260
of differences in regeneration, growth, and mortality among species and individuals of different sizes,
the models are useful in simulating mixed species
and mixed age vegetation dynamics. Shugart
(1984) describes the early formulation and application of these models. Urban and Shugart (1992)
and Shugart and Smith (1996) provide comprehensive recent reviews for forest models.
The more than two dozen model versions vary
somewhat in emphasis and the manner in which
processes are simulated, but all share certain assumptions and model structures. Individuals are
tracked by species, size, and vigor (Urban and
Shugart, 1992). The size of the plot is scaled to the
zone of influence of a mature individual of a
canopy-dominant species. The death of such an individual creates a gap in resource space that can be
filled by other individuals (gap-phase regeneration)
(Watt, 1947); hence the models are often called gap
models.
For most gap models, horizontal placement of
individuals within a plot is not specified (Dale and
Shugart, 1985). Competition for light occurs
through shading of shorter individuals by taller individuals. In modeling the growth of an individual,
a maximum potential response is constrained by environmental conditions such as available light,
growing-degree-days temperature, soil moisture,
and soil fertility (Shugart and Smith, 1996). The
diversity of formulations of tree growth responses
in the models is described in Bugmann et ai. (1996).
Plant establishment is a stochastic function based
on species-specific responses to the plot environment, such as light, temperature, and moisture conditions. Mortality occurs as a result of plant age,
loss of vigor, and, in some models, disturbances
such as fire, insect attack, windthrow, flooding,
hurricanes, and timber harvesting for forests (Urban and Shugart, 1992). Disturbances modeled for
a grassland include ant and small mammal dirt
mounds and cattle fecal pats (Coffin and Lauenroth, 1990).
The models have incorporated a variety of extensions, including nutrient cycling (e.g., Aber and
Melillo, 1982; Pastor and Post, 1986; Bonan,
1990a, 1990b; Botkin, 1992) and detailed representation of soil moisture and soil thermal conditions (Bonan, 1989a, 1989b). Plots in the forest gap
model ZELIG (Urban, 1990) can be linked in a grid
or transect to represent spatial interactions among
plots. ZELIG has been used to investigate spatial
phenomena such as shading effects (Urban et aI.,
1991), seed dispersal (Urban and Smith, 1989), and
spatial pattern in comparison with remotely sensed
data (Weishampel et aI., 1992).
Ecosystem Structure and Function Modeling
Most gap models use simple functions that are relatively easy to parameterize (Urban and Shugart,
1992). For trees, species parameter values can often
be obtained from the silviculture and forestry literature. The models are relatively computationally efficient (Keane et al., 1996b). They have been employed
successfully in a wide variety of systems, from tropical to boreal forests and from floodplains to alpine
vegetation. Locations that have been modeled include
many areas in North America, as well as in Europe,
South Africa, Australia, and New Zealand.
The simplified nature of the functions in a gap
model, an advantage for rapid model parameterization and implementation, may be a limitation for
some applications. In particular, the growth functions are descriptive rather than mechanistic; as a
consequence, the models may be inadequate for
predicting some kinds of responses to global
change, such as how tree growth might differ under changed climate and increased CO2 (Friend et
aI., 1993). In addition, processes occurring on very
short time scales are not considered. Friend et ai.
(1993) developed the model HYBRID by modifying a gap model (ZELIG) to include physiological
growth processes for individual trees using a daily
time step. However, the incorporation of functionally realistic processes for carbon fixation and partitioning required many species-specific physiological parameters and greatly increased model
processing time. A similar approach was taken in
the model FORCLIM (Bugmann and Fischlin,
1996) to explicitly model the environmental constraint on photosynthesis and respiration.
The lack of plot-to-plot spatial interactions, a
limitation of many gap models, has been overcome
in ZELIG, which provides a framework for modeling spatial interactions for forests (Urban, 1990).
The size of a modeled plot (0.01 to 0.2 ha for
forests) may be a limitation for some applications,
because it is very small compared to many areas of
interest in ecological assessments. Continuous coverage of large areas using gap models could require
simulating many thousands of plots. This problem
has been addressed by running models in representative subareas and generalizing results to larger
areas (Shugart, 1998).
Gap models are useful for considering variability within and between forest and grassland systems, including examination of age structure,
species diversity, and disturbance effects (Dale and
Shugart, 1985; Coffin and Lauenroth, 1990). Output from gap models has also been coupled to other
models to predict outcomes of management activities. For example, ZELIG was used to model the
effects of alternative silvicultural regimes on for-
of differences in regeneration, growth, and mortality among species and individuals of different sizes,
the models are useful in simulating mixed species
and mixed age vegetation dynamics. Shugart
(1984) describes the early formulation and application of these models. Urban and Shugart (1992)
and Shugart and Smith (1996) provide comprehensive recent reviews for forest models.
