Simple models for ecological systems with complex patterns.

PASCUAL, M. AND J. P. APARICIO.

Portland, OR, USA

Conferencia; Ecological Society of America (ESA) 89th Annual Meeting.; 2004

ESA

Monday, August 2, 8:00 AM to 11:30 AM, Meeting Room F 152. Simple models for ecological systems with complex patterns. Pascual, Mercedes *,1, Aparicio, Juan2, 1 University of Michigan, Ann Arbor, Michigan2 Universidad Metropolitana, San Juan, Puerto Rico ABSTRACT- Simple (mean field) ecological models ignore spatial and other forms of network structure. At the opposite extreme, high-dimensional models that are both individual-based and stochastic incorporate the local nature of ecological interactions. In between, are different types of approximations that incorporate the effect of correlations (or second-order moments) to represent the effects of spatial or network heterogeneity on mean quantities of interest. As an alternative closer to the typical temporal models used in ecology, we present results on "modified mean-field equations" for predator-prey and disease dynamics. With a spatial individual-based model, a relationship is shown between local and global densities allowing a simple power-law modification of the functional response which provides an approximation for both the transient and long-term dynamics at the population level. With a network model of disease, a temporal model is derived based on the basic reproductive number (Ro) which also captures well both transients and long-term dynamics. Key words: network and spatial heterogeneity, modified mean-field models, spatial scaling, individual-based models