Discrete-event simulation of forest landscape response to fire disturbances

Ecological Modelling, 65 (1993) 177-198

177

Elsevier Science Publishers B.V., Amsterdam

Discrete-event simulation of forest landscape response to fire disturbances Maria J. Perestrello de Vasconcelos ~ and Bernard P. Zeigler b a Aduanced Resource Technology Program, SRNR, Uniuersity of Arizona, Tucson, A Z 85721, USA Department of Electrical and Computer Engineering, Uniuersity of Arizona, Tucson, A Z 85721, USA (Received 21 October 1991; accepted 21 May 1992)

ABSTRACT Vasconcelos, M.J.P. de and Zeigler, B.P., 1993. Discrete-event simulation of forest landscape response to fire disturbances. Ecol. Modelling, 65: 177-198. The objective of this work is to illustrate the potential of discrete-event simulation methodologies and object-oriented hierarchical models to simulate landscape dynamics. We formalized the Noble and Slatyer vegetation replacement scheme in a modular, object-oriented formalism to simulate vegetation dynamics. Based on this module, we suggest a framework for simulating vegetation dynamics in spatially complex landscape systems composed of interacting patches. As illustrated with the simulations performed for a two-patch landscape, patch components are organized in a hierarchical structure, with information flow in the form of messages passing among the hierarchically arranged components. System behavior can be analyzed from any level of organization. Finally, we briefly discuss the implementation of this framework in a Geographic Information System.

INTRODUCTION

Vegetation dynamics involves the changes in composition and spatial arrangement of vegetation with the passage of time. Natural vegetation replacement through time is defined as vegetation succession, and several approaches have been used to describe and model it (see Shugart, 1984, for a review). In the last two decades, a school of succession theory that Correspondence to: M.J.P. de Vasconcelos, Instituto Superior de Agronomia, DEF, Tapada da Ajuda, 1399 Lisboa codex, Portugal. Research work supported by JNICT Portugal. 0304-3800/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

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emphasizes individual attributes has made important contributions for modelling vegetation dynamics (Horn, 1975; Grime, 1979; Noble and Slatyer, 1981; Shugart, 1984). More recently, the importance of individual oriented models has been enhanced by the need to integrate information and processes at different scales for global change studies (IGBP, 1990). Noble and Slatyer (1981) proposed a model of vegetation replacement for a wet sclerophyllous rainforest subject to recurrent fire that is based on the attributes of key component species. Their approach has been successfully used in a one-patch context in several different studies (Noble and Slatyer, 1977; Kessel, 1979; Noble and Slatyer, 1981; Shugart, 1984). A landscape where fire is the primary disturbance factor can be thought of as a set of patches, corresponding to different areas burned at different times. Vegetation dynamics within each of these patches can be described by Noble and Slatyers's replacement sequences. Consequently, we can design a set of several models running in parallel, one for each patch. However, this is insufficient because species re-establishment in a patch after fire is influenced by its neighbors' ability to provide propagules. To be able to derive whole landscape dynamics one has to include intercomponent coupling so that the information (in this case propagules) can flow between patches. In this project the vegetation replacement scheme of Noble and Slatyer (1981) was formalized in a modular, object-oriented format (Zeigler, 1990). To illustrate how landscape dynamics can be simulated based on modular models of components and a knowledge-based hierarchical structure, we simulated the dynamics of a two-patch landscape in the DEVS-Scheme environment. DEVS-Scheme is a knowledge-based, object-oriented simulation environment for modelling and design that facilitates construction of families of models in a form easily reusable by retrieval from a model-base (Zeigler, 1990, p. xiv). It is engineered in a set of layers so that all of the underlying Lisp-based and object-oriented programming language features are available to the user. BACKGROUND

Discrete-et~ent simulation and object-oriented hierarchical, modular models The Discrete Event System Specification (DEVS) formalism introduced by Zeigler (1976) provides a means of specifying a mathematical object called a system. The system has a time base, inputs, states and outputs, and functions for determining next states and outputs, given current states and inputs (Zeigler 1984, pp. 62-79). DEVS focuses on the changes of variable

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values and generates time segments that are piecewise constant. It defines how to generate new values for variables and the times at which new values should take effect. In discrete-event simulation the value of the time increment is not stipulated in advance (as it would be in a discrete time specification), but determined individually for each time step, based on the component actions of the model. Discrete-event simulation formalisms and Artificial Intelligence (AI) knowledge-representation schemes form a powerful combination, called knowledge-based simulation (Zeigler, 1990, pp.l-16). Several languages are being developed to express both the dynamic knowledge of discrete-event formalisms and the declarative knowledge of AI paradigms (Klahr, 1986; Ruiz-Mier and Talvage, 1989). In contrast to other knowledge-based simulation systems, DEVS-Scheme is based on the Discrete Event Simulation (DEVS) formalism, a theoretically well grounded means of expressing hierarchical, modular discrete-event simulation models (Zeigler, 1989, 1990). Systems theory distinguishes between system structure (the inner constitution of a system) and behavior (its outer manifestation). Decomposition, i.e. how a system may be broken down into component systems, and coupling, i.e. how these components may be combined to reconstitute the original system, are important concepts related to systems structure. DEVS knowledge representation scheme, the System Entity Structure, combines not only decomposition and coupling but also taxonomy, which deals with the admissible variants of a component and their specializations (Zeigler, 1989). The entities of the system entity structure refer to the conceptual components of reality for which models may reside in the model base. The model base contains models expressed in the dynamical discrete-event formalisms. An entity may have several aspects, each denoting a decomposition and therefore having several entities. An entity may also have several specializations, each representing a classification of the possible variants of the entity. This knowledge base is a compact representation scheme that can be unfolded to generate the family of all possible models synthesizable from all models in the model base (Zeigler, 1989, 1990). The user, a goal-oriented agent, can interrogate the knowledge base and synthesize a model using pruning operations that ultimately reduce the structure to a composition tree. From the composition tree the model can be synthesized by retrieving the components from the model base (Fig. 1). It is necessary to define one additional concept related to the system entity structure, the multiple entity. A multiple entity represents the set of all members of an entity class. Multiple entities always have an aspect, which is the multiple decomposition into the individual entities of the class.

