Estimating gene conversion rates from population data using multi-individual identity by descent

1 In humans, h omologous gene conversions occur at a higher rate than crossovers, however gene 2 conversion tracts are small and often unobservable. As a result, estimating gene conversion rates is more 3 difficult than estimating crossover rates. We present a method for multi -individual identity-by-descent 4 (IBD) inference that allows for mismatches due to genotype error and gene conversion. We use the 5 inferred IBD to detect alleles that have changed due to gene conversion in the recent past. We analyze 6 data from the TOPMed and UK Biobank studies to estimate autosome-wide maps of gene conversion 7 rates. For 10 kb, 100kb, and 1 Mb windows, the correlation between our TOPMed gene conversion map 8 and the deCODE sex-averaged crossover map ranges from 0.56 to 0.67. We find that the strongest gene 9 conversion hotspots typically die back to the baseline gene conversion rate within 1 kb. In 100 kb and 1 10 Mb windows, our estimated gene conversion map has higher correlation than the deCODE sex-averaged 11 crossover map with PRDM9 binding enrichment (0.34 vs 0.29 for 100 kb windows and 0.52 vs 0.34 for 1 12 Mb windows) , suggesting that the effect of PRDM9 is greater on gene conversion than on crossover 13 recombination. Our TOPMed gene conversion maps are constructed from 55-fold more observed allele 14 conversions than the recently published deCODE gene conversion maps. Our map provides sex-averaged 15 estimates for 10 kb, 100 kb, and 1 Mb windows, whereas the deCODE gene conversion maps provide sex-16 specific estimates for 3 Mb windows. 17

18 In meiosis, the two haplotypes of a parent are combined via recombination to produce the gamete’s 19 haplotype. Recombination takes the form of crossovers and gene conversions. Crossovers are positions 20 at which switches occur between the two haplotypes, and the average distance between crossovers is 21 approximately 100 million base pairs in humans .1 In h omologous gene conversion , a tract of tens or 22 hundreds of base pairs is copied onto the transmitted haplotype from the parent’s other haplotype.2 Gene 23 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint conversion changes the allele on the transmitted haplotype only at positions where alleles on a parent’s 24 two haplotypes differ, that is, at positions of heterozygosity in the parent. Since the heterozygosity rate 25 in human populations is around 1 per thousand base pairs, 3 many gene conversions are not observable. 26 If an allele on the transmitted haplotype is changed by gene conversion, it can be difficult to determine 27 whether the changed allele is due to gene conversion or genotype error.4 28 One approach to studying gene conversions is sperm-typing.2 By typing many sperm from one or more 29 fathers, one can determine the haplotype phase of the fathers and detect possible alleles changed by 30 gene conversion in the gametes. An advantage of this approach is that many meioses can be observed. A 31 disadvantage is that genotype errors can produce miscalled alleles that look like alleles changed by gene 32 conversion.4 In contrast, the use of m ulti-generational families enables resolution of genotype error as 33 well as phase determination.4; 5 The use of nuclear families with more than one sibling does not address 34 genotype error but does allow for phase determination. 6 Collecting a large number of families is 35 challenging. The largest such analysis to date included 10,840 meioses from 2132 nuclear families and 36 identified 62,762 alleles changed by gene conversio n. The resulting gene conversion map s provide 37 estimated gene conversion rates in 3 Mb windows.6 38 Population-genetic models such as the coalescent can be used to investigate rates of gene conversion 39 from genetic data from unrelated individuals.7; 8 The resolution of such methods is not high; for example, 40 the resolution of one such analysis is one estimated rate per chromosome.9 41 In 2024, w e proposed the use of multi -individual identity by descent (IBD) to detect alleles changed by 42 gene conversion in population data .10 Application to a data from 125,361 individuals found 9,313,066 43 alleles changed by gene conversion, which was 2877 times as many allele conversion s compared to the 44 largest family study at that time, and 148 times as many allele conversions compared to a recently 45 published study, which is the largest family study to date.5; 6 Our approach to detecting alleles changed by 46 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint gene conversion from IBD data is robust to genotype error, because it requires that each allele conversion 47 be observed in two or more identical-by-descent individuals. However, the IBD segment detection in our 48 earlier method does not account for discordant alleles caused by genotype error or gene conversion. As 49 a result, the power to detect IBD segments in regions with a high rate of gene conversion is reduced, which 50 reduces power to detect allele conversions in these regions . This limitation makes our earlier method 51 unsuitable for estimating gene conversion rates. Although our earlier approach can detect alleles changed 52 by gene conversion, the analysis is cumbersome. Disjoint sets of markers must be used for detecting IBD 53 and for detecting allele conversion, and multiple analyses with different marker sets must be performed 54 in order to interrogate all markers for allele conversions. 