Abstract
The aim of this paper is to investigate the evolution of body size of population subject to dispersal and advection. For this purpose, we consider a reaction-diffusion system for competing species with hostile boundary conditions, which models population dynamics in advective environments. First, with the methods of adaptive dynamics, we discuss the stability of evolutionary singular strategy; specifically, evolutionary conditions for continuously stable strategy and evolutionary branching are obtained. Second, by theoretical analysis and numerical simulations, we investigate the influence of dispersal and advection on the evolution trend of body size and high-level polymorphism. Our results show that in environments without advection, the result of evolution mainly depends on competition coefficients, intrinsic growth rates and biological dispersal. In particular, the evolution of the body size will tend to the slow disperser with the increase in the dispersal rate if regardless of the influence of body size on competitiveness and growth rate. But there will be different results in advective environments, the increasing dispersal rate may lead to the evolution of the body size toward a intermediate level. A small or a moderate dispersal rate is likely to stimulate the emergence of evolutionary branching. In addition, our results predict that for hostile boundary conditions, advection can promote evolutionary stability, which prevent the emergence of evolutionary branching.