated with expansion of the male map. We attempted to identify specific autosomal loci and estimate their effects by performing genome scans for both the number of crossovers observed and magnitude of crossover interference in the G₂ generation, but no locus reached genome-wide significance. The generational difference in sex-specific map lengths (Table 3) is consistent with a model in which the genotypes of the X chromosome and autosomes influence total map length additively but in opposite directions. In generation G₁ the X and autosomal loci are tightly coupled and the increasing effect of CAST/EiJ autosomal loci offsets the decreasing effects of the CAST/EiJ X chromosome. The same kind of balance occurs in the PWK/PhJ background but with directions of X and autosomal effects reversed. In generation G₂ the segregation of X and autosomal genotypes is less tightly coupled, giving rise to transgressive allelic combinations such as CAST/EiJ autosomal genotypes in combination with a PWK/PhJ X chromosome and leading to increased difference between the two sexes.

Sex and strain effects on spatial distribution of crossovers and interference

In addition to the sex differences in map length, we observe dramatic sex differences in the spatial pattern of crossovers along the autosomes. The raw distribution is presented in Figure 4, left, while Figure 4, right, displays a smoothed representation of their spatial distribution after standardizing chromosomes to unit length and estimating the density of crossovers on all autosomes jointly. Because mouse chromosomes are acrocentric and the function of their short arms is poorly understood, we follow the convention of taking “distal” and “telomeric” to refer to position on the long arm. Approximately half of the crossovers occur in the distal quarter of the chromosomes and almost one-third of events occur in the distal 10% of the autosomes in male meioses (Figure S4A). To demonstrate that this effect is independent of chromosome size or identity, we used quantile regression to assess the effect of sex on the cumulative spatial distribution of events along chromosomes. Figure S4B confirms that the distal portions of all 19 autosomes bear a disproportionate number of crossovers in male vs. female meioses.

Figure 4.

Spatial distribution of crossover events in male and female meioses in the CC G₂:F₁. (A) spatial distribution of crossover events in each experiment: each dot represents the midpoint between the proximal and distal boundaries of a unique crossover event occurring in a female (pink) or a male (blue) meiosis. Chromosomes are aligned at the distal ends of their long arms. (B) Kernel density estimates of crossover frequency across all autosomes in female (pink lines) or male (blue lines) meioses, after scaling all chromosomes to equal length. Note the dramatic difference in distribution of events in female vs. male meioses: crossover events are distributed almost uniformly across autosomes in females, but are concentrated in the distal end of autosomes in males.

The spatial distribution of crossovers on single- and double-recombinant chromosomes differs as expected due to interference, but preserves the excess of crossovers in the distal ends of chromosomes in males (Figure 5). Considering only single-recombinant chromosomes to reduce the confounding effect of interference, the distribution of events is indistinguishable from a uniform distribution in females for 11 of 19 autosomes (chromosomes 2, 4, 5, 6, 8, 9, 10, 11, 12, 13, and 18) at false-discovery rate 0.05 (by a Kolmogorov–Smirnov test) and is qualitatively uniform and symmetric on the remaining autosomes. The distribution in males for single-recombinant chromosomes differs from the uniform case for all chromosomes (median P = 1.7 × 10⁻⁸). To confirm these results using independent data we performed a similar analysis of 192 intercross offspring from two types of F₁ males [(CAST/EiJ × PWK/PhJ)F₁ and (WSB/EiJ × PWK/PhJ)F₁] that were genotyped with the 77,000-SNP MegaMUGA array. In this cross only crossovers in male meioses are observable, but their distribution (bottom row of Figure 5) closely mirrors that in the G₂:F₁ population. Notably, the spatial pattern of crossovers in male meiosis is significantly different from the distribution of DSBs and of the X chromosome effect described in the previous section (Figure S5 and File S5). This pattern is consistent with a model in which recombination is spatially polarized in the male but not the female germline (see Discussion).

Figure 5.

