Within the 34 three-generation pedigrees, we considered transmissions from a total of 98 first generation meioses (49 paternal, 49 maternal). This analysis revealed a total of 103 SNP sites (henceforth ‘NCO sites’) putatively affected by autosomal NCO events: 97 with standard ascertainment, and an additional six that are detectable but do not meet all the criteria for inclusion in the rate calculation (Figure 1C; Source code 1; ‘Materials and methods’—‘Determination of informative sites’). Most (76/103) NCO events derive from a single SNP, while others contain two or three NCO sites that delimit a tract. The NCO sites have roughly equal numbers of homozygous and heterozygous genotype calls in the recipient (53% heterozygous sites, p = 0.56, two-sided binomial test, this and other statistical analyses included in Source code 2), as expected, providing further confidence that the calls are not spurious. Furthermore, we confirmed genotype calls for a subset of the putative NCO events using whole genome sequence data generated by the T2D-GENES Consortium. Sequence data were available for 52 of these NCO sites, of which 50 are concordant with the SNP array calls (‘Materials and methods’—‘Validating NCO events’, Source code 1). Of the two discordant sites, one shows evidence of being an artifact in the sequence data rather than the SNP array data, and for the other, the source of error is unclear (see ‘Materials and methods’—‘Validating NCO events’). Overall, the error rates in these data are low, and so in what follows we assume that all 103 detected NCO events are real.

Meiotic NCOs are thought to localize to the same hotspots as COs (Baudat et al., 2013), and studies at specific loci in sperm have supported this hypothesis (Berg et al., 2011). To evaluate this question using genome-wide data, we utilized CO rates that Kong et al. estimated based on events identified in an Icelandic pedigree dataset (Kong et al., 2010). This genetic map omits telomeres, and thus these rates are only available for a subset of our identified NCOs. The overlapping de novo NCOs show strong enrichment in sites with sex-averaged CO rate ≥10 cM/Mb (Figure 2—figure supplement 1). Indeed, 18 of the 72 events that we can examine (26%) localize to such regions (using only one SNP per NCO event), while 4.2% of informative sites have this high a rate. This co-localization is unlikely to occur by chance (p = 8.2 × 10⁻¹⁰, one-sided binomial test), indicating that NCOs are strongly enriched in CO hotspots, and providing further validation that the detected NCO events are real.

The enrichment of NCO in regions with high rates of meiotic CO suggests that the NCO resolutions are meiotic in origin. To explore this question further, we compared the locations of the NCO events with a recently reported genome-wide map of meiotic DSB hotspots in human spermatocytes (Pratto et al., 2014). We focused our analysis on NCO events transmitted by individuals likely to carry only the PRDM9 zinc finger A or B alleles (see ‘Materials and methods’—‘PRDM9 variants’), since individuals with different PRDM9 zinc finger domains are known to have hotspots in distinct locations (Baudat et al., 2010). We further omitted NCO sites that occur near COs (and are consequently ambiguous as to which homolog converted; see below and ‘Materials and methods’—‘Inclusion criteria’). For this analysis, we considered NCO events rather than single NCO sites, and report an event as overlapping a DSB if any NCO site within it overlaps a DSB. By these criteria, there are 51 events, of which 26 (51%) overlap a meiotic DSB hotspot. Moreover, when focusing on events transmitted by males (because the DSB map is for spermatocytes), 19 of 27 events (70%) overlap a DSB hotspot. This enrichment is highly significant, as only 5.5% of informative sites overlap a DSB hotspot (p < 10⁻⁸, calculated from 10⁸ permutations; see ‘Materials and methods’—‘Inclusion criteria’). Thus, the NCOs tend to occur at sites of meiotic DSB.

Moreover, the rate at which the NCO events overlap (sex-averaged) historical hotspots inferred from LD is almost identical to the rate at which meiotic DSBs occur in such locations. Considering all unambiguous NCO event locations in male PRDM9 A/B-only carriers, 56% (15/27) overlap the (population-averaged) LD-based hotspots (The International HapMap Consortium, 2007), when between 52% and 63% of DSB hotspots from spermatocytes do, depending on the source population of the LD map analyzed (Pratto et al., 2014). The overlap for NCO events from both sexes is similar, with 55% (28/51) of events overlapping LD-based hotspots. Finally, there is no overlap of the NCO events with putative fragile sites (Fungtammasan et al., 2012), one of the important sources of mitotic recombination (see Song et al., 2014). Given these observations, we conclude that most (possibly all) of our events arose in meiosis.

The observation of 97 ascertained NCO sites out of 12.1 million informative sites provides an estimate of the rate of NCO per bp. Assuming the set of informative sites is unbiased with respect to the recombination rate, the rate of NCO is equivalent to the number of sites affected by NCO divided by the number of informative sites. This represents the proportion of the genome affected by NCO, or equivalently the probability that a given site will be part of a NCO tract per meiosis.

As Figure 2A shows, however, our SNP array data are enriched for regions of high recombination relative to the full genome, and it is necessary to account for this bias. We therefore estimated the rate of NCO in each of six recombination rate intervals based on the HapMap2 recombination map (Figure 2A), by dividing the number of NCO sites by the number of informative sites observed in each bin. The overall NCO rate is then the sum of these rates, each weighted by the proportion of the autosomes that occurs in the bin. This procedure yields a sex-averaged rate of R = 5.9 × 10⁻⁶ per bp per meiosis (and a 95% confidence interval [CI] of 4.6 × 10⁻⁶–7.4 × 10⁻⁶, calculated by 40,000 bootstrap samples with 10 Mb blocks).

