A Model for the Dynamics of a Plant Population Containing Individuals Classified by Age and Size

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Abstract
In many populations of plants, reproduction and mortality depend both on age and size. This paper develops a model to describe the dynamics of such a population, classifying individual both by age and size. It is based on a model originally proposed by Goodman (1969) as an extension to the Leslie matrix. The model allows a projection of the transient dynamics of a population from an arbitrary set of starting numbers. It also allows some asymptotic properties of the population to be determined, namely, the finite rate of increase, the stable age/size distribution, and the reproductive values. In the special case of reproduction and survival being independent of size, the model reduces to a Leslie matrix. In the special case of reproduction and mortality being independent of age, it yields results which approximate to a form of the stage projection matrix (Lefkovitch matrix). The main results of the model are illustrated with an example based on a plant with a monocarpic life history.