The “minimal boundary curve for endothermy” as a predictor of heterothermy in mammals and birds: a review

According to the concept of the “minimal boundary curve for endothermy”, mammals and birds with a basal metabolic rate (BMR) that falls below the curve are obligate heterotherms and must enter torpor. We examined the reliability of the boundary curve (on a double log plot transformed to a line) for predicting torpor as a function of body mass and BMR for birds and several groups of mammals. The boundary line correctly predicted heterothermy in 87.5% of marsupials (n = 64), 94% of bats (n = 85) and 82.3% of rodents (n = 157). Our analysis shows that the boundary line is not a reliable predictor for use of torpor. A discriminate analysis using body mass and BMR had a similar predictive power as the boundary line. However, there are sufficient exceptions to both methods of analysis to suggest that the relationship between body mass, BMR and heterothermy is not a causal one. Some homeothermic birds (e.g. silvereyes) and rodents (e.g. hopping mice) fall below the boundary line, and there are many examples of heterothermic species that fall above the boundary line. For marsupials and bats, but not for rodents, there was a highly significant phylogenetic pattern for heterothermy, suggesting that taxonomic affiliation is the biggest determinant of heterothermy for these mammalian groups. For rodents, heterothermic species had lower BMRs than homeothermic species. Low BMR and use of torpor both contribute to reducing energy expenditure and both physiological traits appear to be a response to the same selective pressure of fluctuating food supply, increasing fitness in endothermic species that are constrained by limited energy availability. Both the minimal boundary line and discriminate analysis were of little value for predicting the use of daily torpor or hibernation in heterotherms, presumably as both daily torpor and hibernation are precisely controlled processes, not an inability to thermoregulate

Mass‐independent maximal metabolic rate predicts geographic range size of placental mammals

Understanding the mechanisms driving geographic range sizes of species is a central issue in ecology, but remarkably few rules link physiology with the distributions of species. Maximal metabolic rate (MMR) during exercise is an important measure of physiological performance. It sets an upper limit to sustained activity and locomotor capacity, so MMR may influence ability to migrate, disperse and maintain population connectivity. Using both conventional ordinary least squares (OLS) analyses and phylogenetically generalized least squares (PGLS), we tested whether MMR helps explain geographic range size in 51 species of placental mammals. Log body mass alone (OLS r =.074, p =.053; PGLS r =.016, p =.373) and log MMR alone (OLS r =.140, p =.007; PGLS r =.061, p =.081) were weak predictors of log range size. However, multiple regression of log body mass and log MMR accounted for over half of the variation in log range size (OLS R =.527, p <.001). The relationship was also strong after correcting for the phylogenetic non-independence (PGLS R =.417, p <.001). In analyses restricted to rodents (34 species), neither log body mass alone (OLS r =.004, p =.720; PGLS r =.003, p =.77) nor log MMR alone was useful in predicting log geographic range size (OLS r =.008, p =.626; PGLS r =.046, p =.225), but multiple regressions of log body mass and log MMR accounted for roughly a third to a half of the variation in log range size (OLS R =.443, p <.001, PGLS R =.381, p <.001). Mass-independent MMR is a strong predictor of mass-independent geographic range size in placental mammals. The ability of body mass and MMR to explain nearly 50% of the variation in the geographic ranges of mammals is surprising and powerful, particularly when neither variable alone is strongly predictive. A better understanding of MMR during exercise may be important to understanding the limits of geographic ranges of mammals, and perhaps other animal groups.M.B.A. is funded through the NICHE project (CGL2011‐26852) of the Spanish Ministry of Economy and Competitiveness and the Spanish Research Council (CSIC), the Rui Nabeiro Biodiversity Chair and the Danish NSF. M.B.A. acknowledges support from FCT project PTDC/AAG‐MAA/3764/2014.Peer Reviewe