A general minimum principle for competing populations: Some ecological and evolutionary consequences

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The principle introduced by MacArthur (1969. Proc. Natl. Acad. Sci. U.S.A., 64, 1369–1375) that the stable positive equilibrium of an exploitative competition system minimizes the mean squared deviation between available and utilized resources is generalized. It is shown that under less stringent assumptions, the global attractor of a competition system consists of species assortments that minimize a function of consumers' abundances, called inefficient energy utilization. If the minimum is unique (whether or not lying on the boundary of the state space) the global attractor reduces to a globally stable equilibrium. The inefficient energy utilization is the sum of two terms: one, called unutilized productivity, is the squared difference between maximum resource production and consumers' consumption, while the second, called basal energy consumption, is the caloric income to a community necessary for maintaining it at a steady state. The minimum principle is then used to solve some ecological and evolutionary problems. It is demonstrated that if an inverse correlation is assumed between consumers' efficiency and width of the trophic niche, evolution in undisturbed environments leads to assortments of tightly packed specialists.