A STOCHASTIC-THEORY OF COMMUNITY FOOD WEBS .5. INTERVALITY AND TRIANGULATION IN THE TROPHIC-NICHE OVERLAP GRAPH

Reports a new theoretical and empirical information about the overlaps among the diets of organisms in natural communities. On the basis of mathematical calculations, computer simulations, and new analyses of 113 community food webs, the authors show that the larger the number of trophic species in a web, the larger the probability that the dimension of a community's trophic-niche space exceeds one. Equivalently, the larger the number of species in a web, the smaller the probability that it is an interval web. If the dietary overlaps among consumers in a community can be described by the overlaps among intervals of a single variable, the web of the community is said to be an interval web and to have the property of intervality. In addition to intervality, the overlaps among the diets or among the consumers of organisms in natural communities may possess another property called triangulation. The larger the number of trophic species in a web, the smaller the probability that either the overlap graph or the resource graph of the web is triangulated. The mathematical calculations and computer simulations use a stochastic model of community food webs called the cascade model. -from Authors