Model-free inference of evolution from allele frequency timeseries using permutation tests

Allele frequency (AF) timeseries allow us to directly observe the dynamics of evolution at a genetic level. However, extracting useful inferences from AF timeseries has proved difficult due to the model uncertainties and noisiness inherent in AF change at fine temporal scales. Here we present three new permutation tests — which do not assume a model of evolutionary change or a parametric statistical model — to detect AF timeseries features of evolutionary interest. The features identified by these approaches are: 1) any evolutionary change (as opposed to apparent change due to measurement error); 2) directional selection; 3) fluctuating selection with a propensity to change sign (negative autocorrelation). We are not aware of existing tests for features 1 and 3. Feature 2 is commonly tested using standard evolutionary models such as the Wright-Fisher; we show that the permutation approach has comparable statistical power. We apply our new approaches to AF timeseries data from D. melanogaster and D. pulex.