| Abstract: | Some empirical consequences of an isomorphism between the Lotka-Volterra competitive model and a coevolutionary competitive model are developed. In both the Lotka-Volterra and coevolutionary models, four competitive outcomes are possible: 1) species one wins, 2) species two wins, 3) indeterminate outcome, and 4) stable coexistence. These two models are isomorphic in the sense that the inequalities associated with a particular competitive outcome of the Lotka-Volterra model correspond in a one-to-one manner with similar inequalities associated with the same competitive outcome of the coevolutionary model. The inequalities of the Lotka-Volterra model involve the competition coefficients themselves, while the inequalities of the coevolutionary model involve the genetic variances and covariances of the competition coefficients. The isomorphism suggests some alternative interpretations of the results of classical laboratory studies of competition. The Lotka-Volterra (or ecological) hypotheses postulate that the competition coefficients are constant and that genetic considerations play no role in determining the competitive outcome. By contrast, the evolutionary hypotheses derived from the coevolutionary model postulate that the competition coefficients are variables and that the genetic variances and covariances of the competition coefficients determine the competitive outcome. The isomorphism is applied to competitive exclusion and coexistence, and to competitive indeterminacy in Tribolium. In particular, the evolutionary hypotheses isomorphic to the two classical explanations of competitive indeterminacy, the demographic stochasticity and genetic founder effect hypotheses, are constructed. The theory developed here and in a previous paper (Pease, 1984) provides one perspective on the relation among the Lotka-Volterra competition theory, quantitative genetics, competitive exclusion, the reversal of competitive dominance, coexistence, competitive indeterminacy in Tribolium, and experiments investigating the relation between genetic variability and the rate of evolution of fitness. |
