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Is there any mathematical model to predict the behaviour and long-term consequence of counter-acting selection at different time scale?

For example, let's consider the bi-allelic gene $A$, with alleles $A1$ and $A2$. During a long period of $n1$ generations $A1$ is slightly beneficial (differential of selection: $s1$). After this period, follows a short period of $n2$ generations when $A2$ is highly beneficial (differential of selection: $s2$).

What mathematical model describes the frequency fluctuations of alleles and which allele will get fixed at the long term given the initial frequency ( $f_{0}$ ), assuming infinite population size and random mating.

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Unsmooth changes like you describe are normally hard to use in an analytical model. You could build a model of smoothly changing selection using a sine wave or simulations (which would be easy to build). –  timcdlucas Aug 23 '13 at 7:25
That remainds me the famous case of Biston betularia –  Miguel Ángel Naranjo Ortiz Aug 24 '13 at 11:41
Biston betularia is a moth that lives in England and has a light color in order to mimetize with the bark of trees. However, about 1% of the population presents melanism, and its camouflage fails. During the industrial revolution, the trees became dark as a result of the pollution. When that happened, the proportion of melanistic moths inverted, to almost 99%. During the 20st century, when the industry independized of the coal, the trees got light again, and the proportions restored once again. –  Miguel Ángel Naranjo Ortiz Aug 25 '13 at 14:01
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