The 'covariation method' for estimating the parameters of the standard Dynamic Energy Budget model I: Pilosophy and Approach.

The Dynamic Energy Budget (DEB) theory for metabolic organisation captures the processes of development, growth, maintenance, reproduction and ageing for any kind of organism throughout its life-cycle. However, the application of DEB theory is challenging because the state variables and parameters are abstract quantities that are not directly observable. We here present a new approach of parameter estimation, the covariation method, that permits all parameters of the standard Dynamic Energy Budget (DEB) model to be estimated from standard empirical datasets. Parameter estimates are based on the simultaneous minimization of a weighted sum of squared deviations between a number of data sets and model predictions or the minimisation of the negative log likelihood function, both in a single-step procedure. The structure of DEB theory permits the unusual situation of using single data-points (such as the maximum reproduction rate), which we call "zero-variate" data, for estimating parameters. We also introduce the concept of "pseudo-data", exploiting the rules for the covariation of parameter values among species that are implied by the standard DEB model. This allows us to introduce the concept of a generalised animal, which has specified parameter values. We here outline the philosophy behind the approach and its technical implementation. In a companion paper, we assess the behaviour of the estimation procedure and present preliminary findings of emerging patterns in parameter values across diverse taxa. © 2011 Elsevier B.V.