Turnover shapes evolution of birth and death rates

Abstract

Population turnover, a key trait shaped by the organisms life history strategy, plays an important role in eco-evolutionary dynamics by fixing the timescale for individual birth and death events as well as in determining the level of demographic stochasticity related to growth. Yet, the standard theory of population genetics, and the models heavily used in the related data analysis, have largely ignored the role of turnover. Here we propose a reformulation of population genetics starting from the first principles of birth and death and show that the role of turnover is evolutionarily important. We derive a general stochastic differential equation for the frequency dynamics of competing birth-death processes and determine the appropriate turnover corrections for the essential results regarding fixation, establishment, and substitution of mutants. Our results reveal how both the absolute and relative turnover rates influence evolution. We further describe a deterministic turnover selection, the turnover flux, which operates in small populations. Finally, we analyse the evolution of mean turnover and show how it explains the key eco-evolutionary mechanisms underlying demographic transitions. In conclusion, our results explicitly show how competing life-history strategies, demographic stochasticity, ecological feedback, and evolution are inseparably intertwined, thus calling for a unified theory development starting from the underlying mechanisms of birth and death.