Some Progress on Single Species Models with Nonlocal Dispersal Strategies in Heterogeneous Environments (Journal of Mathematical Study, 2024)
In this paper, we consider a single species model with nonlocal dispersalstrategy and discuss how the dispersal rate and the distribution of resources affectthe total population and survival chances by summarizing some previous results anddemonstrate some relevant progress. The first topic is about the monotonicity of totalpopulation upon dispersal rate. For the nonlocal model, we prove a new result, whichreveals essential difference between local and nonlocal models for certain distributionof resources. Secondly, we discuss optimal spatial arrangement for survival chancesand total populations. The results for both local and nonlocal models demonstrate thatthe concentration of resources is beneficial for species.
Keywords: Total population; nonlocal dispersal; heterogeneity