SPREADING PROPERTIES FOR A PREDATION-COMPETITION SYSTEM WITH NONLOCAL DISPERSAL IN SHIFTING HABITATS

. This paper is concerned with the propagation phenomenon of a three species predation-competition system with nonlocal dispersal and climate change effects. That is to say, there is not only competition for food, but also competitive interaction between two preys. The growth rate of each prey is nondecreasing along the x-axis and shifts rightward at a speed s. We mainly consider the population dynamics for three cases: (i) the predator spreads faster than the two preys, (ii) the predator spreads between two preys and (iii) the predator with slower speed spreads behind the two preys, including multiple layers with different speeds to achieve a complete picture. Due to lack of comparison principle in the prey-predator system and compactness of the nonlocal operator, we give some priori estimates of the solutions to obtain the persistence for three species, which depends on improving the regularity of the dispersal kernels and proposing some parameter conditions of the considered system.