Su W. Et Al 2001 - Agent-based Dynamic Modelling of Forest Ecosystems at the Warra LTER Site

129Tasforests Vol. 13 No. 1 December 2001

Abstract

A spatially explicit, dynamic simulation modelof forest ecosystems at the Warra LTER Sitewas prepared. The advantage of this formof modelling is that one can not only explore thedynamic interactions of the sub-components ofthe ecosystem but also experiment with differentdisturbance regimes and management options.

The simulation model was built using an agent-based modelling approach. The approach buildsa virtual landscape ecosystem and simulates howthe various components of the forest ecosystem fittogether and interact with each other. Fire is themain disturbance source in the succession of theeucalypt forest ecosystem in this area and playsa critical role in the process of patterning theforested landscape. The emergent patterns fromthe simulation are in accord with the successiontheory for the type of the forested ecosystembeing modelled. Fuel dynamics are the maincontributing factors to the definition of the fireregime of the forest ecosystems, and study of fuelsin relation to topographic features is needed tofurther improve the simulation result.

Introduction

A critical issue for native forest managementis the accumulated and long-term ecological

impacts of silvicultural regimes and forestmanagement practices. Forecasting thesepotential impacts is very difficult for anumber of interrelated reasons. Forestecosystem processes are played out on alandscape-wide basis, whereas traditionalforest survey is limited to networks of smallsample field plots. Thus, we generally lackdata about the larger scaled patterns andprocesses. Furthermore, the patterns ofbiodiversity and vegetation structure varythrough time in response to fire regimesand ecological processes that govern forestsuccessional pathways.

Simulation modelling provides a tool forexploring how forest pattern and process mayvary through time on a landscape-wide basis.However, no suitable landscape dynamicmodel has been available for application inAustralia. Consequently, this project aimedto develop a prototype landscape dynamicmodel suitable for exploring the long-termimpacts of land use and global changeperturbations, and to investigate the abilityof the model to replicate current forestecosystem pattern in a test landscape inthe Southern Forests of Tasmania. The workreported here forms part of a PhD projectundertaken by the senior author at theAustralian National University.

An ecosystem is a self-organised, complexadaptive system (Brown 1994). Theecological processes acting within anecosystem create patterns at different spatial

Agent-based dynamic modellingof forest ecosystems at the WarraLTER Site

W. Su1, 2*, M.J. Brown3 and B. Mackey11 Department of Geography, Australian National University, ACT

2 Current address for correspondence: Department of Primary Industries,Water and Environment, GPO Box 44, Hobart, Tasmania 7001

3Forestry Tasmania

* Corresponding authore-mail: [email protected]

[email protected]@dpiwe.tas.gov.au


and temporal scales. The nature of thesepatterns will vary depending upon dynamicinteractions among the constituent biota ofthe ecosystem and the environment. Thecomplexity of ecosystem phenomena resultsfrom dynamic interactions of hierarchicallystructured components. Thus phenomenaat one level may be the result of interactiveprocesses among components at other levels.

Object-oriented modelling is a technologywhich can assist in formulating a modelof a complex system in the real world. Thebasic elements of design in object-orientedmodelling are the objects and objectinteractions. Objects formulated in a modelare largely abstractions of the objects inthe real world ecosystem. In computerprogramming, data and operations aregrouped into a self-sufficient modularunit as a subprogram which representsan equivalent abstraction of objects in thesystem being modelled. A model can beformed by combining the objects intostructured networks in a hierarchy. Withobject-oriented modelling, the nature ofthe interactions among the hierarchicallystructured components can be explored,and the emergent properties resulting fromthese interactions can be experimented with.

This study is based on the wet eucalyptand rainforest ecosystems at the WarraLong-Term Ecological Research (LTER)Site in southern Tasmania. The ecology ofthese types of forest has been well studied(e.g. Gilbert 1959; Jackson 1968; Brown andPodger 1982; Jarman and Brown 1983; Readand Hill 1988; Kirkpatrick et al. 1988; Hickey1994; Read and Brown 1996; Reid et al. 1999)giving an empirical and theoretical base forthe formulation of the simulation model.The study examines the complex ecologicalsuccession paths in response to environmentalresource gradients and fire regimes, as wellas the main ecological processes.

