Mathematical Biology Seminar Joel Brown, Moffitt Cancer Center Wednesday, November 15, 2023 1:45pm in LCB 323 Title: Why Darwin would have loved evolutionary game theory Abstract: When natural selection is density-independent and density-dependent, adaptations maximize population growth rates and sizes, respectively. But when it is frequency-dependent ?. well, who knows? Frequency-dependent selection is certainly more interesting, yet it is the ?miscreant? of evolution. What does evolution maximize? This is particularly perplexing for interactions like sexual selection, sociobiology, predator-prey interactions and habitat selection. Evolutionary game theory provides the logic behind adaptations emerging from frequency-dependent selection. A fitness generating function, G(v,u,x) can be used to define the expected per capita growth rate of an individual with strategy, v, where others use strategy u in a population of size x. Building on this formalism it is possible to model 1) species with quantitative traits, 3) speciation, niche coevolution, and coexistence, 4) predator-prey coevolution, and 4) formalize key stability concepts such as evolutionarily stable strategy (ESS), convergence stability, and neighborhood invader strategy (NIS). Game theory not only models natural selection, it may be the formal language of natural selection.