Asymmetric spatial distribution of crossovers in male meiosis in singly vs. multiply recombinant chromosomes. Shown are kernel density estimates of crossover frequency across single-recombinant (left) and double-recombinant (right) autosomes in female (pink lines) and male (blue lines) meioses. The sharp peak in crossover density observed at the distal end of autosomes in males is present in both single- and double-recombinant autosomes. An additional broader peak is present in the proximal region of double-recombinant chromosomes. This effect is independent of the distribution of double-strand breaks (DSBs) in male meiosis reported by Brick et al. (2012), plotted in gray.

The large-scale (>5 Mbp) recombination landscape and differences between males and females in the distribution of crossovers are conserved across all eight strain backgrounds. However, at the fine scale (<0.5 Mbp) we begin to observe heterogeneity in the distribution of crossovers with respect to strain genotypes at the recombination breakpoint (Figure S6). While our study lacks the resolution required to identify individual hotspots of recombination or recombination-associated sequence motifs, these fine-scale patterns almost certainly reflect the strain-specific nature of most hotspots. Tightly clustered strain- and sex-specific breakpoints are observed for both male and female meiosis across all chromosomes. A male-specific PWK/PhJ cluster on chromosome 15, in which a physical region of <0.1 Mbp encompasses 6 cM, is a notable example (Figure S7).

Identification of cold regions in the G₂:F₁ population

We define cold regions as long (>500 kbp) contiguous genomic intervals that have a >10-fold reduction in crossovers compared to the genome-wide average. Given the total number of crossovers in our experiment (21,993) we established this 500-kbp threshold in the initial identification of cold regions to minimize the number of false positives (i.e., on average we expect 4.4 crossovers per 500 kbp).

We initially identified the 50 coldest regions in male and female meioses separately to allow for possible cold regions on chromosome X. Because of the substantial overlap between these sets, we took their union, totaling 68 regions, as our candidate set. Candidate regions underwent several filtering steps. First, we excluded regions in which N’s in the reference genome sequence represent a large fraction (>12.5%) of the nominal length. We refined the boundaries of the 59 remaining cold regions, using the crossover uncertainty intervals in the G₂:F₁ population. After refinement, 51 of these regions have no crossovers; they are bounded proximally by the distal boundary of the proximal crossover and distally by the proximal boundary of the distal crossover (File S4). The remaining 8 cold regions have only one or two crossovers. Overall, cold regions span 124.1 Mbp (≈5% of the genome), distributed along 18 chromosomes (all chromosomes except 10 and 11), with an enrichment for proximal and distal sections of the chromosomes. On average, cold regions are almost 2.1 Mbp in length (range 582,221–10,217,265 bp). Importantly, cold regions are consistently “cold” across strains, sexes, and generations. The refined cold regions are plotted against their genomic position in Figure 6.

Figure 6.

A catalog of 59 cold regions of dramatically reduced crossover frequency. Cold regions are represented as yellow-shaded boxes. Local rate of crossing over (in arbitrary units) is plotted as a dark blue line.

External validation of cold regions:

To determine whether the cold regions seen in the G₂:F₁ population are cold in other populations, we examined these regions in the HS used to construct a recent linkage map of the mouse (Cox et al. 2009). On average, there is a fourfold reduction in crossover density in cold regions (0.14 cM/Mbp vs. the expected 0.5 cM/Mbp that is observed genome-wide; File S4). In fact, 57 of the 59 regions are below the genome-wide average and for 16 regions the recombination density in the HS is zero. The two exceptions are located on chromosome 7 (positions 7,231,821–12,298,098 and 110,909,130–111,734,201). The extent of validation is striking given the differences in genetic background between the two populations: of the eight strains contributing to the HS, only A/J, C57BL/6J, 129S1/SvImJ, NOD/ShiLtJ, and NZO/HILtJ—all of which are of nearly pure M. m. domesticus origin—are shared with the G₂:F₁ population. The strains not shared include two wild-derived strains representing subspecies (CAST/EiJ, M. m. castaneus; and PWK/PhJ, M. m. musculus, respectively) that are rare or absent in the genetic makeup of the strains in the Cox study and are separated from M. m. domesticus by 500,000 years of evolution (Yang et al. 2011). Furthermore, marker density and methods used to estimate local recombination density were quite different between the present study and the Cox study.