Figure 2 with 1 supplement see all

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Sperm-typing data have also been used to examine the number and tract length of NCO events. Notably, a study by Jeffreys and May that examined three hotspots in detail (Jeffreys and May, 2004) found the number of NCO events to be 4–15 times that of COs, with a mean tract length of 55–290 bp. The rate R can be calculated as the number of NCO tracts in a meiosis multiplied by the tract length and divided by the genome length. Using the estimates from Jeffreys and May yields R = 2.6 × 10⁻⁶ to 5.2 × 10⁻⁵/bp/generation (for a genome-wide CO rate of 1.2 cM/Mb), a range that includes our estimate. Our results are therefore concordant with those from sperm-based analyses; they are also consistent with several LD-based studies of genome-wide levels of NCO (Ardlie et al., 2001; Frisse et al., 2001; Gay et al., 2007).

Considering the parent of origin of each NCO event, we found that the two SNP arrays differ significantly in number of events detected per sex (p = 5.1 × 10⁻⁴, χ² one degree of freedom [df] test), with the lower density SNP dataset uncovering fewer male-specific events than expected. This bias may be caused by a lower coverage of the telomeres in the low density SNP array, and makes the analysis of potential differences in NCO rate between the sexes difficult. Nevertheless, considering the position of events captured by genotype arrays reveals broad-scale localization differences, with male events more prevalent in the telomeres and female events relatively dispersed throughout the genome (Figure 1C,D). These sex differences in localization are similar to those seen for CO events (Kong et al., 2010), as expected from a shared mechanism for the broader-scale (e.g., megabase-level) control of both types of recombination.

Deviations from the Mendelian expectation of 50% transmission of each allele at a polymorphic site have been observed a number of recombination hotspots in humans. Many of these asymmetries result from polymorphisms that occur within motifs bound by PRDM9 (Webb et al., 2008). Recombinations at these sites typically show under-transmission of the allele that better matches the PRDM9 motif, a phenomenon thought to arise through initiation bias due to more frequent breakage of the homolog with a better match to the motif. We identified four NCO events that overlap sequences that match at least six of the eight predictive bps in the degenerate 13-mer motif bound by PRDM9 (Myers et al., 2008) (in all four cases, there are exactly 6 of 8 matching bps) and in which a SNP occurs at one of the non-degenerate positions. Because the PRDM9 motif is GC rich, initiation bias would be expected to predominantly transmit AT alleles, but instead all four of these events transmit GC alleles. Notably however, for three of the events, sequences that match the PRDM9 motif at seven of eight positions occur at other positions within 2 kb of the NCO site, and for the fourth, another motif with 6 of 8 matching bps occurs within 2 kb. Thus, these four events may not be caused by initiation bias.

A distinct form of bias in transmission that does not depend on the presence of polymorphisms in the PRDM9 binding motif is thought to occur when AT/GC heteroduplex DNA arises during the resolution of recombination and is preferentially repaired towards GC alleles (Duret and Galtier, 2009). A recent sperm-typing study reported on two loci that exhibit such biased gene conversion, associated with NCO but not CO events (Odenthal-Hesse et al., 2014). This sperm-based study is, to our knowledge, the first to demonstrate direct evidence of gBGC in mammals. In the NCO events identified here, we saw no evidence for a difference in GC transmission rate between the two SNP density datasets (p = 0.18, χ² 1-df test), or between males and females (p = 0.79, χ² 1-df test), and so considered the data jointly. For this calculation, we again omitted the ambiguous NCO events (described below and ‘Materials and methods’—‘Inclusion criteria’) and we excluded the four sites that occur within PRDM9 motifs. The remaining 92 NCO sites all have an AT allele on one homolog and GC on the other, a consequence of the fact that only ≤1% of sites on the Illumina SNP arrays are A/T or C/G SNPs. We observed a strong bias towards the transmission of G or C: of the 92 sites, 63 transmit G or C alleles (68%, 95% CI 58–78%; p = 5.1 × 10⁻⁴, two-sided binomial test). SNP variants at CpG dinucleotides account for 39 of these 92 sites, and these also show GC bias, with 25 CpG sites (64%) transmitting GC alleles, and no evidence of rate difference between transmissions at CpG and non-CpG sites (p = 0.58, χ² 1-df test). By comparison, the sperm-typing study noted above found that two of six assayed hotspots exhibited detectable levels of gBGC, and these two loci transmitted GC alleles in ∼70% of NCO transmissions (Odenthal-Hesse et al., 2014). Across recombination rate bins, we observed consistent GC transmission rates (p = 0.67, χ² 5-df test Figure 2B). Since the strength of gBGC depends on both the degree of bias and the rate of recombination, this finding implies that the effects of gBGC will be strongest in high recombination rate regions, as seen in analyses of polymorphism and divergence (Duret and Galtier, 2009).

The data allow us to estimate NCO tract lengths, with upper bounds derived from informative SNPs that flank a NCO tract and lower bounds given by the distance spanned by SNPs involved in the same tract. As previously noted, most NCO events involve only one SNP, but a total of twelve regions (ten with information from SNP array data only, and two including information from the sequence data) have tracts that include multiple SNPs (as plotted in Figure 3). From these data, we deduced that five of these events have a lower bound on tract length of at least 1 kb while the smallest is at least 94 bp. In turn, one tract is at most 144 bp—only slightly longer than the minimum tract involving more than one SNP (≥94 bp)—and four events have tracts that must be shorter than 1400 bp. These observations, coupled with the variable length in tracts that occur in the clustered NCO events described below (see Figure 4A), suggest that tract lengths span at least an order of magnitude (i.e., 100–1000 bp).

