A review of forest gap models

Forest gap models, initially conceived in 1969 as a special case of individual-tree based models, have become widely popular among forest ecologists for addressing a large number of applied research questions, including the impacts of global change on long-term dynamics of forest structure, biomass, and composition. However, they have been strongly criticized for a number of weaknesses inherent in the original model structure. In this paper, I review the fundamental assumptions underlying forest gap models, the structure of the parent model JABOWA, and examine these criticisms in the context of the many alternative formulations that have been developed over the past 30 years. Four assumptions originally underlie gap models: (1) The forest is abstracted as a composite of many small patches of land, where each can have a different age and successional stage; (2) patches are horizontally homogeneous, i.e., tree position within a patch is not considered; (3) the leaves of each tree are located in an indefinitely thin layer (disk) at the top of the stem; and (4) successional processes are described on each patch separately, i.e., there are no interactions between patches. These simplifications made it possible to consider mixed-species, mixed-age forests, which had been difficult previously mainly because of computing limitations. The structure of JABOWA is analysed in terms of the functional relationships used for formulating the processes of tree establishment, growth, and mortality. It is concluded that JABOWA contains a number of unrealistic assumptions that have not been questioned strongly to date. At the same time, some aspects of JABOWA that were criticized strongly in the past years are internally consistent given the objectives of this specific model. A wide variety of formulations for growth processes, establishment, and mortality factors have been developed in gap models over the past 30 years, and modern gap models include more robust parameterizations of environmental influences on tree growth and population dynamics as compared to JABOWA. Approaches taken in more recent models that led to the relaxation of one or several of the four basic assumptions are discussed. It is found that the original assumptions often have been replaced by alternatives; however, no systematic analysis of the behavioral effects of these conceptual changes has been attempted to date. The feasibility of including more physiological detail (instead of using relatively simple parameterizations) in forest gap models is discussed, and it is concluded that we often lack the data base to implement such approaches for more than a few commercially important tree species. Hence, it is important to find a compromise between using simplistic parameterizations and expanding gap models with physiology-based functions and parameters that are difficult to estimate. While the modeling of tree growth has received a lot of attention over the past years, much less effort has been spent on improving the formulations of tree establishment and mortality, although these processes are likely to be just as sensitive to global change as tree growth itself. Finally, model validation issues are discussed, and it is found that there is no single data source that can reliably be used for evaluating the behavior of forest gap models; instead, I propose a combination of sensitivity analyses, qualitative examinations of process formulations, and quantitative tests of gap models or selected submodels against various kinds of empirical data to evaluate the usefulness of these models for assessing their utility for predicting the impacts of global change on long-term forest dynamics.