Information encoded in gene-frequency trajectories

In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded within gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard diffusion approximation result, for the probability of fixation, systematically emerges when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.