PREDICTING THE OUTCOME OF COMPETITION USING EXPERIMENTAL-DATA - MAXIMUM-LIKELIHOOD AND BAYESIAN APPROACHES

Lotka-Volterra (LV) equations have been used extensively to explore th e possible dynamic outcomes of interspecific competition. But while th ere have been hundreds of papers on the mathematical properties of Lot ka-Volterra models, there have been only a handful of papers that expl ore techniques for fitting these models to actual data, and no papers that explore the interface of experimental design and statistical infe rence when fitting LV equations to census data. In this paper we prese nt a statistical analysis of Gause's experimental cultures of Parameci um aurelia and P. caudatum, using analytical methods based on maximum likelihood and Bayesian statistics. We compare the effectiveness of th ese two approaches in addressing several questions about competition f rom experimental data: Are the mutual effects of competing populations substantial? Are these competitive effects symmetrical? Are two popul ations expected to coexist or to eliminate each other by competition? We show that even a laboratory-derived data set with minimal variabili ty can entail significant levels of uncertainty about the nature of th e competitive interaction. We assess the errors involved in estimating the strength and symmetry of competition, and find that one's conclus ions depend critically on assumptions about sources of variability in the data. We also estimate the probabilities of alternative dynamic be haviors for competing species. We use simulations to evaluate how part icular experimental designs might improve our power to characterize th e dynamic; outcome of competition. We show that much more information is gained by running competition experiments at different starring con ditions than by replicating the same experiment for a particular start ing condition.