Ecology, 95(2), 2014, pp. 553–562 Ó 2014 by the Ecological Society of America The metabolic theory of ecology convincingly explains the latitudinal diversity gradient of Neotropical freshwater fish DAYANI BAILLY, 1,5 FERNANDA A. S. CASSEMIRO, 2 CARLOS S. AGOSTINHO, 3 ELINEIDE E. MARQUES, 3 AND ANGELO A. AGOSTINHO 4 1 State University of Maringa ´, UEM/PEA/NUPELIA, Avenida Colombo, 5790, 87020-900, Maringa ´, PR, Brazil 2 Systema Naturae Environmental Consulting, 58 st, 217, 74810-250, Jardim Goia ´s, Goi ˆ ania, GO, Brazil 3 Federal University of Tocantins, UFT/NEAMB, Jardim dos Ipˆ es, 77500-000, Porto Nacional, TO, Brazil 4 State University of Maringa ´, UEM/DBI/NUPELIA, Avenida Colombo, 5790, 87020-900, Maringa ´, PR, Brazil Abstract. In the context of diversity gradients, the metabolic theory of ecology (MTE) posits that the logarithm of species richness should decrease linearly with the inverse of temperature, resulting in a specific slope. However, the empirical validity of this model depends on whether the data do not violate certain assumptions. Here, we test the predictions of MTE evaluating all of its assumptions simultaneously. We used Neotropical freshwater fish and tested whether the logarithm of species richness varied negatively and linearly with temperature, resulting in the slope value specified by the MTE. As we observed that the assumption of the energetic equivalence of populations was not achieved, we also analyzed whether the energetic nonequivalence of populations could be responsible for the possible lack of fit to the MTE predictions. Our results showed that the relationship between richness and the inverse of temperature was linear, negative and significant and included the slope value predicted by the MTE. With respect to the assumptions, we observed that there was no spatial variation in the average energy flux of populations or in the body size and abundance of species. However, the energetic equivalence of populations was not achieved and the violation of this assumption did not affect the predictive power of the model. We conclude that the validity of the assumptions (spatial invariance in the average flux energy of populations and spatial invariance in the body size and abundance, especially) is required for the correct interpretation of richness patterns. Furthermore, we conclude that MTE is robust in its explanation of diversity gradients for freshwater fish, proving to be a valuable tool in describing ecological complexity from individuals to ecosystems. Key words: abundance; assumptions; average flux energy of populations; body size; energetic equivalence rule; metabolic hypothesis; richness pattern; spatial invariance; temperature. INTRODUCTION One of the oldest recognized patterns in ecology is the increase in species richness from the poles towards the equator (Ricklefs 2004, Jablonski et al. 2006, Mittelbach et al. 2007). Although this pattern is widely accepted, there is still no consensus on the processes underlying this trend. Identifying the mechanisms that govern this pattern has become an important challenge for ecolo- gists and has been the focus of intense debate (Willig et al. 2003, Currie et al. 2004, Rahbek 2005). Many hypotheses have been proposed to explain biological diversity gradients at broad spatial scales (Rohde 1992, Hawkins et al. 2003, Willig et al. 2003, Mittelbach et al. 2007), but many of them are neither robust nor testable (Rohde 1992, Hawkins et al. 2003). Currently, one of the most widely accepted hypotheses is related to climate effects, which appears to be the strongest predictor of species richness at broad scales in a correlative sense (Hawkins et al. 2003). However, the mechanisms that link variation in species richness to climate have not yet been elucidated (Currie et al. 2004, Algar et al. 2007). In the context of the climatic hypothesis, Allen et al. (2002) proposed the ‘‘metabolic hypothesis,’’ based on the first principles of thermodynamics and biochemical kinetics, within the context of the more general metabolic theory of ecology (MTE hereafter; see Brown et al. 2004). The MTE proposes to address how the relationship between organismal metabolism, body size, and temperature scales up to population, community, and ecosystem properties. Specifically, metabolic theory, when applied to understanding diversity gradients, applies only to ectothermic organisms and proposes that log-transformed species richness, S, should decrease linearly with the reciprocal of temperature according to the formula lnðSÞ } 1=kT, where k is the Boltzmann factor (8.62 3 10 5 eV/K) and T is temperature in Kelvin (see Allen et al. 2002). Note that the temperature is multiplied by k, which is a conversion factor between thermodynamic temperature and energy. Thus, in the Manuscript received 14 March 2013; revised 8 July 2013; accepted 30 July 2013. Corresponding Editor: D. E. Schindler. 5 E-mail: dayanibailly@gmail.com //xinet/production/e/ecol/live_jobs/ecol-95-02/ecol-95-02-22/layouts/ecol-95-02-22.3d  14 January 2014  5:37 pm  Allen Press, Inc.  Page 553 MS#13-0483 553