Figure 1. Hypothetical forms of a positive macroecological relationship between basal metabolic rate (BMR) and geographic range size.

(a) Expected relationship if low BMR (low performance capacity) is a constraint on achieving large range size (upper bound with positive slope) and high BMR is an advantage for achieving large range size, but not a constraint on persisting with small range size (constant lower bound). This pattern would be consistent with the Thermal Plasticity Hypothesis and Activity Levels/Dispersal Hypothesis. (b) Expected relationship if high BMR (high energy demand) is a constraint on persisting with large range size (lower bound with positive slope), but not a requirement for achieving large range size (constant upper bound). This pattern would be consistent with the Energy Constraint Hypothesis, and is the same pattern described previously for the relationship between body size and range size. (c) Expected relationship if constraints on range size operate at both ends of the BMR spectrum. At low BMR, species are constrained against achieving large ranges as in (a). At high BMR, species are constrained to have large ranges as in (b). See text for details.