As proposed by Macarthur and Levins in 1967, the theory of limiting similarity is rooted in the Lotka-Volterra competition model. This model describes two or more populations with logistic dynamics, adding in an additional term to account for their biological interactions. Thus for two populations, x1 and x2: Macarthur and Levins examine this system applied to three populations, also visualized as resource utilization curves, depicted below. In this model, at some upper limit of competition α, between two species x1 and x3, the survival of a third species x2 between the other two is not possible. This phenomenon is termed limiting similarity. Evolutionary, if two species are more similar than some limit L, a third species will converge towards the nearer of the two competitors. If the two species are less similar than some limit L, a third species will evolve an intermediate phenotype. The key weakness of the Theory of Limiting similarity is that it is highly system specific and thus difficult to test in practice. In actual environments, one resource axis is inadequate and a specific analysis must be done for each given pair of species. In practice it is necessary to take into account: individual variations in resource utilization curves within a species and how these should be weighted in calculating a common curve whether the resource in question is a present in a deterministic or stochastic distribution and if this changes over time effects of intraspecific competition vs interspecific competition While these complications don't invalidate the concept, they render limiting similarity exceedingly difficult to test in practice and useful for little more than didacticism.
As proposed by MacArthur and Levins in 1967, the theory of limiting similarity is rooted in the Lotka-Volterra competition model. This model describes two or more populations with logistic dynamics, adding in an additional term to account for their biological interactions. Thus for two populations, x1 and x2: MacArthur and Levins examine this system applied to three populations, also visualized as resource utilization curves, depicted below. In this model, at some upper limit of competition α, between two species x1 and x3, the survival of a third species x2 between the other two is not possible. This phenomenon is termed limiting similarity. Evolutionary, if two species are more similar than some limit L, a third species will converge towards the nearer of the two competitors. If the two species are less similar than some limit L, a third species will evolve an intermediate phenotype. The key weakness of the theory of limiting similarity is that it is highly system specific and thus difficult to test in practice. In actual environments, one resource axis is inadequate and a specific analysis must be done for each given pair of species. In practice it is necessary to take into account: individual variations in resource utilization curves within a species and how these should be weighted in calculating a common curve whether the resource in question is a present in a deterministic or stochastic distribution and if this changes over time effects of intraspecific competition vs interspecific competition While these complications don't invalidate the concept, they render limiting similarity exceedingly difficult to test in practice and useful for little more than didacticism.
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Theory of Limiting
theory of limiting