The model built in this study is an agent-based, discrete event, simulation modelbased on a generic object-orientedsimulation framework called Swarm

developed by the Santa Fe Institute (Minaret al. 1996). It provides a group of reusablesoftware objects for managing, analysing,displaying and controlling simulationexperiments. With Swarm, an agent-baseddiscrete event simulation model of acomplex system can be built. In thissimulation model, an individual tree isthe basic agent. There are also other objectsrepresenting the environments where theagents live.

Model design

The purpose of this simulation model is toobserve how species diversity emerges fromthe interactions of individual trees with theenvironment and disturbances due to fire,to determine the regeneration process.

The individual tree was chosen as a keyagent in this simulation because speciesdiversity is both an emergent property fromindividual trees and an important featureof forest ecosystems. The model simulatesthe biological processes of birth, growthand death for each individual tree. Theseprocesses in turn are controlled through theinteractions of each of the individual treeswith their local environment.

The environmental objects are treated asa series of two-dimensional lattice objectsrepresenting the environmental conditionsin which the trees live. A two-dimensionaldiscrete lattice defines the spatial locationof the tree objects. Models built in this waycan be viewed as a virtual landscape insidethe computer.

The objects in the simulation model areable to dynamically update their propertiesaccording to events such as regeneration,growth, death and fire during each of thesimulation time steps. Each of the objectshas its own life span and schedule forchange through time. Some of them arestatic since they slowly respond to time orother events. For instance, a topographicfeature is relatively static over a 100-yearperiod, and therefore can be treated as


constant during the simulation. Others suchas trees grow every year and their propertiesneed to be updated in every simulation timestep. The simulation was designed to runusing a yearly time step over periods ofhundreds of years.

The model also incorporates the effects ofregeneration, mortality and fire processes.

Model development

The ecosystem in the study area has beendivided into three distinctive subsystems:the climate, the environment and the forest.

1. Climate subsystem

The climate is a broadscale phenomenon,and is treated as a constant and globalconstraint on the local physical environmentprocesses in this model.

The local environment variables such astemperature, rainfall, surface hydrologicaldynamics and soil moisture condition etc.are interpolated from topographicallyrelated physical and ecological processes.These variables and related processes weremodelled through ANUCLIM and used asinputs to the simulation model as part ofthe environment component.

MacArthurs (1962, 1967) forest fire dangerindex (FDI) is used to characterise theclimate condition of the fire season in thissimulation. The FDI is used as a variable forthe risk of forest fire during the fire seasonin the study area. Under a specific weathercondition, the fire occurrence and thebehaviour depend on local conditions suchas topographic features, fuel load, etc. TheFDI is used here as a general qualificationof the weather condition, it is not spatiallyexplicit in this model.

Fire has a critical impact on the dynamicdevelopment of the wet sclerophyll forestecosystem. It consists of four componentvariables: temperature, air humidity, wind

speed, and drought factors in soil. The formof the FDI is:

FDI = 1.25 . D . e(TH)/(30+0.234w)

where FDI is the forest fire danger index, D isdrought factor (1 to 10), which is a functionof soil water deficit; T is air temperature;H is air humidity; and W is the wind speedin the open, 9 m above ground.

2. Environment subsystem

In the environment subsystem, four objectshave been identified to act as the maincontrollers of species diversity in southernforests: elevation, aspect, slope and soilmoisture. Each effect is discussed below.

Elevation.Elevation gradients affectenvironmental variables such astemperature and rainfall, and thus maydefine the distribution of the different typesof the vegetation community and speciesdiversity. The elevation is represented in athree-dimensional surface in the simulationmodel just as a digital elevation model(DEM) does in geographic informationsystems (GIS).

Aspect.Aspect is modelled as a spatiallydistributed, two-dimensional, passive objectand has strong effects on fire and firebehaviour. The north-west aspect is drierthan others because the prevailing wind isnorth-westerly. Three aspect directionshave been sampled, based on the effectsof the aspect on fuel load properties of theecosystem in the study area. The effects ofthe aspect on fire behaviour through rateof spread and intensity of the fire havealso been spatially explicitly modelled.