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M. PERES'rREI.IX3 DE VASCONCELOS A N D B.P. Z E I G L E R - - model

-

-

I

I

F--1

I

I

I

I

K N O W L E D G E BASE

ENTITY STRUCTURE ~]

\

M O D E L BASE

/

Composition tree

Fig. 1. The knowledge base framework: system entity structure, model base, and composition tree. The composition tree is generated by pruning the system entity structure, and retrieving the models corresponding to the tree entities from the model base. An experimental frame specifies the form of the experimentation that is required to obtain answers to questions of interest (Zeigler 1990, pp. 99-105). It generally consists of a coupled-model (a model composed of lower level models linked by coupling). The experimental f l a m e generates input external events, monitors the simulation, and processes output. The design of an experimental frame reflects the objectives one has in experimenting with a model. An object-oriented program contains components called objects. Each object has its own variables and procedures to manipulate these variables, called methods. Only the methods owned by the object can access and change the values of its variables. The variables of the object constitute its state. Consequently, only the methods of an object can alter its state. Different objects can have variables and methods having the same name,

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Fig. 2. M o d e l s A a n d B are m o d u l a r models and are available in the model base. A m o d u l a r m o d e l C can b e c r e a t e d by m a p p i n g the input and o u t p u t ports of A and B in a p r o c e d u r e called coupling.

and these can have equivalent meaning and purpose but operate in different ways. In object-oriented programming, objects are not usually defined individually. Instead, a class definition provides a template for generating any n u m b e r of instances, each one an identical copy of a basic prototype. Objects can be organized into a family of h o m o g e n e o u s classes, which affords an economy of definitions. In addition to their own methods, objects of a given class inherit all the methods of other classes, automatically obtaining their definitions. M o d u l a r system models can have a hierarchical structure in which c o m p o n e n t systems are coupled together to form larger ones. The term modularity means the description of a model in such a way that it has recognized input and output ports through which all the interaction with the external world is mediated (Zeigler, 1989, 1990). For any set of c o m p o n e n t models, a new model can be created by specifying how the input and output ports of the components are to be connected to each other and to external ports, in an operation called coupling. Once included in the model base, the new model can itself be employed to construct yet larger models in the same manner (Fig. 2). In modular discrete-event models, the values appearing on input and output ports are determined by events. In D E V S one has to specify atomic models from which larger ones are built, and how these models are connected together in a hierarchical fashion (Zeigler, 1990, pp. 69-88). An atomic model contains: a set of input ports through which external events are received a set of output ports through which external events are sent -

-

-

-

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M. P E R E S T R E L L O D E V A S C O N C E L O S A N D B.P. ZIEIGLER

- - a set of state variables and parameters a time advance function which controls the timing of external events an internal transition function which specifies the next state to which the system will transit after the time given by the time advance function has elapsed - - an external transition function which specifies how the system changes state when an input is received an output function which generates an external output just before an internal transition takes place. Two state variables are usually present in atomic models: phase and sigma. In the absence of external events the system remains in the current phase for the time given by sigma. W h e n an external event occurs the external transition function places the system in a new phase and sigma thus scheduling it for the next internal transition (Zeigler, 1990, p. 72). The next state is c o m p u t e d on the basis of the present state, the input port and value of the external event, and time elapsed in the current state. -

-

-

-

-

-

The Noble and Slatyer model Noble and Slatyer (1981) developed a qualitative successional model based on individual key-species' properties. Their scheme defines a set of species' attributes that are vital to the reproduction and survival of a species within a community. The vital attributes defined as most important to a species' success on a site subject to recurrent fires are the m e t h o d of arrival (or persistence) to the site following a disturbance; the conditions in which a species establishes itself and grows to maturity; and the time taken to reach critical stages (maturity, senescence and extinction) in its life history. Noble and Slatyer summarize all the important species information in a table of vital attributes. To depict shifts in a community composition after disturbances (fire events) this scheme uses replacement sequences. F o r a detailed description of this model see Noble and Slatyer (1981, pp. 315-319). The vital attributes described below refer exclusively to those relevant for the present study. It should also be noted that some discrete-event concepts are introduced in this description. Establishment conditions important in this study correspond to establishment immediately and exclusively after disturbance (I species) and establishment at any time (T species). The first group corresponds to species intolerant to competition in established communities (competition can apply to light, soil, nutrients, or other physiological requirements). The second group of species is tolerant to competition.

