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 former Applied Math student who generalized these travelling waves into two dimensions, representing two different beneficial traits. The first model considers the simple case where in each of two kinds of mutations has the same characteristics, to characterize emergent covariance and timescales of fluctuation. 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, to characterize the conditions under which one trait proceeds unaffected while the other “stalls”. The third considers environmental change that must be countered by one trait to avoid extinction, while the other trait represents a zero-sum contest that can act as a distraction, including the possibility that larger habitats could actually reduce the adaptedness of a population. I will end with two possible directions for new students. One 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.