population bottleneck - senecio7の日記

Wilson BA, Petrov DA & Messer PW 2014 Soft selective sweeps in complex demographic scenarios. Genetics 198:669-684.

population bottlenecks can lead to the removal of all but one adaptive lineage from an initially soft selective sweep
"hardening” of soft selective sweeps

even in the global human population, adaptation has produced soft selective sweeps, as evidenced by the parallel evolution of lactase persistence in Eurasia and Africa through recurrent mutations in the lactase enhancer
some of these sweeps arose from standing genetic variation while others involved recurrent de novo mutation
we focus on the latter scenario of adaptation arising from de novo mutation

our current understanding of the likelihood of soft sweeps relies on the assumption of a Wright-Fisher model with fixed population size, where Θ remains constant over time
this assumption is clearly violated in many species

strong selection is often more likely to produce soft sweeps than weak selection when population size fluctuates

population bottlenecks were simulated through a single-generation downsampling to size N₂ (without selection) every ΔT generations
empirical probabilities of observing a soft sweep in a given simulation run were obtained by calculating the expected probability that two randomly drawn adaptive lineages are not identical by decent, based on the population frequencies of all adaptive lineages in the population at the time of sampling

we ignore back mutations and consider the dynamics of the two alleles at this locus in isolation
there is no interaction with other alleles elsewhere in the genome
the distinction between a hard and a soft sweep is based on the genealogy of adaptive alleles in a population sample
it is therefore possible that the same adaptive event yields a soft sweep in one sample but remains hard in another, depending on which individuals are sampled

Θ = 2NU_A is the population-scale mutation rate—twice the number of adaptive alleles that enter the population per generation
the probability of a soft sweep is primarily determined by Θ and is nearly independent of the strength of selection
when Θ ≪ 1, adaptive mutations are not readily available in the population and adaptation is impeded by the waiting time until the first successful adaptive mutation arises
this regime is referred to as the mutation-limited regime
adaptation from de novo mutation typically produces hard sweeps in this case
when Θ ≥ 1, by contrast, adaptive mutations arise at least once per generation on average
in this non-mutation-limited regime, soft sweeps predominate

mutation and selection operate only during the phases when the population is large
the two alleles, a and A, are neutral with respect to each other and no new mutations occur during a bottleneck
this assumption is justified for severe bottlenecks with N₂ ≪ N₁ and when bottlenecks are neutral demographic events
many effects of a population bottleneck depend primarily on the ratio of its duration over its severity
most of the results we derive below should therefore be readily applicable to more complex bottleneck scenarios by mapping the real bottleneck onto an effective single-generation bottleneck, provided that the real bottleneck is not long enough that beneficial mutations appear during the bottleneck
adaptive mutations establish during the large phases at an approximate rate Θs
successfully establishing mutations reach their establishment frequency fast compared to the timescale ΔT between bottlenecks
establishment can be effectively modeled by a Poisson process
this assumption is reasonable when selection is strong and the establishment frequency low
those adaptive mutations that do reach establishment frequency typically achieve this quickly in ~γ/s generations, where γ ≈ 0.577 is the Euler–Mascheroni constant

τ'_est = 1 / (Θs) + log(N₁s / N₂) / s ... (2)
hardening should occur whenever Θ ≥ 1 and at the same time ΔT < τ'_est ... (3)

in the scenario where Θ = 2, N₁/N₂ = 10⁴, and ΔT = 100 generations, an adaptive allele with s = 0.056 almost always (90%) produced a hard sweep in our simulations, whereas an allele with s = 0.1 mostly (57%) produced a soft sweep

even in the same demographic scenario, the probability of observing soft sweeps can differ substantially for weakly and strongly selected alleles
the stronger the selective sweep, the higher the chance that it will be soft in a population that fluctuates in size
Otto and Whitlock (1997) showed that the fixation process of an adaptive allele depends on the timescale of the fixation itself
only short-term demographic changes encountered during the fixation event matter for strongly selected alleles
slower changes affect only weakly selected alleles
Otto and Whitlock (1997) therefore concluded that “there is no single effective population size that can be used to determine the probability of fixation for all new beneficial mutations in a population of changing size” (p. 728)

our own species has likely experienced population-size changes over more than three orders of magnitude within the past 1000 generations (Gazave et al. 2014)

the fitness advantage during the evolution of drug resistance in pathogens or pesticide resistance in insects can be on the order of 10% or larger

let us consider another example, motivated by the proposed recent demographic history of the European human population (Coventry et al. 2010; Nelson et al. 2012; Tennessen et al. 2012; Gazave et al. 2014)
we assume demographic parameters similar to those estimated by Gazave et al. (2014), i.e., an ancestral population size of N_anc = 10⁴, followed by exponential growth over a period of 113 generations, reaching a current size of N_cur ≈ 520,000 individuals
we further assume that exponential growth halts at present and that population size remains constant thereafter
this scenario is qualitatively different from the previously discussed models in that population-size changes are nonrecurring
for determining whether a given selective sweep will likely be hard or soft in this model, its starting time becomes of crucial importance
we assume an adaptive mutation rate of U_A = 5 × 10⁻⁷ for this example to illustrate the transition between mutation-limited behavior in the ancestral population, where Θ_anc = 4N_ancU_A ≈ 0.02, and non-mutation-limited behavior in the current population, Θ_cur = 4N_curU_A ≈ 1.0
this adaptive mutation rate is higher than the single nucleotide mutation rate in humans
it may be appropriate for describing adaptations that have larger mutational target size, such as loss-of-function mutations or changes in the expression level of a gene
all sweeps that start prior to the expansion are hard in a sample of size 10, as expected for adaptation by de novo mutation in a mutation-limited scenario
sweeps starting in the current, non-mutation-limited regime are almost entirely soft, regardless of the strength of selection
sweeps starting during the expansion phase show an interesting crossover behavior between hard and soft sweeps
the strength of selection becomes important in this case
sweeps that start during the expansion have a higher probability of producing soft sweeps when they are driven by weaker selection than when they are driven by stronger selection
in a growing population, a weaker sweep will experience larger population sizes during its course than a stronger sweep starting at the same time, increasing its probability of becoming soft

the effective Θ determining the probability of soft sweeps is not the same for different loci across the genome
mutational target sizes and huts adaptive mutation rates vary at different loci
no single value of Θ will be appropriate for describing the entire adaptive dynamics of a population
estimators based on the levels of neutral diversity in a population, such as Θ_π and Watterson's Θ_W (Ewens 2004), can be strongly biased downward by ancient bottlenecks and recurrent linked selection

if adaptation is limited by mutational input, then most adaptive mutations should arise during the population booms, biasing us toward seeing more soft sweeps
it is also possible—maybe even more probable—that adaptation will be common during periods of population decline
if adaptation is more common during population busts, this should lead us to observe more hard sweeps

we have considered only scenarios in which population size and selection coefficients are independent of each other
models that consider population size and fitness in a unified framework will be necessary to fully understand signatures that adaptation leaves in populations of variable size