On investigating local–regional species richness relationships

Abstract

Most authors (e.g. Hugueny & Paugy 1995; Caley & Schluter 1997; Griths 1997; Oberdor€ et al. 1998) have concluded that local species richness is directly proportional to regional species richnessÐthe proportional sampling hypothesis (Cornell & Lawton 1992). Others (see Cornell & Karlson 1997) have found evidence for a levelling o€ in local richness as regional richness increases, consistent with the saturation of communities with species in some regions. Figure 1a shows the expected relations for the proportional sampling hypothesis and one version of the saturation curve. Here I consider the e€ects of inadequate sampling, inadequate pool identi®cation and statistical methodology (polynomial vs logarithmic and unconstrained vs constrained regression) on the shape of the local±regional relation detected, and examine other possible interpretations of a claimed non-interactive assemblage (Oberdor€ et al. 1998). The position of the intercept and the degree of curvature of the regression line are central to shape identi®cation. Inadequate sampling can a€ect where the local± regional relation crosses the ordinate. It is conceivable that local diversity at any given site could be zero when some species occur in the region. Whether or not this is the case will depend, in part, on the sample e€ort. Sampling e€ort that is inadequate but uniform across regions will move the intercept below zero by shifting the regression line to the right but should not a€ect the shape of the relation. If the degree of undersampling is a function of regional richness, the intercept might not pass through the origin (Fig. 1b). Changes in species rank-abundance patterns (or dispersion patterns) with regional richness could also a€ect the type of relation detected; for example, a shift from a geometric to a log-normal series pattern with increasing regional richness will result in a smaller fraction of the assemblage being sampled. A trend of reduced dominance with increasing species richness, which is plausible (Gray 1987; Whittaker 1975), will increase the chance of falsely detecting a saturating relationship. Correctly identifying regional pools can be problematic; for example Oberdor€ et al. (1998) de®ned their regional pool in ecological terms, noting that `a regional but ecologically based species richness would include only those species that are able to maintain populations within the sites studied'. The ecological pools were identi®ed from a more geographically widespread correspondence analysis (Verneaux 1981) which divided a species continuum into nine categories. How the sample sites were related to Verneaux's categories was not explained. This step is important because identifying an assemblage as indicative of, for example, Verneaux's metarhithron rather than the adjacent mesorhithron category would increase the regional pool size from 10 to 15 (i.e. by 50%) or if only the two most common abundance classes were used from 5 to 9 (by 80%). Moreover the 10 species found by Oberdor€ et al. (1998) do not appear to come from a single habitat because they divide into two ecological assemblages, one characteristic of relatively fastowing conditions (salmon, trout, minnow, bullhead, stoneloach) and the other of much slower ows (gudgeon, roach, chub and dace). Misidenti®cations of pools will shift the intercept up or down, depending on whether they have been underor overestimated: incorrect inclusion seems more likely than exclusion, favouring subzero intercepts. Two methods have been used to test the shape of the local±regional relation. 1. Fit a second-order polynomial regression, the lower order, linear, model being used to test for linearity if the second-order term is not signi®cant (Hawkins & Compton 1992). Some authors (Hugueny & Paugy 1995; Caley & Schluter 1997; Cornell & Karlson 1997; Oberdor€ et al. 1998) have omitted the constant, thereby constraining the line to pass through the origin, because `when regional diversity is zero, so too is local diversity' (Caley & Schluter 1997). It is correct that local richness must, by de®nition, be equal to or less than regional richness but the line need not pass through the origin, for the reasons outlined above. Accordingly when using polynomial regression the intercept a should be R 0 but not necessarily Correspondence: University of Ulster Freshwater Laboratory, Traad Point, Ballyronan, Co. Londonderry, UK, BT45 6LR. E-mail: D.Griths@ulst.ac.uk Journal of Animal Ecology 1999, 68, 1051±1055