Maximum entropy models reveal spatial variation of metabolic scaling in stream fish communities

Abstract

Metabolic scaling provides valuable information about the physiological and ecological functions of organisms, although few studies have quantified the metabolic scaling exponent (b) of communities under natural conditions. Maximum entropy theory of ecology (METE) is a constraint-based unified theory with the potential to empirically assess the spatial variation of the metabolic scaling. Our main goal is to develop a novel method of estimating b within a community by integrating metabolic scaling and METE. We also aim to study the relationships between the estimated b and environmental variables across communities. We developed a new METE framework to estimate b in 118 stream fish communities in the north-eastern Iberian Peninsula. We first extended the original maximum entropy model by parameterizing b in the model prediction of the community-level individual size distributions and compared our results with empirical and theoretical predictions. We then tested the effects of abiotic conditions, species composition and human disturbance on the spatial variation of community-level b. We found that community-level b of the best maximum entropy models showed great spatial variability, ranging from 0.25 to 2.38. The mean exponent (b = 0.93) resembled the community-aggregated mean values from three previous metabolic scaling meta-analyses, all of which were greater than the theoretical predictions of 0.67 and 0.75. Furthermore, the generalized additive model showed that b reached maximum at the intermediate mean annual precipitation level and declined significantly as human disturbance intensified. The parameterized METE is proposed here as a novel framework for estimating the metabolic pace of life of stream fish communities. The large spatial variation of b may reflect the combined effects of environmental constraints and species interactions, which likely have important feedback on the structure and function of natural communities. Our newly developed framework can also be applied to study the impact of global environmental pressures on metabolic scaling and energy use in other ecosystems.

Keywords: Shannon entropy; body size; constraint-based model; information theory; maximum likelihood method; metabolism; model parameterization.