The Influences Of Allee Effects On Predator-prey Interaction At Different Spatial Scales

Allee effects have been much studied in ecology, reservation biology and biological invasion. In the past tens of years, a lot of studies have been done to investigate the influences of Allee effects on population dynamcs, species interaction, conservation, species range expansion and alien species invasion. As more and more ecologists have reconganized that space plays a very important role in almost all aspects of ecology, ecologists are now making efforts to extend the researches on Allee effects from local to regional scales. It has been shown that there are Allee-like effects at metapopulation level, which is similar to that of Allee effects at the local population level. However, most research has been focused on the Allee effects of local populations and both theoretical and experimental studies on Allee-like effects at the metapopulation level remain much too limited. On the other hand, identifying what regulates population dynamics and allows ecological interactions to persist has vexed ecologists for almost 100 years. Predation is a very common process in natural ecosystems. It can affect the distribution, abundance, and dynamics of species in ecosystems. Hence, researches on influences of Allee effect s and Allee-like effects at different spacial scales on predator-prey interactions appear very important. In this paper, I constructed theoretical predator-prey models including Allee effects/Allee-like effects, and then investigated the effects of Allee effects and Allee-like effects on predator-prey systems by mathematical analysis, phase-plane analysis and numerical simulation. The main conclusions in this paper are as follows:In this paper, I selected two classical models describing predator-prey systems and introduce the Allee effects into the dynamics of both the predator and prey populations in these models respectively. By combining mathematical analysis with numerical simulation, we have shown that the Allee effect may be a destabilizing force in predator-prey systems: the equilibrium point of the system could be changed from stable to unstable or otherwise, the system, even when it is stable, will take much longer time to reach the stable state. We also conclude that the equilibrium of the prey population will be enlarged due to the Allee effect of the predator, but the Allee effects of the prey may decrease the equilibrium value of the predator, or that of both the predator and prey. It should also be pointed out that the impact of the Allee effects of predator and prey due to different mechanisms on different predator-prey systems may also vary.We then extended our researches from local population scale to metapopulation scale. We investigated the influences of Allee-like effects of both predator and prey on predator-prey metapopulation dynamics by theoretical analysis. The results indicate that the predator is more vulnerable than the prey to Allee-like effects of both predator and prey. In presence of these Allee-like effects, the equilibrium fractions of predator-prey patches are decreased, and the predator generally becomes more vulnerable to habitat destruction. We conclude that either the coexistence or extinction of predator and prey at the metapopulation level should not be solely as a result of metapopulation dynamics and habitat destruction, rather, Allee-like effects may likewise play a role of its own.