Figure 3

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Because NCOs identified using SNP arrays are sparsely sampled, our data may be enriched for events with longer tracts since such tracts impact a larger number of sites. This effect would bias an estimate of the mean tract length using the data from this study. It is also possible that some of the longer events result from clustered but disjoint tracts, as described below. Due to these potential sources of bias, our data cannot be used to learn about mean tract lengths without strong assumptions.

We used Complete Genomics resequencing data generated by the T2D-GENES Consortium to examine variants surrounding several of the identified NCO events at closer resolution. In order to confidently phase these regions, we required sequence data for both parents and three children (including the NCO event recipient); such data were available for two pedigrees. In these pedigrees, there are a total of 15 regions with evidence for a NCO event in the SNP array data. Two of these regions are not included in this analysis: for one, the sequence data do not contain a genotype call for the site putatively affected by NCO, while in the other, genotype calls do not match the sequence data. Neither locus contains other sites affected by NCO in the sequence data.

Figure 4A shows the phase for the 13 regions included. In four cases (haplotypes 10–13), multiple disjoint NCO tracts occur within a short interval of less than 30 kb, with the discontinuities evident from informative sites located between the NCO tracts. Two of these events (haplotypes 11 and 13) occur near COs, and the transmitted haplotypes do not allow us to determine unambiguously which sites experienced the NCO event. (This determination depends on whether the haplotype upstream or downstream of the CO is considered the ‘background.’) Figure 4A plots the NCOs that result in shorter tracts. The four cases occur in a single pedigree, three in the mother, and one in the father (haplotype 11). Using the LD-based genetic map length of the 100 kb around these four regions, we found that this clustering is highly unexpected, with a probability of observing two independent tracts within the four regions ranging from p = 2.9 × 10⁻⁶ to 1.9 × 10⁻⁴ (for each region independently; see ‘Materials and methods’—‘Examination of regions containing clustered NCOs’).

Figure 4

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To check for possible artifacts, we performed Sanger sequencing of the three-generation pedigrees for six regions in three of these four haplotypes, indicated by boxes in Figure 4A. The Sanger sequence data are concordant with the genotypes from the whole genome sequence data at every site and in all individuals for which we were able to call genotypes (see ‘Materials and methods’—‘Examination of regions containing clustered NCOs’). We also examined these regions for overlap with segmental duplications, but found none (‘Materials and methods’—‘Examination of regions containing clustered NCOs’). Finally, to evaluate whether an uncharacterized paralogous sequence variant could confound the results, we considered the genotype status (homozygous or heterozygous) of variants within these regions. Haplotypes 10 and 12 include heterozygous and homozygous genotypes both within and outside the NCO tracts. For haplotypes 11 and 13, the genotypes at all NCO sites are homozygous whereas the genotypes at other sites (blue in Figure 4A) are heterozygous. This observation raises the concern of a structural variant or duplicated sequence that has not been identified and spans the nearby CO breakpoint. In this case, heterozygous genotypes could be mismapped to the wrong side of the CO and possibly mimic a NCO tract. Reassuringly, at all these positions, the non-transmitting parent is homozygous, one sibling is heterozygous, the other is homozygous, and neither of the other children received a recombinant haplotype. Thus, all four events appear to comprise true NCOs, but caution is warranted in interpreting two of the four cases.

Intriguingly, the alleles within the NCO events show strong GC bias: For the two unambiguous events (haplotypes 10 and 12), GC alleles were transmitted at 9 out of 10 heterozygous AT/GC SNPs affected by NCO. Moreover, considering all sites in haplotypes 10–13 contained within or between the NCO tracts and irrespective of NCO status, G or C was transmitted at 32 of 43 (74%) heterozygous AT/GC SNPs (‘Materials and methods’—‘Examination of regions containing clustered NCOs’). These findings raise the possibility that the patchy repair resolutions observed in the four events result from a GC biased repair process that operates discontinuously within long stretches of heteroduplex DNA. Alternatively, these results could be explained by repeated template switching, as has been observed in Saccharomyces cerevisiae (Tsaponina and Haber James, 2014).

Further examination of our array-based data revealed additional events: three more clustered NCO events as well as six NCO events near but disjoint from CO resolutions (Figure 4B). Two of these haplotypes (numbers 18 and 19) are the same cases that show clustered NCO in sequence data (Figure 4A, haplotypes 11 and 13); all other events were seen in distinct pedigrees. These complex CO resolutions shed light on the distances over which such events may occur. The complex CO events previously described in humans were seen in assays of relatively short intervals of ≤4 kb around CO breakpoints, and yielded an estimated frequency of 0.17% (Webb et al., 2008). The results from the current study indicate that complex resolutions also occur farther from the CO breakpoint, so may be more common. Whether the observations at short and longer distances result from the same phenomenon remains to be elucidated.

To our knowledge, this is the first observation of clustered but discontinuous NCO gene conversion tracts in mammals, although patterns that resemble those shown in Figure 4A have been reported in meiosis (Martini et al., 2011; Globus, 2013) and mitosis (St Charles and Petes, 2013; Yin and Petes, 2013) in S. cerevisiae. We further note that some events classified as complex CO in humans (based on a limited number of markers) may in fact be complex NCO (Webb et al., 2008). The observed complex NCOs and distant forms of complex CO (Figure 4B, haplotypes 17–22) both point to a property of mammalian recombination that is poorly understood and in need of further characterization.

