Decomposing Frequency Dependence on Selection and Population Growth: Implications for Carrying Capacity and...

The phenotypes of individuals within a population create a dynamic social environment that influences phenotypic selection and population growth. Fluctuations in the frequencies of these phenotypes can influence population mean fitness and the relative fitness of phenotypes, and thus impact both population dynamics and phenotypic evolution. Various theoretical frameworks have been used to study the impact of frequency dependence on ecological and evolutionary dynamics. However, their diversity and mathematical complexity have obscured the relationship between theoretical models and empirical work. To bridge this gap, we discuss the effects of frequency dependence on phenotypic selection and population growth from a statistical perspective. We classify frequency-dependent effects on fitness according to their additive, relative or multiplicative effects, and explore how their interaction with population density can affect the eco-evolutionary dynamics of continuous traits. We show how these different effects can be mapped onto the parameters of simple linear regression models and derive how their magnitude is expected to affect the population carrying capacity and equilibrium mean phenotype. We then use individual-based simulations to complement our analytical results and demonstrate that quantifying frequency-dependent effects on fitness is key for understanding how populations will respond to environmental change.