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UBC Theses and Dissertations

Theoretical studies of the limiting similarity of competitors Abrams, Peter Arnold


This study consists of several theoretical investigations which bear on the question, "How similar may competing species be and still coexist?" It evaluates two previously suggested generalities, and suggests several factors which are important in determining the limiting similarity of competitors in a particular type of community. The first part is a study of the limits to overlap in resource utilization for competitors which are linearly arranged. The question of whether there is a limit to the similarity of species competing on a one-dimensional resource axis has previously been investigated by a number of authors. These studies have all used the Lotka-Volterra model of competition, and have assumed that the competition coefficient a., may be calculated using MacArthur and Levins' (1967) expression, [Chemical Equation] where U[sub i](R) is the resource utilization curve of species i. The generality of this formula is questioned, and two [missing text] alternative expressions for α[sub ij] are proposed. When these expressions are used in an analysis of limiting similarity, qualitatively different conclusions emerge regarding the existence and nature of this limit. The two alternative formulae considered suggest that under some circumstances very high overlap is possible in a linear array of competing species. The available experimental evidence does not strongly support the validity of MacArthur and Levins' formula for α[sub ij]. Since a given method of calculating α[sub ij] must be derived from a higher level model, it is suggested that the Lotka-Volterra model is not sufficient in an investigation of limiting similarity. Different assumptions about the nature of the resource utilization curves result in major differences in the limiting similarity. If the resources at a given position on the resource axis consist of a number of resource types, it seems likely that very close species packing should be possible. The second part investigates the question of whether several forms of environmental variability will limit niche overlap in a group of competing organisms. A simulation methodology was used to answer this question for the Lotka-Volterra model of competition. The basic result of this analysis is that systems where competition coefficients are relatively high can tolerate nearly as high a level of environmental variability as systems where niche overlap is low if, (i) environmental variability means variation in the supply of the resource for which the animals are competing, or (ii) there is a high level of correlation in the fluctuations in the rates of increase of different species (which, in turn, will be the case if the competitors share the same predators or have similar tolerances to physical stresses in the environment). High levels of variability may preclude the persistence of systems with a high level of competition when variations in the per capita rates of increase are uncorrelated or negatively correlated, or when increased variability is correlated with a lower average per capita rate of increase. The third chapter develops and analyzes a simple model of exploitative competition in which the resource consumers do not influence the rate at which resources become available to them. The goal of this analysis is to determine what factors allow relatively high (or low) resource overlap among competitors. The basic results are that: (1) The maximum overlap which will allow coexistence of two species, one of which has a slight competitive advantage, is usually greater when exploitation is efficient (i.e. when a large fraction of the resources entering the system are consumed when the consumer populations are at equilibrium). (2) The effect of density independent predation on this type of system is always to increase the niche separation necessary for coexistence, and thus to decrease species diversity. Predation increases the intensity of competition and decreases the maximum overlap consistent with coexistence for a pair of species. Environmental fluctuations which result in a reduction of population levels will have a similar effect. These results appear to be fairly general, so it would be desirable to try to determine whether the basic assumption of the model is actually met in those natural systems where it seems plausible.

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