Establishment in a new habitat by polygenic adaptation
Maladapted individuals can only colonise a new habitat if they can evolve a
positive growth rate fast enough to avoid extinction, a process known as evolutionary
rescue. We treat log fitness at low density in the new habitat as a
single polygenic trait and thus use the infinitesimal model to follow the evolution
of the growth rate; this assumes that the trait values of offspring of a
sexual union are normally distributed around the mean of the parents’ trait
values, with variance that depends only on the parents’ relatedness. The
probability that a single migrant can establish depends on just two parameters:
the mean and genetic variance of the trait in the source population.
The chance of success becomes small if migrants come from a population
with mean growth rate in the new habitat more than a few standard deviations
below zero; this chance depends roughly equally on the probability
that the initial founder is unusually fit, and on the subsequent increase in
growth rate of its offspring as a result of selection. The loss of genetic variation
during the founding event is substantial, but highly variable. With
continued migration at rate M, establishment is inevitable; when migration
is rare, the expected time to establishment decreases inversely with M.
However, above a threshold migration rate, the population may be trapped
in a ‘sink’ state, in which adaptation is held back by gene flow; above this
threshold, the expected time to establishment increases exponentially with M. This threshold behaviour is captured by a deterministic approximation,
which assumes a Gaussian distribution of the trait in the founder population
with mean and variance evolving deterministically. By assuming a constant
genetic variance, we also develop a diffusion approximation for the joint distribution
of population size and trait mean, which extends to include stabilising
selection and density regulation. Divergence of the population from its
ancestors causes partial reproductive isolation, which we measure through
the reproductive value of migrants into the newly established population.
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110-127
110-127
Academic Press
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