Recently, several maps of recombination-initiation sites in the mouse have been published (Smagulova et al. 2011; Brick et al. 2012). These studies identified regions with significant enrichment of DSBs in the male germline of mice of different genetic backgrounds [(C57BL/10.S × C57BL/10.F)F₁, 9R, 13R, C57BL/6, and (9R × 13R)F₁]. The initial study (Smagulova et al. 2011) identified 21 recombination deserts >3 Mbp, but noted that it was not possible to identify DSBs in some regions due to gaps in the reference sequence or highly repetitive DNA. Eleven of the cold regions identified in the G₂:F₁ population overlap with those described previously in one of these two studies. This level of concordance is even more remarkable in light of the fact that one of the Smagulova deserts was eliminated from our analysis because of a complete lack of sequence (chromosome 7, 39 Mbp; see also new GRCm38 assembly of the mouse genome), and 9 additional regions that fail to pass thresholds for inclusion in our list nonetheless show low levels of recombination in the G₂:F₁ population. More importantly, data from the second study (Brick et al. 2012) can be used to estimate the density of DSBs in any given region. On average, there is an 18-fold reduction in DSB density (range 14- to 24-fold; Wilcoxon’s rank-sum test, P = 1.4 × 10⁻⁵⁰; H₀: equal number of DSBs per 500-kbp window in cold regions vs. noncold regions) in cold regions compared to the genome-wide average (Figure S8), with the caveat that DSBs in repetitive sequence typically cannot be mapped via high-throughput sequencing. Across the four strain backgrounds of these two studies, an average of 9 (range 8–11) of our cold regions have no DSBs and less than half of these have low-complexity or nonunique sequence that may interfere with sequencing-based DSB identification (File S4).

We conclude that the vast majority of cold regions identified in the G₂:F₁ population represent bona fide regions of suppressed recombination that are independent of genetic background and strongly associated with a reduction in density of recombination-precursor sites.

Genomic analysis of cold regions:

We analyzed cold regions with regard to several genomic features that have been associated with suppressed crossing over in other regions (such as centromeres): low C+G content, low gene content, and enrichment for complex duplications and repeated sequences (López-Flores and Garrido-Ramos 2012). The results are presented in File S4.

The overall C+G content in cold regions is lower than the genome-wide average (38.7% vs. 42%), but the distribution is multimodal (Figure S9). We observed a marked enrichment for relatively long (>20 kbp) segmental duplications, either in tandem or inverted, in cold regions. On average, almost 32% of the sequence of a single cold region is composed of segmental duplications; but in aggregate, segmental duplications account for 47.7% of the total sequence spanned by the 59 cold regions. In fact, the size and segmental duplication content of cold regions are correlated (r² = 0.664). However, 16 cold regions are completely devoid of segmental duplication.

