Spatiotemporal Dynamics Of Allee Effect And Multiple Allee Effect

Allee effect,the positive relationship between individual's fitness and population density at low population density Allee effect is the hotstops in the research of ecology,biological invasion and conservation ecology.Due to various ecological mechanisms leading to Allee effect,there have been a large number of experimental evidences that species are subjected to multiple Allee effects in recent years.Therefore it is necessary to study the influence of multiple Allee effects on population dynamics and persistence.But theoretical studies on multiple Allee effect are very few.In this paper,the influence of the Allee effect and multiple Allee effect on the temporal and spatial dynamics of the population are discussed theoretically.We firstly discuss the concept,forming mechanisms,types,models of the Allee effect in details,as well as the applications in conservation ecology.Secondly,we construct the multiple Allee effect model of spatial structure population by combining mechanistic modeling and phenomenological modeling,and investigate the interaction of two component Allee effect.Based on the cellular automaton model(CAM)and probability transition model(PTM)we study how local dispersal affects the multiple Allee effect and the stability of population.Finally,we construct the Lotka-Volterra model subjected to Allee effect,and investigate the influence of Allee effect on the stability of mutualistic population under global and local dispersal.Two approaches will be utilized in this dissertation.One is the differential dynamical system,and we will use the phase plane analysis and numerical solution to illustrate the equilibriums and their stability of the system.The other is constructing the spatially explicit simulation,and then to achieve the explicit graphic model of the spatial pattern,structure and dynamics,which can make up for the deficiency of spatially implicit model.We have obtained the following new results.(1)Habitat restoration induced by the organism itself plays a crucial role to trigger the Allee effect(the bistability).Organism-environment positive feedback will incur weak,strong and fatal Allee effect.(2)The interaction between Allee effect caused by the organism-environment feedback(AE-by-OEF)and by other ecological mechanisms(AE-by-OM)could largely increase the extinction risk of population either due to the enlargement of Allee threshold or the change of inherent characteristic of Allee effect.(3)The multiple Allee effects could be stronger than the simple sum of involved individual Allee effects.This implies that the interaction of multiple Allee effects could be nonlinear.(4)The AE-by-OM is an unstable factor for population dynamics,larger intensity will destroy population.Under the certain strength of the AE-by-OM,the AE-by-OEF is a stable factor for population dynamics.The positive organismenvironment feedback is greater,the more favorable for population persistence.(5)Spatially local interaction between organism and environment can make both individual and superimposed Allee effects mitigate greatly and even disappear.(6)Although low-density local regions are subjected to Allee effect and make sub-populations extinct,high-density local regions save the population globally.Pattern formation could prevent population extinction.(7)In general,the mutualistic interaction makes the system unstable.When the system is subjected to Allee effect,the system can be stabilized.Therfore,Allee effect may play a stabilizing effect in mutualistic system.(8)Allee effect is a stabilizing or a destabilizing force in mutualistic systems could be determined by its intensity.The strong Allee effect leads to the extinction of one of the species or both species,but the mutualistic interaction between species reduces the Allee threshold of the system and reduces the risk of extinction.