Genealogical process on a correlated fitness landscape

We study with extensive numerical simulation the genealogical process of 2N haploid genetic sequences. The sequences are under selective pressure, and fitness values are assigned at random, but with a tunable degree of correlation to the fitness values of closely related sequences. The genealogies that we observe can be classified into three different categories, corresponding to different regimes of the mutation rate. At low mutation rates, the sequences remain localized around a small number of central sequences, which leads to trees with short pairwise distances and slow turnover of the most recent common ancestor of the population. At high mutation rates, we observe trees similar (but not identical) to those of neutral evolution. In this regime, the population drifts rapidly, and selection does not influence the distribution of fitness values in the population. The third regime, for intermediate mutation rates, is only found in strongly correlated landscapes. It resembles the one for high mutation rates in that the population drifts rapidly, but nevertheless selection still shapes the distribution of fitness values.