Supplementary material from "Integrating morphology and kinematics in the scaling of hummingbird hovering metabolic rate and efficiency"

Wing kinematics and morphology are influential upon the aerodynamics of flight. However, there is a lack of studies linking these variables to metabolic costs, particularly in the context of morphological adaptation to body size. Furthermore, the conversion efficiency from chemical energy into movement by the muscles (mechanochemical efficiency) scales with mass in terrestrial quadrupeds, but this scaling relationship has not been demonstrated within flying vertebrates. Positive scaling of efficiency with body size may reduce the metabolic costs of flight for relatively larger species. Here, we assembled a dataset of morphological, kinematic, and metabolic data on hovering hummingbirds to explore the influence of wing morphology, efficiency, and mass on hovering metabolic rate (HMR). We hypothesize that HMR would decline with increasing wing size, after accounting for mass. Furthermore, we hypothesize that efficiency will increase with mass, similarly to other forms of locomotion. We do not find a relationship between relative wing size and HMR, and instead find that the cost of each wingbeat increases hyperallometrically while wingbeat frequency declines with increasing mass. This suggests that increasing wing size is metabolically favourable over cycle frequency with increasing mass. Further benefits are offered to larger hummingbirds due to the positive scaling of efficiency.