History Can Matter: Non-Markovian Behavior of Ancestral Lineages

Although most of the important evolutionary events in the history of biology can only be studied via interspecific comparisons, it is challenging to apply the rich body of population genetic theory to the study of interspecific genetic variation. Probabilistic modeling of the substitution process would ideally be derived from first principles of population genetics, allowing a quantitative connection to be made between the parameters describing mutation, selection, drift, and the patterns of interspecific variation. There has been progress in reconciling population genetics and interspecific evolution for the case where mutation rates are sufficiently low, but when mutation rates are higher, reconciliation has been hampered due to complications from how the loss or fixation of new mutations can be influenced by linked nonneutral polymorphisms (i.e., the Hill-Robertson effect). To investigate the generation of interspecific genetic variation when concurrent fitness-affecting polymorphisms are common and the Hill-Robertson effect is thereby potentially strong, we used the Wright-Fisher model of population genetics to simulate very many generations of mutation, natural selection, and genetic drift. This was done so that the chronological history of advantageous, deleterious, and neutral substitutions could be traced over time along the ancestral lineage. Our simulations show that the process by which a nonrecombining sequence changes over time can markedly deviate from the Markov assumption that is ubiquitous in molecular phylogenetics. In particular, we find tendencies for advantageous substitutions to be followed by deleterious ones and for deleterious substitutions to be followed by advantageous ones. Such non-Markovian patterns reflect the fact that the fate of the ancestral lineage depends not only on its current allelic state but also on gene copies not belonging to the ancestral lineage. Although our simulations describe nonrecombining sequences, we conclude by discussing how non-Markovian behavior of the ancestral lineage is plausible even when recombination rates are not low. As a result, we believe that increased attention needs to be devoted to the robustness of evolutionary inference procedures that rely upon the Markov assumption.