Pattern formation, outbreaks, and synchronization in food chains with two and three species

We study the dynamics of populations of predators and preys using a mean field approach and a spatial model. The mean field description assumes that the individuals are homogeneously mixed and interact with one another with equal probability, so that space can be ignored. In the spatial model, on the other hand, predators can prey only in a certain neighborhood of their spatial location. We show that the size of these predation neighborhoods has dramatic effects on the dynamics and on the organization of the species in space. In the case of a three species food chain, in particular, the populations of predators display a sequence of apparently irregular outbreaks when the predation neighborhood has intermediate values, as compared to the size of the available space. Nonetheless, further increasing their size makes the outbreaks disappear and the dynamics approach that of the mean field model. Our study of synchronization also shows that the periodic behavior displayed by the average populations in a spatially extended system may hide the existence of patches that oscillate out of phase in a highly coordinated fashion.756

Patch exploitation strategies of parasitoids: The role of sex ratio and forager's interference in structuring metapopulations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)We use a mathematical model to explore the effects of parasitoid reproductive strategies and foraging behavior in response to spatio-temporal variations in the patch quality of a host-parasitoid metapopulation system. The variations of patch quality over the landscape were measured by the presence of parasitoid competitors and the density of hosts. The parasitoid responses to patch quality are given by three different foraging behaviors: (i) the decision to remain in or leave the current patch; (ii) the control of progeny's sex ratio and (iii) competitive abilities, measured by changes in the potential to attack hosts due to interference from conspecifics in the exploited patch. We study the dynamics of host and parasitoid populations characterized by different levels of density-dependent sex ratio adjustment and interference competition. Our results show that population stability increases when parasitoid growth is correlated with patch conditions. The effect of sex ratio adjustment alone does not account for qualitative changes to system dynamics or to the distribution patterns of species. In contrast, the degree of competitive interference among the parasitoids plays a crucial role in constraining the parasitoids' potential to reduce host populations and in determining the species' distribution in the landscape. We found that high levels of interference competition disrupt the population dynamics within a patch and allows hosts to completely dominate the landscape. This study shows that the inclusion of life history traits and the co-evolutionary aspects of host-parasitoid interaction can help researchers to understand species distribution patterns in the landscape. (C) 2012 Elsevier B.V. All rights reserved.2301121Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES [0004428/2010