The Influence Of High-order Interactions And Spatial Diffusion Structures On A Class Of Intransitive Competitive Systems

The stability of ecosystems and species coexistence is one of the classic issues in theoretical ecology research,and also an important theoretical basis for biological invasion and biodiversity conservation.Competition is an important interaction in ecology,and the exploration of the coexistence mechanism of competitive systems has always been a hotspot in ecological research.Intransitive competition can promote the coexistence of species by considering the cycle of competition among multiple species,which is usually a oscillaling coexistence mode.Intransitive competition combining ecological niche overlap and competitive symmetry can obtain a large range of stable coexistence areas.High-order interaction among species is a factor that has been ignored for a long time.In recent years,scholars have paid attention to the spatial structure between species.It is also a basic element of spatial ecology.The study of intransitive competitive systems considering high-order interactions and spatial structure is relatively scarce,and there is no general result.In this paper,I take intransitive competitive systems with overlapping ecological niche as the object to study the effects of high-order interactions of species and spatial network structure on system stability and coexistence.In order to investigate the effects of high-order interactions among species,the Lotka-Volterra intransitive competition model with high-order interactions is constructed.By analyzing the stability of equilibrium points,the conditions for stable coexistence are obtained.Furthermore,the influence of high-order interactions on stable coexistence regions is investigated through numerical solutions.After that,based on the local characteristics of species interactions in reality,the pair approximation model with high-order interactions is constructed.According to this approximate deterministic differential equation system,the effects of high-order interactions on species coexistence and population size are studied.In order to study the effects of species spatial structure,intransitive competition models with regular network,random network and scale-free network structures are established respectively.By rules updated according to the state of cellular automata,the changes in species coexistence and population size under different network structures is analysized.Based on the above model,through mathematical analysis and numerical simulation,the following results are obtained:(1)In the Lotka-Volterra intransitive competitive system without spatial structure,high-order interactions reduce the region of stable coexistence of species.(2)Under the condition of local interactions,high-order interactions promote species coexistence,However,the magnitude of this promotion effect is affected by the degree of local relationships(the number of neighbors).As the local relationships become larger(the number of neighbors becomes smaller),high-order interactions promote the coexistence of species.(3)The higher the degree of heterogeneity of the spatial network structure(the degree of heterogeneity increases in order of regular networks,random networks,and scale-free network),the more conducive to species coexistence;The spatial structure with low heterogeneity is not conducive to the development of population size.The mechanism and specific presentation of high-order interactions and species spatial structures in ecology are complex,and exploring their effects is a systematic and massive task.In this paper,I only reveal the impact of these two factors on intransitive competitive systems from one side,through a simple manifestation.The conclusions obtained will help enrich the theory of the stability of ecosystems and the species coexistence.