In addition to the NCO events with tracts that span no more than 5 kb, we identified five longer-range recombination events: three continuous tracts, and two that showed a clustering pattern (see Figure 5). Each event occurred in a different pedigree; the continuous tract that spans ∼79 kb was transmitted by a male, and the four other events occurred in females. The long continuous tracts could conceivably reflect double COs in extremely close proximity, as might arise from a CO-interference independent pathway (Fledel-Alon et al., 2009), but the clustered events cannot be explained in this way. For two events, sequence data are available and validate the genotype calls, indicating that the case that spans at least 9 kb in the genotype data is in fact at least 18 kb long (haplotype 23), and confirming the case in which clustered events span ∼203 kb (haplotype 26).

Figure 5

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Haplotypes 23, 24, and 27 reside on the p arm of chromosome 8 where a long inversion polymorphism occurs (Antonacci et al., 2009). Single COs within inversion heterozygotes can be misinterpreted as more than one CO event (Broman et al., 2003), yet these three recombination events are >1.7 Mb outside the inversion breakpoints, so should not be affected. One possibility is that the large inversion polymorphism leads to aberrant synapsis during meiosis, leading to complex repair of DSBs. In that regard, we note the transmitter of haplotype 23 is heterozygous for tag SNPs for the 8p23 inversion polymorphism (Antonacci et al., 2009), and that a sibling inherited a haplotype from the same parent with a CO at the same position as the end of the tract for haplotype 23. This co-localization may be due to effects of the inversion on synapsis; alternatively, this could indicate that the sites are incorrectly positioned, resulting in inaccurate inference of breakpoint locations (Broman et al., 2003). The pattern in haplotype 27 is even more complex and difficult to explain.

This study analyzed Mexican American samples from the San Antonio Family Studies (SAFS) pedigrees. SNP array data were generated for these individuals as previously described (Mitchell et al., 1996; Duggirala et al., 1999; Hunt et al., 2005). Our study design required the use of three-generation pedigrees with SNP array data for both parents in the first generation, three or more children in the second generation, one or more grandchildren, and data for both parents for any included grandchildren. Within the entire SAFS dataset of 2490 individuals, there are 35 three-generation pedigrees consisting of 496 individuals that fit these requirements. As noted below, one of these pedigrees was not included in the analysis, so the overall sample consisted of 34 pedigrees and 482 individuals.

Each sample was genotyped using one of the following Illumina arrays: the Human660W, Human1M, Human1M-Duo, or both the HumanHap500 and the HumanExon510S (these latter two arrays together give roughly the same content as the Human1M and Human1M-Duo).

Most of the samples—21 out of the 34 analyzed pedigrees containing 293 individuals—have SNP data derived from arrays with roughly equivalent content and ∼1 million genotyped sites. We analyzed all these samples across the SNPs shared among these arrays, with data quality control applied collectively to all samples and sites (see below). After quality control filtering, 896,375 autosomal SNPs remained for the analysis of NCO.

Data for the other 13 out of 34 analyzed pedigrees comprise 189 individuals and were analyzed on a lower density SNP arrays. The majority of the samples in these pedigrees (105 individuals) have SNP array data from ∼660,000 genotyped sites. The other samples (84 individuals) have higher density genotype data available, but because other pedigree members have only lower density data, we omit these additional sites from analysis. After quality filtering, this lower SNP density dataset contained 513,283 autosomal sites.

Initially, sites with non-Mendelian errors, as detected within the entire SAFS pedigree, were set to missing. We next ensured that the locations of the SNPs were correct by aligning SNP probe sequences to the human genome reference (GRCh37) using BWA v0.7.5a-r405 (Li and Durbin, 2009). Manifest files for each SNP array list the probe sequences contained on the array and we confirmed that these probe sequences are identical across all arrays for the SNPs shared in common among them. We retained only sites that (a) align to the reference genome with no mismatches at exactly one genomic position and that (b) do not align to any other location with either zero or one mismatches.

We updated the physical positions of the SNPs in accordance with the locations reported by our alignment procedure and utilized SNP rs ids contained in dbSNP at those locations. We omitted sites for which multiple probes aligned to the same location. Some sites had either more than two variants or had non-simple alleles (i.e., not A/C/G/T) reported by dbSNP, and we removed these sites. We also filtered three sites that had differing alleles reported in the raw genotype data as compared to those reported for the corresponding sites in the manifest files. We filtered a small number of sites for which the manifest file listed SNP alleles that differed from those in dbSNP at the aligned location.

Some SNPs are listed in dbSNP as having multiple locations or as ‘suspected,’ and we removed these sites from our dataset. We also removed sites that occur outside the ‘accessible genome’ as reported by the 1000 Genomes Project (The 1000 Genomes Project Consortium, 2012, roughly 6% of the genome is outside this), and sites that occur in regions that are segmentally duplicated with a Jukes-Cantor K-value of <2% (this value closely approximates divergence between the paralogs; Bailey et al., 2002). Finally, we removed sites that occur within a total of 17 Mb of the genome that receive excess read alignment in 1000 Genome Project data (Genovese et al., 2013).

We next conducted more standard quality control measures by performing analyses on two distinct datasets: (1) including individuals that were genotyped at ∼1 million SNPs (1932 samples) and (2) including all 2490 samples. On the more densely typed dataset, we first removed any site with ≥1% missing data and those for which a χ² test for differences between male and female allele frequencies showed |Z| ≥ 3. We then removed 29 samples with ≥2% missing data. Next we examined the principal components analysis (PCA) plots (Patterson et al., 2006) generated using (a) the genotype data and (b) indicators of missing data at a site. These plots generally show an absence of outlier samples, and the genotype-based PCA plot appears consistent with the admixed history of the Mexican Americans (results not shown).

