polygenic adaptation - senecio7の日記

Weissman DB, Feldman MW & Fisher DS 2010 The rate of fitness-valley crossing in sexual populations. Genetics, in press.
doi:10.1534/genetics.110.123240

ISSUE HIGHLIGHTS
how do populations acquire complex adaptations that require multiple mutations before providing a fitness benefit?
the authors investigate the dynamics of complex adaptation across a broad range of population parameters and find expressions for the rate of adaptation
while frequent recombination can render complex adaptation effectively impossible, lower recombination rates can greatly increase the rate of complex adaptation relative to that in an asexual population

complex adaptations may be acquired through successive individually beneficial mutations
it is likely that some adaptations require a combination of mutations that are each individually neutral or deleterious in the absence of the other mutations

in general, the dynamics of complex adaptation will depend on the population size, the mutation rates, the recombination rates between the different loci, the selective advantage provided by the adaptation, and the selective disadvantages of each of the intermediate genotypes

it is not known (even in simple models) under what circumstances adaptation proceeds primarily via the fixation of alleles that provide a selective advantage in a wide range of genetic backgrounds
or when, instead, adaptation primarily involves formation and selection of particularly advantageous combinations of alleles

simulations have usually found that recombination reduces the rate of valley crossing (e.g., Takahata 1982; Kim 2007)
although some have found a slight increase for small amounts of recombination (Takahasi and Tajima 2005; Weinreich and Chao 2005; De Visser et al. 2009)

except in very large populations, the time that it takes for AB to sweep to fixation in the population will be a negligible component of τ
which will be dominated by the waiting time before the selective sweep begins (Weissman et al. 2009)
we therefore ignore the sweep time and refer to the beginning of the sweep (when the double mutants establish and begin to increase in number exponentially) as the point at which the population has crossed the valley

the time τ for the population to acquire the adaptation is usually minimized at an optimum level of recombination r ≲ s
which balances the two effects of recombination on valley crossing
bringing together single mutants
breaking up double mutants

Figure 3
single mutants are effectively neutral
τ decreases with increasing r until it reaches a minimum at r ≈ s / 2
after which it quickly increases back to roughly its asexual value

Figure 4
selection against single mutants is strong enough to affect the dynamics
but not so strong to prevent the two single-mutant genotypes from occasionally arising together and recombining to produce double mutants
τ decreases with increasing r until it reaches a minimum at r ≈ s / 2 ~20
after which it quickly increases to a maximum ~200

equation 4 remains valid for intermediate recombination rates r ≲ s if we replace s with š ≡ s − r
τ generally decreases with increasing rš
meaning that a recombination rate r ≈ s / 2 maximizes the rate of valley crossing

for the interplay between the asexual and sexual processes, Lynch's (2010) Equation 1 for τ is incorrect
it relies on the assumption that for each single-mutant lineage, success via the asexual path occurs independently from success via the sexual path
it follows from our heuristic arguments that the converse is true, since for neutral single mutants both paths depend primarily on the same random variable T, the time that the lineage drifts
since drifting to fixation is also primarily dependent on T, earlier asexual versions of this equation such as Equation 3b in Lynch and Abegg 2010 are also incorrect

for neutral single mutants and r « s, Equation 2 in Lynch (2010) is similar to the second line of our Equation 13 and is found using a method that appears to be similar to our heuristic argument
the approximations given for the two parts of the process are valid in opposite limits and thus inconsistent

for r » s and large population sizes, Nμ » 1, Lynch (2010) claims τ » τ_{r = 0}, in contrast with our result τ ≈ τ_{r = 0}
although it is not clear in this case how he has defined τ or the boundaries of the regime

for deleterious single mutants and r « s, Equation 5 in Lynch (2010) is clearly incorrect
it adds Equation 4b, which is valid only for strongly deleterious single mutants, and Equation 4a, which overcounts the asexual path across the valley that is already included in Equation 4b
the (fairly poor) agreement with simulations is obtained only by the use of a fitting parameter with no biological meaning

for very closely linked loci, adaptive double substitutions should actually increase as a function of the genetic distance between the loci
this signal is likely to be harder to detect in data from natural populations, because it is difficult to identify adaptive double substitutions
Piskol and Stephan 2008 do observe that the rate of double substitutions at a certain set of interacting sites does increase with genetic distance at short distances
this is unlikely to be due to recombination, as the double substitutions in question are expected to be only compensatory, not adaptive

we should expect to see a transition from selection acting on some combinations of mutations at tightly linked loci to selection acting roughly independently on different haplotype blocks at longer genetic distances
because the genetic length scale at which this transition occurs depends on the strength of selection, we expect that complex adaptations that provide large selective advantages may involve longer regions of chromosomes than adaptations providing smaller advantages