Slope.Like the aspect object, the effect ofslope is only considered on fire behaviour.It is assumed here to have little effect onthe modelled species diversity of theecosystem. There may be other complexinteractions which exist between the slopeand the ecosystem but the effect on fire isconsidered to be most important for thissimulation model.


Soil moisture index.Soil moisture affectsvarious aspects of the ecosystem and has asignificant effect on fuel moisture content(Cheney 1981). The effect of fuel moisturecontent on the behaviour of fire has beenmodelled in relation to soil moisture inthis simulation model.

3. Forest subsystem

There are four objects (and two sub-objects)identified and considered the major sourcesto contribute to the emergence of thecharacteristics of the ecosystem: trees, species,forest (including young and mature subsets)and seed space. Each is discussed below.

Tree object.The simulation model is builtunder the assumption that the individualsare the major source of emergent propertiesof the ecosystem. The species diversityor species composition at a particular sitearises from the contribution of each of theindividual trees.

Species object.Each tree belongs toa species, which is also identified in themodel. The species object is designed tocapture the similarity of features at thespecies level. The separation of the featuresof a species from a tree is a level of

abstraction since the features at species levelnever change on a basis of each individualtree. Examples include shade tolerance,seeding and seedling features, age tomaturity, longevity and reproduction.

Forest object.The forest object is a levelof hierarchy above the tree and species. Thepurpose of the forest class forms a virtualforest ecosystem (Figure 1). Therefore, theforest class consists of a two-dimensionallattice, which identifies the location of eachindividual tree and the trees that are spatiallydistributed on the two-dimensional lattice.

In order to distinguish the differentaspects of the age of a tree in the process ofregeneration, and the process in response tofire, the forest object has been sub-classifiedinto young forest and mature forest objects.

The young forest objects grow and gettransferred to mature forest objects, leavinga space for new seedling establishment.Young forest objects are killed by fire andold forest objects eventually die, also leavinga space for a new seedling.

Seed space object.The seed spaceobject is designed to keep track of the seedavailability for the regeneration process. It

Figure 1. A visual presentation of the forest object.


is a dynamic mechanism to let speciescompete for available locations. Seed spaceassociates with each of the species andinteracts with regeneration processes. It alsohas a feedback effect from fires because firestimulates seed germination for some species.

Ecological process related objects.Thereare two main linked ecological processeswhich are critically important to the wetsclerophyll forest ecosystem dynamics.The first is the regeneration process andthe second is fire.

The seven species chosen in this simulationmodel have distinctive ecologicalcharacteristics in response to the twoimportant processes. Regeneration ofE. obliqua and E. delegatensis relies on fire,whereas the rainforest species do not.Therefore two types of regeneration mustbe simulated differently in response tofire and non-fire events during thesimulation. In terms of function, thesetwo types of regeneration processes havedistinctive differences.

The regeneration object.The regenerationobject is designed to model the regenerationprocess of the rainforest species in theecosystem at each simulation time step.This object is scheduled in a yearly timestep and interacts with the seed spaceobject, species object and forest object tocarry out the regeneration process. Theregeneration process object gives uniformcontrol of the regeneration process in thesimulation and ensures every species getsthe same opportunity to compete forregeneration space.

The responsibility of the regeneration object isto trigger the regeneration process (by sendinga message or invoking an operation) of theforest object at each time step during thesimulation. It is scheduled in Forest ModelSwarm against the global clock each year toemulate the season for seedling establishment(spring), during which the seeds from lastyear will be ready for germinating if there isa spare site and the condition at that site is

suitable. A suitable condition is where thereis a site available for occupation by a properspecies which has sufficient seeds. If morethan one species is suitable for the site, othercontrols or rules are introduced to decidewhich one has the establishment advantage.Final decisions on an unresolved conflict areby random selection. However, this is notcommon since the species chosen in thisstudy have distinctive ecological preferenceswhich hardly ever conflict.