For the dataset that included samples typed at lower density, we first removed sites with ≥1% missing data and sites with male-female allele frequency differences with |Z| ≥ 3. This filtering step yields SNPs of high quality that are shared across all SNP arrays, including the lower density Human660W array. Next we removed 30 samples with ≥2% missing data. Lastly, we examined PCA plots generated using (a) genotype and (b) missing data at each site, and these plots are again generally as expected with an absence of outlier samples (results not shown).

We performed minimum-recombinant phasing on the three-generation pedigrees using the software HAPI (Williams et al., 2010), but with minor modifications because this program phases nuclear families independently. Specifically, our approach phased nuclear families starting at the first generation family. After this completed, we phased the families from later generations while utilizing the haplotype assignments from the first generation. Our approach assigned the phase at the first heterozygous marker to be consistent across generations in the individuals shared between the two nuclear families. (Shared individuals are members of the second generation who are a child in one family and a parent in another.) This approach helps produce consistent phasing across generations and does not introduce extra recombinations since the phase assignment at the first marker on a chromosome is arbitrary.

After phasing, our method for detecting NCO events also handled sites with inconsistent phase between the families (though in practice nearly all sites have consistent phase assignments between families). This method excluded individual sites that have inconsistent phase and that occur within a background of flanking markers with consistent phase; we examined these sites individually and confirmed that they do not represent NCO events, but are likely driven by genotyping errors. When 10 or more informative SNPs in succession are inconsistent across families, we assumed that a CO event went undetected in one of the generations, and inverted the phase for the relevant individuals in order to identify putative NCO events.

We analyzed the inferred haplotype transmissions to identify sites that exhibit recombination from one haplotype to the other and then back again. The detection approach identified any recombination events that switch and revert back to the original haplotype within ≤20 informative SNPs.

Genotypes are only informative for which haplotype a parent transmits—and therefore recombination—at sites where the parent is heterozygous. We employed a pedigree-specific quality control measure by only considering sites in which all individuals in the full three-generation pedigree have genotype calls and no missing data; other sites are omitted. This requirement helps address possible structural or other complex variants that are specific to a particular pedigree and that may adversely affect genotype calling (as evidenced by a lack of a genotype call for some individual in that pedigree at the given site).

Because NCOs occur relatively infrequently, it is unlikely that the same position will experience NCO in multiple generations. We therefore excluded sites that exhibit NCO in any grandchild (i.e., locations with potential NCO events transmitted from the second generation). We applied this filter regardless of the NCO status in earlier generations in order to obtain unbiased ascertainment of events and informative sites. We also excluded sites that exhibit potential NCO events from a given parent and where that parent only transmits one haplotype. In this case, the genotype from the transmitting parent is likely to be in error and to be homozygous; given this consideration, we considered the site as invalid for both parents.

In principle, all children in the second generation are useful for studying meiosis in their parents, but to reduce false positives, we only analyzed a subset of these children. Specifically, we only considered a child if data for his/her partner and one or more of their children (grandchildren in the larger pedigree) were available.

We counted a site as informative (or not) relative to a given parent and a given child if sufficient data for relatives were available and if it satisfied six requirements. First, we required the parent to be heterozygous at the site. Second, as shown in Figure 1B, we required the allele that the given parent transmitted to the child also be transmitted to at least one grandchild. Third, in any series of otherwise informative sites, we counted all but the first and last sites as informative since we detect NCO events as haplotype switches relative to some previous informative site. Fourth, except at sites that are putatively affected by NCO, we required a second child to have received the same haplotype as the child that is potentially informative. This requirement helps to ensure the validity of the heterozygous genotype call of the parent. As an example, consider a pedigree with four children, three of whom received a haplotype ‘A’ at some site and the fourth of whom received haplotype ‘B’. If the fourth child were to receive a NCO at some subsequent position, it would receive haplotype ‘A’, and thus all four children would receive the same haplotype. This scenario violates the requirement that the alternate allele (not transmitted in the putative NCO) be transmitted to at least one second-generation child. Thus, at this example site, the fourth child is not informative (where it is the sole recipient of haplotype ‘B’). Note however that this site could be informative in the other children if they meet the other requirements listed here.

Fifth, we required that the site be phased unambiguously across two generations, and that if a NCO had occurred, the phase at the site would remain unambiguous in the first generation. Sites in which all individuals in a nuclear family are heterozygous have ambiguous phase. Thus, if a given child is homozygous at a marker but all other individuals in the family are heterozygous, the child is not informative at that site since a NCO event would lead the child to be heterozygous. We note that it is possible to identify putative NCOs when a child receives a haplotype that has recombined from otherwise ambiguous phase to be homozygous at this type of marker. Indeed, we identified five such putative NCO sites, but did not include them when calculating the rate of NCO since the denominator does not include ambiguously phased sites and is therefore ascertained differently.

Finally, we imposed further conditions on the transmitted haplotypes and the genotype calls in the third generation. Our focus for these filters was the erroneous case in which a NCO recipient is called homozygous but is truly heterozygous, and his/her partner and children are all heterozygous. Here, the phasing procedure may incorrectly infer that an allele transmitted by the recipient was instead transmitted by his/her partner; thus the potential NCO allele is not necessarily observed in the grandchildren. To address this issue, we filtered sites that have two properties: (1) the recipient is called homozygous, but the partner and grandchildren are all heterozygous, and (2) both parents transmit only one of their haplotypes to the third generation. If, in contrast to property (2), either the recipient or the partner transmits both his/her haplotypes, this type of erroneous NCO genotype call will produce haplotype assignments in the grandchildren with apparent recombination events relative to flanking markers. As a result, there will be an apparent NCO in the third generation and a filter noted above will remove the site from consideration.

