Effects of Organismal and Distance Scaling on Analysis of Species Distribution and Abundance

Abstract

As communities and populations become increasingly fragmented, much theoretical and some empirical research has focused on the dynamics of metapopulations. Many metapopulation models describe dynamics among populations in a region, yet the scale of the ''region'' to which different models apply often is undefined. Because the spatial scale is undefined, testing predictions and assumptions of these models is problematic. Our goal is to present two scaling concepts relevant to these models, distance scaling and organismal scaling, and to apply these scaling notions to patterns of species distribution. To determine distance effects, we analyzed patterns of distribution of four taxonomic groups in tallgrass prairie (grasshoppers, small mammals, vascular plants, and breeding birds) at two spatial scales. To assess organismal effects, we held spatial scale constant and we compared patterns of distribution and abundance among these taxonomic groups.Using long-term data from Konza Prairie, Kansas, there were significant differences in the pattern of distribution of grasshoppers, small mammals, vascular plants, and breeding birds within a single spatial scale. The number of core species (species occupying Ͼ90% of the sites in a region) of plants and birds was less than the number of satellite species (those occupying Ͻ10% of the sites in a region). The opposite was true for grasshoppers and small mammals. All four distribution patterns were significantly nonrandom, but only grasshoppers and small mammals were significantly bimodal at this scale. Plants and birds were unimodal. The patterns of distribution within these taxonomic groups at two spatial scales were significantly different as well. In all cases, the percentage of species in the core group declined, and the percentage of species in the satellite group increased as spatial scale increased. These results demonstrate the difficulty of testing theoretical models with only one taxonomic group at a single spatial scale. One should not accept or reject a model until the spatial domains of organismal and distance scaling have been properly evaluated.

Metapopulation Extinction Thresholds in Rain Forest Remnants

“…In particular, species with large local populations are regionally common (i.e., high probability of occurring at any given habitable site), whereas those characterized by small population sizes are regionally rare. Although several hypotheses, ranging from niche-breadth differences to sampling artifact, provide equally plausible explanations for this relationship (Gotelli and Simberloff 1987;Collins and Glenn 1997;Gaston et al 1997;van Rensberg et al 2000), only one hypothesis predicts how modifications to the regional distributional extent of a species assemblage is expected to alter both demographic and community-level processes.…”

A typing error in Tokeshi's test of bimodality

“…We found a typing error in Collins & Glenn (1997), in which '(1 − h ) N-i ' was replaced by '(1 − h ) N -1 '. Unfortunately, at least three recent studies (Guo et al ., 2000;Van Rensburg et al ., 2000;Perelman et al ., 2001) have referred to the incorrect equation in Collins & Glenn (1997).…”

“…Coincident with the growing interest in macroecology (see Gaston, 1994;Brown, 1995;Maurer, 1999;Gaston & Blackburn, 2000), the availability of this type of statistical test greatly improves the description and interpretation of frequency distribution patterns. Collins & Glenn (1997), among others, applied Tokeshi's statistical test to test for bimodality in range-size distributions for grasshoppers, small mammals, plants and birds, but introduced a typing error in the formula used to calculate the probability of the left-and right-most classes. Although such errors may occur easily during manuscript preparation, final printing, or other associated processes, as we will show below, this particular error has had some consequences in recent applications of the model.…”

“…Unfortunately, at least three recent studies (Guo et al ., 2000;Van Rensburg et al ., 2000;Perelman et al ., 2001) have referred to the incorrect equation in Collins & Glenn (1997). Applying the correct equation to the data of Van Rensburg et al .…”

“…bimodality vs. unimodality) remain the same, most P -values are now larger than those originally reported, in the case of unimodal distributions rendering the mode less significant following Tokeshi's (1992) diagnosis in Table 1 ( p. 260). Moreover, we believe somewhat different results would be produced if the correct model were used in Collins & Glenn (1997), unless the typing error was simply a printing error (i.e. all the calculations actually used the correct equation).…”