Gap Models of Forests

Gap models describe the change of species composition on a gap in the forest that was created by the death of a canopy tree. Typical gap size in early gap models is 0.01 ha. The entire forest is assumed to be an ensemble of gaps with temporally and spatially independent dynamics. The purpose of gap models is to understand long-term species composition and succession and how they depend on environmental variables. Gap models were thus developed by ecologists, not forest managers.

The representation of the individuals, the trees, is extremely simple: they have only one state variable, trunk diameter at breast height (dbh), which is a standard measure ofsize in forestry. Tree height is calculated from dbh using an empirical relationship. The structure of gap models is extremely simple: each tree grows according to a sigmoidal potential growth curve. Potential annual growth is then reduced by multipliers which reflect the influence of competition and environmental factors. Competition is only considered vertically and calculated from the vertical distribution of light that is determined by the trees existing in the gap.

Thus, at each time step of the model, which usually represents a year, first the vertical light profile is calculated, and then the growth increment. Different species are characterized by different parameters of the growth equation and the relationship between dbh and height. Mortality depends on the growth rate: trees that do not grow for a certain time span, that is, are suppressed by larger trees, will die sooner or later.

Starting from the pioneering model JABOWA, at least 19 gap models have been developed for a wide range of forest types and questions. More recent gap models try to be more realistic in some way, for example, by including spatial interactions between neighboring gaps. The great success of gap models has three main reasons: they are conceptually very simple, their growth equations are relatively easy to parametrize, and they make important testable predictions regarding species composition and dynamics of real forests. Gap models have, however, also many limitations, and other types of individualbased forest models exist, which are based on physiological processes or empirical relationships that are drawn from long-term observations of thousands of trees.

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