Distribution of recombination crossovers and the origin of haplotype blocks: the interplay of population history, recombination, and mutation

Abstract

Recent studies suggest that haplotypes are arranged into discrete blocklike structures throughout the human genome. Here, we present an alternative haplotype block definition that assumes no recombination within each block but allows for recombination between blocks, and we use it to study the combined effects of demographic history and various population genetic parameters on haplotype block characteristics. Through extensive coalescent simulations and analysis of published haplotype data on chromosome 21, we find that (1) the combined effects of population demographic history, recombination, and mutation dictate haplotype block characteristics and (2) haplotype blocks can arise in the absence of recombination hot spots. Finally, we provide practical guidelines for designing and interpreting studies investigating haplotype block structure.

Figure 1

Diagram of the FGT and haplotype block identification. A, Consider two loci A and B, each with two alleles (denoted as A₁, A₂, B₁, and B₂). On the left, only three gametes (A₁B₁, A₁B₂, and A₂B₁) are observed between loci A and B (which arise from mutations; suppose A₁B₁ is the wild type). On the right, recombination has occurred between A₁B₂ and A₂B₁ haplotypes, which leads to all four gametes being observed in a sample. B, Haplotype block identification. The FGT is conducted between pairwise loci, and 0 and 1 denote the absence and presence, respectively, of all four gametes between locus pairs. In this example with eight loci, three haplotype blocks were identified, with the first block including SNPs 1, 2, and 3; the second block including SNPs 4, 5, and 6; and the last block including SNPs 7 and 8.

Figure 2

The effect of recombination and demographic history on haplotype block characteristics; average haplotype block size ± SE versus recombination level for a sample size of 100. If we assume 1 cM = 1 Mb, the recombination rate r is ∼10⁻⁸ per generation per intersite. The average block size decreases with the increasing recombination level. The effective population size was adjusted by fixing the ratio of R/θ and allowing θ to vary from 5, 10, and 25 (which corresponds to effective population sizes of 2,000, 4,000, and 10,000).

Figure 3

The effect of sample size on haplotype block characteristics; average haplotype block size versus sample sizes. Under the same parameters θ=25 and R=10, which corresponds to a general population with mutation rate 10⁻⁹ per site per year, and recombination rate 10⁻⁸ per generation, given effective population size as 10⁴, each generation time as 25 years, and total sequence length as 25 kb, changing the sample size from 20 to 50, 100, 200, 400, 600, 800, and 1,000, respectively. Small sample size reveals increased haplotype block sizes. Each simulation is based on 1,000 replications.

Figure 4

The effect of SNP density of haplotype block characteristics. A, Average block size versus θ. By fixing R, the average block size increases slightly when θ is very small and then decreases until an equilibrium value of θ is reached. If we assume the mutation rate is constant across a local region, changing θ also corresponds to changing the SNP density. The five arrows denote positions where the SNP density is equal to 0.5, 1, 2, 3, and 5 SNPs/kb, respectively. B, An explanation of why θ influences average block size. Each X represents a recombination position, and each ↓ represents an identified SNP marker. When θ is small, two markers are identified and constitute one block as shown in (a); (b) θ increases, three markers are identified, and they form one block whose size is larger compared with (a); (c) As θ continues to increase, six markers are identified to resolve this region into two blocks, whose average block size has now decreased in comparison with (b). Each simulation is based on 1,000 replications.

Figure 5

Haplotype block size distribution of published chromosome 21 data and simulations identified by FGT method. For the simulated data, each parameter combination is based on 1,000 replications. A, Distribution of haplotype block length in real data, simulated data assuming r=1.0^*10^-8, and simulated data assuming r=4.0^*10^-8. B, Distribution of haplotype block length in real data and simulated data assuming a mixture model of recombination (see text for details).