55 In this work , we present a new method for detecting IBD that is robust to discordant alleles and that 56 eliminates the need for multiple analyses with different sets of markers. Our new method, implemented 57 in the ibd-cluster software package, employs a probabilistic model that accounts for genotype error and 58 other sources of discordant alleles. We apply the method to infer 17,404,902 alleles changed by gene 59 conversion across two data sets of sizes 39,961 and 125,361 individuals . We use the detected allele 60 conversion to estimate the gene conversion rate at resolutions of 10 kb, 100 kb, and 1 Mb. We estimate 61 the probability that a position in the genome is part of a gene conversion tract, rather than the gene 62 conversion tract initiation rate. If the average length of gene conversion tracts is the same throughout the 63 genome, these two rates will be proportional to each other. Our method estimates the relative rate of 64 gene conversion as the rate varies along the genome; it does not estimate the genome-wide rate, which 65 can be obtained from other pedigree-based or IBD-based methods.4; 11 66 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint Subjects and Methods 67 Multi-individual IBD inference 68 A set of haplotypes form an IBD cluster at a locus if they share a recent common ancestor. In inferring 69 multi-individual IBD, i.e. IBD clusters, there is an implicit or explicit dependence on underlying pairwise 70 IBD segments.10; 12; 13 However, in spite of this dependence, the inferred multi-individual IBD is not easily 71 described in terms of segments and is more readily expressed as sets of IBD haplotypes at a locus.10 Locus-72 based multi-individual IBD is ideal for detecting alleles changed by gene conversion.10 73 We previously developed a method for multi-individual IBD inference that can be applied to large samples 74 of individuals.10 The method did not allow for discordant alleles in IBD sequences. In this work, we develop 75 a multi-individual IBD inference method that is designed to handle discordant alleles in IBD segments, 76 while still retaining the computational efficiency necessary to analyze biobank-scale data. 77 The new method retains important features of our previous method, such as the use of IBD transitivity to 78 obtain linear scaling with sample size, and the application of a trim to the ends of pairwise IBD segments 79 before applying transitivity to reduce false-positive IBD. Transitivity is the property that if haplotypes ℎ1 80 and ℎ2 are IBD at a locus , and if haplotypes ℎ2 and ℎ3 are IBD at the locus , then haplotypes ℎ1 and ℎ3 81 must also be IBD. This is a natural property that multi -individual IBD should have, but the application of 82 this property to inferred pairwise IBD segments can propagate false-positive errors in detected IBD. Thus, 83 it is necessary to have a low rate of false positive error in the pairwise IBD segments that are used to infer 84 multi-individual IBD. The endpoints of IBD segments tend to be difficult to determine accurately, 14 so 85 application of a trim results in a significant reduction in false positive IBD. 86 We provide a brief description of our new multi-individual IBD inference method here and provide further 87 details in Section 1 of Supplemental Information. 88 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint We first apply a minor allele frequency (MAF) filter that excludes all markers whose second largest allele 89 frequency is less than a threshold (0.1 by default). The MAF filter retains the most informative markers, 90 reduces computation time, and reduces the number of discordant alleles in IBD segments. 91 We then identify a set of candidate pairwise IBD segments in the MAF -filtered data . The candidate -92 generating step uses four disjoint, interleaved sets of markers. The 𝑘-th marker (1 < 𝑘 ≤ 4) set contains 93 every fourth marker beginning with the 𝑘-th marker. The use of interleaved marker sets protects against 94 loss of power due to discordant alleles, since a discordant allele will be present in only one of the four 95 sets. We apply the Positional Burr ows-Wheeler Transform (PBWT)15 to each marker set to identify 96 identity-by-state (IBS) segments in the marker set that exceed a specified length ( 𝐿 = 1 cM, unless 97 otherwise stated) and that are on adjacent haplotypes when the haplotype are lexi cographically sorted 98 by the sequence of alleles looking backwards from the last marker in the IBS segment. 99 For each pair of adjacent haplotypes with IBS segment length exceeding 𝐿 cM, we use the ibd -ends 100 algorithm with all markers that pass the MAF filter to estimate the endpoints of the underlying IBD 101 segment.14 Each IBD segment endpoint is estimated as the median of the posterior endpoint distribution. 