Ref ID : 1787
Frank M. Stewart and Bruce R. Levin; Partitioning of resources and the outcome of interspecific competition: A model and some general considerations. The American Naturalist 107:171-198, 1973
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In the existing mathematical theory of the growth of populations in limited environments, with some exceptions (e.g., Kostitzin 1939), limited consideration has been given to the nature of the mechanisms which lead to the inhibition of growth as densities increase. Models for the growth of single populations in limited environments usually take the form dN/dt=NF(N), where N is the number of individuals in the population and F(N) is some decreasing function of N. The biological assumption is that, as a population becomes more dense, the "conditions of life" become more severe, thus increasing the rate of mortality or reducing the rate of reproduction or both. Whether the conditions of life become more severe due to pestilence, wars, psychological effects, or lack of resources is not specified in the models. Models for more than one population of the same trophic level inhabiting the same limited environment (i.e., models for interspecific or intergenotypic competition) generally take the form dNi/dt=NiFi (N1, N2...), where Ni is the size of the (i)th population and of the other populations in this limited environments. The mechanisms by which one individual inhibits the growth of another-of his own or of a different, competing species-have usually been left vague and unspecified. Although the models themselves are not very definite, the biological interpretation is most often phrased in terms of resources. In other words, it is generally assumed that rates of population growth decrease because the available quantities of one or more resources decrease as the populations increase (see, for example, the often-cited paper of Hairston, Smith, and Slobodkin 1960). Thus, interspecific competition is generally studied as a situation which results from the sharing of essential resources by two or more populations. In fact, one of the most common forms of the so-called principle of competitive exclusion (a principle derived directly from the mathematical theory) is expressed in terms of resources: The number of species cannot exceed the number of resources (see Levins 1968). Here we present models in which the interaction between competing populations is dependent solely upon the abilities of individual members of these populations to take up and convert resources. The mechanisms by which resources are presented to the individuals and the manner in which they exploit these resources are specified precisely. The general properties of such models are examined and particular emphasis is given to the conditions of resources sharing under which two species can coexist. Among other things, we demonstrate that it is possible to obtain stable states of coexistence when the number of species is greater than the number of resources and when the conditions for stability of the equilibrium in the Gause form of the Volterra interspecific-competition model (Gause 1934) are violated.