The state-space point of view can clarify the various approaches to growth modelling. In this view the behaviour of a time-varying system is described by a state that characterises the system at any point in time, and a transition function that specifies how the state changes over time.
A multidimensional state is required to adequately model forest stand growth. Growth models are commonly classified into three types that differ in the level of detail in the state description. In stand-level models the state consists of a small number of summary variables, for example basal area, stocking, and top height. Individual-tree distance-dependent models include in the state the size and location of every tree in a piece of land. Individual-tree distance-independent models use a state description based on a size (usually diameter) distribution.
The most appropriate type of model to use depends on the circumstances. The homogeneity of the stands and the kind of treatments to be analysed determine how detailed a state description needs to be. In addition, the state description also determines the quantity and quality of inventory data required for growth projections.
The development of growth models presents special statistical problems. An approach involving stochastic differential equations and maximum likelihood estimation has been developed and used successfully in New Zealand.