Some Progress on Single Species Models with Nonlocal Dispersal Strategies in Heterogeneous Environments

In this paper, we consider a single species model with nonlocal dispersal strategy and discuss how the dispersal rate and the distribution of resources affect the total population and survival chances by summarizing some previous results and demonstrate some relevant progress. The first topic is about the monotonicity of total population upon dispersal rate. For the nonlocal model, we prove a new result, which reveals essential difference between local and nonlocal models for certain distribution of resources. Secondly, we discuss optimal spatial arrangement for survival chances and total populations. The results for both local and nonlocal models demonstrate that the concentration of resources is beneficial for species.