The more than two dozen model versions vary
somewhat in emphasis and the manner in which
processes are simulated, but all share certain assumptions and model structures. Individuals are
tracked by species, size, and vigor (Urban and
Shugart, 1992). The size of the plot is scaled to the
zone of influence of a mature individual of a
canopy-dominant species. The death of such an individual creates a gap in resource space that can be
filled by other individuals (gap-phase regeneration)
(Watt, 1947); hence the models are often called gap
models.
For most gap models, horizontal placement of
individuals within a plot is not specified (Dale and
Shugart, 1985). Competition for light occurs
through shading of shorter individuals by taller individuals. In modeling the growth of an individual,
a maximum potential response is constrained by environmental conditions such as available light,
growing-degree-days temperature, soil moisture,
and soil fertility (Shugart and Smith, 1996). The
diversity of formulations of tree growth responses
in the models is described in Bugmann et ai. (1996).
Plant establishment is a stochastic function based
on species-specific responses to the plot environment, such as light, temperature, and moisture conditions. Mortality occurs as a result of plant age,
loss of vigor, and, in some models, disturbances
such as fire, insect attack, windthrow, flooding,
hurricanes, and timber harvesting for forests (Urban and Shugart, 1992). Disturbances modeled for
a grassland include ant and small mammal dirt
mounds and cattle fecal pats (Coffin and Lauenroth, 1990).
The models have incorporated a variety of extensions, including nutrient cycling (e.g., Aber and
Melillo, 1982; Pastor and Post, 1986; Bonan,
1990a, 1990b; Botkin, 1992) and detailed representation of soil moisture and soil thermal conditions (Bonan, 1989a, 1989b). Plots in the forest gap
model ZELIG (Urban, 1990) can be linked in a grid
or transect to represent spatial interactions among
plots. ZELIG has been used to investigate spatial
phenomena such as shading effects (Urban et aI.,
1991), seed dispersal (Urban and Smith, 1989), and
spatial pattern in comparison with remotely sensed
data (Weishampel et aI., 1992).
Ecosystem Structure and Function Modeling
Most gap models use simple functions that are relatively easy to parameterize (Urban and Shugart,
1992). For trees, species parameter values can often
be obtained from the silviculture and forestry literature. The models are relatively computationally efficient (Keane et al., 1996b). They have been employed
successfully in a wide variety of systems, from tropical to boreal forests and from floodplains to alpine
vegetation. Locations that have been modeled include
many areas in North America, as well as in Europe,
South Africa, Australia, and New Zealand.
The simplified nature of the functions in a gap
model, an advantage for rapid model parameterization and implementation, may be a limitation for
some applications. In particular, the growth functions are descriptive rather than mechanistic; as a
consequence, the models may be inadequate for
predicting some kinds of responses to global
change, such as how tree growth might differ under changed climate and increased CO2 (Friend et
aI., 1993). In addition, processes occurring on very
short time scales are not considered. Friend et ai.
(1993) developed the model HYBRID by modifying a gap model (ZELIG) to include physiological
growth processes for individual trees using a daily
time step. However, the incorporation of functionally realistic processes for carbon fixation and partitioning required many species-specific physiological parameters and greatly increased model
processing time. A similar approach was taken in
the model FORCLIM (Bugmann and Fischlin,
1996) to explicitly model the environmental constraint on photosynthesis and respiration.
The lack of plot-to-plot spatial interactions, a
limitation of many gap models, has been overcome
in ZELIG, which provides a framework for modeling spatial interactions for forests (Urban, 1990).
The size of a modeled plot (0.01 to 0.2 ha for
forests) may be a limitation for some applications,
because it is very small compared to many areas of
interest in ecological assessments. Continuous coverage of large areas using gap models could require
simulating many thousands of plots. This problem
has been addressed by running models in representative subareas and generalizing results to larger
areas (Shugart, 1998).
Gap models are useful for considering variability within and between forest and grassland systems, including examination of age structure,
species diversity, and disturbance effects (Dale and
Shugart, 1985; Coffin and Lauenroth, 1990). Output from gap models has also been coupled to other
models to predict outcomes of management activities. For example, ZELIG was used to model the
effects of alternative silvicultural regimes on for-