The season triggers the regeneration process.The species are checked annually one byone. If it is, for example, a eucalyptspecies, and there is no fire at the sites, noregeneration process occurs. If it is a non-eucalypt species, the regeneration processwill start. As was discussed earlier, thecompetition for sites depends on the seedavailability and other ecological propertiesof the species such as shade tolerance. Arandom shuffle is used to decide how manyseeds for a species can be germinated if thereare many sites suitable for that species.

Fire regeneration object.The fireregeneration object is responsible for the fire-related regeneration process of the species.

Fire is a highly variable event both inspace and time. The occurrence of the firedepends on ignition source, seasonal localclimate and weather conditions, topographiceffects and vegetation.

Fire object.A fire object models theprocess of fire in relation to the developmentof the ecosystem. Since the occurrence offire relies on the weather condition duringthe fire season, the weather condition isgenerated based on the distribution ofthe fire danger index (FDI) during the fireseason from real data. The fire object servesas a spatial and temporal generator of theoccurrence of random fire in the simulation.The occurrence and behaviour of fires willdepend on the fuel load and time since lastfire. The effects of the fire on the forest willdepend on the species characteristics as wellas the status of each of the individual trees.


In order to create a generic scenario of theclimate condition during the fire seasonin the study area, two years of daily basedweather data were obtained from the Bureauof Meteorology in Tasmania. These datawere used to calculate the monthly spread ofFDI values. This distribution of FDI valueswas then used to randomly generate thelocal weather conditions in the fire object.In future models, the distributions wouldincorporate more extreme events to includesummers of very low FDI as well as highextreme events such as in February 1967.

Fuel load object.The fuel load objectrepresents the fuel accumulation dynamics.Although the occurrence of the fire dependson the local climate and weather conditionsduring the fire season, the behaviour ofthe fire will largely be decided by the fuelload of the site and topography as wellas topographic-related features such as soilmoisture condition. The fuel load is closelyrelated to the intensity of the fire, while thetopographic feature decides how the firespreads across the forested landscape.

For the fuel load dynamics, there are manymodels to describe the fuel accumulationover time in Eucalyptus forest. The equationis used also in various mathematical formssuch as polynomial (Hutson and Veitch1985) and linear equations. The mostcommonly used form of fuel load modelis as follows:

Wt = Wmax (1 e-kt)

where Wt is the fuel load at time t, Wmaxis the maximum fuel load under the staticcondition, k is the fuel decomposition rate,and t is the time since last fire.

The fuel space spread of the fire is calculatedusing the following algorithm in the fuelspace:

F(x,y) ? F( i, j)

(i ? x?1 ,j ? y?1)

x? 1,y ?1

?

where F(x,y) is the fire at location (x, y).

The fuel space object is a dynamic objectwith feedback effects from the environmentobjects and the fire object. Therefore, thefuel dynamics of the forest floor in the studyarea is not only a function of time since lastfire but also of the variables describingthe topographic features of the study area.Calculations are based on observationsmade in the Southern Forests of Tasmania.The strong influences of the topographicfeatures, mainly slope and aspect, on fireintensity and rate of spread across the wetsclerophyll forest have been discussed byCheney (1981).

The fuel load object is also used to calculatethe rate of spread and intensity of the fireat the specific location based on thetopographic features and the fuel loadof that site. The rate of spread on flatground is calculated by using Noblesequation (Noble et al. 1980),

Ros = a . Wf . FDI

where Ros is the rate of spread (m/hr), andWf is the fuel load (t/ha), FDI is the forestfire danger index (MacArthur 1962) and a isconstant (1.2).

Time since last fire object.In the fuelload object, the fuel load is a function oftime since last fire. Therefore, another objectwhich records the variation of time since lastfire has been created to indicate the elapsedtime of the fire at each location in the studyarea. It is dynamically updated during eachsimulation time step.

Simulation control related objects.Objects do not stand alone, they must beput together and interact to make a usablemodel. The objects interactions come intoplay only when we put them together inthe correct way. This is the final task insimulation modelling.

At the final stage of the modelling, theForest Model Swarm object initialises theobjects created from the modelling processand schedules them in a logical order. It


also establishes the overall interactionsof the objects. Figure 2 describes theinteraction relationship of the objects of the

Forest Model Swarm object, and Figure 3gives an overview of the overall structure ofthe simulation model.

