Dispersion fields, diversity fields and null models: uniting range sizes and species richness

One of the cornerstones of macroecological research is theongoing effort to understand large-scale patterns of speciesrichness. These patterns are emergent properties of thedistributional ranges of individual species, as they areformed by the overlap of species ranges in a given area.As such, the sizes of ranges, and the processes controllingtheir geographical location, are key determinants of richnesspatterns. However, a satisfactory link between range sizedistributions, the spatial location of individual ranges, andspecies richness has been slow to emerge.To forge this link, a central part is the role of speciesassociations in determining the composition of species ina defined area. Overlap between species ranges may arisebecause species have similar ecologies (Webb 2000), forhistorical reasons of dispersal (Svenning et al. 2008), ormay simply be random, because ranges are constrained bythe shape of the geographical domain (Colwell and Lees2000, Jetz and Rahbek 2001). However, although speciesinteractions have consistently been shown to affect speciesco-occurrence at local scales (Gotelli and McCabe 2002),the importance of species associations for distributionaloverlap at biogeographical scales remains a central questionfor macroecology (Gotelli et al. 1997, in press).Species’ ranges are usually continuous at large scales, andas a consequence, the species richness values of closelylocated sites are not independent. This means that thespatial pattern of species richness cannot be explained byanalyzing sites as a set of independent points in a regression(Legendre 1993). Spatial regression methods solve thestatistical issue of autocorrelation (Rangel et al. 2006),but a simplistic use of these statistics risks missing the mainpoint. Spatial patterning is not a statistical issue it is aninherent quality of biogeographical data (Rahbek andGraves 2000, Diniz-Filho et al. 2003). In the light ofthis, recent attention has focused on developing conceptualand analytical tools for macroecological analysis that dealexplicitly with species’ ranges.One important advance is the concept of the ‘‘dispersionfield’’, developed by Graves and Rahbek (2005). Thedispersion field is the set of geographical ranges of allspecies that occur in a given site. Just as the continentalspecies richness pattern is created by the overlap of allspecies in a continent, the dispersion field can be visualizedas the pattern created by overlapping the ranges of allspecies occurring in a given cell (Fig. 1). These dispersionfields have striking geometric shapes, and have a number ofpromising applications.First, it has been argued that the geometric shape ofdispersal fields are an approximation to the regional speciessource pool (Graves and Rahbek 2005). The source poolplays a key role in theories of community assembly, butthe concept has been consistently difficult to pin down(Gotelli and Graves 1996). Even more importantly,dispersion fields visualize the species associations thatcreate richness patterns. Hence, they provide an opportu-nity for more stringent tests of ecological hypotheses forspecies richness than standard regression methods. Agrowing research paradigm in macroecology is to replacecurve-fitting methods with mechanistic models of rangeplacement (Rahbek et al. 2007, Rangel et al. 2007, Gotelliet al. 2009). Such models also generate predictions on thestructure of dispersion fields. Comparing both richnesspatterns and dispersion fields to modeled patterns thusconstitutes an opportunity for validation of these modelsat two hierarchical levels, a standard for pattern-orientedmodeling (Grimm et al. 2005).A promising approach for investigating the linkbetween range sizes and richness patterns has recentlybeen developed by Arita et al. (2008). This approach isbased on dispersion fields, and starts with the presenceabsence matrix of sites versus species. In this matrix, thecolumns are sites, rows are species, and the matrixelements represent the presence (1) or absence (0) ofa given species in a particular site (Gotelli 2000). Thestrength of the presence absence matrix is that it com-bines information on species richness (which are thecolumn sums), range sizes (which are the row sums),and the co-occurrence of species (which can be mea-sured by the degree of co-variance in the matrix). How-ever, the presence absence matrix is not easy to visualizegraphically.