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There are three critical events within the life history of a species following a disturbance (time 0): Maturity (m) is the time at which individuals will have recovered or grown sufficiently to be regarded as established. By definition it is the time when the individual is able to contribute propagules into the propagule pool that will enable the species to persist through another disturbance. Before reaching maturity the species is in the juvenile phase. - - Senescence and loss of the species individuals from the community (l). A species is in phase mature from the time it reaches maturity until just before senescence occurs. - - Loss of propagules from the site so that the species is extinct (ex). A species is in phase propagule from the time it senesces until just before extinction. After extinction the species is in phase extinct. The three methods of persistence relevant for this particular application are: - - persistence by arrival of widely dispersed seeds (D species). Seeds are considered to be available all the time (permanent propagule viability). This means that phase extinct is never reached persistence of seeds with short viability that often survive disturbance within protective fruits or cones stored in the canopy (C species) mechanism such as long lived seed storage in the soil that is not destroyed by fire (S species). Propagules are available not only during the mature phase, but also at juvenile and propagule phases. The propagule phase is not indefinitely available after senescence like in the D species. If enough time elapses without establishment the species becomes extinct. Noble and Slatyer (1981) applied the above-described scheme to a wet sclerophyll rainforest (tall open and closed forests). Four key component species of the ecosystem were identified and their life history used to derive replacement sequences under different fire regimes. The key components identified were Eucalyptus sp., Acacia sp., Nothofagus sp., and Antherosperma sp. with the life histories summarized below. The capital letters in front of each species correspond to persistence and establishment attributes, respectively. - -

- -

-

-

a

METHODS The approach utilized for simulating the dynamics of the wet sclerophyll forest (one and two patches) in the DEVS-Scheme environment can be summarized in the following steps: - - Formalization of species' atomic models (components of a patch) and testing. Couplings for a one-patch landscape.

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Life phase (years)

0

10

30 70

Acacia Eucalyptus

SI CI

m - - I

Nothofagus

CI

m

Antherosperma

DT

m

400

500

ex l ,ex l ,ex

m

l ,ex

Scheme 1. - - Formalization of an experimental frame (EF) for simulations of onepatch dynamics and testing. - - Definition of assumptions for interactions between two patches. Formalization of interactions between two patches by coupling. Formalization of the experimental frame for simulations of two interactive patches. --Design of a system entity structure applicable to simulation of the dynamics of one patch or of two interacting patches. - - Pruning and simulation of one patch using the fire frequencies (inputs) described in Noble and Slatyer (1981). Verification of outcomes (outputs) and comparison of system behavior, sequences of system's states, with those described in Noble and Slatyer (1981). --Pruning and simulations of two interacting patches. Interpretation of results. T h e species' a t o m i c m o d e l s a n d the o n e - p a t c h m o d e l

From the vital attributes described above one can derive that the life history characteristics of a species correspond to the set of internal states generated in case where there are no fires. Accordingly the times of internal events are given by rn, l, and ex, which can be regarded as parameters of a model of the species. Fires are external events that will determine a new sequence of states for each species. The rules governing the new sequences are dependent on the persistence and establishment characteristics of the species. A single atomic model was created to be used for all the component species (Eucalyptus, Nothofagus, Antherosperma and Acacia). Figure 3 shows a diagram representing the species' atomic model and respective pseudo-code. The variable n a m e is the species identifier; m, l and ex are parameters that correspond to the time that this species takes to reach maturity,

S I M U L A T I O N OF F O R E S T LANDSCAPE R E S P O N S E T O F I R E D I S T U R B A N C E S

,n I

out

SPECIES

fire /

phasel sigma I clock I m [ I I ex I name I temp

PSEUDO-CODE STATE

VARIABLES:

PARAMETERS:

s~gma phase

= i0 name = juvenile m = i0 1 = 60 ex = 3 3 0

FOR

SP

= Acacia

clock = 0 temp = none

EXTERNAL TRANSITION FUNCTION: If n a m e is Acacia if p o r t is f i r e , c a s e v a l u e is f i r e l if p h a s e i s n ' t p a s s i v e t e m p = p h a s e a n d c l o c k = s i g m a - e hold-in send 0 otherwise continue c a s e v a l u e is e n d p a s s i v a t e c a s e v a l u e is f i r e 2 if p h a s e i s n ' t p a s s i v e h o l d in j u v e n i l e f o r m if p o r t is in c a s e v a l u e is A C A C I A a n d p h a s e is p a s s i v e h o l d in a r i v 0 If n a m e is e u c a l y p t u s (or n o t h o f a g u s ) c a s e p o r t is f i r e c a s e v a l u e is f i r e l if p h a s e is m a t u r e t e m p = p h a s e c l o c k = s i g m a - e h o l d in s e n d 0 otherwise continue c a s e v a l u e is e n d p a s s i v a t e c a s e v a l u e is f i r e 2 if p h a s e is m a t u r e h o l d in j u v e n i l e f o r m o t h e r w i s e if p h a s e is n o t p a s s i v e h o l d in p r o p a g u l e 0 c a s e p o r t is in c a s e v a l u e is e u c a l y p t u s (or n o t h o f a g u s ) if p h a s e is p a s s i v e h o l d in a r i v 0 If n a m e is a n t h e r o s p e r m a c a s e p o r t is f i r e if v a l u e is e n d p a s s i v a t e if v a l u e is f i r e 2 h o l d - i n j u v e n i l e for m INTERNAL TRANSITION FUNCTION: c a s e p h a s e is j u v e n i l e h o l d in m a t u r e f o r 1 c a s e p h a s e is m a t u r e h o l d in p r o p a g u l e f o r ex c a s e p h a s e is p r o p a g u l e p a s s i v a t e c a s e p h a s e is s e n d s e t p h a s e t o t e m p a n d s i g m a c a s e p h a s e is a r i v h o l d in j u v e n i l e f o r m

