Modelling pasture mass through time in a managed grazing system subject to perturbations resulting from complexity in natural biological processes
1997
Pleasants, A.B. | Wake, G.C. | McCall, D.G. | Watt, S.D.
Variation is a characteristic of biological systems which may be due to both inaccuracies in measurement and the complexity of the interactions involved. The complexity of the interactions means that any abstraction of a biological system into a model often includes considerable uncertainty. Traditionally this uncertainty has been modelled by probabilistic methods. When dynamical systems are used to describe the evolution of biological processes it is necessary to consider the variation resulting from the impact of variables that are ignored in the formulation. Typically these variables are ignored because they act on a time scale faster than that of the abstraction. However, these fast variables can still affect the evolution of the system. This fast variable affect can be modelled using stochastic differential equations which incorporate the uncertainty due to complexity in the natural system. Solutions of stochastic differential equations may differ from the corresponding deterministic equations. Stochastic differential equations introduce a number of modelling issues not present in the deterministic case. These issues are reviewed using a model of pasture grazing system. It is shown that the mode of the probability density which is the solution of the stochastic differential equation is an important statistic in the dynamical case. The importance of the first passage time in modelling complex ecological systems subject to uncertainty is also discussed.
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