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In a study of the feeding ecology of several species of diving ducks wintering together off the coasts of Sweden, Nilsson (1969) concluded that there was considerable overlap in the food species taken.

The proportions of certain food organisms in the diet of four lake-dwellng flatworms (Poly eel is tenuis. P. nigra, Dugesia polychroa and Dendrocoelum lacteum) was determined, by serological means, by Reynoldson and Davies (1970). Again, there proved to be considerable overlap between the species.

Such examples do not necessarily invalidate Cause's theorem, however. For the idea that two species with the same °r similar ecologies cannot coexist (and that one will thus be excluded or will evolve away), is based, as we will see later, on the assumption ^at the species are actually in direct competition. In the examples above, the resource in question (food) is superabundant and intense competition for any resource can only exist, by definition, if the resource in question is actually or potentially limiting. In general, where niche overlap does occur as described this is indeed only when the resource in question is superabundant.

As soon as resources become limiting, each species withdraws from the zone of overlap and ecological separation is re­established. Thus, in our 'food niche' examples above, each species has one particular food type or set of food types characteristic to itself: its 'food refuge' (Reynoldson and Davies, 1970).

The overlap is not total, but more as in Figure. Amongst the lake-dwelling triclads studied by Reynoldson and Davies, the food niches of Polycelis, Dugesia and Dendrocoelum overlap, but Polycelis species feed to a greater extent on oligochaetes, Dugesia on gastropods and Dendrocoelum on Asellus; within the oligochaete refuge, P. nigra has a specific refuge in Naididae, P. tenuis in Lumbricidae (Reynoldson and Davies (1970), revised Reynoldson and Bellamy (1970)).

Even here the extent of dietary difference between each species and all the others averages less than 46.2 per cent of total food at the most competitive season, when food becomes shortest; and there are many further examples where organisms appear to co-occur even in a potentially competitive situation with even greater overlap between their niches.

MacArthur's study of a guild of five similar species of warbler (Dendroica) found together as insectivores in New England provides a classic example (MacArthur, 1972).

This being the case, how much niche overlap is permissible? MacArthur and Levins (1964) examined the relative efficiency of exploitation of a range of examined the relative efficiency of exploitation of a range of resources by a single generalist species and by two comparative specialists.

Clearly that point at which a generalist become more eficient at exploiting a combined niche than two specialists might be considered the point beyond which niche overlap becomes impossible (for a single) generalist could them exploit the double niche more efficiently and would therefore outcompete either specialist). If we follow through their arguments therefore we can reach some conclusion as to the maximum tolerable degree of niche overlap.

Suppose there is some resource which varies over a simple continuum. A large number of species may exploit different parts of this continuum; each will have an optimum point (e.g., optimum size of insect, related perhaps to a bird's beak size).

Its total area of action will of course be over a range around this optimum, due to variability within the species, and, as we have already determined, each species' exploitation of the resource will be in the form of a normal distribution about its optimum point (Figure).

Thus niche relationships among potentially competiting species may be visualised and are conventionally represented as a series of bellshaped resource utilisation curves along the resource continuum (Figure). Each separate distribution may be defined in terms of its mean and standard deviation.

MacArthur and Levin's consider the efficiency of exploitation of a pair of overlapping resources by a single 'Jack-of-all-trades' and by a pair of specialists.

The degree of overlap between the resources influences the outcome. If we start with tw6 resource distributions which are very similar, so that an animal which is good at exploiting one of them is at least moderately good at exploiting the other, we can draw two curves representing harvesting efficiency with respect to resource parameter (in our example, insect size) for animals specialising in each resource, i.e. for using the two resource units separately. If our environment is a fine-gained mixture, in equal proportions, of the two resource units a line plotted at half height indicates the harvesting efficiency of each specialist on the mixture (dotted line).

The efficiency of a generalist operating over the whole resource and with an optimum between those of the two specialists is also indicated, and in such an environment may be seen to be greater than that of either specialist (and, it may be shown, than both specialists in combination).

Suppose the resources are less similar-sufficiently separate that the (dotted) curve for the mixed resource now has two peaks separated by a through (Fig). The generalist (J) now lies in the trough and it is clear that in this case the two specialists are superior, even on the mixed resource, to the generalist.

It may be calculated that the breakpoint-that equilibrium point where the trough appears and disappears and generalist and specialists are equally efficient at exploiting the 'double niche'-occurs when the separate resource distributions overlap within two standard deviations of their means.

As we have noted, these same deliberations may also be taken to suggest that there is a limiting similarity possible between the resource utilisation distributions of two coexisting species, and that at a certain degree of overlap exclusion must occur. Clearly, this too must occur at the point where one generalist becomes more efficient than two specialists, i.e., if niche overlap is within two standard deviations of the 'niche mean'.

Such considerations are based purely on analysis of the relative efficiency of exploitation of a given set of unlimited resources. In a later consideration, MacArthur and Levins (1967) have calculated the limiting similarity/overlap between species due to competitive exclusion when resources may be presumed to be limiting; they calculate a limiting similarity between the niches of 54 percent: a point beyond which competition would lead to exclusion of one or other species. More recent models have refined this analysis still further (May and MacArthur, 1972; May, 1975a; Fenchel and Christiansen, 1976) while the extent of overlap to be observed in practice may be measured by a variety of derived formulae.

Whatever the maximum possible overlap in theory, in the real community overlap will rarely extend to this theoretical potential. Real overlap will always be less than the maximum theoretically possible, because of the effects of competition within the community.

Even if potential competition between the actual species primarily concerned is taken into account in calculation of overlap (as MacArthur and Levins, 1967) effects of 'diffuse' competition from other members of the community may still have a further (unpredictable) effect on permissible overlap. Maximum possible overlap, as calculated here, should in theory remain a constant; maximum tolerable overlap in the real community has been shown to depend on the number of species in the community and the pattern of species packing.

Such analysis in any case refers to highly special cases where competing species differ only in their use of some single resource continuum. In practice, real organisms differ in their use of just one resource relatively infrequently however and if we consider two or more dimensions of the niche, pairs of species may have substantial or even complete overlap along one common dimension and still avoid competition by some degree of niche separation along another dimension (Figure, from Pianka, 1976).

(This is, after all, only putting into general terms the evidence from studies of ecological separation like those of Lamprey (1963) and Leuthold (1978) quoted in which, while overlap in the food niche might be quite considerable separation in the overall niche was ensured by differences in habitat use.) Ideally, therefore, an analysis of resource utilisation and niche separation/overlap should consider and quantify separation along all dimensions of the niche.

In such a case it is possible to show that, provided niche dimensions are independent, overall multidimensional utilisation (or full niches) is the product of the separate unidimensional functions. Estimates of niche parameters (niche width, niche overlap) along each separate dimension can simply be multipled together to produce the full niche picture (May, 1976; Pianka, 1976).

If niche dimensions are not entirely independent, such a calculation leads to an overestimation of the actual degree of overlap between two niches, while if niche dimensions are totally interrelated a more accurate estimate derives as the arithmetic mean of the component niche parameters (May, 1975a).