recombination & adaptation - senecio7の日記

Neher RA, Shraiman BI & Fisher DS 2010 Rate of adaptation in large sexual populations. Genetics 184:467-481.

adaptation often involves the acquisition of a large number of genomic changes that arise as mutations in single individuals
in asexual populations, combinations of mutations can fix only when they arise in the same lineage
for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later
when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously
v is linear in NU_b only in sufficiently small populations
in large populations, v increases much more slowly as log NU_b
this acceleration of adaptation by recombination implies a strong evolutionary advantage of sex

the crucial point that must be addressed is the balance between selection and recombination of existing variation and the injection of additional variation by new mutations

a novel beneficial mutation can arise on different genetic backgrounds and its establishment probability will thus vary
being greater if it arises in a well-adapted individual
to avoid extinction, descendants of the novel mutation thus have to move to fitter genetic backgrounds via recombination in outcrossing events

a grossly simplified model of recombination in which a randomly chosen individual is replaced by an individual whose genome is assembled by choosing the alleles at each locus according to the allele frequencies in the entire population, independent of the "parents"
it turns out that this communal recombination model, even if unrealistic, behaves similarly to the free recombination model while being much easier to analyze mathematically

a third model in which only a single locus is exchanged with a mating partner in an outcrossing event or, equivalently, is picked up from DNA in the environment and randomly replaces the initial allele at the same locus
this model is reminiscent of lateral gene transfer among bacteria and related to, but not the same as, the model studied by Cohen et al. (2005)
this model does not approximate the position-dependent crossing over of chromosomes

the fate of a new allele during the stochastic phase, when it exists only in a small fraction of individuals, can be described well by a branching process that accounts for stochastic birth, death, and, crucially, recombination events that move some of its descendants from one genetic background to another
to establish, its descendants have to switch repeatedly to fitter genomic backgrounds
this general idea (see Rice 2002 for review) applies to the accumulation of beneficial as well as deleterious mutations

at very high recombination rates, we will obtain that w(x) ~ (1 + 2x/r)
almost independent of x for x ≪ r
in this limit, the T acting on w(y) vanishes and the population average establishment probability is just the solution to the right-hand side, giving simply w(x) ≈ s
this is the conventional result (obtained by the simple branching process) in the absence of linkage to the rest of the genome
more generally, the fixation probability of a new mutation that can arise in any individual is the population average of the x-dependent establishment probability over the approximately Gaussian distribution of the fitness, x

in the high recombination limit and moderate N the conventional analysis of independent fixations holds and the rate of adaptation (and concomitantly the variance of fitness) is proportional to the total production rate of beneficial mutations, NU_b
for large populations (with recombination rates in the intermediate regime) we find adaptation rate v ~ r²logNU_b
this change from linear to logarithmic dependence on NU_b indicates that the rate of adaptation is limited by interference among multiple simultaneously segregating beneficial mutations rather than by the supply of beneficial mutations
this reduction in the rate of adaptation due to linkage is, qualitatively, the Hill-Robertson effect
while logarithmic in population size, the rate of adaptation increases with the rate of recombination as r²
our results confirm the heuristic arguments by Fisher and Muller and provide a quantitative framework for identifying conditions favoring sexual reproduction

with any amount of recombination, the diversity and distribution of allele frequencies are absolutely crucial
it matters a great deal whether the advance of the fitness wave occurs via small amounts of each of several new alleles or all from a single allele
in general this is also true for adaptation from standing variation

some of the most interesting extensions of the present models would include epistasis
in the limit of very strong epistasis (Neher and Shraiman 2009) the establishment probability of an allele is described by a model that reduces to the communal recombination
in general, how to set up−never mind analyze!−instructive models of evolutionary dynamics with epistasis between many segregating loci is largely an open field