A spatiotemporal model for the effects of toxicants on the competitive dynamics of aquatic species

In this paper, we develop a reaction-diffusion model with negative toxicant-taxis that incorporates spatiotemporally inhomogeneous toxicant input to investigate the impact of toxicants on the competitive dynamics of two species in a polluted aquatic environment. Here the negative toxicant-taxis models the evasive movement of avoiding toxicants by species. We establish the global well-posedness of the model, analyze the existence and stability of spatially homogeneous steady states, and derive sufficient conditions for species extinction and coexistence. Through linear stability analysis, we identify sufficient conditions on model parameters that destabilize spatially homogeneous steady states under spatiotemporally uniform toxicant input. Numerical experiments reveal the influence of key toxicant-related factors (input rate, taxis intensity, and diffusivity) on competition outcomes and species distributions. Notably, strong negative toxicant-taxis can induce spatial aggregation and segregation patterns between the species and the toxicant under uniform toxicant input. Our findings suggest that toxicant-taxis may promote population persistence and coexistence, particularly when the toxicant input is not uniform in space and time and the toxicant does not diffuse fast (i.e. weak diffusivity). However, strong toxicant diffusion can diminish the impact of taxis, adversely affecting population persistence and species coexistence.