A Geometry of Regulatory Scaling

Over recent years, data have accumulated for an ecologically and taxonomically diverse range of animals showing that the mechanisms of feeding regulation prioritize a balanced gain of multiple nutrients. This emerging generality calls for an approach, equivalent to multidimensional morphometrics in the field of evolutionary morphology, in which regulatory systems are represented in more than one dimension. We use geometry to provide a quantitative metric of such regulatory phenotypes, which enables us to empirically address the evolutionarily interesting question of how the parameters of regulatory systems reflect performance outcomes. First, we develop a parameter-efficient geometry characterizing regulatory scaling strategies in two nutrient dimensions. We then take empirical data from several species (insects, birds, and mammals, including humans) in which individuals were limited to one of a small number of diets varying in the balance of macronutrients, and we explore which metrics and scaling techniques best unite within a common descriptive framework their patterns of regulation. We next show how a similar approach might be applied in the context of equilibrium models of operant conditioning and briefly discuss the potential for integrating such an approach into evolutionary and ecological studies.