Limiting Similarity Species Packing How Close Can Species Be to Each Other

Hutchinson states that a species' realized niche is exclusive, that is, no two species can share a single niche and no overlap in the realized niches is possible in a stable environment. In other words, were there to be an overlap in, say, the trophic 'dimension' of the niche, species would differ in other dimensions, for example in their tolerance to abiotic factors, or avoidance of predators. Now, the (rather vague) consensus is that a little overlap between niches is consistent with coexistence, whereas somewhat larger overlap is not. The theory of 'limiting similarity', formalized by Robert MacArthur and Richard Levins, predicts the minimum permissible degree of overlap in the resource utilization curve. They showed that coexistence between species utilizing a continuous resource is possible when the ratio between the niche width (see Box 1) and the distance between species' optima is approximately unity or smaller. (This has been derived using the Lotka-Volterra equations describing the growth rates and hence stability of populations of competing species, where the competition coefficients were determined by the proximity of species' bell-shaped utilization curves.) However, the result is sensitive to the assumptions about the form of the resource utilization function and population growth rate:

Box 1 Niche width

Niche width describes the dispersion of population resource use along a niche dimension. As such, it is very laborious to measure: more often, we get estimates of niche width from the morphological traits related to the resource use: for example beak dimensions, jaws or teeth size. However, this measure delivers only a part of the information: both phenotypic variation in the traits important for food gathering and the ability of an individual to exploit a range of resources generally contribute to the niche width. For example, the niche breadth of Anolis lizards, studied by Joan Roughgarden, is mostly determined by variation in jaw size within species, but any individual still contributes to the total niche width, having its own range of prey sizes. Importantly, Roughgarden shows that a measure of the total niche width can be calculated as a sum of a 'within-phenotype component', the average variance of the individual's utilization function, and a 'between-phenotype component', the variance in population resource utilization function. Often, the range of two standard deviations (twice the square root of the sum), comprising about 95% of resource used, is denoted as the niche width.

The related term 'niche breadth' is originally due to Richard Levins. Levins' measures of niche breadth reflect the diversity of species' use of available resources: niche breadth is determined by the Shannon index (i.e., information entropy), or Simpson's index (i.e., the inverse of the sum of squared frequencies of the focal species over all resources). Although niche breadth intuitively captures differences between generalists and specialists, the measure is very sensitive to the categorization of resources and their frequency distribution.

notably, highly peaked resource utilization functions show actually almost no limits to coexistence (as their overlap is always minute) and niches can overlap broadly when fitness increases as the frequency of individuals carrying the respective trait decreases (negative frequency dependence). Also, coexistence between species can be facilitated by fluctuations in the environment generating frequency or density-dependent selection, or when the response of competitors to the common fluctuations is nonlinear. Note that the predictions ofthe theory oflimiting similarity cannot be directly corroborated by observation: by definition, the population density of one of the species is close to zero if the species pair is close to limiting similarity, and thus the utilization functions are not observable in such a situation. On the other hand, finding a similarity higher than predicted would clearly indicate that some ofthe assumptions of the model are violated.

The spacing between species in niche space, resulting from partitioning the available resources ('species packing'), differs considerably between sexually and asexually reproducing species. In asexual species, clones bearing favorable combinations do not recombine, and therefore those adapted to the various resource combinations can be arbitrarily spaced in the niche space. In sexual populations, individuals share common gene pool which does not allow divergence in adaptive response to varying resource combination. (Over time, of course, tradeoffs in utilizing the resource spectrum can lead to disruptive selection strong enough to drive evolution of reproductive isolation and evolution of distinct species.) Due to the necessity of finding a mating partner, population growth rate of sexual populations can sharply decrease at low densities ('Allee effect'), limiting both adaptation to marginal conditions and invasion to a new area. Both these effects contribute to discontinuities in distribution of resource use of sexually reproducing species.

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