Fitness landscapes for species interactions: when do population genetics and adaptive dynamics diverge?

Multiple frameworks have been developed to investigate the evolution of species interactions on fitness landscapes, each with unique strengths and weaknesses. These include adaptive dynamics, which uses linear stability analyses to predict eco-evolutionary outcomes resulting from the invasion of rare mutants into a resident population, and population genetics, which mechanistically models finite populations and stochastic processes in finite time. Though there are some known correspondences between these frameworks, it is not clear that they will always result in the same eco-evolutionary outcomes. Moreover, while adaptive dynamics is very powerful for predicting outcomes, it is not always straightforward to relate these predictions to the data generated in experimental evolution studies. Here, we use a data-driven model of microbial species interactions to compare and contrast the predictions of population genetics and adaptive dynamics. We derive expected outcomes for one-species and two-species evolutionary trajectories by using the invasion fitness landscape concept from adaptive dynamics, and then use analytical theory and forward-in-time simulations to set these predictions within the context of population genetic models. In the context of our one-species models, we show that the timescale of evolution depends on mutation supply and effect sizes, when populations are initialized both along and off a trade-off function. For two-species competition models, we show that mutation supply, effect sizes, and asymmetries between competing species result in discrepancies between adaptive dynamics and population genetics, especially in cases where adaptive dynamics predicts stable coexistence. Our study provides insight into the role of finite timescales, mutation supplies and population sizes in the evolution of species interactions, and facilitates further research that leverages the invasion fitness landscape concept within the realm of population genetics.