102 The ibd-ends algorithm uses a probabilistic model that allows for mismatches that arise from genotype 103 error, mutation, and gene conversion . The ibd -ends algorithm also accounts for inter -marker distances 104 which can be large in regions with unmapped sequence reads, such as centromeres. Standard methods 105 for detecting IBD segments based on IBS segment length can produce many false-positive IBD segments 106 that span long inter-marker gaps.16 The ibd-ends algorithm accounts for these inter-marker gaps and does 107 not have high false positive rates in these regions.14 We retain the IBD segment if the length estimated by 108 the ibd -ends algorithm exceeds the 𝐿 cM length threshold. We then trim 𝑇 cM (𝑇 = 0.5 cM, unless 109 otherwise stated) from each end of each IBD segment. 110 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint The preceding algorithm for identifying IBD segments will not find all IBD pairs since it only considers pairs 111 of haplotypes that are adjacent when haplotypes are sorted by the PBWT. We fill in the missing IBD by 112 enforcing IBD transitivity. When applying IBD transitivity, we take all the trimmed IBD segments that 113 overlap a position and apply transitivity to define IBD haplotype clusters at that position. 114 Gene conversion detection 115 We use the methodology described previously to detect alleles changed by gene conversion using multi-116 individual IBD.10 At each marker with MAF larger than a minimum, which is 0.1 in this work, we examine 117 the IBD clusters at the position closest to the marker. We look for IBD clusters for which at least two 118 haplotypes carry one allele and at least two haplotypes carry a different allele. These are the potential 119 allele conversions (i.e., alleles changed by gene conversion). Each haplotype belongs to an individual, and 120 that individual may be homozygous or heterozygous at the marker. If all the individuals with haplotypes 121 in the cluster are homozygous at the marker, we do not record an allele conversion because the discordant 122 alleles could be caused by the haplotypes in the IBD cluster carrying a cryptic deleted allele which results 123 in the individuals carrying those haplotypes being called as homozygous for the individuals’ non -deleted 124 alleles. 125 Analysis of gene conversion 126 We estimate gene conversion rates in non-overlapping windows that have a fixed base pair length. In each 127 window, we count the number of detected allele conversions. We divide the count by the expected 128 heterozygosity, which is ∑ 2 × 𝑓𝑖 × (1 − 𝑓𝑖)𝑖 where 𝑓𝑖 is the MAF of marker 𝑖 and the sum is across the 129 analyzed markers in the window (i.e., those passing the MAF filter) . In homogeneous populations, the 130 expected heterozygosity is proportional to the expected number of allele conversions, because alleles are 131 only changed by gene conversion if the parent individual is heterozygous. In heterogenous populations, 132 such as the TOPMed data analyzed in this study, the expected heterozygosity does not have this property 133 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint but can still serve as a proxy for marker densi ty. Our procedure provides relative rather than absolute 134 rates of gene conversion, so we normalize the gene conversion rates . In the real human data, we 135 normalize the rates to have mean 6 × 10−6 per bp across the autosomes,4; 11 while in the simulated data 136 we normalize the rates so that the baseline simulations have mean 1 per bp in the region to facilitate 137 comparison across different multiples of the baseline rate. 138 When calculating the correlation between an estimated gene conversion map and a crossover map, we 139 ignore windows in which the IBD rate is more than 1.4 times or less than 0.6 times the median. The IBD 140 rate at a locus is the proportion of pairs of haplotypes that are in the same IBD cluster, and the IBD rate 141 for a window is the average IBD rate over loci in the window. A high IBD detection rate indicates natural 142 selection.14; 17; 18 Natural selection leads to higher rates of IBD and hence a larger number of meioses in 143 which gene conversions can be detected through IBD. Thus, natural section will tend to lead to increased 144 gene conversion detection even if the gene conversion rate is not elevated. A low IBD detection rate can 145 occur at chromosome ends, at centromeres and other regions devoid of genotypes, and in regions of high 146 genotype error, and will lead to decreased gene conversion detection. Similarly, when calculating 147 correlations between two estimated gene conversion maps, we ignore windows in which the IBD rate for 148 either data set is more than 1.4 times or less than 0.6 times the median for that data set. We also ignore 149 regions of low expected heterozygosity (i.e., low marker density) because these regions have less data 150 and will have noisy results. If the expected heterozygosity is less than the window size divided by 10 kb 151 (e.g. less than 1 for 10 kb windows or less than 100 for 1 Mb windows) we ignore the window. In the 152

