Transition and gap models of forest dynamics Page: 1,041
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TRANSITION AND GAP FOREST MODELS
We will concentrate on the possibilities of including
some of the vegetation history by using a semi-Markov
model, which makes the transitions dependent on the
time spent in a given state (Howard 1971). This type
of formulation could, for example, account for the de-
pendency on the age structure suggested as necessary
by Hulst (1980) and Hobbs and Legg (1983). The semi-
Markov model has been relatively less used in ecolog-
ical modeling research; Marcus et al. (1979) proposed
its use for compartment models, Acevedo (1981a) used
its correspondence to electrical networks for modeling
forest successional dynamics, Moore (1990) used its
discrete formulation to relate disturbance and manage-
ment strategies of vegetation dynamics, and Matis et
al. (1992) applied it to shrimp migration.
Gap models have been modified and adapted to site-
specific applications but have lost generic capabilities
(Urban et al. 1991, Urban and Shugart 1992). While
this trend has helped us to understand the dynamics of
several forests, it is still necessary to infer general be-
havior and formulate general hypotheses. Deriving
transition models from gap models can help to extract
basic features and closed-form solutions for gap mod-
els.
Modeling species-rich forests and landscape-scale
forest patterns can be simplified by aggregating species
according to convenient criteria. For example, species
can be classified according to their light-dependence
or gap-requirement characteristics, such as "pioneer"
or "gap-requiring" species and "climax" or "shade-
tolerant" species (Acevedo 1980, 1981a, b, Swaine and
Whitmore 1988, Whitmore 1989). These classes have
been the subject of much research and discussion (Bro-
kaw 1982, 1985, 1987, Hubbell and Foster 1986, Bro-
kaw and Scheiner 1989), and permit a dynamic inter-
pretation of the forest as an ever-changing mosaic of
patches cycling through gap, building, and mature
phases (Watt 1947, Oldeman 1978, Whitmore 1989) or
similar phases (Whittaker and Levin 1976, Bormann
and Likens 1979). Even though this classification may
be simplistic (Barton 1984, Hubbell and Foster 1986,
Denslow 1987, Brokaw and Scheiner 1989, Canham
1989, Lieberman et al. 1989, Smith et al. 1992), it
allows for a practical modeling methodology able to
answer questions related to the coarse-scale dynamics
of the forest mosaic.
Other examples include: definition of cover-states
according to successional status for simulating large
regions (Shugart et al. 1973); definition of types ac-
cording to shade and drought tolerance (Smith and Hus-
ton 1989); definition of functional groups based on
physiological, reproductive, and life history character-
istics (Moore and Noble 1990); and identification of
several tree species roles based on patterns observed
in FORET-type simulations (Shugart et al. 1981, Shu-
gart 1984, 1987). This last approach combines the gap-
creating properties of trees (derived from the mortality
process) with the gap-requiring properties (derivedfrom the regeneration process), to obtain four main
groups of tree species that play functional roles in the
dynamics of the forest. This scheme associates size
with gap creation and therefore is similar to the clas-
sification proposed by Swaine and Whitmore (1988)
for tropical forests. Shugart and Urban (1989) have
used simulated forests with single species representing
the four roles to infer typical dynamical patterns. Tran-
sition models based on these four roles and their cor-
respondence to gap simulators have been explored in
detail by Acevedo et al. (1995a).
In the following pages, transition models using semi-
markovian transitions among cover types are developed
and parameterized. First, the conceptual basis of the
approach is presented, emphasizing the semi-Markov
transition model. Next, an example of state definition
incorporating both species functional roles and canopy
layers is developed. Third, the method to parameterize
the transition model from the gap model is described
using four functional roles as an example. Next, the
basis for simulating landscape dynamics using the tran-
sition model is described. Lastly, the ideas presented
in the previous sections are applied to the H. J. Andrews
forest in the Western Cascades of Central Oregon;
states are defined by species and vertical position in
the canopy, a transition model is parameterized from
a gap model, and the transition model is used to explore
landscape dynamics.
MARKOV AND SEMI-MARKOV MODELS
A Markov chain describing the transitions of a forest
plot among states is used to establish a semi-Markov
model that also considers the different longevities and
growth rates of the tree species. A gap-size forest plot
is assumed to make transitions among several states
defined on the basis of dominance of one of the several
cover types. These types can be species, functional
roles, structural roles, or a combination of both. Ex-
plicit consideration of the unoccupied gaps can be done
very simply by defining them as another type. At time
t, the total coverage in a collection of n gap-size plots
will be distributed among the N types according to
proportions X,(t), which should be approximately equal
to the probabilities pi(t) that a plot is covered by type
i at time t.
The Markov chain is given by a matrix P of transition
probabilities. An entry p, of this matrix is associated
with the transition from state j to state i. These prob-
abilities are defined from known relationships among
the cover types or from the output of gap simulators.
Examples of these methods, using four functional roles
to define the states, are described in Acevedo et al.
(1995a).
The steady-state derived from a Markov chain to
infer the long-term forest composition fails to account
for the time spent in a given state before making a
transition, which is important given the different lon-
gevities and growth rates of the tree species. Therefore,This content downloaded from 129.120.92.148 on Fri, 6 Jun 2014 13:14:57 PM
All use subject to JSTOR Terms and ConditionsNovember 1995
1041
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Acevedo, Miguel F.; Urban, D. L. & Ablan, Magdiel. Transition and gap models of forest dynamics, article, November 1, 1995; [Washington, D.C.]. (https://digital.library.unt.edu/ark:/67531/metadc303220/m1/2/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.