Allee effects of local populations and the synchrony of metapopulation
LIU Zhiguang1,,ZHAO Xue2,ZHANG Fengpan1,CHEN Aimin1 1 Institute of Applied Mathematics,School of Mathematics and Information Sciences,Henan University,Kaifeng 475004,China 2 Medical college of Henan University,Kaifeng 475004,China
A metapopulation describes a system of many small and extinction-prone fragmented local populations that are connected via migration.Spatial synchrony of oscillating populations has been observed in many ecological systems,and identifying its causes has attracted the interest of ecologists.Theory has shown that spatially autocorrelated environmental noise,dispersal,and trophic interactions are capable of producing spatial synchrony.Synchrony of a metapopulation has been shown to be detrimental to its persistence because all local populations may go extinct simultaneously. Allee effects at the local population level and Allee-like effects at the metapopulation level are important topics in ecology and conservation.Allee effects result in the existence of a threshold density below which the population goes extinct.At low density,fecundity may decrease while mortality may increase because of a range of factors including difficulties in finding mates,social dysfunction and inbreeding depression.These demographic changes lead to negative population growth rates and ultimately extinction.Many studies have demonstrated the potential importance of Allee effects for the dynamics of small populations,range expansion,community composition and biological invasion.It is widely accepted that Allee effects may increase the extinction risk of low density populations.However,insufficient attention has been paid to the relationship between metapopulation synchrony and Allee effects within local populations.By incorporating detailed information on dispersal strategy in a heterogeneous landscape,we were able to address the following questions:(1) how do Allee effects affect the synchrony of metapopulations?(2) Does the impact of the Allee effect depend on the dispersal strategy? In this paper,we begin by assuming that local populations experience Allee effects and construct a coupled map lattice model of connected local populations,i.e.a metapopulation model.A stability criterion for synchrony involving the Lyapunov number of the local population system,the frequency of dispersal and the network configuration matrix was obtained by Earn et al.We extend these ideas to the situation of a metapopulation comprising local populations subject to Allee effects.Using analysis and simulations,the results suggest that when the intensity of the Allee effect on local populations is strong,the metapopulation goes extinct;(2) when the intensity of the Allee effect on local populations is relatively weak,the local populations fluctuate in synchrony.In this latter case,the metapopulation persists,but the synchronous fluctuations of the local populations cause it to be more susceptible to environmental and demographic stochasticity,which increases metapopulation extinction risk;(3) the connectivity of the network has an important effect on metapopulation synchrony,and fragmented habitat is beneficial for metapopulation survival.Global migration combined with Allee effects increases the possibility of synchronous oscillation,and therefore enhances extinction risk of the metapopulation.As a result,when local populations are subject to Allee effects,the metapopulation quickly goes extinct or has a relatively high extinction risk.Allee effects have a deleterious effect on metapopulation persistence.These results may play an important role in understanding the mechanism underlying population synchrony as well as in developing conservation management plans and controlling the abundance of pest species.
【Fund】： 河南省教育厅基金项目(2011A180003);; 河南大学基金项目(2009YBZR027);; 国家自然科学基金项目(11105040)
【CateGory Index】： Q14
【CateGory Index】： Q14