Dynamic energy budget representations of stoichiometric constraints on population dynamics

Metabolism, and thus population dynamics, can be limited by energy, carbon, nitrogen, and/or other nutrients. This is due to homeostasis, the relatively constant composition of biomass. Yet growth-rate-dependent changes in the composition of biomass do exist. The dynamic energy budget (DEB) theory provides the framework to deal with these simultaneous limitations and stoichiometric restrictions. We illustrate the application with three examples. First, we discuss simple single-species growth of a chemolithoautotroph to illustrate the interactions between nutrients and substrates in growth. We show how the macrochemical reaction equation with variable yield coefficients can be decomposed in a number of subprocesses with constant yield coefficients. We then discuss a simple predator-prey system, where nutrients are accumulated in the prey, which no longer have a constant composition of biomass. The implication is a varying conversion efficiency from prey to predator, with consequences for qualitative aspects of population dynamics. We illustrate the principles with a grazer (a heterotrophic consumer) feeding on algae (autotrophic producers). The algae frequently have an excess of energy in the form of carbohydrates, which are excreted and serve as food supplements for the heterotroph. This exchange of carbohydrates against nutrients is basic to a symbiosis, our third example of application of DEB theory for solving stoichiometric problems in species interactions. The algae are no longer grazed as long as the grazer is able to extract nutrients from other sources. Depending on parameter values of the system, the coexistence can be very stable and further integrate into a single entity with mixotrophic properties. This process is basic to the evolution of the eukaryotic cell and to the organizational structure of metabolism. Mixotrophs can specialize under particular environmental conditions into autotrophs or heterotrophs, which again can associate in symbiotic relationships. The chemical composition of membranes testifies to the frequent occurrence of this process, which can now also be understood quantitatively.