to

clock

OUTPUT FUNCTION: c a s e p h a s e is j u v e n i l e s e n d v a l u e " m a t u r e " t o p o r t O u t c a s e p h a s e is m a t u r e s e n d v a l u e " l o n g e v i t y " t o p o r t o u t c a s e p h a s e is p r o p a g u l e s e n d v a l u e " e x t i n c t " to p o r t o u t c a s e p h a s e is s e n d s t a t e - n a m e t o p o r t s e n d c a s e p h a s e is a r i v s e n d s t a t e - n a m e to p o r t a r i v e d

Fig. 3. Species' atomic model box diagram and respective pseudo-code.

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fire

>

DE VASCONCELOS

A N D B.P. Z E I G L E R

PATCH

~re

in+

~fire n+

,o+ ~ire i~~l i NOTHOFAGUS I ANTHEROSP.

+send+arlut n~ed

out

>

Fig. 4. Couplings in onc patch. longevity and extinction. The variable phase holds the species' phases. It will have the values juvenile (from time 0 to time m), mature (from time m to l), propagule (from l to ex) and passive (after the species reached extinction time ex). If no external events (fires) occur, the species will passivate after ex has elapsed. This description s h o w s how the internal transition function can be the same for all species. All have the same sequence of phases and differ only in the time taken to reach it (this includes the possibility of infinite time for ex). D e p e n d i n g on name different sets of rules are applied when external events (fires) occur arriving in port fire. The rules applied are a consequence of the species (name) life history, and will set the variables phase to the appropriate phase, and sigma to time of next internal event. Before each internal transition an output goes to port out with the value of the phase reached. A patch is composed of four atomic models, one for each c o m p o n e n t species. The coupling is of a broadcast type, where messages received by patch in port fire or port in are broadcast to a corresponding port in all components (Fig. 4). Additionally, the output ports of each c o m p o n e n t species are coupled with patch output ports only. Thus, there is no internal coupling among patch components. The ports in and send are never accessed in the case of one patch only, since there is no interaction between species in a patch. This is a consequence of the assumptions in Noble and Slatyer's approach. As discussed above each species' adaptive traits (including competition abilities) are addressed in its life history description.

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Assumptions for two interacting patches It is assumed that when a fire occurs in one patch, and the second patch has available propagules, these can be instantaneously sent to the first (burned) patch. It is also assumed that if a species was locally extinct in the just b u r n e d receiving patch and propagules arrive, the species will reestablish instantaneously. The first assumption may or may not be true. Particularly, it may be true for some species and false for others. However, the second assumption is certainly valid u n d e r the constraints of this model. If a species is available

fire in

PATCH

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Fig. 5. Couplings in two patches.

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M. P E R E S T R E L L O DE VASCONCELOS A N D B.P. Z E I G L E R

in the propagule pool immediately after a fire, then its life history can proceed as if it had been available by other mechanisms. The formalization of these assumptions is reflected in the atomic model behavior, and in the couplings described below and shown in Fig. 5.

Multipatch modelling A landscape model of several interacting patches can be built as a coupled-model of several one-patch models. In this example there are two interacting patches, however, the same coupling types could be used for any number of interacting patches. As illustrated in Fig. 5, the two-patch system has internal coupling between patches. As a consequence, there is access to ports in and send of the species' atomic models. Port arrive is also accessed due to external output couplings between component species and their patch. The variable phase in each atomic model can hold the additional values "send" and "arrive". An event arrived in port fire of a species in patchl can be either " f i r e l " or "fire2" (fire in patchl or fire in patch2). If the value is "fire2" and the species has viable propagules, it will go to the temporary phase "send" and place an output in port send. Conversely, when the value is " f i r e l " (a fire occurs in this patch) and an event arrives in port in (a propagule sent by the corresponding species in patch 2), if the species is extinct (passive), it can re-establish. The species will go to a temporary phase "arrive" that puts out a value in port arrive. This is necessary in order to acknowledge the species re-establishment in patchl. The basic experimental frame consists of a generator that generates fires at different points in time, and a transducer that keeps track of extinctions and respective times (Fig. 6). In the case of two interacting patches the transducer keeps track of extinctions and re-establishments in both patches separately.