Figure 2. The relationship of the objects inside the Forest Model Swarm object. Solid linesindicate that, for example, fuel space is a function of moisture, slope etc. Dotted lines indicatean association relationship; for example, each tree and seed belong to only one species.

Figure 3. The overall structure of the simulation model.


Simulation

The characteristics of tree species as individualagents

The simulation is based on seven species.Each of them represents an importantecological or functional group within theecosystem. The characteristics of the sevenspecies are given below.

Eucalyptus obliqua.Eucalyptus obliquais a widespread and dominant species inwet sclerophyll forests. It lives for 350450years. The site preference for E. obliqua iscomparatively mesic, well-drained, lowlandhabitats on a variety of substrates andterrain associated with relatively higher firefrequency. The substrates often are dolerite,sandstone and mudstone. The altituderange is below 400 m in the study area. Itrepresents various types of communities,from wet sclerophyll to mixed forestthrough combinations with other species.It displaces E. regnans on deep, well-drainedsoils on fertile sites which are relatively drierwith moderate to high fire frequency, and isitself replaced by E. delegatensis at higheraltitudes on similar sites.

Regeneration of E. obliqua in wet forestsrelies on fire (Hickey 1994). The successionpathway is decided by fire regimes, especiallythe interval between fires, or fire-free periodafter the fire. At the stage of wet sclerophyllforest, if the fire regime changes and theinterval between fires becomes long enough,the succession is towards rainforest throughthe mixed forest stage. However, if the fireregime remains the same, wet sclerophyllforest types would be maintained. The fireintensity and season also play an importantrole in deciding the species compositionand age structure of the forest community.

The species composition and communitystructure often correspond to the soil fertilityand moisture gradient of the sites. Heathyunderstoreys are typical on siliceous soils.On fertile soils, a tall scrub understorey willbe present. On moist fertile sites, a pure

stand can be formed. With decrease of soilmoisture, it coexists with other eucalyptspecies such as E. viminalis.

Eucalyptus obliqua has canopy-stored seedswhich are available each year and aredispersed through gravity. Regenerationoccurs only after fire.

Eucalyptus delegatensis.Ecologically,E. delegatensis is similar to E. obliqua, exceptit has a higher altitude distribution thanE. obliqua (between 400 and 600 m). It occupiescomparatively fertile, moist, well-drained siteswith Jurassic dolerite soil parent material.

Eucalyptus delegatensis can dominate a rangeof community types. It forms pure standsbut frequently associates with E. obliqua atlower altitudes. This species is more firesensitive than E. obliqua.

Nothofagus cunninghamii.Nothofaguscunninghamii is a cool temperate rainforestspecies. It lives for 400600 years.Rainforest can perpetuate itself withoutbroadscale disturbance (Jarman andBrown 1983). It is fire sensitive and maybe converted into Eucalyptus forest after fire,if there is an available seed source. Thealtitude range of N. cunninghamii is verywide. It can grow from sea level to 1500 mbut grows best below about 700 m. Thecurrent distribution of rainforest in thestudy area is in moist, sheltered gulliesalong drainage lines where humidity is high,and on well-drained, moderate to steepslopes topographically protected from fire.

In the model, this species is the mainrepresentative of rainforest components andcan either form a pure rainforest alone or inassociation with Phyllocladus aspleniifolius, oroccur as a subordinate stratum to eucalyptswithin mixed forests. It is less shadetolerant than Atherosperma moschatum, whichmay replace it in small stands in wet gullies(Read and Hill 1988). We do not take thissituation into account in the simulation sincethere is little pure Atherosperma forest foundin the study area.


Nothofagus cunninghamii seeds every year,although mast years do occur. Seeds areground stored with a longevity of threeyears. Seed dispersal is by gravity and wind.The regeneration is continuous without fire.

Phyllocladus aspleniifolius. Phyllocladusaspleniifolius is another rainforestcomponent. Its altitude range is from sealevel to 800 m and it lives for more than800 years. It has a wide topographic rangeand is often associated with Nothofaguscunninghamii, Atherosperma moschatum,Eucryphia lucida and Acacia melanoxylon.Also it can be present in mixed forest withE. obliqua and E. delegatensis.

