The bijection from data to parameter space with the standard DEB model quantifies the supply–demand spectrum

The standard Dynamic Energy Budget (DEB) model assumes that food is converted to reserve and a fraction κ of mobilised reserve of an individual is allocated to somatic maintenance plus growth, while the rest is allocated to maturity maintenance plus maturation (in embryos and juveniles) or reproduction (in adults).

The add_my_pet collection of over 300 animal species from most larger phyla, and all chordate classes, shows that this model fits energy data very well. Nine parameters determine nine data points at abundant food: dry/wet weight ratio, age at birth, puberty, death, weight at birth, metamorphosis, puberty, ultimate weight and ultimate reproduction rate.

We demonstrate that, given a few other parameters, these nine data points also determine the nine parameters uniquely that are independent of food availability: maturity at birth, metamorphosis and puberty, specific assimilation, somatic maintenance and costs for structure, allocation fraction of mobilised reserve to soma, energy conductance, and ageing acceleration.

We provide an efficient algorithm for mapping between data and parameter space in both directions and found expressions for the boundaries of the parameter and data spaces. One of them quantifies the position of species in the supply–demand spectrum, which reflects the internalisation of energetic control.

We link eco-physiological properties of species to their position in this spectrum and discuss it in the context of homeostasis. Invertebrates and ray-finned fish turn out to be close to the supply end of the spectrum, while other vertebrates, including cartilaginous fish, have stronger demand tendencies.

We explain why birds and mammals up-regulate metabolism during reproduction. We study some properties of the bijection using elasticity coefficients. The properties have applications in parameter estimation and in the analysis of evolutionary constraints on parameter values; the relationship between DEB parameters and data has similarities to that between genotype and phenotype