The system entity structure The system entity structure is shown in Fig. 7. For this particular application (one or two patches) a simple system entity structure was utilized. The landscape is composed of land-units (landscape-dec indicates this decomposition), and each land-unit is either composed of one or of two patches. This is illustrated by the specialization lands-units-spec. The three parallel vertical lines indicate that each patch is a multiple entity, meaning that each patch can have any number of similar components (in this case species). The number of component species is specified by the user during the pruning process, and in this case there are four

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EXPERIMENTAL FRAME

stopJ

GENERATOR

I-

-1

F

result

out

............ <

out >

out

fire

TRANSDUCER l j extin~..............

extinct

C |~arrived

[~rdved

Fig. 6. The experimental frame is composed of atomic models Generator and Transducer. The Generator sends a message out when fires occur and the Transducer keeps track of the times of fire occurrences, species extinctions and global simulation.

key-species in each patch. All component species inherit the same methods, and as a consequence they are all functionally similar. However, each species also has its own particular methods and behaves differently under identical circumstances.

LANDSCAPE

[

landscape~Jec

[ EXPERIMENTAL-FRAME

LANDS-UNITS

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Fig. 7. The system entity structure.

I

I TRANSDUCER

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The system entity structure was pruned and two pruned entity structures (composition trees) were created, one for the one-patch situation and the other for the two-patch scenario. For applications in more complex landscapes a generalized system entity structure could be created with landscape-units several layers deep. Each patch would consist of several lower level patches in a multiple entity and this structure can be r e p e a t e d down to a given level of hierarchical complexity. Simulations

All simulations were performed for a period of 1600 years. This n u m b e r was chosen because it includes two complete life cycles of the longest lived species, excluding Antherosperma. A n t h e r o s p e r m a never reaches the phase extinct, being an ubiquitous DT species. Additionally, all simulations considered that the c o m p o n e n t species were at the starting point of their life cycle (clock = 0, phase = juvenile). The beginning of each simulation involved setting each atomic model to a species and the corresponding state-variables and parameters to the appropriate values. For example, the atomic models set to A C A C I A have the initial variable values: name = A C A C I A , sigma = 10 (time of next event), phase = juvenile; and p a r a m e t e r values: m = 10, l = 60, and e x = 400. This procedure was performed in batch format. The generator in the Experimental Frame (Fig. 5) generates fires at specific points in time and the transducer keeps track of extinctions and respective times. In the two-patch case the transducer also keeps track of re-establishments and respective times. The first simulation corresponded to the one-patch situation under the fire regimes described in Noble and Slatyer (1981). Then simulations for two interacting patches were p e r f o r m e d as follows: - - same fire regimes as in the one-patch case for both patches. If patch1 had a fire regime of 5 to 9 years, so would patch2. However, fires did not necessarily occur in the exact same year in both patches - - same fire regimes were applied differentially to patches 1 and 2. For example, patch1 with fire regime 5 - 9 years and patch 2 with fire regime 10-29 years finally, randomly generated fires (within a likely interval of 1000 years) were utilized in five simulations. -

-

RESULTS The results are summarized in Tables 1 through 4. Table 1 shows the results for the simulations with one patch; Tables 2, 3, and 4 show the

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TABLE 1 Results of the simulations for one single patch Fire c y c l e

Extinctions

Final system

Community type

5-9

Eucalyptus Nothofagus

Acacia + Antherosperma

Acacia/ Antherosperma

10-29

Nothofagus

Acacia Antherosperma Eucalyptus

Mixed forest

30-69

None

All species

Sclerophyll scrub

70-399

None

All species

Sclerophyll scrub

400-499

Acacia Eucalyptus

Nothofagus Antherosperma

Juvenile rain forest

500-1000

Nothofagus Eucalyptus Acacia

Antherosperma

Pure rain forest

No fire

Nothofagus Eucalyptus Acacia

Antherosperma

Pure rain forest

results for the three different simulations with two interacting patches. In Tables 2 and 3, each entry has two values of fire cycle corresponding to the fire cycles in patch1 (top) and patch2 (bottom). It should be noted that when the two patches have the same fire cycle, that does not mean they have simultaneous fires. Fires were randomly, and independently, generated for each patch within the specified fire interval. Consequently, a patch and its neighbor can have fires occurring at different times even though they are subject to the same fire cycle. It is not possible to show the sequences of states obtained for every simulation. For the two-patch case there is one transducer file in the Appendix. Nevertheless, it can be acknowledged that for the particular case of one patch, the state sequences obtained were consistently the same as those described by Noble and Slatyer (1981, pp. 326-333). W h e n equal fire cycles were applied to both patches in the two-patch landscape, system behavior was equivalent to that observed with one patch only, and consequently equivalent to the replacement sequences presented by Noble and Slatyer (1981). There were transitions to corresponding states within the same time intervals, and the final outcomes are the same (see Tables 1 and

2).

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TABLE 2 Results of the simulations for two interacting patches with the same fire cycles Fire cycle

