An effective Allee effect may induce the survival of low-density predator

Abstract

Allee effect, as one of the research hotspots in ecology and conservation biology, extremely easily affects the distribution of population in space, especially for the low-density population. In the ecosystem, the spatial distribution of predator is more vulnerable to Allee effect since the density of predator is always smaller than that of prey, but the relevant attention paid to it is few. In this paper, we establish and analyze a spatial predator–prey system incorporating Allee effect on predator population. Theoretically, we use multi-scale analysis to derive the amplitude equation and obtain the different Turing patterns under different intensities of Allee effect. Numerically, we verify the theoretical results. We also find that the growth rate of predator is significantly inhibited and the time of reaching equilibrium tends to be slower with the increase of Allee effect intensity within certain limits. More interestingly, it is discovered that the predator under Allee effect in a certain extent is more stable although Allee effect on predator may lead to more complex dynamic behaviors. Our results help better understand species invasion and nature conservation in ecology.

Keywords

• Allee effect
• Predator–prey system
• Multi-scale analysis
• Turing pattern