with 10 kb, 100kb, and 1Mb windows, application of this heterozygosity filter removes 10%, 5%, 153 and 2% respectively of the windows remaining after the application of the IBD rate filter. 154 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint Simulated data 155 We simulate data from a growing population that is designed to be similar to modern human populations 156 that have not gone through recent bottlenecks. The historical size of the population is 10,000 diploid 157 individuals. The population has been growing at 3% per generation for the past 200 generations, for a 158 current size of 3.7 million. Our simulation has a mutation rate of 1.5 × 10−8 per bp per generation, a 159 recombination rate of 10−8 per bp per generation, and gene conversions. Gene conversions have mean 160 length 300 bp and a baseline initiation rate of 2 × 10−8 per bp per generation. Data simulated with 161 msprime (see below) have gene conversion lengths following a geometric distribution, while data 162 simulated with SLiM (see below) have gene conversion lengths distributed as a sum of two geometric 163 random variables. As described below, some simulations include gene conversion hotspots with a higher 164 rate of gene conversion, while other simulations have a higher rate of gene conversion across the entire 165 simulated region. We add cryptic deletions to the data, in which individuals carrying the deletion allele 166 are called as homozygous for their other allele. One percent of the simulated variants with frequency <167 1% are turned into uncalled deletions with length drawn from an exponential distribution with mean 500 168 bp, and genotypes carrying the deletion are called as homozygous for the non-deleted allele.10 We add 169 genotype error at rate 2 × 10−4. Genotypes affected by error have one of their alleles chosen at random 170 to be changed. We phase the data using Beagle 5.4.19 171 We simulated 10,000 individuals across 20 regions of length 10 Mb using msprime v1.2 with the baseline 172 level of gene conversion. 20; 21 For these data, we generated ground -truth IBD and gene conversion 173 information in order to calculate false discovery rates, using the methods described in our previous 174 work.10 175 We simulated 125,000 individuals across 20 regions of length 10 Mb using msprime v1.2 with the baseline 176 level of gene conversion (gene conversion tract initiation rate of 2 × 10−8 per bp), and a further 20 regions 177 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint of length 10 Mb with 1.5 times the baseline level of gene conversion (gene conversion tract initiation rate 178 of 3 × 10−8 per bp). 179 We also simulated data with gene conversion hotspots, for which we used SLiM v4 since msprime is 180 limited to a constant gene conversion rate.22; 23 Our code for generating gene conversion hotspots follows 181 suggestions in the SLiM manual and can be found in Section 2 of Supplementary Methods. We simulated 182 the past 5000 generations with SLiM and then recapitated the simulations (added further generations as 183 needed to complete coalescence) and added mutations using pyslim and msprime. 24 We simulated 184 125,000 individuals across 10 regions of length 10 Mb, with the central 10 kb of those regions having twice 185 the baseline gene conversion rate, and a further 10 regions with the same parameters except for a ten -186 fold rather than two-fold hotspot gene conversion rate. 187 PRDM9 binding enrichment 188 We used published PRDM9 binding enrichment scores that were obtained from expressing PRDM9 in a 189 human cell line and performing ChIP-seq to assess binding (see Web resources).25 The data that consisted 190 of 170,198 PRDM9 binding peaks across the genome. We lifted the positions over from hg19 to GRCh38 191 to match the sequence data described below. When partitioning and analyzing the data in windows, we 192 summed the enrichment scores for peaks having their centers in each window. 193 TOPMed data 194 We analyzed phased whole autosome sequence data from a previous phasing of 39,961 TOPMed 195 individuals,19 but with 1882 individuals from the withdrawn SARP study removed, with a resulting size of 196 38,079 individuals. The analyzed individuals are multi-ethnic with a predominance of European ancestry 197 and are mostly from the USA.26 198 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint UK Biobank data 199 We analyzed phased whole autosome data on 125,361 individuals of White British ancestry from a 200 previous phasing of UK Biobank individuals.27; 28 201

202 Length and trim parameter settings 203 Using the simulated data on 10,000 individuals that have true IBD and gene conversion information, we 204 calculated detection rates and false discovery rates for IBD and allele conversions (Table S1). IBD false 205 discovery rates are less than 1% and allele conversion false discovery rates are less than 2% for all settings 206 with 𝑇 ≥ 0.75. IBD and allele conversion false discovery rates are both less than 3% for all settings with 207 𝑇 ≥ 0.5. 208 Using the simulated data with 125,000 individuals with a constant gene conversion rate of 1.5 times the 209 baseline rate, we investigated the level of bias in estimation of the relative gene conversion rate (Table 210 S2). We find that there is a small downward bias when the gene conversion rate is high, but that for 𝑇 ≥211 0.5 the bias is small, with the estimated relative rate being 1.48 while the true relative rate is 1.5. 212 Increasing the length threshold ( 𝐿) to values larger than 1 has little effect on bias, and it reduces the 213 number of detected allele conversions (Table S1). 