Temporal Variation, Spatial Heterogeneity, and Competition for Resources in Plankton Systems: A Theoretical Model

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Abstract
A model of 2 spp. competing for 2 resources in a spatially nonuniform (i.e, spatially disaggregated) environment is presented. The formulation is based experience with phytoplankton competing for nutrients in lakes and the ocean. The organisms may diffuse, be carried by currents, grown (controlled by the resources), sink, and die; the resources may diffuse, be carried by currents, be taken up by growing organisms, and be regenerated from dying organisms. External sources (or sinks) of resources are allowed. For reasonable choices of parameters, the model shows much more variable behavior in space and time than the usual smooth approach to coexistenc (or exclusion of one of the species) seen in previous resources competition models. For example, damped oscillations and "limit-cycle-like" behavior are exhibited. These are not the result time delays or varying environmental factors, but are inherent in the theory in which sinking plays a larger role. Diffusion in the spatially heterogeneous environment can allow coexistence of 2 species for situations in which dominance of one is predicted by other models. Conversely, through Turing instabilitiy, diffusion can destabilize an otherwise stable, uniform coexistence situation. Turing-type behavior may occur when organisms and nutrients diffuse at different rates and when perturbations in species densities or nutrient concentrations occur at intermediate spatial scales. The upper and lower limits of the intermediate scale region are set by the interaction of physical and biological processes; such regions (and thus Turing behavior) may be common in lake and ocean environments. The results of other models of resource-based competition depend upon behavior found near equilibrium. The conclusions of these equilibrium models may not apply in environments with realistic temporal and spatial variation.