evolutionary rescue

Orr HA & Unckless RL 2014 The population genetics of evolutionary rescue. PLoS Genet 10:e1004551.

  • evolutionary rescue from new mutation takes longer and involves a smaller minimum population size than rescue from the standing genetic variation
  • it is easy to find the conditions under which evolutionary rescue is more likely to involve the standing genetic variation versus a new mutation, where both types of allele enjoy selective advantage s
  • this occurs when p0 > u / r ... (4)
  • a result that seems not to have been noted in the literature
  • loss of rare beneficial alleles affects not only the probability of evolutionary rescue but expected population size when the beneficial allele is not lost
  • successful alleles are disproportionately those that rise by genetic drift to higher than expected copy number in the first few generations of their evolutionary histories [18]
  • Maynard Smith showed that this oversampling effect could be taken into account in otherwise-deterministic selection equations by a simple, albeit approximate, approach
  • it is, he argued, as though the alleles that successfully fix began with higher copy number than they actually did
  • a finding that often plays a part in hitchhiking theory
  • this point is also well known in the branching process literature, at least in certain limiting cases
  • Nmut,t = Pr{Nmut,t > 0} E[Nmut,t | Nmut,t > 0] + Pr{Nmut,t = 0} 0
  • Pr{Nmut,t > 0} = Pr{fixation}
  • E[Nmut,t | Nmut,t > 0] = Nmut,t / Pr{fixation} ... (7)
  • Pr{fixation} = 1 − Pr{all k copies lost} = 1 − [1 − 2(s − r)]k ... (8)
  • Pr{fixation} ≈ 2k(s − r)
  • E[Nmut,t | Nmut,t > 0] = k[(1 + s)(1 − r)]t / 2k(s − r) ≈ e(s − r)t / 2(s − r) ... (9)
  • in words, the expected number of mutant individuals at time t conditional on ultimate fixation equals the deterministic expectation for a single new mutation normalized by its probability of fixation
  • the expected number of copies present at time t conditional on ultimate fixation is therefore the same as that for a single mutation normalized by its probability of fixation