In this simulation model, it acts as a speciesto form both rainforest and mixed foresttypes. It is assumed to produce good seedevery year, seed longevity is between fiveto seven years, and seeds are dispersed bybirds. Regeneration is assumed to becontinuous in the absence of fire.

Acacia melanoxylon.Acacia melanoxylon isa widespread species that appears in manydifferent communities. It usually dies after80120 years. It ranges from sea level to800 m on a wide range of topography, fromlow-lying swamps to mountain slopes. It isfound in rainforests, mixed forests and wetsclerophyll forests.

In the model, A. melanoxylon representsspecies related to a range of time scalesof disturbance and can associate with wetsclerophyll forests as well as rainforest. Itseeds annually in huge quantities and relieson gravity and small animals for dispersal.Regeneration is rare without disturbance.

Pomaderris apetala. Pomaderris apetalarepresents the broad-leaved shrub componentassociated with wet sclerophyll forests. Itlives for 6080 years. Its seeds are gravitydispersed and ground stored. Regenerationoccurs after broadscale disturbance.

Gahnia grandis.Gahnia grandis is an earlycoloniser after fire and only persists with

frequent fire. It lives for 1525 years. Itsseeds are ground stored and dispersed bybirds and gravity.

The simulation was carried out for an areaof 9 km by 6 km in the Southern Forests atthe Warra LTER Sitein Tasmania. The modelwas set to run for 500 years. The spatialpattern of the species diversity can be clearlyviewed by converting the result into images.

Results

The result of this simulation is a seriesof snapshots taken from the simulation at25-year intervals. The output of the speciesdistribution data is put into text files andimported into a GIS and presented as a grid.The pattern of the species distribution canthen be viewed in image form.

The simulation result can be viewed as areassemblage of the species distribution inthe real world. For example, classificationmethods can be applied to obtain a vegetationmap since the vegetation type is defined bythe species composition. Sometimes thereare clear boundaries and sometimesboundaries are unclear and can only bedefined by statistical classification techniques.

Patterns readily emerge from the simulation.Figures 4 and 5 are snapshot images takenat 100 and 500 years from commencementof the simulation. Different shades representdifferent species, with black being recentlyburnt (newly available habitat) areas.

Figure 4 is the snapshot at 100 years. Fromthis image, there are clear patterns emergingafter fire disturbance. A few fires haveoccurred in the area, creating patchesof varying species composition and agestructures. The large central grey patch isE. delegatensis regenerated from an earlyfire. The black patch on the right is a freshlyburned patch. The species are in the recoveryphase. The light grey colour inside the blackpatch is Gahnia, which is a pioneer speciescolonising the latest burned patch.


The result at 300 years is similar to that at100 years, but the pattern evolves at thelocal scale since succession is happeningwithout major fire disturbance. Thespecies composition in the area undergoesprogressive change. More and more wetsclerophyll species invade the ecosystem.A close examination of the simulation showsthat clear natural boundaries are related tosharp topographic changes and abrupt fire-disturbance events. The successionelsewhere takes the form of changes inrelation to local environmental gradientsand competition for resources.

The snapshot at 500 years (Figure 5) is thefinal stage of the simulated forest ecosystem.Eucalyptus delegatensis is dominant athigh elevations. In the gullies, high soilmoisture content and low terrain featureslimit fire spread and therefore provide theopportunity for rainforest species to develop.Similar trends appear in the area near thecentre: as the eucalypt forests grow, the forestecosystem follows the successional pathtowards rainforest, with Acacia melanoxylonand Pomaderris apetala gradually decreasingdue to their relatively short life span.

Conclusions

The agent-based simulation approachprovides some new insights into thedynamic aspects of the forest ecosystem.The approach enables one to build a virtuallandscape ecosystem to simulate how thevarious components of the forest ecosystemfit together and interact with each other.It also provides a way to explore theinterrelationship between patterns andecological processes. The combination ofthe parameters can be used experimentallyand the output can be validated with realdata, or subjected to statistical analysis.Individual trees contribute to speciesdiversity through the process of dynamicinteractions with each other as well aswith their environment. Fire is the maindisturbance source in the succession of theeucalyptrainforest ecosystem in this areaand plays a critical role in the process ofpatterning the forested landscape. Thesimulated result demonstrates that theemergent pattern in the form of thevegetation type defined by speciescomposition or diversity conforms withsuccession theory for the type of the forested

F i g u r e 4 . S i m u l a t i o n a t 1 0 0 y e a r s .


