Modeling and analysis of stoichiometric two-patch consumer-resource systems

Ecological stoichiometry studies the balance of energy and multiple chemical elements in ecological interactions to establish how the laws of thermodynamics affect food-web dynamics and nutrient cycling in ecosystems. In this paper, we incorporate stoichiometric principles in a model with habitat heterogeneity and dispersal in order to better understand population growth dynamics. This model describes a situation where a resource is separated into two patches by a barrier. Growth of the resource in each patch is limited by soil fertility and self-crowding. The consumer disperses between the two patches and is not affected by the barrier. The consumer's growth is potentially limited by the phosphorus content of the acquired resource. Mathematical analysis of this model and simulations are performed. Several biological implications, including an observed "stoichiometric extinction effect," are demonstrated with simulation where the stoichiometric mechanism appears to promote extinction in a patchy environment. This is in sharp contrast to the notion that stoichiometry mechanism promotes diversity in spatially homogeneous settings. Another important result is the rediscovery of a simple and plausible biological mechanism that generates local and global extinction. In this setting, which can be considered a spatially mediated form of apparent competition, the dispersal of the consumer from the rich patch can des the growth of the resource in the poor patch and in some situations can lead to the extinction of the resource in the poor patch.