Spreading speeds of a three-species predator–prey model with nonlocal dispersal in a shifting environment

This paper is concerned with the spreading speeds of solutions for a three-species predator–prey model with nonlocal dispersal in a shifting environment. Specifically, we consider the survival or extinction of species in the following three situations: (i) both preys spread faster than predator; (ii) the predator spreads faster than both preys; (iii) the predator spreads between two preys. In order to obtain the persistence of species, we first provide some priori estimates of solutions to overcome the difficulties caused by the lack of comparison principle of the predator–prey model and the compactness of nonlocal operators. Then, the asymptotic behavior of the solutions can be obtained by constructing a suitable weighted Lyapunov function.