  It is likely that the strength of selection acting upon a mutation varies
through time due to changes in the environment. However, most population
genetic theory assumes that the strength of selection remains constant. Here we
investigate the consequences of fluctuating selection pressures on the
quantification of adaptive evolution using McDonald-Kreitman (MK) style
approaches. In agreement with previous work, we show that fluctuating selection
can generate evidence of adaptive evolution even when the expected strength of
selection on a mutation is zero. However, we also find that the mutations,
which contribute to both polymorphism and divergence tend, on average, to be
positively selected during their lifetime, under fluctuating selection models.
This is because mutations that fluctuate, by chance, to positive selected
values, tend to reach higher frequencies in the population than those that
fluctuate towards negative values. Hence the evidence of positive adaptive
evolution detected under a fluctuating selection model by MK type approaches is
genuine since fixed mutations tend to be advantageous on average during their
lifetime. Never-the-less we show that methods tend to underestimate the rate of
adaptive evolution when selection fluctuates.
