"The allele frequency spectrum in a non-equilibrium world"Müller-Widmann, RebekkaA typical assumption of many models in theoretical population genetics are equilibrium conditions. However, natural populations generally evolve in unstable environments that are changing over time, and are also subject to demographic changes, such as fluctuations in population size and population structure. As a consequence, empirically testing theories that rely on equilibrium assumptions can confound interpretation of empirical observations. To improve inference from data, it is crucial to extend existing models and methodology to account for non-equilibrium conditions. As a step in this direction, we explicitly model the effects of fluctuations in population size and/or fluctuations in the fitness landscape on allele frequency trajectories. Specifically, we use the Poisson random field framework to model allele frequency trajectories, where we first consider single, instantaneous changes in population size or selection pressure, and also examine periodical fluctuations and transient pulses of strong selection pressures. Within this setting, we obtain analytical solutions of the non-stationary allele frequency spectrum, and derive exact results of measures of natural selection and effective population size for non-equilibrium conditions. By studying the time-dependent relationship of these measures, we show a substantial deviation from the equilibrium selection-drift balance in a non-equilibrium world. Besides, we establish an application of our approach to model changes in recombination rate over time. In conclusion, we present a flexible, analytical framework to study the effect of non-stationary dynamics of various evolutionary processes on allele frequency trajectories and highlight practical consequences for the interpretation of empirical observations. |
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