Synchrony in tritrophic food chain metacommunities

Abstract

The synchronous behaviour of interacting communities is studied in this paper. Each community is described by a tritrophic food chain model, and the communities interact through a network with arbitrary topology, composed of patches and migration corridors. The analysis of the local synchronization properties (via the master stability function approach) shows that, if only one species can migrate, the dispersal of the consumer (i.e., the intermediate trophic level) is the most effective mechanism for promoting synchronization. When analysing the effects of the variations of demographic parameters, it is found that factors that stabilize the single community also tend to favour synchronization. Global synchronization is finally analysed by means of the connection graph method, yielding a lower bound on the value of the dispersion rate that guarantees the synchronization of the metacommunity for a given network topology.

Synchrony in Metapopulations with Sporadic Dispersal

“…Proof. The proof directly follows from the one given in [Belykh et al, 2009] for the two-patch static network (3) (see Appendix in [Belykh et al, 2009]) where the coupling ε is replaced with pε and the network is extended to the all-to-all configuration with n patches.…”

“…Before proceeding with the study of the stochastic network, we should first understand the synchronization properties of the averaged network. Following [Belykh et al, 2009], we explore several scenarios of possible migration schemes between ecological patches when all three trophic levels (x, y, z-coupling) or only one trophic level can migrate. Figure 3 presents the Master Stability function [Pecora & Carroll, 1998] for synchronization in the averaged network.…”

“…The cause for spatial synchrony is believed to be a combination of correlated atmospheric conditions (the Moran effect) [Ranta et al, 1997;Cazelles & Boudjema, 2001;Colombo et al, 2008;He et al, 2010] and the presence of migration between population patches. Synchronization of Canadian lynx was initially attributed to the Moran effect; however, several studies have indicated that sufficiently strong dispersal in networks of tritrophic food chain models, related to the Canadian boreal forest, can induce synchrony without common atmospheric conditions (see for example, [Blasius et al, 1999;Belykh et al, 2009]). These studies supported by the DNA analysis [Schwartz et al, 2002], revealing high dispersal of Canadian lynx over large distance between the East and West Coasts, suggest that dispersal plays a key role in the spatial synchronization of the Canadian lynx.…”

“…Under this assumption, the metapopulation model is an n-patch network of linearly coupled food-chain models with a static graph. The static interaction is typically assumed to be of diffusive nature (on an arbitrary coupling graph) and defined by a zero-row sum connection matrix (see, for example, [Belykh et al, 2009]). There has also been a fair amount of work focused on density dependent migration models (for example, a model where predator migration is dependent on the prey density in a given patch [Huang & Diekmann, 2001]).…”

Asymptotic transversal stability for synchronized attractors in a metapopulation model

“…Indeed, each patch corresponds to a vertex of a graph; the local reproduction function f operates at each vertex, and there is an interaction along the edges of the graph due to the dispersal mechanisms. Although we are restricted to a metapopulation model, it is worth noticing that CMNs appear in several areas as electronics, neurology, chemistry, cryptography and others [36][37][38][39][40]. In particular, CMNs where the network dynamic and the coupling are time varying have an intrinsic interest [41].…”