Extinctions

Interchanged species

Final system

Community type

Eucalyptus Nothofagus Eucalyptus Nothofagus

None

Acacia + Antherosperma

Acacia/ Antherosperma forest

10-29

Nothofagus

None

Mixed forest

10-29

Nothofagus

Acacia Antherosperma Eucalyptus

30-69 30-69

None None

None

All species

Sclerophyll scrub

70-399 70-399

None None

None

All species

Sclerophyll scrub

Acacia Eucalyptus Acacia Eucalyptus

None

Nothofagus Antherosperma

Juvenile rain forest

Nothofagus Eucalyptus Acacia Nothofagus Eucalyptus Acacia

None

Anthcrosperma

Pure rain forest

Nothofagus Eucalyptus Acacia Nothofagus Eucalyptus Acacia

None

Antherosperma

Pure rain forest

5-9 5-9

400-499 400-499 500-1000

500-1000

No fire

No fire

W h e n d i f f e r e n t fire r e g i m e s a r e a p p l i e d in the two i n t e r a c t i n g p a t c h e s s e v e r a l d i f f e r e n t b e h a v i o r s a n d o u t c o m e s occur. T h e r e m a y b e p r o p a g u l e flow in b o t h d i r e c t i o n s , in o n e d i r e c t i o n or n o n e , a n d t h e final s y s t e m m a y consist of two d i f f e r e n t i a t e d p a t c h e s or o f o n e single p a t c h ( w h e n the two p a t c h e s b e c o m e e q u a l to e a c h o t h e r ) . A d d i t i o n a l l y , t h e r e a r e s i t u a t i o n s w h e r e n e w o u t c o m e s , not s e e n in the p r e v i o u s two s i m u l a t i o n s , o c c u r ( A c a c i a a n d j u v e n i l e rain forest) T h e results p r e s e n t e d c o r r e s p o n d to t h e e x p e c t e d l a n d s c a p e c o m p o s i t i o n

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TO FIRE DISTURBANCES

TABLE 3 Simulations for two patches with different fire cycles Fire cycle

Extinctions

Interchanged species "

Final system

Community type b

10-29

Nothofagus

Eucalyptus (1 -0 2)

(a) Mixed forest

5-9

Nothofagus Eucalyptus

Acacia Antherosperma Eucalyptus

Eucalyptus and Nothofagus (1 -0 2)

All species

(c) Sclcrophyll scrub

Acacia (2 -0 1) Eucalyptus and Nothofagus (1 -02)

Acacia Nothofagus Antherosperma

(c) Juvenilc rain forest and Acacia

Nothofagus (1-o2)

All species

(c) Sclerophyll scrub

None

All species

(a) Sclerophyll scrub (b) Pure rain forcst

70-399

None

5-9

None

400-499

Eucalyptus

5-9

Eucalyptus

70-399

None

10-39

None

70-399 No fires

None Acacia Nothofagus Eucalyptus

400-499

Eucalyptus Acacia Acacia Nothofagus Eucalyptus

No fires

Nothofagus Antherosperma None

(b) Acacia/ Antheroperma forest

(a) Juvenile rain forest (b) Pure rain forest

a The arrows within parentheses indicate the direction of the flow between patches 1 and 2. b When two distinct patches emerge in the final system, (a) is used for patch 1 and (b) for patch 2. When one uniform patch results, (c) is utilized.

a f t e r 1600 years. H o w e v e r , l a n d s c a p e e v o l u t i o n to that p o i n t is k n o w n a n d the system c a n be a n a l y z e d at any p o i n t in time. DISCUSSION Since t h e r e was total c o r r e s p o n d e n c e o f states b e t w e e n the o n e - p a t c h D E V S m o d e l a n d N o b l e a n d Slatyer's, we can say t h a t t h e r e is an i s o m o r p h i c r e l a t i o n s h i p (Zeigler, 1990) b e t w e e n the two models. N o b l e a n d S l a t y e r ' s m o d e l has an h o m o m o r p h i c r e l a t i o n s h i p to the real system ( S a m p son, 1984) b e c a u s e c h r o n o l o g y is p r e s e r v e d a n d t h e r e is an h o m o m o r p h i c m a p p i n g f r o m states o f the system to states o f the m o d e l . C o n s e q u e n t l y , it

194

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TABLE 4 Simulations for two patches with fire cycles randomly generated Patch a

Extinctions

Interchanged species

Final system

Community type

1

None

All specics

(c) Sclerophyll scrub

2

None

Eucalyptus, Nothofagus and Acacia (1 ~ 2)

1

Acacia Eucalyptus Acacia Eucalyptus

Nothofagus, Acacia and Eucalyptus (1 ~ 2)

Nothofagus + Antherosperma

(c) Juvenile rain forest

Acacia Eucalyptus Acacia Eucalyptus

Nothofagus (1 ~ 2)

Nothofagus + Anthcrosperma

(c) Juvenile rain forest

Acacia Eucalyptus Nothofagus Acacia Eucalyptus Nothofagus

Nothofagus, Acacia and Eucalyptus (1 ~ 2)

2 1 2 1

2

1

2

Acacia Eucalyptus Nothofagus Acacia Eucalyptus

Acacia

(c) Pure rain forest Antherosperma

Nothofagus + Antherospcrma

Eucalyptus (2 -~ 1)

(a) Pure rain forest

(b) Juvenile rain forest

'~ Fire occurrence years in both patches arc listed below: Fire occurrences Simulation

Patch

Fire occurrences (years)

