The comparative topology of energy allocation in budget models

The standard Dynamic Energy Budget (DEB) model assumes that assimilates of an isomorphic individual are first added to reserve, a fraction κ of mobilised reserve is allocated to soma (somatic maintenance plus growth of structure), and the rest to maturity maintenance and maturation or reproduction. Food, reserve and structure have constant chemical composition. We here discuss all possible topological alternatives to the standard DEB model, and compare them on the basis of seven properties: the ability to capture weak homeostasis and general empirical growth and reproduction patterns. We selected a reserve dynamics such that reserve mobilisation rate is independent of assimilation, somatic maintenance is proportional to the amount of structure, maturity maintenance to the level of maturity, and assimilation to the surface area. The alternatives only differ from the standard DEB model in topology, but we drop the κ-rule and allow κ to vary with the amount of structure. For this purpose we introduce the concept ‘generalised von Bertalanffy growth rate’ and study how it behaves as a function of the ultimate structural length, both intra- and inter-specifically. The 21 derived topological alternatives of the standard DEB are classified into five classes of models, depending on the first allocation event for the assimilation flux. The possibilities of the first allocation event for the assimilation flux are: splitting (κ-models), storing (A-models), both maintenance fluxes simultaneously (P-models), somatic maintenance (S-models) or maturity maintenance (J-models). We conclude that the standard DEB model with constant κ is the only one that passes all our tests successfully. Only assimilation (A) models can naturally accommodate embryo development. The κ-models, which after splitting the fraction 1-κ of assimilates is allocated to maturity maintenance and maturity/reproduction while the fraction κ of assimilates is first stored in reserve or allocated to somatic maintenance, pass most tests, but have maturation and reproduction directly from food. So, embryos have to do this differently and reproduction is prohibited during starvation in these models.