We excluded one of the 35 available three-generation pedigrees from our analysis. The NCO recipient in this pedigree has a missing data rate that is more than double any other NCO recipient, suggesting genotype quality issues; accordingly, we observed an excessive rate of NCO event calling in this pedigree (results not shown).

Our method identified all double recombination events (defined as switches from one haplotype to the other and then back again) that span 20 informative sites or fewer. We examined the haplotype transmissions at each such reported event by hand to ensure that segregation to all children and grandchildren matches expectations. A few sites exhibited NCO events in the same interval in two or more children. Because NCO is relatively rare, it is unlikely that these are true events. Additionally, some sites were consistent with NCO events transmitted to the same child from both parents; these are again unlikely to be real and are more likely caused when a child is homozygous for one allele but called homozygous for the opposite allele. We therefore considered these cases false positives and excluded them from consideration.

Although we omitted sites in which grandchildren exhibit putative NCO events that occur at a single site, the software did not filter putative NCOs that span multiple sites. We examined all events by hand, and excluded three reported NCO events in which the grandchildren either exhibit putative NCOs longer than one SNP (therefore undetected) or show aberrant genotype calls.

The main text describes five long-range recombination events shown in Figure 5. For all these events, the recombined alleles at every site were transmitted to the third generation with no apparent recombinations or NCO events in the third generation. We excluded two other events with unexpected transmissions to the grandchildren. Specifically, one 4-SNP contiguous tract shows transmission to the third generation for three of the four recombined SNPs, but one SNP in middle of the tract was not transmitted and shows an apparent NCO in the third generation. The other 18-SNP long contiguous tract shows a putative NCO transmitted from the opposite parent across this same interval. We also excluded an event in which two sites separated by ∼27 kb exhibit NCO in the second generation, but where one site has ambiguous phase in the third generation and would not be expected to have such phasing on the basis of flanking markers.

We tested for overrepresentation of either heterozygous or homozygous genotype calls in the recipient of the putative NCOs. Overrepresentation would suggest bias and possibly artifactual detection of NCOs, but we saw no evidence of bias (p = 0.56, two-sided binomial test, this and other statistical analyses included in Source code 2). This analysis excludes the five sites identified using non-standard ascertainment and which are homozygous by detection, and also excludes a sixth non-standard site (described below in ‘Inclusion criteria’).

Of the 482 individuals that we analyzed using SNP array data, 98 were whole genome sequenced by the T2D-GENES Consortium and we were therefore able to check concordance of genotype calls. We attempted validation on all sites for which data were available for the transmitting parent or a recipient (either the child or a grandchild) of the putative NCO site (Source code 1). Within these 98 samples, genotype calls were available for 52 of the putative NCO sites (103 total); 42 of these sites include data for both the transmitting parent and a NCO recipient. One additional site had data available for relevant samples, but the sequence data do not contain calls for that position. We compared genotypes for every available parent, child, partner of the NCO recipient, and children of the recipient (grandchildren in the larger pedigree). For ambiguous NCOs, we required data for both possible NCO orientations to be concordant in order to count as validated. The genotype calls for all inspected individuals are concordant between the two sources of data for 50 of the 52 sites. One of the inconsistent sites shows a discordant genotype call between the datasets for the recipient of the NCO, but a concordant call for his child (the grandchild in the pedigree). This inconsistency suggests that the genotype data may in fact be correct. The other discrepancy occurs at a site where sequence data were unavailable for the recipient of the NCO. Here, the genotype call for the transmitting parent is discordant between the two sources of data, and the error source is ambiguous; we retained this site in the analyses.

CO rates are those reported by deCODE (Kong et al., 2010) based on COs detected in large Icelandic pedigrees. The original map is reported for human genome build 36 and was lifted over to build 37 coordinates. This map is estimated to have resolution to roughly 10 kb, and we therefore computed recombination rates in cM/Mb at each site using the genetic distances from the map at the 10 kb surrounding a site and divided by this (10 kb) window size. Because this map omits relatively large telomeric segments, we did not have rates for many sites from the SNP arrays and from the identified NCO events. We used linear interpolation to obtain rates at sites within the range of the map but not directly reported. The proportion of sites in the ‘autosomal genome’ in Figure 2—figure supplement 1 derives from all sites within the reported positions in the autosomal genetic map.

The HapMap2 LD-based recombination rates are from the genetic map generated by the HapMap Consortium (The International HapMap Consortium, 2007) using LDhat (McVean et al., 2004) that was subsequently lifted over to human genome reference GRCh37. We used analogous methods for calculating recombination rates from this map as for the CO map mentioned above, including a window size of 10 kb and linear interpolation. A few sites on the higher density SNP data (12 of 896,387) fall outside the interval of positions reported in the map and were not included in our analyses.

