Chaos and pattern formation in a spatial tritrophic food chain

The model of Hastings and Powell describes a tritrophic food chain that exhibits chaotic dynamics. The model assumes that the populations are homogeneously mixed, so that the probability that any two individuals interact is uniform and space can be ignored. In this paper we propose a spatial version of the Hastings and Powell model in which predators seek their preys only in a finite neighborhood of their home location, breaking the mixing hypothesis. Treating both space and time as discrete variables we derive a set of coupled equations that describe the evolution of the populations at each site of the spatial domain. We show that the introduction of local predator-prey interactions result in qualitatively distinct dynamics of predator and prey populations. The evolution equations for the predators involve averages over the local density of preys, whereas the equations for the preys involve double averages, where the local density of both preys and predators appear. Our numerical simulations show that local predation also leads to spontaneous pattern formation and to qualitative changes in the global dynamics of the system. In particular, depending on the size of the predation neighborhoods, the chaotic strange attractor present in the original model of Hastings and Powell can be replaced by a stable fixed point or by an attractor of simpler topology. (c) 2005 Elsevier B.V. All rights reserved.191229130

Biodiversity, species interactions and ecological networks in a fragmented world

Biodiversity is organised into complex ecological networks of interacting species in local ecosystems, but our knowledge about the effects of habitat fragmentation on such systems remains limited. We consider the effects of this key driver of both local and global change on both mutualistic and antagonistic systems at different levels of biological organisation and spatiotemporal scales. There is a complex interplay of patterns and processes related to the variation and influence of spatial, temporal and biotic drivers in ecological networks. Species traits (e.g. body size, dispersal ability) play an important role in determining how networks respond to fragment size and isolation, edge shape and permeability, and the quality of the surrounding landscape matrix. Furthermore, the perception of spatial scale (e.g. environmental grain) and temporal effects (time lags, extinction debts) can differ markedly among species, network modules and trophic levels, highlighting the need to develop a more integrated perspective that considers not just nodes, but the structural role and strength of species interactions (e.g. as hubs, spatial couplers and determinants of connectance, nestedness and modularity) in response to habitat fragmentation. Many challenges remain for improving our understanding: the likely importance of specialisation, functional redundancy and trait matching has been largely overlooked. The potentially critical effects of apex consumers, abundant species and super-generalists on network changes and evolutionary dynamics also need to be addressed in future research. Ultimately, spatial and ecological networks need to be combined to explore the effects of dispersal, colonisation, extinction and habitat fragmentation on network structure and coevolutionary dynamics. Finally, we need to embed network approaches more explicitly within applied ecology in general, because they offer great potential for improving on the current species-based or habitat-centric approaches to our management and conservation of biodiversity in the face of environmental change