Articles
STOCHASTIC MODELS FOR FRUIT GROWTH
We describe here a method by which information on the mean and variance of fruit growth rates can be used to model the changing fruit size distribution through the growing season.
Models for changes in mean fruit size can be written in the form of ordinary differential equations.
However, we are often interested in the entire size distribution of the fruit; in this case we cannot use ordinary differential equations because they do not take into account the fact that the growth rate can be significantly variable in a cohort of fruit all of the same size at a given time.
In the approach described here, we add some ‘noise’ and describe fruit growth by a stochastic differential equation, which requires us to measure not only the mean growth rate of fruit in any size class, but also the variance of the growth rate.
The solution of a stochastic differential equation is a probability distribution at any time, rather than just a single value.
In this paper, some special cases are illustrated where analytical solution using the Îto calculus is possible.
For more general cases, a numerical approach using a partial differential equation formulation, known as the Fokker-Planck Equation, is described.
This approach allows the fruit size distribution at any time to be calculated from the initial size distribution, and can take into account modification of the size distribution by fruit drop.