1

1 2

529, 1474 35,204, 705, 1034, 1066, 1125, 1285

2

1 2

553, 1513 58, 410, 1051, 1514

3

1 2

39, 373,495, 1286, 1519 943

4

1 2

579, 1283, 1319 289, 1162

5

1 2

646, 1583 294, 327, 661, 1141, 1463, 1579

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195

is assumed that this is a validated model. In addition, the model implemented in the DEVS-Scheme environment was verified. The results obtained for two interacting patches under the same fire regimes show that the system as a whole behaves as a single patch under these circumstances. Since in this case replacement sequences are the same as in the one-patch landscape, this is yet another verification of the model. However, it really goes one step further because it shows that the patterns of response of two interacting patches (two landscape elements) do give rise to a verifiable pattern at the higher, whole system level. When different fire regimes are applied to the two interacting patches there are situations where the final system (after 1600 years) becomes composed of two identical patches. In this case it can be considered that one single patch emerges out of the two initial ones. The two initial patches can effectively be considered different because they progress to their final stages though different pathways and are behaviorally different from each other, reflecting the different timings imposed by fires. However, at the end of the simulation time, and still under different fire regimes, they either became behaviorally equivalent (and equivalent to the whole) or they reached a steady state of species interchange that reflects itself as an equivalent behavior with intermediate states of species' "sending" and "receiving". Additionally, it should be noted that the emerging patch may have a different composition from what would occur if there was no interaction, and fire events were the same. On the other hand, there are circumstances that lead to two totally distinct patches. For example, when a sclerophyllous scrub and a "climax", undisturbed rain forest are obtained. In this case, one can conclude that those different fire regimes do shape a landscape with two interactive, dynamically different patches. CONCLUSIONS AND FUTURE DIRECTIONS In spite of the simplicity of the application presented, it is apparent that landscape dynamics can be simulated using DEVS, and concepts of hierarchical, modular, object-oriented systems. The ability to derive landscape behavior at one level based on the behavior of components at lower levels was demonstrated. The general objectives of landscape modeling are to predict changes in land cover patterns across large geographic areas over long time scales as a result of very site-specific natural, or management-induced changes (Costanza et al., 1990). There is an increasing interest in the ability to derive whole landscape dynamics based on models of local dynamics. This approach has a parallel in the field of ecology where ecologists studying

196

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DE VASCONCELOS

A N D B.P. Z E I G L E R

complex interactions in ecological systems have turned increasingly to computer models based on simulations of many individuals (Huston et al., 1988; Pickett et al., 1989; Costanza et al., 1990). Individual models are conceptually simpler, easier to quantify and require fewer unreasonable assumptions than large-scale models (Huston et al., 1988). If the structure of the system is sufficiently known, these lower level models can be used as building pieces of that structure. In addition to discrete state models, such as that utilized in this work, there are situations where continuous models could be utilized. Cellier (1979) surveyed the techniques for combined simulation for systems having properties suitable to both continuous and discrete-event simulation. Additionally, Zeigler (1984, 1990) outlined an approach for constructing a discrete-event abstraction for deterministic continuous systems that are well modeled with conventional differential equation techniques. This technique can have wide applicability for simulating ecological processes usually described by differential equations (e.g., population growth). Although a deeper discussion of this subject is beyond the scope of this paper, just as an illustration we can think of a model where state transitions depend not only on passage of time but on other variables as well. For example, the time of transition to maturity of a species component could be determined by biomass accumulation curves driven by environmental and physiological variables. As a result the same species' model could have different times of maturity in two different patches or, for the same patch, in two different climatic scenarios. A complete framework for modeling landscape dynamics has to incorporate space, as well as time. This explicit spatial aspect is what motivates landscape ecology (Sklar and Costanza, 1990). One of the ways to model spatial dynamics is to arrange a spatial array of models and connect them with fluxes (e.g., water, nutrients, propagules), employing rules to govern changes in the system (Costanza ct al., 1990). This can be achieved with spatially referenced discrete-event, modular models in a Geographic Information System (GIS). GIS incorporate data from such diverse sources as remotely sensed images, maps, aerial photography, and tabular data in a common, georeferenced data base. Additionally, GIS provide means for manipulating the data, deriving new mapped information by applying standard algorithms to maps (e.g., computation of erosion maps based on topography, vegetation cover, soil type and treatment by applying the Universal Soil Loss Equation). Modelling of spatially explicit dynamical processes using GIS as been done for several applications (Berry and Sailor, 1987; Kessel, 1990; Pereira and Vasconcelos, 1990; Vasconcelos and Pereira, 1991). However, the

SIMULATION

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197

APPENDIX Log file resulting from the first simulation with randomly generated fires

FIRES 1:(1474 529) FIRES 2:(1285 1125 1066 1034 705 204 35) The arrived listl: ((EUCALYPTUS 1474) (ACACIA 1474) (NOTHOFAGUS 1474) (ACACIA 529) (NOTHOFAGUS 529) (EUCALYPTUS 529)) The arrived list2: ((NOTHOFAGUS 705) (EUCALYPTUS 705) (ACACIA 705)) The extinctions listl: ((NOTHOFAGUS 1029) (EUCALYPTUS 929) (ACACIA 929) (NOTHOFAGUS 500) (EUCALYPTUS 400) (ACACIA 400)) The extinctions list2: ((NOTHOFAGUS 704) (ACACIA 604) (EUCALYPTUS 604)) Note: the number in parentheses indicates the year of extinction or arrival in a patch. Even though the extinctions lists in both patches include Eucalyptus, Nothofagus and Acacia, these species are re-established at the end of the simulation period (see arrived lists).