Mexican Americans were previously shown to carry primarily PRDM9 A and B alleles (Parvanov et al., 2010), and admixture with African descent groups may have led to the presence of PRDM9 C variants. The derived allele at SNP rs6889665 is in strong LD with this PRDM9 C variant: 96% of haplotypes with the ancestral allele contain <14 zinc fingers, with most being A or B alleles; 93% of haplotypes with the derived allele contain PRDM9 variants with ≥14 zinc fingers, including primarily the PRDM9 C variant. With a larger number of zinc fingers, the PRDM9 C variant binds a degenerate 17 bp motif distinct from the motif bound by PRMD9 A and B (Hinch et al., 2011). The higher SNP density arrays include genotypes for this site, providing information about the likely PRDM9 variant of the transmitting parent for 76/103 of the NCO sites. Of these, 11 events are transmitted by a likely PRDM9 C carrier, with a total of five carrier parents within the 48 parents for which we have genotypes. The remaining 65 events are transmitted by individuals that are homozygous for the ancestral allele at rs6889665 and thus likely to carry only the PRDM9 A or B alleles, both of which bind the common 13-mer motif (Baudat et al., 2010).

Five NCO events were identified with a non-standard ascertainment and are inappropriate for inclusion in estimating the rate of NCO. A sixth, non-standard event is part of a three SNP long tract but has ambiguous phase in the third generation; it appears to be to be a NCO site on the basis of its presence in a tract and the fact that the ambiguous phase in the third generation is consistent with neighboring sites and not suggestive of artifact. None of these sites are expected to show bias with respect to allelic composition and we therefore included them when calculating the strength of GC-bias.

Somewhat more complex cases are NCO sites that occur near CO events (Figure 4B, haplotypes 17–22). In most, a single site appears to have been involved in the NCO event, and is followed by a single site that reverts to the first haplotype, and then by a CO. Depending on whether one considers the ‘background haplotype’ to be the one upstream of the NCO and CO, or downstream of these, the site in the NCO tract differs. Thus the sites affected by NCO are ambiguous. To simplify the examination of GC-bias, we excluded these sites from consideration. The excluded haplotypes are 17–22 (Figure 4B); haplotypes 11 and 13 are the same as 18 and 19 and are thus excluded, whereas haplotypes 10 and 12 and 14–16 are unambiguous NCO tracts and are included. (Haplotypes 23–26 in Figure 5 are long-range events that are not included in any analysis.) Additionally, to avoid confounding biased repair with initiation bias driven PRMD9 binding, we omit four events that overlap partial matches to the PRDM9 motif as described in ‘Results’ (‘GC-biased gene conversion’).

To estimate the rate of NCO genome-wide, rather than exclude the ambiguous NCO sites noted above—which would bias our rate calculation downwards—we instead included both possibilities in the rate calculation, and gave each of them a weight of 0.5, while other sites have a weight of 1. There are two effects of this weighting. First, if the recombination rate bin differs across these sites, they each contribute the weight of half a site to the rate calculation for those bins. Most sites fall into the same rate bin and therefore have the same effect as counting a single site. The second effect of weighting these sites is that, in one case, we cannot tell whether the NCO was two SNPs or only one SNP long. In this case, we counted the event as 1.5 NCO sites. Finally, we observed one instance of two adjacent putative NCO sites separated from a CO by three informative sites. The three informative sites span 19.6 kb—longer than our threshold for NCO events. In this case, we considered the two sites (which form a tract of length at least 264 bp) as part of a definitive NCO with weight 1.

For estimating the number of sites with CO rate ≥10 cM/Mb, we included only one SNP per tract and weighted ambiguous cases by 0.5 as above. Additionally, two ambiguous sites have CO rates that straddle this threshold, with one site slightly less, the other slightly more. To be conservative in estimating a p-value, we considered these sites as falling below the threshold.

We checked overlap between DSB hotspots from PRDM9 A/A and A/B type individuals determined by Pratto et al. (2014) and the set of NCO sites that are unambiguous (i.e., omitting haplotypes 17–22 from Figure 4B) and for which the transmitting parent is likely to carry only PRDM9 A or B alleles (see ‘PRDM9 variants’ above). A secondary analysis of these DSB hotspots included only events transmitted by males. To calculate overlap with LD-based hotspots (The International HapMap Consortium, 2007), we again included only unambiguous events but did not further restrict the analysis. For both DSB and LD hotspots, we counted overlap with respect to events (some of which include multiple converted SNPs) rather than single NCO SNP sites, and we defined a NCO event as overlapping a hotspot if any of its sites overlap. To assess the significance of the overlap, we performed permutation by randomly sampling NCO sites among all informative sites, selecting the same number of adjacent SNPs as observed for each event. We repeated this process 10⁸ times, each time calculating the proportion of NCO events that overlapped a DSB. Out of 10⁸ permutations, no samples obtained at least the level of overlap seen for the actual NCO events; thus p < 10⁻⁸.

To examine tract lengths, we omitted all but one ambiguous event. For the one included ambiguous event, the two possibilities have tract lengths ≥1615 bp and ≥365 bp (upper bounds are more than 25 kb for both). We included the shorter of these lengths (365 bp) since this lower bound holds for both possibilities. We note that the addition of the sixth, non-standard NCO site that is part of a three-SNP tract (see above) leads to a minimum tract length of 629 bp instead of 520 bp (obtained for the two-SNP tract identified with standard ascertainment).

We calculated the probability of two NCO events occurring within the four intervals in which we observed clustered NCO by rescaling the genetic distances of 100 kb surrounding these regions as reported in the LD-based map. (Note that this map includes some of the historical effects of NCO McVean et al., 2004.) We earlier estimated the per bp rate of NCO R, and R = N × l/G where N is the number of NCO events that occur in a meiosis, l is the average tract length of these events, and G is the total genome length. The genome-wide average rate of initiation of NCO at a bp is simply N/G = R/l. For an interval with genetic map length d cM, we estimated the rate of initiating a NCO by rescaling this rate as r = d/c × R/l, where c = 1.2 cM/Mb is the average genome-wide rate of CO, and where we assume l = 75 bp. The probability of two independent NCO tracts (conservatively assuming lack of interference among events) is then P = r². This calculation assumes the HapMap2 map accurately represents the relative rate of both CO and NCO events in an interval; a test for difference between the observed locations of NCO sites and expected locations based on this map are generally consistent with this assumption (p = 0.15, χ² 5-df test).