Discussion

Using a unique multiparental intercross design, we have produced a new linkage map for the mouse genome that extends our understanding of the genetic and genomic underpinnings of meiotic recombination. Our map has three key features: very dense genotyping, balanced contributions from each sex, and the presence of uniformly high levels of genetic diversity across the genome. We observe that genetic background influences the overall level of recombination in a sex-specific manner. The pattern of genetic effects in G₁ males implicated loci on both the X chromosome and the autosomes. Interestingly, these effects worked additively and in opposition to produce relatively similar levels of recombination across founder strains. We were unable to precisely map any QTL and it appears likely that multiple unmapped autosomal loci may contribute to the overall recombination rate, a conclusion in line with previous QTL-mapping experiments (Murdoch et al. 2010; Dumont and Payseur 2011). However, our measure of recombination in each individual, the number of crossovers inferred in at most two offspring, is substantially noisier than cytological approaches to estimate recombination used in those previous studies. Such techniques usually involve visualization and counting of crossover-associated proteins via immunofluorescence in a sample of single spermatocytes (Anderson et al. 1999) and yield tens of observations (i.e., independent meioses) per individual. In practice, such techniques are difficult to apply in the female germline and cannot precisely resolve the genomic location of crossovers. Our design, by contrast, allows both the counting of crossovers (through both male and female meioses) and the localization of those events with great precision, enabling us to analyze the effects of sex on both the level and the genomic distribution of recombination and to identify cold regions for recombination. Larger sample sizes and experimental designs that randomize the autosomal allelic combinations more efficiently, such as the diversity outbred (DO) population (Svenson et al. 2012), will be required to map loci affecting overall recombination rates.

We observe an increase in crossover density in the distal ends of every mouse autosome in male meiosis. This observation holds independent of the genetic background, chromosome size, and number of crossovers per chromosome and leads to the concentration of almost one-third of all crossover events in the distal 10th of autosomes in male meiosis. Similar patterns are observed in humans and chimpanzees (Broman et al. 1998; Auton et al. 2012).

Sex effects on overall map length in eutherian mammals (Dunn 1920; Dunn and Bennett 1967), and to a lesser extent sex differences in regional crossover density (Broman et al. 1998; Dumont and Payseur 2011), are not novel observations. However, the spatial and temporal precision with which we identify crossover events in this experiment allows us to link meiotic outcomes to their generating processes. We do so by exploiting the asymmetry of peaks of crossover density among chromosomes with different numbers of crossover events (Figure 4). That both the chromosomal position and the shape of the distal peak in male meiosis are identical on single- and double-recombinant chromosomes—independent of strain background, chromosome size, or sequence content—suggests that the distal event occurs via a regulated process. A process that consistently results in a concentration of crossover events in the distal portion of chromosomes must be polarized either in space or in time. Remarkably, the distribution of crossover events is clearly different from the density and individual strength of hotspots identified through high-resolution analysis of DSBs (Brick et al. 2012; Khil et al. 2012) (Figure S5). The fact that nonrecombining regions of the sex chromosomes are nonetheless marked by DSBs in male germ cells (Wojtasz et al. 2012) provides further evidence for an additional layer of regulation between DSB formation and their resolution as crossovers in males.

The conservation of the broad-scale features of the recombination landscape across divergent species strongly suggests that the recombination landscape in male meiosis is controlled in large part at the chromosomal level. Such a model is consistent with the observation that in many organisms, including male mammals, chromosome pairing and synapsis progress from the telomeres inward (reviewed in Hunter 2003). The early steps of meiosis thus provide a simple and universal mechanism for identifying chromosome ends independently of the number, morphology, and sequence composition of the chromosomes in a given species. It is attractive to speculate that enrichment for crossovers in the distal ends of chromosomes in males evolved as a result of the obligation for a crossover in the short and subtelomerically located region of homology between the X and Y chromosomes known as the pseudoautosomal region (PAR) (Burgoyne 1982; Mohandas et al. 1992). Once the mechanism that ensures the presence of a crossover in the PAR evolved in males, it is easy to imagine that it was co-opted to act in every other chromosome. The absence of this constraint in females would explain the sex differences in crossover density. Marsupials, an outgroup to eutherian mammals whose sex chromosomes lack a PAR, provide preliminary support for this hypothesis. The program for pairing and segregating the sex chromosomes in marsupials differs in important ways from that in eutherians (Page et al. 2005), and the most recent linkage maps for marsupial species including wallaby (Zenger et al. 2002) and opossum (Samollow 2004) show no evidence for male-specific expansion in subtelomeric regions. The evolution of eutherian sex chromosomes may thus be intimately linked to chromosome-scale behavior of the recombination machinery.

