A population genetics model with recombination hotspots that are heterogeneous across the population

Abstract

Both sperm typing and linkage disequilibrium patterns from large population genetic data sets have demonstrated that recombination hotspots are responsible for much of the recombination activity in the human genome. Sperm typing has also revealed that some hotspots are heterogeneous in the population; and linkage disequilibrium patterns from the chimpanzee have implied that hotspots change at least on the separation time between these species. We propose a population genetics model, inspired by the double-strand break model, which features recombination hotspots that are heterogeneous across the population and whose population frequency changes with time. We have derived a diffusion approximation and written a coalescent simulation program. This model has implications for the ''hotspot paradox.'' A nalysis of the Seattle SNP, Perlegen, and HapMap data sets has suggested that the fine-scale recombination rate varies with position across the chromosome (1-3). Indeed 80% of the recombination activity is believed to occur in as little as 10-20% of the sequence. So-called recombination hotspots, narrow regions generally 1 kb wide with elevated recombination rates, have been estimated approximately every 100 kb across the human genome. Sperm typing (4-6) (for reviews, see refs. 7 and 8) has confirmed the presence of recombination hotspots. Although more recent population genetic modeling efforts (9-11) have included recombination hotspots, these methods, like their predecessors (12-16), assume that the recombination rate is (i) homogeneous across the population, and (ii) constant throughout time. However, sperm typing has also demonstrated that some hotspots are heterogeneous in the population (17). Moreover, analysis of linkage disequilibrium patterns in the human and chimpanzee populations (18,19) has shown little congruence between the location of hotspots in the two species, implying that recombination rates change at least on the order of the separation time between these species.The predominant mechanistic model of recombination is the double-strand break model illustrated in Fig. 1 (20) (for a review see ref. 21). In this model, there is a break through both strands of one of the chromosomes. On this chromosome there is a loss of several hundred base pairs around the break. This loss is then replaced by copying from the other chromosome. The break can be resolved as either a crossover or a conversion event. In most population genetic models, this loss and copy of DNA has been ignored: in these models there is an exchange of DNA between chromosomes, but, despite this rearrangement, all sections of the chromosome are assumed to retain their original quantities. Because the length of this loss is relatively small, this simplification had seemed benign.However, this loss is the key factor in the ''hotspot paradox'' (e.g., refs. 22 and 23). This paradox states that if the hotspot is caused by some motif in the DNA sequence that elevates the local double-strand break rate, then this motif will often be lost in a reco...

A Combination of cis and trans Control Can Solve the Hotspot Conversion Paradox

“…This is because under these conditions the standard mutation-selection balance assumption that selection is a much stronger force than mutation is violated: the total strength of selection in this model is on the order of b H 3 ðs À t=2Þ, which may be quite small under reasonable parameter values. One consequence of this is that it potentially allows for hotspot polymorphisms to be maintained deterministically; however, because this tends to occur when selection is weak, drift may be more important than selection under these parameter values (Calabrese 2007;Coop and Myers 2007). A comparison of these approximate results to the exact solutions, along with confirmation through numerical results, can be found in the supplemental material.…”

“…Unlike recent stochastic models (Calabrese 2007;Coop and Myers 2007), it allows for the fixation of very-hot hotspots, assuming selection is strong enough (in fact, very-hot modifiers are more likely to fix under a given selection strength than less-hot modifiers; see Figure 3). Of course, this model requires several simplifying assumptions.…”

“…The continued existence of recombination hotspots in the face of this biased gene conversion has been termed the ''hotspot conversion paradox'' (Boulton et al 1997). 1 This paradox has been addressed in several recent theoretical studies (Boulton et al 1997;Pineda-Krch and Redfield 2005;Calabrese 2007;Coop and Myers 2007), but a general solution to the problem remains elusive. Simulation studies show that selection favoring DSBs can counteract the process of biased gene conversion and slow or stop the loss of a hotspot, but only if there is a strong fitness benefit directly associated with activity at the hotspot itself (Boulton et al 1997;Pineda-Krch and Redfield 2005).…”

“…Given that the conversion paradox is likely to be at its strongest when a hot allele is rare (so that the hot allele is always found in heterozygotes and is therefore constantly being lost to conversion), explaining the spread of a new hotspot is more difficult than explaining the existence of an old one. Recent theoretical studies exploring the action of genetic drift on modifiers undergoing biased gene conversion suggest that only when the force of conversion (that is, the product of the DSB rate and the probability that the control allele is converted when a DSB occurs) is weak can a hotspot spread or be maintained at high frequency (Calabrese 2007;Coop and Myers 2007). That is, very-hot cis-controlled hotspots act essentially as strongly deleterious mutations, which almost never fix due to drift.…”

“…Theoretical approaches to the hotspot conversion paradox to date have consisted of simulations of finite populations (Boulton et al 1997;Pineda-Krch and Redfield 2005) and diffusion approximations focusing on the stochastic fate of hotspots (Calabrese 2007;Coop and Myers 2007). Here, I present an analytical model of the deterministic processes underlying the evolution of a single recombination hotspot, to clearly define the conditions under which selection can overcome the effects of biased gene conversion and allow the maintenance of an existing hotspot and/or the spread of a new one.…”