On the Ecology of Mountainous Forests in a Changing Climate: A ...

14 Chapter 2
Individual-based models (DeAngelis & Gross 1992) such as forest gap models have
obvious relationships to DEVS: For example, in forest gap models an individual tree
shows up (much like a customer in the classical DEVS example of a grocery), it grows
and enters complex relationships with its environment (does his/her shopping), and it
dies (leaves the shop). Thus, a conventional forest gap model (Botkin et al. 1972a,b,
Kienast 1987) formally may be considered as a set of coupled models with two components:
1) a discrete event model (DEVS) for tree population dynamics (sapling establishment,
tree growth, and tree mortality) as a function of the biotic and abiotic
environment
2) a discrete time model (SM) for the calculation of the abiotic environment based
on a monthly time step, aggregating most of the output to the annual time scale.
One of the advantages of DEVS compared with the sequential machine approach is that
the model can be ignored at those time steps when “nothing significant happens” (Zeigler
1976). However, no tree population dynamics submodel in a forest gap model was implemented
according to the DEVS formalism. The reason is that, unfortunately, in forest
gap models something “significant” happens to every object in every year, i.e. either tree
growth or mortality. This has led modellers to implement the population dynamics part of
forest gap models as discrete time models, too.
The other criteria proposed by Zeigler (1976) allow the following categorization of forest
gap models: they are stochastic (they contain random variables), and time invariant (time
does not enter explicitly as an argument of the rules of interaction in the models). Part of
their state variables are continuous (e.g. the diameter of a tree), and others are discrete
(e.g. the memory for “slow growth”). The population dynamics model is nonautonomous
(it requires abiotic input data), and the same goes for the discrete time model (it
requires monthly weather data). The latter property is concealed in most models because
they incorporate a stochastic weather generator (Botkin et al. 1972a,b).
For the following analysis, I adopt the view that the submodel of tree population dynamics
in forest gap models is a discrete-time model (t = 0, 1, 2, ...), usually with a time step
(∆t) of one year. This means that establishment, growth and death of trees must depend
only on the current state vector x(t) and input vector u(t) since they are time invariant
(Zeigler 1976, Eq. 2.1).