214 We then investigated which length and trim settings give the highest accuracy when estimating the gene 215 conversion rate in the TOPMed and UK Biobank data . The primary metric that we use is Pearson’s 216 correlation between the estimated gene conversion rate and the sex -averaged crossover rate. Previous 217 work has shown that the gene conversion rate tends to be high in regions where the recombination rate 218 is high, 2; 6 so a higher correlation indicates more accurate estimation of gene conversion rate s. As a 219 secondary metric, we consider the correlation between the gene conversion rate estimates from the two 220 data sets. Although there may be some population differences in the maps, we expect them to be similar. 221 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint We found that 𝐿 = 1 with 𝑇 = 0.5 gave the best or close to best results on these metrics across the two 222 data sets when considering windows of size 10 kb and of size 1 Mb (Tables S3 and S4) . Since th ese 223 parameter settings were also supported by the simulated data, we use these settings for subsequent 224 analyses. 225 Detection of hotspots and inter-window differences in gene conversion rates 226 We use d simulated data with gene conversion hotspots to investigate the power to detect gene 227 conversion hotspots, and we used simulated data with baseline and 1.5x baseline gene conversion rates 228 to investigate the accuracy of estimated gene conversion rates in 100 kb and 1 Mb windows. 229 Using the simulated data with 125,000 individuals and gene conversion hotspots, we investigate d the 230 ability to estimate the relative rate of gene conversion in 10kb windows. We removed windows within 1 231 cM of each end of the analyzed region before presenting results, because IBD rates are zero or significantly 232 reduced in these end regions. 233 Figure 1A shows that the median estimates for hotspots with twice (2x) and ten times (10x) the baseline 234 gene conversion rate are close to their true values. There is some overlap in the distribution of estimates 235 from baseline gene conversion rate windows compared with estimates from windows with twice the 236 baseline gene conversion rate, however 100% (10/10) of the 2 x estimates exceed the 9 9th percentile of 237 the baseline distribution. Estimated gene conversion rates in hotspots with 10x gene conversion rate are 238 completely separated from both the baseline and the 2x gene conversion rates. An increase in downward 239 bias is seen in Figure 1A as the hotspot intensity increases. High gene conversion rates can reduce IBD 240 detection power, both directly due to creating allele mismatches in IBD segments and indirectly through 241 the impact of these mismatches on haplotype phasing accuracy. 242 Using the simulated data with 125,000 individuals and constant gene conversion rate, we investigated the 243 ability to estimate gene conversion rate s in long windows. Figure 1B shows that with 100 kb or 1 Mb 244 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint windows, there is no overlap between the baseline and 1.5x results, so there is very high power to 245 distinguish a 1.5 factor difference from baseline. 246 Gene conversion maps from TOPMed and UK Biobank autosome data 247 We detected 3,503,072 allele conversions in the TOPMed data and 13,901,830 allele conversions in the 248 UK Biobank data. For comparison, an analysis of the UK Biobank data with our previous multi -individual 249 IBD detection method found 9,313,066 allele conversions. We collated the allele conversions into non-250 overlapping windows of length 10 kb, 100 kb, or 1 Mb, and we estimated the gene conversion rate in each 251 window as described in Methods. We removed from further analysis any window that had an IBD rate 252 more than 40% higher or 40% lower than the median IBD rate in either data set. We also remov ed 253 windows with expected heterozygosity less than the required minimum in either data set (100 for the 1 254 Mb windows, 10 for the 100 kb windows, and 1 for the 10 kb windows). 255 In humans, gene conversion hotspots tend to co -occur with crossover hotspots. 2; 4 Table 1 shows the 256 correlation between our two gene conversion rate maps (TOPMed and UK Biobank) and the deCODE sex-257 averaged crossover map,29 as well as the correlation between our two gene conversion maps. Correlations 258 increase with increasing window size because larger windows contain more data and thus have higher 259 relative accuracy. At a 1 Mb resolution, our TOPMed gene conversion rate map has a correlation of 0.667 260 with the deCODE sex-averaged crossover map. For comparison, we averaged the maternal and paternal 261 non-crossover (gene conversion) deCODE maps, 6 which are based on overlapping 3 Mb windows, and 262 found a correlation of 0.553 with the deCODE sex -averaged crossover map. This reduced correlation for 263 the deCODE gene-conversion map compared to our TOPMed gene conversion map may be due to our 264 TOPMed map being based on more than 55 times more observed allele conversions than the deCODE 265 map. 266 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint Our UK Biobank gene conversion rate map has lower correlation than our TOPMed gene conversion rate 267 map with the deCODE crossover map, especially at finer scales of resolution (10 kb or 100 kb). When we 268 restrict the analysis to windows in which our two gene conversion rate maps are similar, we