Stochastic theory of ecological interactions

It is possible, using the distribution of random numbers of random variables, to derive bimodal vertical distributions of phytoplankton biomass similar to those observed in nature. On the basis of the distribution of pseudorandom events, equations for the probability of individual mortality from one of several reasons, and for the capture of one of several preys by the predators were obtained. From these theoretical formulations the empirical equations of Beverton and Holt, Ricker and Ivlev were derived. An equation for the average feed intake of one individual interacting in a swarm, feeding on aggregated food, is derived from an estimate of the average interval between the random encounters of aggregates, in the nodes of an α-dimensional net.