The observed sex differences in map length and spatial distribution of recombination have practical implications for the design of mapping experiments. While the female map is longer, mapping through males will provide improved resolution for loci in the distal regions of chromosomes. Furthermore, the field of mouse genetics is increasingly embracing the use of multiparental reference populations such as the CC (Collaborative Cross Consortium 2012), the HS (Valdar et al. 2006), and the DO (Svenson et al. 2012). Genetic analysis in these populations relies on the accurate identification of the founder haplotype inherited locally by each individual, a task that becomes increasingly difficult in the chromosome ends and in the presence of increasing levels of recombination. Genotyping platforms can be designed to overcome these challenges: the new MegaMUGA array spaces markers on a grid defined by genetic rather than physical distance (Rogala et al. 2014), allowing precise and accurate detection of subtelomeric crossovers.

Finally, we have identified >50 regions of dramatically reduced recombination that we term cold regions. These regions represent the left tail of the sampling distribution of local recombination rate. If cold regions are purely artifacts of sampling, then we would expect their location to be random, such that they should not be replicated in independent experiments and that their number and size should decrease as an increasing number of meioses are sampled. However, a majority of our cold regions are replicated in three independent experiments—the HS, the DO, and an intercross between CAST/EiJ, PWK/PhJ, and WSB/EiJ—representing at least an order of magnitude more independent meioses than were captured in the G₂:F₁ (summarized in File S4). Furthermore, our cold regions are depleted for DSBs (Wilcoxon’s rank-sum test, P = 1.4 × 10⁻⁵⁰; H₀: equal number of reads per 1-Mbp window in cold regions vs. noncold regions) in a range of genetic backgrounds. In an F₂ or backcross design a cold region could arise due to a simple inversion, but this is unlikely to be case in our experiment: all eight G₀ founder strains would have to carry a different large inversion allele.

One-third of cold regions span genomic regions enriched for segmental duplications, and local recombination rate and density of segmental duplications are inversely correlated genome-wide [Pearson’s ρ = −0.26, 95% C.I., (−0.28, −0.23); Figure S10 and File S6]. In fact, some of the larger and more complex tandem duplications and rearrangements in mice are among the coldest regions for recombination (Figure S11). As in pericentromeric regions, accumulation of repeated sequences could be either a cause or an effect of suppressed recombination. Either case leads to a paradox: tandem duplications are generated through unequal (i.e., nonallelic) recombination, but levels of crossing over in these regions are exceedingly low. A simple explanation for this paradox is that some cold regions can be hotspots for de novo structural variation. This hypothesis predicts that cold regions with segmental duplications should be enriched for structural variants and that multiple independent variants should arise over short evolutionary times.

Support for this hypothesis can found first and foremost in a previous study that observed de novo structural variants within a single inbred strain, C57BL/6J, in four of our cold regions, using tiling arrays (Egan et al. 2007). In fact, structural variants are twice as common in cold regions as in the rest of the genome—in the eight founders of the CC; in the five founders that are classical laboratory strains; and in comparisons between two sister inbred strains, C57BL/6J and C57BL/6NJ (File S4). However, the true relative incidence of structural variants in cold regions likely exceeds this estimate. The best available catalog of structural variants in 18 laboratory inbred strains (Yalcin et al. 2011) has limited coverage of regions rich in segmental duplications (including our cold regions) due to the inherent difficulty in accurately aligning short reads to repeated sequences (Figure S12).

