Mass scaling of metabolic rates in carabid beetles (Carabidae) – the importance of phylogeny, regression models and gas exchange patterns

The origin of the allometric relationship between standard metabolic rate (MR) and body mass ( M ), often described as MR= aM b , remains puzzling, and interpretation of the mass-scaling exponent, b may depend on the methodological approach, shapes of residuals, coefficient of determination ( r 2 ) and sample size. We investigated the mass scaling of MRs within and between species of Carabidae beetles. We used ordinary least squares (OLS) regression, phylogenetically generalized least squares (PGLS) regression and standardized major axis (SMA) regression to explore the effects of different model-fitting methods and data clustering caused by phylogenetic clades (grade shift) and gas exchange patterns (discontinuous, cyclic and continuous). At the interspecific level, the relationship between MR and M was either negatively allometric ( b <1) or isometric ( b =1), depending on the fitting method. At the intraspecific level, the relationship either did not exist or was isometric or positively allometric ( b >1), and the fit was significantly improved after the analyzed dataset was split according to gas exchange patterns. The studied species originated from two distinct phylogenetic clades that had different intercepts but a common scaling exponent (OLS, 0.61) that was much shallower than the scaling exponent for the combined dataset for all species (OLS, 0.71). The best scaling exponent estimates were obtained by applying OLS while accounting for grade shifts or by applying PGLS. Overall, we show that allometry of MR in insects can depend heavily on the model fitting method, the structure of phylogenetic non-independence and ecological factors that elicit different modes of gas exchange.