Stability and evolution of networks on networks

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The project investigates how structure, stability, and dynamics of spatially extended food webs depend on the arrangement of and the coupling between the different patches, on the heterogeneity of the patches, on the local dynamics, and on the addition of new species. To this purpose, models for metacommunities of up to 60 species on 60 patches coupled by migration will be generated and investigated. Four work packages are planned: (1) We will investigate how the heterogeneity of the patches (in terms of different mortality or different amount of resources) and the type of migration (stochastic or continuous) affect the suvrival of species and the local and global diversity. We will generate allometrically scaled food webs and initialize them with random initial biomasses. Evaluations will be done with stochastic and continuous migration. (2) We will use the generalized modelling approach, which is based on a linear stability analysis of a suitably scaled system, in order to evaluate the linear stabilty, the variability (i.e., the global oscillation of the populations) and the occurrence of critical tranisitions in metacommunities. Variability will be determined based on the phases of the entries of the eigenvector to the largest eigenvalues. Critical transitions will be identified based on saddle node bifurcations, and they will be studied further in other projects of the RU. (3) The body-mass based evolutionary food web model developped during the first funding period will be investigated on several patches coupled by migration in order to study the influence of spatial structure and migration strength on the survival of species and on the local and global diversity. We will investigate the case of stochastic migration as well as the case of continuous migration. (4) In order to simulated many species on many patches, we will simplify the evolutionary model such that it does not contain explicit population dynamics. The rule for deciding which species survive and die out, will be based on estimates of biomass flows and competition, and will also take into account that specialists have higher attack rates. The emergent properties of the metacommunity will be investigated, and local and global diversities and other structural signatures shall be conpared to empirical systems and to the colonization-extinction models studied in other projects of this RU.