find that 269 correlations with the crossover map increase slightly for our TOPMed map and increase significantly for 270 our UK Biobank map, so that the UK Biobank correlations become similar to the TOPMed correlations 271 (Table S5). This suggests that our UK Biobank map contains more artifacts than our TOPMed map. 272 Figure 2 shows estimated gene conversion rates from the TOPMed data along the autosome for 1 Mb 273 windows. The estimated rates of gene conversion are elevated near the chromosome ends. In males, 274 crossover recombination occurs at greatly elevated rates in the subtelomeric regions, 30 thus leading to 275 high sex-averaged crossover rates in these regions (Figure S1), so it is not surprising to see this effect for 276 gene conversion recombination as well. Our TOPMed gene conversion maps for 10 kb, 100 kb, and 1 Mb 277 windows are provided as Supplemental Information. 278 We plotted gene conversion rates in the vicinity of the strongest gene conversion hotspots (Figure 3 and 279 Figure S2). These figures show that hotspot peaks die away over very short distances, typically within 1 280 kb. 281 PRDM9 binding enrichment 282 One question of interest is whether PRDM9 binding enrichment is more strongly predictive of gene 283 conversion or of crossovers. To answer this question, we estimated the correlation of PRDM9 binding 284 enrichment (see Methods) with our gene conversion rate estimates from the TOPMed data and with the 285 deCODE sex-averaged crossover rates. For windows of size 100 kb or 1 Mb, we find higher correlation 286 between PRDM9 binding enrichment and the gene conversion rate than between PRDM9 binding 287 enrichment and the crossover rate (Figure 4). For example, with 1 Mb windows, the Pearson correlation 288 coefficient is 0.52 for gene conversion and 0.34 for crossovers. 289 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint For 10 kb windows, crossover rates have a higher correlation than gene conversion rates with PRDM9 290 binding enrichment (0.24 for crossovers and 0.22 for gene conversion) . The total number of crossovers 291 used to build the crossover map is 4.5 million, or approximately 15 crossovers per 10 kb on average.29 The 292 total number of allele conversions used to build our TOPMed gene conversion map is 3.5 million, or 293 approximately 11 allele conversions per 10 kb on average. The lower number of allele conversion events 294 compared to crossover events combined with the fact that the variance will be high relative to the mean 295 at the 10 kb scale due to the low average numbers of events in 10 kb windows may be the primary factor 296 underlying the lower correlation of the gene conversion map at this scale. 297 We used enrichment peak centers as the locations for this analysis; the PRDM9 binding map also provides 298 confidence intervals for the peak locations. These have a median length of 55 bp (in hg19 coordinates) , 299 which is much shorter than the window sizes that we are considering. 300 Computing times 301 Inferring multi-individual IBD on chromosome 1 with 𝐿 = 1 and 𝑇 = 0.5 took 73 minutes on a 24 -core 302 compute node for the 38,079 -individual TOPMed data and 191 minutes on a 96 -core compute node for 303 the 125,361-individual UK Biobank data. 304

305 We presented a new method for multi -individual IBD detection and applied it to detecting allele 306 conversions and estimating gene conversion rates in 10 kb, 100 kb, and 1 Mb windows. 307 The first stage of our multi-individual IBD detection method generates a candidate set of pairwise IBD 308 segments that are evaluated in the second stage using the ibd-ends probabilistic model. The challenge of 309 detecting IBD segments in the presence of discordant alleles caused by mutation, gene conversion, and 310 genotype error is addressed in the first stage by performing IBS segment detection separately on four 311 disjoint, interleaved marker sets and in the second stage with a probabilistic mod el that allows for 312 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint discordant alleles. The probabilistic ibd-ends algorithm also allows our algorithm to model uncertainty in 313 IBD segment endpoints. Our two-stage method avoids the problem of quadratic scaling of pairwise IBD 314 segment detection with sample size through the use of the Positional Burrows-Wheeler Transform and 315 IBD transitivity. The result is an algorithm that scales linearly with sample size in both computing time and 316 output file size. 317 We generated gene conversion rate maps using both UK Biobank data, and TOPMed data. Although the 318 UK Biobank data contained 3.3 times as many individuals and resulted in detection of almost 4 times as 319 many allele conversions, we found that the map generated from the TOPMed data had higher correlation 320 with the deCODE crossover map , which suggests that the TOPMed map is superior. This difference may 321 be due to differences in the sequencing and QC pipelines between the two data sets. We also found that 322 our TOPMed gene conversion map was more highly correlated than the deCODE gene conversion map 323 with the deCODE crossover map, which suggests that the TOPMed gene conversion map is more accurate 324 than the deCODE gene conversion map. Our TOPMed map is sex-averaged and has reasonable accuracy 325 in 10 kb windows, whereas the deCODE gene conversion map s are sex-specific and use 3 Mb windows. 