vol. 171, no. 6 the american naturalist june 2008  Scale Dependence of Species-Energy Relationships: Evidence from Fishes in Thousands of Lakes Tariq Gardezi * and Andrew Gonzalez † Department of Biology, McGill University, Montreal, Quebec H3A 1B1, Canada Submitted May 7, 2007; Accepted November 19, 2007; Electronically published April 11, 2008 Online enhancements: appendixes. abstract: Variation in the shape of relationships between species richness and different measures of energy may be linked to variation in the spatial scale on which such relationships are measured. We examine scale dependence in the relationship between potential evapotranspiration and the species richness of fishes in 7,885 post- glacial lakes. The strength of this relationship is weak across lake communities but strong and positive across groups of lakes or regions. In addition, the strength and slope of this relationship in- crease significantly as the regional scale of analysis is increased. We interpret the observed patterns in terms of a simple model whereby energy influences the linear character of the species-energy relation- ship through its influence on spatial turnover in the species com- position (beta diversity). Our results suggest that if energy is strongly tied to patterns of site occupancy or abundance, the parameters of species-energy relationships will depend, to a considerable extent, on the scale of measurement. Furthermore, the ability of high-energy regions to accommodate relatively large numbers of rare or infre- quent species may underlie any general tendency for the strength or shape of species-energy relationships to change with scale. Keywords: species richness, species-energy relationships, potential evapotranspiration, spatial scale, beta diversity, fishes. The role of energy in accounting for the heterogeneous distribution of species richness across the earth has been a core focus of ecology (Rosenzweig 1995; Gaston 2000; Evans et al. 2005), and patterns of species richness have been tied more consistently and convincingly to energy * Corresponding author; e-mail: tariq.gardezi@mail.mcgill.ca. † E-mail: andrew.gonzalez@mcgill.ca. Am. Nat. 2008. Vol. 171, pp. 800–815.  2008 by The University of Chicago. 0003-0147/2008/17106-42590$15.00. All rights reserved. DOI: 10.1086/587520 than to other factors (Wright et al. 1993). Decades of in- vestigation have revealed, however, that there is a great deal of variation in the shape of species-energy relation- ships (Mittelbach et al. 2001), and their underlying mech- anisms have remained largely unresolved (Currie et al. 2004; Evans et al. 2005). Some variation in the shape of species-energy relation- ships is undoubtedly due to differences in the scale of measurement, like variation in many other ecological pat- terns (Levin 1992). Species-energy relationships may differ depending on whether they are assessed at small grain sizes (e.g., a few square kilometers or less) or large ones (hun- dreds of square kilometers or more) and are more likely to be positive and linear in the latter case (Evans et al. 2005 and references therein; see also Gaston 2000), es- pecially when species have a common historical context and potentially confounding areal and sampling effects are controlled for (see Abrams 1995). Thus, the grain of an analysis—that is, the size of the geographic units for which species richness is estimated—can influence the form of the relationship between species richness and energy (Scheiner et al. 2000) and has received explicit attention in a growing number of investigations (e.g., Lyons and Willig 2002; Scheiner and Jones 2002; van Rensburg et al. 2002; Bailey et al. 2004; Chalcraft et al. 2004; Storch et al. 2005; Harrison et al. 2006). Grain size will delimit the mechanisms that mediate the interaction between species richness and energy (Tonn 1990; Kaspari et al. 2003). In particular, processes that influence species survival within communities are important in determining the nature of the species-energy relationship at a grain size of a single community or smaller, while consequences of these pro- cesses for spatial turnover in species composition come into play when regions or groups of communities are com- pared (Scheiner et al. 2000; Chase and Leibold 2002). An understanding of the link between species turnover and regional variation in species richness is, furthermore, vital for an understanding of large-scale biodiversity patterns (Ricklefs 2004). We investigate the influence of spatial grain on the form of species-energy relationships, and we use the terms “scale” and “grain size” interchangeably.