Using differential equations in biological modelling – a case study for clover

K Louie; H Clark; PCD Newton

Abstract

Biological scenarios are given in which it is more appropriate to use differential equations, rather than the more commonly used difference equations, to model the processes occurring. The relative merits of small simple models and large-scale simulation models are compared. A simple differential equation model (dynamical system) for clover, based on meristem numbers, is outlined and analysed mathematically. The model possesses two steady states, and a threshold condition dictating which of these steady states is ultimately achieved is presented. The advantages in nondimensionalising the model are demonstrated, highlighted by reduction of parameter dependence and increased efficiency over conventional means of sensitivity analysis.

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