approaches utilized are generally based on discrete time paradigms and use GIS only as a means for retrieving data and displaying final and intermediate results. The need for truly dynamic spatial modeling capabilities within GIS is particularly important in the field of landscape ecology. Recent developments in supercomputers and parallel/vector processing (Casey and Jameson, 1988), together with the accessibility of large time series sets of remotely sensed images, stimulate the idea of true dynamic modeling within GIS environments. Additionally, ecosystem understanding and modeling in a stuctured hierarchical approach is necessary for the more general goal of incorporating ecological information in global change models. We suggest that the approach followed in this study provides a set of concepts appropriate for dealing with the hierarchical structure and function of complex landscape systems. It provides the necessary capabilities for handling and analyzing systems' spatial dynamics at several levels of organization, temporal and spatial resolution. REFERENCES Berry, J.K. and Sailor, J.K., 1987. Use of a Geographic Information System for storm runoff prediction from small urban watersheds. Environ. Manage., 11(1): 21-27. Casey, R.M. and Jameson, D.A., 1988. Parallel and vector processing in landscape dynamics. Appl. Math. Comput., 27(1): 3-23. Cellier, F.E., 1979. Combined continuous/discrete system simulation languages - - usefulness, experiences and future development. In: B.P. Zeigler, M.S. Elzas, G.J. Klir and T.I. Oren (Editors), Methodologies in Systems Modelling and Simulation. North-Holland, Amsterdam, pp. 93-99. Costanza, R., Sklar, F.H. and White, M.L., 1990. Modeling coastal landscape dynamics. BioScience, 40(2): 91-107.

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Grime, J.P., 1979. Plant Strategies and Vegetation Processes. John Wiley, Chichester. Horn, H.S., 1975. Markovian properties of forest succession. In: M.L. Cody and J.M. Diamond (Editors), Ecology and Evolution of Communities. Harvard University Press, Cambridge, pp. 196-211. Huston, M., DeAngelis, D. and Post, W., 1988. New computer models unify ecological theory. BioScience, 38(10): 682-691. IGBP, 1990. A Study of Global Change. The Initial Core Projects. International Council of Scientific Unions (ICSU), Rep. No. 12, 1990. Kessel, S.R., 1977. Gradient modelling: a new approach to fire modelling and resource management. In: C.A.S. Hall and J.W. Day Jr (Editors), Ecosystem Modelling in Theory and Practice: An Introduction With Case Histories. John Wiley, New York, pp. 575-605. Kcssel, S.R., 1979. Gradient Modeling. Resource and Fire Management. Springer-Verlag, Berlin. Kessel, S.R., 1990. An Australian geographical information and modelling system for natural area management. Int. J. Geogr. Inf. Syst., 4(3): 333-362. Klahr, P., 1986. Expressibility in Ross, an object-oriented simulation system. In: G.C. Vansteenkiste, E.J.H. Kerckhoffs and B.P. Zeiglcr (Editors), Artificial Intelligence in Simulation. SCS Publications, San Diego, CA. Noble, I.R. and Slatyer, R.O., 1981. Concepts and models of succession in vascular plant communities subject to recurrent fire. In: A.M. Gill, R.H. Groves and I.R. Noble (Editors), Fire and the Australian Biota. Australian National Commitee for SCOPE. Australian Academy of Science, pp. 311-335. Pereira, J.M. and Vasconcelos, M.J., 1990. Fire propagation modelling in heterogeneous environments and a new spread algorithm for FIREMAP. In: Proc. Int. Conf. Forest Fire Research, University of Coimbra, 19-22 November 1990, Coimbra, Portugal. Comissa6 de Coordena~a6 de Regiao Centro, pp. B.14-I-B.14-15. Pickett, S.T., Kolasa, J., Armesto, J.J. and Collins, S.L., 1989. The ecological concept of disturbance and its expression at various hierarchical levels. Oikos, 54: 129-136. Ruiz-Mier, S. and Talvage, J., 1989. A hybrid paradigm for modeling of complex systems. In: L.A. Widman, K.A. Loparo and N. Nielsen (Editors), Artificial Intelligence, Simulation and Modelling. John Wiley, New York, pp. 381-395. Sampson, J.R., 1984. Biological Information Proccssing. Current Theory and Computer Simulation. John Wiley, New York. Shugart, H.H., 1984. A Theory of Forest Dynamics. The Ecological Implications of Forest Succession Models. Springer-Verlag, Berlin. Sklar, F.H. and Costanza, R., 1990. The development of dynamic spatial models for landscape ecology: a review and prognosis. In: M.G. Turner and R.H. Gardner (Editors), Quantitative Methods in Landscape Ecology: Analysis and Interpretation of Landscape Heterogeneity. Springer-Verlag, New York, pp. 239-288. Vasconcelos, M.J. and Pereira, J.M., 1991. Spatial dynamic fire behavior simulation as an aid to forest planning and management. In: Proc. Fire and the Environment Symp., March 20-24, 1990, University of Tenessee, Knoxville. USDA Forest Service General Technical Report SE-69, pp. 421-426. Zeigler, B.P., 1976. Theory of Modeling and Simulation. John Wiley, New York. Zeigler, B.P., 1984. Multifacetted Modeling and Discrete Event Simulation. Academic Press, London. Zeigler, B.P., 1989. Knowledge-based design of artificial worlds. BioSystems, 23: 95-112. Zeigler, B.P., 1990. Object Oriented Simulation with Hierarchical, Modular Models. Intellegent Agents and Endomorphic Systems. Academic Press, New York.