We performed Sanger sequencing on individuals from the three-generation pedigrees in which clustered NCOs occurred. Assayed samples included both parents, all children (including the NCO recipient), the partner of the NCO recipient, and all (four or five) grandchildren of that couple. Overall, sequencing included 11 or 12 samples for each of the three regions examined. We manually examined chromatograms to determine genotype calls. For haplotype 10 (Figure 4A), Sanger sequence data overlaps five SNPs called in the Complete Genomics data. For three of these five positions, the sequence data quality was sufficient to easily call genotypes in all samples, whereas for two positions, we called genotypes only in the four grandchildren. Three of the four grandchildren received the haplotype that resulted from a NCO, providing validation of the event at these sites. In all cases, the Sanger-based genotypes are concordant with the Complete Genomics genotypes. For haplotype 11, the Sanger sequence overlapped four SNPs called in the Complete Genomics data. For one of these sites, we called genotypes in all samples, and for two others, we omitted genotypes for one sibling of the recipient but called all other samples. For the fourth site, we could not determine the genotype of the transmitting parent and were uncertain of three of the four siblings of the recipient, but still obtained genotypes for the recipient, one sibling, and four grandchildren. At all four sites, the genotypes that we obtained are consistent with those in the Complete Genomics data. Finally, for haplotype 12, the Sanger sequence overlaps eight sites from the Complete Genomics data. We called genotypes in the five grandchildren at seven of the eight sites, and call four of the five grandchildren at the eighth site. Data quality for other individuals in the pedigree was high for four of the eight sites, but low for the other four sites. In all cases for which we obtained genotype calls, the Sanger data are concordant with the Complete Genomics data. Overall, the Sanger sequence data provided genotype calls for three (haplotypes 11 and 12) or four (haplotype 10) NCO sites (Figure 4A) as well as one (haplotype 11) and at least two sites (haplotypes 10 and 12) that descend from the background haplotype (red in Figure 4A).

We also checked the regions for potential mismapping from paralogous sequences elsewhere in the genome. Specifically, we looked for overlap between these regions and the following resources: (a) recent segmental duplications that are <2% diverged (Bailey et al., 2002; http://ftp.1000genomes.ebi.ac.uk/vol1/ftp/technical/reference/phase2_reference_assembly_sequence/); (b) the 35.4 Mb ‘decoy sequences’ released by the 1000 Genomes Project (http://ftp.1000genomes.ebi.ac.uk/vol1/ftp/technical/reference/phase2_reference_assembly_sequence/), which contain regions of the genome that are paralogous to sequence from Genbank (Benson et al., 2014) and the HuRef alternate genome assembly (Levy et al., 2007); and (c) regions of the genome with excess read mapping in the 1000 Genomes Project (Genovese et al., 2013). Our quality control procedure already removed individual SNPs that overlap several of these resources (‘Materials and methods’—‘Quality control procedures’), and this additional analysis revealed no overlap with the regions containing these clustered events.

We examined GC transmission rates for sites within and between NCO tracts in haplotypes 10–13 (‘Results’—‘Complex clustered NCO tracts’). As previously noted, haplotypes 11 and 13 are ambiguous with respect to NCO status; for these, we included all sites between NCO tracts for both possible recombination outcomes. None of the included sites are definitively on the opposite side of the nearby CO event in the haplotypes.

We ran Primer3 (http://bioinfo.ut.ee/primer3/) using the initial presets on the human reference sequence from targeted regions to obtain primer sequences. For the suggested primer designs, we performed a BLAST against the human reference to ensure that each primer is unique, and ordered primers from Eurofins Operon. We tested each primer using the temperature suggested during primer design on DNA at a concentration of 10 ng/ul and checked on a 2% agarose gel. For any primer with poor performance, we conducted a temperature gradient, and, if needed, a salt gradient until we found a PCR mix that performed well. Next we performed PCR on the samples of interest, running a small quantity on a 2% agarose gel. We then cleaned the PCR sample using Affymetrix ExoSAP-IT and ran sequencing reactions twice for each sample using Life Technologies BigDye Terminator v3.1 Cycle Sequencing Kit. Finally, we purified each sample using Life Technologies BigDye XTerminator Purification Kit and placed these onto the 3730xl DNA Analyzer for sequencing.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We thank Scott Keeney, Maria Jasin, John Schimenti, Laure Ségurel, and Lorraine Symington for helpful discussions and Melanie Carless for bioinformatics support. We thank Swapan Mallick for sharing a version of the deCODE crossover map in GRCh37 coordinates. ALW was supported by the NIH Ruth L Kirschstein National Research Service Award number F32 HG005944 and by NIH GM83098 to MP. This work was partly completed while MP was a Howard Hughes Medical Institute Early Career Scientist. DR is a Howard Hughes Medical Institute Investigator. T2D-GENES project data generation was supported by NIH grants U01 DK085501, U01 DK085524, U01 DK085526, U01 DK085545, and U01 DK085584.

Human subjects: Institutional review board exemption was given for this study from the Broad Institute of Harvard and MIT and the Texas Biomedical Research Institute. The analysis was entirely conducted using anonymous identifiers.

© 2015, Williams et al.

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