326 Our TOPMed-based gene conversion map has an average of 1.1 allele conversions per kb. In contrast, the 327 deCODE gene conversion maps have an average of around 20 allele conversions per Mb combined across 328 both sexes. 329 At scales of 100 kb and 1 Mb, our TOPMed-based gene conversion rate map was more highly correlated 330 than the deCODE crossover map with a map of PRDM9 binding enrichment. Since the deCODE crossover 331 map has high resolution at these scales and is expected to be highly accurate due to its pedigree -based 332 design, this suggests that PRDM9 binding has a stronger local effect on gene conversion than on crossing-333 over. 334 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint The most direct way to estimate gene conversion rates is to observe products of meioses, such as through 335 sperm-typing or family data. In order to achieve highest accuracy with this type of approach, it is necessary 336 to have multi -generational families.4 Even with very large data, such as the recently published deCODE 337 gene conversion data with 10,840 meioses, the number of observed events (62,762 in the deCODE gene 338 conversion data) is not sufficient for obtaining a high-resolution map. An indirect way to estimate gene 339 conversion rates is to construct LD -based gene conversion maps in a similar way to the construction of 340 LD-based crossover maps. 7; 8 However, these LD -based maps also have low resolution. 9 Our IBD-based 341

has both similarities and differences with these alternate approaches . Unlike the LD -based 342 approaches, but like the family -based approaches, we observe specific allele conversions, and like the 343 multi-generational family-based approaches, we have excellent control over false positive observations. 344 However, compared to family-based approaches we observed orders of magnitude more events, allowing 345 for good resolution even at a 10 kb scale with our TOPMed map. 346 A disadvantage of our IBD-based approach compared to family-based approaches is that we cannot assign 347 observed allele conversions to specific meioses. Thus, whereas the recently published deCODE study was 348 able to estimate sex -specific gene conversion rates , age effects, and genetic associations between 349 genome-wide gene conversion rates and specific alleles, we cannot estimate these quanti ties with our 350 method. On the other hand, because we observe a large number of events, we are able to visualize the 351 decay of events around hotspots and to observe a higher correlation of gene conversion than crossovers 352 with PRDM9 binding. 353

354 The methodological and analytical work performed in this study was supported by the National Human 355 Genome Research Institute (NHGRI) under award numbers R01 HG005701 and R01 HG008359. This 356 research has been conducted using the UK Biobank Resource under Application Number 19934. The 357 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint content is solely the responsibility of the authors and does not necessarily represent the official views of 358 the National Institutes of Health or the UK Biobank. 359 Sequence data for the Trans -Omics in Precision Medicine (TOPMed) program was supported by the 360 National Heart, Lung and Blood Institute (NHLBI). Core support including centralized genomic read 361 mapping and genotype calling, along with variant quality metrics and filtering were provided by the 362 TOPMed Informatics Research Center (3R01HL -117626-02S1; contract HHSN268201800002I). Core 363 support including phenotype harmonization, data management, sample-identity QC, and general program 364 coordination were provided by the TOPMed Data Coordinating Center (R01HL -120393; U01HL-120393; 365 contract HHSN268201800001I). We gratefully acknowledge the studies and participants who provided 366 biological samples and data for TOPMed. Funding for the Barbados Asthma Genetics Study was provided 367 by National Institutes of Health (NIH) R01HL104608, R01HL087699, and HL104608 S1. The Framingham 368 Heart Study was supported by contracts NO1 -HC-25195, HHSN268201500001I and 75N92019D00031 369 from the NHLBI and grant supplement R01 HL092577 -06S1; genome sequencing was funded by 370 HHSN268201600034I and U54HG003067. See Supplemental Data for acknowledgments of additional 371 studies in the TOPMed data. 372 Author contributions 373 BLB developed the IBD haplotype clustering method and software; SRB. developed the method for 374 estimating gene conversion rates ; SRB designed and performed the analyses ; SRB and B LB wrote the 375 manuscript. 376 Declaration of interests 377 The authors declare no competing interests. 378 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint Web resources 379 ibd-cluster program (version 0.2): 380 https://github.com/browning-lab/ibd-cluster 381 PRDM9 binding peaks: 382 https://www.ncbi.nlm.nih.gov/geo/download/?acc=GSE99407&format=file&file=GSE99407_ChIPseq_Pe383 aks.YFP_HumanPRDM9.antiGFP.protocolN.p10e-5.sep250.Annotated.txt.gz 384 (accessed August 8, 2024). 385 TopMed sequence data: 386 https://topmed.nhlbi.nih.gov/topmed-data-access-scientific-community 387 UK Biobank sequence data: 388 https://www.ukbiobank.ac.uk/ 389 Data and code availability 390 The TopMed and UK Biobank data sets analyzed in this study are available to researchers upon approval 391 of a data access application. The open source ibd-cluster software and gene conversion rate estimates are 392 publicly available (see Web resources and Supplemental Information). 393

