Adaptive dynamics of a single-species trait under asymmetric competition and chronic critical pollution

The evolution of certain phenotypic traits can be influenced both by natural pressures, such as asymmetric competition, and by anthropogenic pressures, such as the severe and prolonged emission of pollutants generated by human activity. In this study, we propose a new nonlinear and non-autonomous mathematical model to analyze the adaptive dynamics of a continuous phenotypic trait in a single-species population, simultaneously exposed to asymmetric competition and to chronic and critical pollution. The model considers both exogenous sources, such as chemical or acoustic emissions, and endogenous sources derived from compensatory mechanisms, such as metabolic detoxification or the Lombard effect. We employ methods from population and adaptive dynamics, complemented by numerical simulations, to determine the conditions under which a convergently stable evolutionary strategy can remain continuously stable or become an evolutionary branching point that promotes phenotypic diversification. The results show that asymmetric competition drives evolution toward higher trait values, although increasing costs may induce evolutionary branching. In contrast, pollution tends to limit such evolution, favoring its stabilization at lower values. The interaction between both pressures can give rise to different adaptive trajectories depending on how evolutionary costs vary. Finally, we apply our theoretical results to a case of acoustic pollution in species that experience the Lombard effect. This model is presented as a useful tool for anticipating evolutionary trajectories in polluted environments and for supporting adaptive conservation strategies in the face of global change.