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A population can adapt to a rapid environmental change or habitat expansion in two
ways. It may adapt either through new beneficial mutations that subsequently sweep
through the population or by using alleles from the standing genetic variation. We
use diffusion theory to calculate the probabilities for selective adaptations and
find a large increase in the fixation probability for weak substitutions, if alleles
originate from the standing genetic variation. We then determine the parameter regions
where each scenario-standing variation vs. new mutations-is more likely. Adaptations
from the standing genetic variation are favored if either the selective advantage
is weak or the selection coefficient and the mutation rate are both high. Finally,
we analyze the probability of "soft sweeps," where multiple copies of the selected
allele contribute to a substitution, and discuss the consequences for the footprint
of selection on linked neutral variation. We find that soft sweeps with weaker selective
footprints are likely under both scenarios if the mutation rate and/or the selection
coefficient is high.