'•i and has the same quantitative behavior as PS;, that is, ranging from generalization (A = 1) toward qj as an individual specializes on resource j. The precise value of A; is, however, sensitive to sample size of diet items used by individual i (n;), and number of resource categories (r). This can be standardized by
that corrects for this problem. As with PS;, one can use the average W¡ of the sample to estimate the population-wide prevalence of IS (W).
These four indices all vary from values close to 1 -indicating that all individuals have the same diet (may it be broad or narrow diet breadth) - to ~0, indicating strong IS. All these indices yield very similar though not identical values when applied to the same data. But which index should one use? Although the indices are quantitatively very similar, each has particular advantages and disadvantages. Both WIC/TNW and WICs/TNWs offer the attractive advantage of quantifying both relative specialization and population niche width. This can be used when testing hypotheses such as whether niche expansion during competitive release occurs by increased interindividual variation (greater BIC), implying that higher TNW is associated with greater individual specialization (low WIC/TNW). Both WIC/TNW and WICs/ TNWs make assumptions about the resource distribution. The continuous version assumes that niches are normally distributed, whereas the Shannon-Weaver index assumes that resources are evenly distributed. The Shannon-Weaver-based index can also be biased to overestimate IS due to its natural log of a proportion. Additional advantages of the two overlap indices are that they make no assumptions about the shapes of the resource distributions, and they yield estimates of specialization for each individual. The estimate of specialization for each individual further makes it possible to study the variation in specialization among individuals in a population, so one can study the ecological or evolutionary (fitness) consequences of IS. The likelihood measure has not been used to date, but has the advantage of providing a parametric statistical test of whether each individual departs significantly from the population's overall diet.
It is important that the niche axis or diet categories have been chosen appropriately when measuring diet specialization. For example, coarse-grained niche studies that pool functionally distinct resources may underestimate IS. When resources that a forager distinguishes among are lumped together by an ecologist, individuals may appear more generalized than they really are. Conversely, high between-individual variation may not be biologically significant if it is based on 'snapshot' sampling regimes. This risk can be minimized by several sampling schemes that allow one to establish the temporal consistency of diet variation. The most direct method is to follow individuals through time. Alternatively, a significant phenotype-diet correlation in a snapshot sample provides strong inferential support for consistent diet differentiation but does not guarantee that the quantitative measure is accurate. This is because it suggests that diet variation is due to functional morphology rather than random effects such as patchy prey distribution. Stable isotope ratios have been used to estimate the contribution of different prey to a forager's diet, as prey have characteristic isotope signatures. Isotope ratios in a forager's tissues turn over slowly, so isotope signatures thus represent a long-term average of prey use.
Why should we quantify IS? The obvious answer to that question is that there are large-scale trends in diet variation that reveal more fundamental patterns about tradeoffs, character release, and these effects of competition. These trends would not be detected if we simply tested whether diet variation was present or absent using a simple hypothesis-testing approach. For example, one study showed experimentally that IS in three-spine stickleback (Gasterosteus aculeatus) was stronger when competition was more intense. Furthermore, by quantifying IS, we enable broad-scale comparative studies where we can investigate similarities and differences between different taxonomic or geographic groups.
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