To circumvent the limitations of sequencing, we took advantage of data from the MegaMUGA genotyping array to explore the relationship between segmental duplications, coldness for recombination, and structural variation. This approach finds evidence for structural variation in segmentally duplicated portions of our cold regions. A representative example (chromosome 5: 93–96 Mbp) is displayed in Figure 7. This region has complex segmental duplication in the C57BL/6J reference sequence (see dotplot in Figure 7A). The wide variation in sum intensity at probes within the region (Figure 7B) suggests differences in copy number between strains. Inspection of the two-dimensional intensity plots (Figure 7C) demonstrates that the three strains (A/J, C57BL/6J, and NZO/HILtJ) with highest sum intensity carry at least two paralogous alleles at the first two probes, while the remaining classical inbred strains carry only one allele. At the third probe three strains (again A/J, C57BL/6J, and NZO/HILtJ) carry a different allele but in equal copy number to two wild-derived strains, CAST/EiJ and PWK/PhJ. In contrast, three strains (129S1/SvImJ, NOD/ShiLtJ, and WSB/EiJ) have intensities consistent with the presence of zero copies. Finally, the tree derived from principal components analysis of intensities in this region (Figure 7D) clearly segregates the classical inbred strains in a pattern consistent with panel sum intensities (Figure 7B) but inconsistent with local phylogeny based only on SNPs (Figure 7E) (Yang et al. 2011; Wang et al. 2012; Welsh et al. 2012). Taken together, these data provide additional evidence that structural variants arise multiple times in cold regions with segmental duplication. Studies in wild mice, both from Mus and sister clades, can provide further insights regarding the evolutionary significance of cold regions with respect to both genome stability and patterns of linkage disequilibrium.

Figure 7.

Cold regions enriched for complex tandem duplications and inversions show evidence of structural variation between inbred strains. Strain abbreviations are as follows: A, A/J; B, C57BL/6J; C, 129S1/SvImJ; D, NOD/ShiLtJ; E, NZO/H1LtJ; F, CAST/EiJ; G, PWK/PhJ; and H, WSB/EiJ. Color coding of strains is consistent across panels. (A) Dotplot from self-alignment of reference sequence (GRCm38/mm10 assembly) in a representative cold region. A dark dot represents >95% sequence identity between a pair of 100-bp windows. Linear clusters parallel to the main diagonal thus represent tandem duplications, and linear clusters perpendicular to the main diagonal represent duplication with inversion. (B) Profile of sum intensity at the eight probes (GRCm38/mm10 coordinates) within the region, for classical inbred strains only (strains A–E). (C) Two-dimensional intensity plots for three representative probes in the region whose nominal coordinates lie within a segmental duplication. Normalized intensity for the A and B alleles is plotted on the x- or the y-axis, respectively; definition of A and B alleles is arbitrary. Each point represents a single individual. (D) Unrooted tree based on principal components analysis on sum intensities (see Materials and Methods) at the eight probes in the region, for classical inbred strains only. (E) Local phylogeny based on SNPs across the compatible interval (chromosome 5: 91,477,046–96,609,347) spanning the region (Wang et al. 2010, 2012).

In conclusion we report here the newest version of the linkage map for the laboratory mouse, with more precise localization of crossover events and more comprehensive coverage of segregating variation than previous maps. Although a study of this type is the most basic and traditional work in genetics, our results provide several new and important insights into the nature and spatial pattern of recombination across generations. First, we expand knowledge of sex differences in regional crossover density by describing sex-specific properties of the recombination landscape that are general across all autosomes and strain backgrounds. Second, we demonstrate that by selecting a unique experimental design that combines a highly informative population with very dense genotyping we are able to infer dynamic properties from static data. Finally, we provide a catalog of cold regions for recombination that reveals a paradoxical inverse relationship between recombination and segmental duplication. This work provides a foundation for testing specific hypotheses regarding the effect of sex and genetics in recombination.

Data Accession

The recombination maps from the G₂:F₁ population—sex specific, sex averaged, strain specific, and strain averaged—will be made publicly available via the Mouse Map Converter tool (http://cgd.jax.org/mousemapconverter/) hosted by the Center for Genome Dynamics (CGD) at the Jackson Laboratory. Raw genotype data in the form of Affymetrix *.cel files will be made available for download on the CGD repository page (http://cgd.jax.org/datasets/diversityarray/CELfiles.shtml). Code to generate and analyze genetic maps is available via GitHub: http://github.com/andrewparkermorgan/cc-g2f1/.