Figure 5. Simulation at 500 years.

ecosystem being modelled. The role thatfire plays in the succession of wet sclerophyllforest in this area is through its direct effectson the process of species regeneration andthe fire response properties of the species.The life span of species and the firefrequency will contribute to the maintenance

of particular vegetation communities. Thefuel dynamics of the forest ecosystem is themain contributing factor defining the fireregime of the forest ecosystem. Therefore,study of fuels in relation to topographicfeatures is a critical aspect needed toimprove the simulation result.

References

Brown, J.H. (1994). Complex ecological systems. In: Complexity: Metaphors, Models and Reality. SFIStudies in the Sciences of Complexity. Proceedings Vol. XIX (eds G. Cowan, D. Pines and D. Meltzer),pp. 419443. Addison-Wesley, Massachusetts, USA.

Brown, M.J. and Podger, F.D. (1982). Floristics and fire regimes of a vegetation sequence fromsedgeland-heath to rainforest at Bathurst Harbour, Tasmania. Australian Journal of Botany 30:659676.

Cheney, N.P. (1981). Fire behaviour. In: Fire and the Australian Biota (eds A.M. Gill, R.H. Groves andI.R. Noble), pp. 151175. Australian Academy of Science, Canberra.

Gilbert, J.M. (1959). Forest succession in the Florentine Valley, Tasmania. Papers and Proceedings of theRoyal Society of Tasmania 93: 129151.

Hickey, J.E. (1994). A floristic comparison of vascular species in Tasmanian oldgrowth mixed forestwith regeneration resulting from logging and wildfire. Australian Journal of Botany 42: 383404.

Hutson, B.R. and Veitch, L.G. (1985). Relationships between litterfall rate, litter mass and decompositionrate in Eucalyptus forests in southeastern Australia. Australian Journal of Ecology 10: 443450.

Jackson, W.D. (1968). Fire, air, water and earth - an elemental ecology of Tasmania. Proceedings of theEcological Society of Australia 3: 916.

Jarman, S.J and Brown, M.J. (1983). A definition of cool temperate rainforest in Tasmania. Search 14: 8187.Kirkpatrick, J.B., Peacock, R.J., Cullen, P.J. and Neyland, M.G. (1988). The Wet Eucalypt Forests of

Tasmania. Tasmanian Conservation Trust, Hobart.


MacArthur, A.G. (1962). Control burning in eucalypt forest. Commonwealth Forestry and Timber BureauLeaflet 80.

MacArthur, A.G. (1967). Fire behaviour in eucalypt forests. Commonwealth Forestry and Timber BureauLeaflet 107.

Minar, N., Burkhart, R., Langton, C. and Askenazi, M. (1996). The Swarm simulation system: a toolkitfor building multi-agent simulations. Santa Fe Institute Working Paper 96-06-042, Santa Fe, NewMexico.

Noble, I.R., Bary, G.V. and Gill, A.M. (1980). McArthurs fire danger meters expressed as equations.Australian Journal of Ecology 5: 201203.

Read, J. and Brown, M.J. (1996). Ecology of Australian Nothofagus forests. In: Ecology and Biogeographyof Nothofagus Forests (eds T.T. Veblen, R.S. Hill and J. Read), pp. 131181. Yale University Press.

Read, J. and Hill, R.S. (1988). The dynamics of some rainforest associations in Tasmania. Journal ofEcology 76: 558584.

Reid, J.B., Hill, R.S., Brown, M.J. and Hovenden, M.J. (eds) (1999). Vegetation of Tasmania. Flora ofAustralia Supplementary Series Number 8. ABRS, Canberra.

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Su W. Et Al 2001 - Agent-based Dynamic Modelling of Forest Ecosystems at the Warra LTER Site

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