Modelling allocation with transport/conversion processes.

A shoot:root carbon:nitrogen allocation model, based on the two processes of transport and chemical conversion, is described and explored. The view is proposed that all allocation models, whether built for the purposes of theoretical investigation or practical application, should start with this irreducible framework. In the present implementation, the processes operate according to: for substrate sources, dependence on shoot and root sizes, with possible product inhibition; for transport, movement down a substrate concentration gradient; for substrate sinks or utilization, linear bisubstrate kinetics. The dynamic and equilibrium properties of the model are explored. Failure of this approach to allocation will indicate to the modeller that additional mechanisms to control the processes are needed, and the mode of failure will indicate the type of mechanisms required. Additional mechanisms are discussed which may involve hormones or teleonomic (goal-seeking) controls, and may be added to the irreducible framework. However, these additions should not replace the irreducible framework of transport and chemical conversion, because they do not in reality. Modifications to the basic model to reflect some possibilities such as ontogenesis with the transition from exponential growth towards a steady state or with the scaling of within-plant transport resistances, the influence of hormones, and active transport, are described.