In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes in the distribution of types as mutations march toward fixation or extinction. We describe motion as the swapping of individuals on graphs, and also more generally as the shuffling of individuals between reproductive updates. Beginning with a one-dimensional graph, the cycle, we prove that motion suppresses natural selection for death-birth updating or for any process that combines birth-death and death-birth updating. If the rule is purely birth-death updating, no change in fixation probability appears in the presence of motion. We further investigate how motion affects evolution on the square lattice and on weighted graphs. In the latter case, we find that motion can be either an amplifier or a suppressor of natural selection. In some cases, whether it is one or the other can be a function of the relative reproductive rate, indicating that motion is a subtle and complex attribute of evolving populations.
Madison S. Krieger, A. McAvoy and M. A. Nowak, “Effects of motion in structured populations”, Arxiv, PDF
Some of the most critical evolutionary innovations occurred within single-celled prokaryotic organisms in the primitive ocean, such as the development of flagellar motility and the invention of oxidative photosynthesis. Prokaryotes have multiple vectors to exchange genetic material including transduction, transformation and conjugation. Being able to exchange genetic information allows important novel genes to be built up more quickly than if the population were waiting for the proper mutations to arise in a single lineage. However, these methods of genetic exchange require two differing lineages containing subsections of the novel gene to be in close proximity. Here we consider whether the transport properties of the primitive ocean may have accelerated this process. We consider two genetic components which arise via mutation at the same rate within a large background population and afford no selective advantage on their own. Once the pieces are combined via horizontal gene transfer in a single lineage, the selective advantage is immense. We examine the role of different fluid flows and components of complex oceanic flow on the time until the two lineages are united via theory and simulation.