Resource Productivity‐Consumer Species Diversity: Simple Models of Competition in Spatially Heterogeneous Environments

Abstract

The relationship between resource productivity and the number of consumer species that can coexist in a patchy environment was examined using simple models of competition. The analysis seeks to determine when diversity should increase with productivity, and when there should be a unimodel relationship between species diversity and resource productivity. The environment is assumed to consist of a number of independent patches in which competition occurs for one or two resources. In one—resource models, productivity—diversity relationships are increasing unless certain types of interspecific competition other than resource depletion occur. In two—resource models, differentiation with respect to use of the resources provides an additional mechanism for coexistence. The effects of productivity on coexistence conditions via this mechanism are examined using four different models. The models differ in whether resources are nutritionally substitutable or nonsubstitutable, and in whether the consumer species adjust the relative values of their two consumption rate constants to maximize fitness. Results for each model suggest that both increasing and unimodal productivity—diversity relationships are possible, depending on the type of resource growth and the definition of productivity. The conditions for coexistence of three species suggest that resource differentiation alone is unlikely to account for high species diversity, especially in the case of nonsubstitutable resources. This analysis makes different predictions than that of Tilman (1982) for several reasons; a major factor is that Tilman (1982) assumes that increasing productivity implies a decreasing coefficient of variation in productivities. Because there are many processes that can produce unimodal and increasing productivity—diversity curves, one cannot infer the mechanism of competition from this relationship.