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Nat Commun 8, 1-9. 468 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint Figures 469 470 Figure 1: Estimated scaled gene conversion rate in simulated data . Simulated data have 125,000 471 individuals. Boxplots show range, interquartile range, and median. All analyses use a 𝐿 = 1 cM IBD length 472 threshold and a 𝑇 = 0.5 cM end trim. A. 10 kb hotspots with twice (x2) or ten times (x10) the baseline 473 gene conversion rate. W e estimate relative gene conversion rates in 10 kb windows and scale them so 474 that the mean baseline rate is 1. Baseline results are based on 15,678 windows with heterozygosity sum 475 greater than 1 and located at least 1 cM from the ends of the simulated regions, while hotspot results are 476 each based on 10 windows (one window from each of 10 simulated regions). B. 100 kb and 1 Mb regions 477 with baseline gene conversion or 1.5 times (x1.5) the baseline rate. We estimate relative gene conversion 478 rates in 100kb or 1 Mb windows and scale them so that the mean baseline rate for the 1 Mb windows is 479 1. The 100 kb boxplots are each based on 1600 windows located at least 1 cM from the ends of the 480 simulated regions, while the 1 Mb boxplots are each based on 160 windows located at least 1 cM from 481 the ends of the simulated regions. 482 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint 483 Figure 2: Estimate d gene conversion rates for TOPMed data in 1 Mb windows across the autosomes. 484 Estimated relative gene conversion rates have been scaled to have mean 6 per Mb ( 6 × 10−6 per base 485 pair). Estimates are calculated in 1 Mb windows, and windows with expected heterozygosity less than 100 486 or IBD rate more than 40% higher or 40% lower than the median IBD rate are excluded. Chromosomes are 487 separated by vertical gray dashed lines. 488 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint 489 Figure 3: Gene conversion hotspots. We selected the markers with the highest estimated gene conversion 490 rates in the TOPMed data and plotted the gene conversion rates in the UK Biobank data at nearby markers. 491 The gray dashed vertical lines give the locations of the hotspots in the TOPMed data . TOPMed hotspots 492 that are within 10 kb of a marker with a larger gene conversion rate are omitted, as are hotspots at 493 markers for which the TOPMed IBD rate is more than 1.4 times or less than 0.6 times the median. TOPMed 494 hotspots for which there is no UK Biobank marker with MAF > 10% within 100 bp or for which there are 495 fewer than 20 UK Biobank markers with MAF > 10% within the 10 kb region centered on the TOPMed 496 hotspot position are also omitted because the plots do not show sufficient detail. Plots are shown in order 497 of TOPMed hotspot rate with highest first, left to right, then top to bottom. The estimated gene 498 conversion (GC) rate at a marker (in the TOPMed data to select the hotspots, and in the UK Biobank data 499 for the y-axis values in these plots) is the number of detected allele conversions divided by the expected 500 heterozygosity of the marker, normalized so that the autosome-wide average is 6 × 10−6. Estimates are 501 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint plotted as dots, while 95% confidence intervals are given as vertical lines through the dots and are 502 obtained by assuming that the number of detected allele conversions follows a Poisson distribution to 503 obtain the standard error and then adding two standard errors to each side of the estimate. Each plot 504 shows all UK Biobank markers with MAF > 10% within 5 kb on either side of the hotspot location. Positions 505 on the x-axes are in GRCh38 coordinates. This figure shows the top six hotspots meeting the UK Biobank 506 marker density criteria, and Figure S2 shows the top twenty-four such hotspots. 507 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint 508 Figure 4: Comparison of gene conversion rate estimates from the TOPMed data and sex -averaged 509 crossover rates with PRDM9 binding enrichment. Gene conversion rates are shown in the upper row, 510 while crossover rates are shown in the lower row. Each column has a different window size which is 511 notated above the plots. The Pearson correlation coefficient between the gene conversion rate or 512 crossover rate and PRDM9 binding enrichment is shown in the upper right of each plot. 513 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint Tables 514 Table 1: Pearson correlation coefficients between the sex-averaged deCODE 2019 crossover map and 515 our inferred gene conversion maps based on TOPMed and UK Biobank data for 10 kb, 100 kb, and 1 Mb 516 windows. 517 Window TOPMed vs deCODE UK Biobank vs deCODE TOPMed vs UK Biobank 10 kb 0.561 0.426 0.632 100 kb 0.597 0.457 0.665 1 Mb 0.667 0.626 0.855 518 .CC-BY-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted February 27, 2025. ; https://doi.org/10.1101/2025.02.22.639693doi: bioRxiv preprint