A nonautonomous model for the impact of toxicants on size-structured aquatic populations: Well-posedness and long-term dynamics

Abstract

Mathematical models have played a crucial role in understanding and assessing the impacts of toxicants on populations. However, many existing population-toxicant interaction models are physically unstructured and represented by autonomous systems, assuming all individuals are identical and model parameters are constant over time. In this paper, we develop a nonautonomous model describing the interaction between a size-structured population and an unstructured toxicant in a polluted aquatic ecosystem. This model allows us to investigate the influence of size- and time-dependent individual vital rates (growth, reproduction, and mortality), time-varying toxicant input and degradation, and size-specific sensitivity of individuals to toxicants on population persistence. We establish the existence and uniqueness of solutions for this model using the monotone method, based on a comparison principle. We then analyze how time- and size-dependent parameters affect the long-term population dynamics. Specifically, we derive conditions on these parameters that lead to either extinction or persistence of the population. We provide a comparative analysis of numerical solutions between our size-structured model and an unstructured model with size-averaged parameters, emphasizing the significance of incorporating size structure when evaluating the effects of toxicants on populations.