evolutionary rescue - senecio7の日記

Orr HA & Unckless RL 2008 Population extinction and the genetics of adaptation. Am Nat 172:160-169.

some environmental challenges—challenges to which populations must adapt—may depress absolute fitness below 1, causing populations to decline

this scenario, which obviously sits at the intersection of population genetics and ecology, differs fundamentally from that typically considered by population geneticists in that it is a race

we consider the fate of major mutations at one or several loci—not the cumulative effects of many genes that each have a modest effect
our results are most directly relevant to organisms such as microbes, in which a small number of genes can respond to an environmental challenge
a small number of genes, perhaps only one, can confer resistance to the insecticide cyclodiene
adaptation to sudden environmental change is difficult, at least when using new mutations or previously deleterious alleles at one or a few loci

the probability that a new beneficial mutation that arises in generation t goes to fixation and thereby prevents population extinction is 1 minus the probability that all such mutations are lost accidentally
P = 1 − (1 − Π)^{N₀u(1 − r)^t} ... (1)
Π is the probability of fixation of a new beneficial mutation
population size declines deterministically
beneficial mutations are sufficiently rare to enjoy independent fates
Π ≈ 2(s_b − r)
with small to moderate probabilities of fixation, equation (1) becomes P_t ≈ 1 − exp[−2N₀u(s_b − r)(1 − r)^t]

A = N₀uΣ_{T = 0}^t(1 − r)^T = N₀u[1 − (1 − r)^{t + 1}]/r
a mutation that appears by generation t will save a population with probability
P_T≤t ≈ 1 − [1 − 2(s_b − r)]^A ≈ 1 − exp{−2N₀u(s_b − r)[1 − (1 − r)^{t + 1}]/r} ... (2)
P_T≤t levels off with increasing t
as t becomes large (t → ∞) in equation (2), we can find the total probability that a new mutation will save the population
P_new ≈ 1 − exp[−2N₀u(s_b − r)/r] ... (3)
when the term in brackets is small, this is, to a good approximation, P_new ≈ 2N₀u(s_b − r)/r
equation (3) is our most important result
there is a ceiling on the change that new mutations can save a declining population
this reflects the fact that adaptation in a declining population is a race
adaptation must occur before a population becomes extinct

conditional on population survival, how often does a rescuing mutation arise in generation T = 0, 1, 2, ... ?
P(T = t|survival) ≈ r exp(−rt) ... (4)
the population declines approximately exponentially
the adaptive contribution of each generation must also decline approximately exponentially

we can also consider the case in which both "old" alleles from mutation-selection-drift balance and "new" alleles from mutations that arise after the environmental change can contribute to adaptation
we simplify the analysis by defining rescue from the standing genetic variation if any of the haplotypes going to fixation segregated before the environmental change at T = 0
P_total = P_old + (1 − P_old)P_new
P_total ≈ 1 − ((s_b − r + s_d)/s_d)^−2N₀u exp(−2N₀u(s_b − r)/r) ... (6)

absolute copy number of an allele, not its frequency, determines the probability of population survival

how likely is it that an allele that had essentially no effect on fitness in the old environment will have a profound effect in the new environment, that is, will boost absolute fitness above 1?

more loci (any one of which might save the population) provide more material for the genetic rescue of endangered populations and so help mitigate our negative, single-locus conclusions

we have not considered the scenario in which populations survive because of modest allele frequency change at many genes, each having a small effect on fitness, and not because of substitution events at single locus
Gomulkiewicz and Holt's (1995) results suggest that the probability of population survival can often remain low in quantitative genetic models, at least when population size is modest and environmental change abrupt
our approach partly rests on branching process theory