Predicting the Outcome of Competition Using Experimental Data: Maximum Likelihood and Bayesian Approaches

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Abstract
Lotka—Volterra (LV) equations have been used extensively to explore the possible dynamic outcomes of interspecific competition. But while there have been hundreds of papers on the mathematical properties of Lotka—Volterra models, there have been only a handful of papers that explore techniques for fitting these models to actual data, and no papers that explore the interface of experimental design and statistical inference when fitting LV equations to census data. In this paper we present a statistical analysis of Gause's experimental cultures of Paramecium aurelia and P. caudatum, using analytical methods based on maximum likelihood and Bayesian statistics. We compare the effectiveness of these two approaches in addressing several questions about competition from experimental data: Are the mutual effects of competing populations substantial? Are these competitive effects symmetrical? Are two populations expected to coexist or to eliminate each other by competition? We show that even a laboratory—derived data set with minimal variability can entail significant levels of uncertainty about the nature of the competitive interaction. We assess the errors involved in estimating the strength and symmetry of competition, and find that one's conclusions depend critically on assumptions about sources of variability in the data. We also estimate the probabilities of alternative dynamic behaviors for competing species. We use simulations to evaluate how particular experimental designs might improve our power to characterize the dynamic outcome of competition. We show that much more information is gained by running competition experiments at different starting conditions than by replicating the same experiment for a particular starting condition.

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