Abstract: Beyond fitness: evolution in two dimensions
Evolution by natural selection can be modeled in terms of the mutation rate, the expected effect of each mutation on an individual’s propensity to survive and reproduce, and stochastic effects. Especially in an asexual population, one powerful approach considers evolution as a travelling wave, with new beneficial mutations appearing at the leading “nose” where they might or might not escape stochastic loss, and the power of natural selection driving the bulk of the distribution of genotypes forward. I will present work by a recently graduated Applied Math student who generalized these travelling waves into two dimensions. The first model considers the simple case where the two dimensions are equivalent. The second considers what happens when one dimension has a higher rate of beneficial mutations, while the second experiences a larger benefit per beneficial mutation. The third considers environmental change that must be countered in one dimension to avoid extinction, while the other dimension represents a zero-sum contest that can act as a distraction. I will end with possible directions for new students. One possible project is to consider the role of frequent deleterious mutations in something like the third scenario. A second considers the evolution of aging, where competition between cells within an organism helps purge senescent (degraded) cells but can cause the proliferation of “cheater” cells that cause cancer and other problems. Senescent and cheater cells each cause aging, albeit via different modes in tension with each other.