Gap models, also known as forest succession models, simulate seedling establishment, including their transition to sapling and tree status, and individual-tree growth and mortality. They are very well adapted to simulate the development of mixed uneven-aged forest ecosystems. Several gap models were developed in the last few decades, and the majority of them are descendants of JABOWA, originally developed by Daniel B. Botkin and colleagues in the early 1970s. Among gap models that have received much attention, FORET (developed by Herman H. Shugart in the 1970s and 1980s) and ZELIG and SORTIE (developed by Dean L. Urban and colleagues and Steve W. Pacala and colleagues in the 1990s) are similar in concept to JABOWA. They can simulate the natural course of species replacement for several generations, as well as the succession that is initiated when canopy openings occur in forest ecosystems following the death of a dominant tree. Gap models are a compromise between growth and yield models and process-based models. Biotic and abiotic processes occurring in forest ecosystems are modeled, including competition and the effects of PAR conditions, site fertility, temperature, and water on tree growth and seedling establishment. However, the description of the processes and effects of site factors on ecosystem behavior is much simpler than in process-based models discussed above.
Empirical or semiempirical relationships are used to model the growth of individual trees. For JABOWA-type models, the annual growth rate of individual tree species within a forest ecosystem is modeled using the following basic equation form:
where the left-hand term represents the realized annual dbh growth rate, and —Dpot/—t is the maximum or potential dbh growth rate that the tree can achieve under optimal conditions. The relationship for potential growth rate has the following general form:
where D is dbh, H stem height, G a growth rate parameter, Dmax and Hmax the maximum dbh and height that a tree species can reach under optimal conditions, respectively, and f (D) an allometric relationship between dbh and height. The effects of limiting site factors are expressed by functions that describe the influence of abiotic and biotic factors, including PAR, temperature, site fertility, and moisture conditions. These functions constrain the potential growth rate and are based on scalar (0-1) multiplicative relationships. Tolerance or response classes are used to differentiate the response of each species to environmental factors. For instance, ZELIG recognizes five shade-tolerance classes (from tolerant to intolerant), three soil fertility classes (from responsive to stress tolerant), and three soil moisture classes (from drought tolerant to intolerant). The effect of temperature for each species is described by a dimensionless (0,1) response function that scales the growing degree-days computed for a given site relative to the minimum and maximum growing degree-days that exist within the range of distribution of a species. Seedling establishment is modeled stochastically by computing a probability of establishment conditioned by the potential number of seedlings that a site can produce and the prevailing understory PAR conditions, site fertility level, moisture conditions, and growing degree-days. Mortality is also modeled as a stochastic event and may result from natural or stress-related factors.
The advances in computer technology have made it possible to develop integrated modeling tools to simulate forest succession and disturbance at the landscape level. While the JABOWA-type models focus on the simulation of individual-tree development to predict ecosystem dynamics at the forest ecosystem level, forest landscape models simulate the forest dynamics of large regions that include many forest ecosystems. Forest landscape models explicitly consider that ecological processes occur at different scales or units: abiotic and biotic interactions occur among trees within a forest ecosystem as well as among forest ecosystems within a forest region or landscape. Thus, several processes may occur among adjacent or more or less remote forest ecosystems: flow of energy, water and nutrients, species migration or disturbances, such as fire, windthrow, diseases, or insect infestation. One of the objectives in the design of forest landscape models is to integrate the effects of the occurrence of events in individual forest ecosystems on adjacent forest ecosystems. This means that the integration of spatial and temporal complex interactions differing in scale, which may require the use of several variables, must rely on technology, such as geographic information systems for spatialization, in combination with mathematical analysis methods to describe the mechanistic details of the processes. A good example of this relatively recent generation of forest ecosystem models is LANDIS (Figure 2). This basic diagram illustrates the interactions between the information on species composition and ecological characteristics of the forest ecosystems within a landscape or forest region, the processes that are simulated over time, including species establishment, growth, and death, and the integration of different types of disturbances and management scenarios.
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