Fishwick P.A. (editor) Handbook of Dynamic System Modeling

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29-10 Handbook of Dynamic System Modeling

if we have previously seen how the latter were limited in simulating biological processes (Grimm and

Uchmanski, 1994) when we face questions requiring a high level of details, ecological modeling often has

to take into account:

•

the diversity of individuals,

•

the spatial heterogeneity of the environment,

•

the changing interaction network (and changes in biotic structures),

•

the discrete and distant interactions,

•

some random aspects and behavior (i.e., random spatial interactions).

At the end of the 1980s, biologists and computer scientists highlighted the convergence between biological

concepts and object model concepts (Huston et al., 1988). Indeed, IBMs are often implemented by object-

oriented models (Coquillard and Hill, 1997) or by multiagent models when there is a need to represent

an autonomous social behavior of individuals involved in a common goal (Ferber, 1999). It is by the

way remarkable that the Simula language (Dahl and Nygaard, 1966), which introduced the essence of

object-orientation in computer science, is still providing one of the most convenient ways to implement

IBMs without additional libraries. Even if the authors of this chapter have abandoned this language, they

want to emphasize the work done by some of their pioneer colleagues in Germany (Kiel Ecology Center)

who built various models dealing with a wide range of delicate ecological interactions in Simula (Breckling

et al., 1998).

An object-oriented simulation willbe based on individual organisms ratherthan on aggregated variables.

Classes and their relationships can deﬁne the biological taxonomy retained for the model (Baveco, 1997). A

domain analysis will produce an object model tightly associated with the biological model and helping the

communication process between both scientiﬁc communities (Computer Science/Biology) (Hill, 1996).

Coupling object-oriented concepts with individual-based modeling has the main following advantages:

•

It avoids difﬁcult or impossible mathematical modeling (i.e., a competition between three different

species including spatial constraints). It is also possible to enrich a model using inheritance, which

recovers all its original meaning. In addition, object classes can take into account a part of mathe-

matical modeling to obtain combined simulations if needed (mixing the discrete and continuous

approach as explained in the methodological chapters of this book).

•

It avoids keeping scrupulous track of stands over longtime periods, which are necessary to feed

Markovian analysis. However, a lot of ﬁeldwork is necessary as well as a substantial knowledge of

the species modeled by object classes. Class attributes can reﬂect the current expert knowledge; the

detail level will depend on the expected model result.

•

It takes into account the spatial aspects of ecosystems, which is hardly possible with partial

differential equations (compartment models), or with classical Markovian analysis except with

time-dependent matrix (nonhomogeneous chains) which sets (i) the problem of the investigation

time cost and (ii) initialization difﬁculties in variable conditions (i.e., combinatorial exploration).

•

It provides the possibility to manage, for each individual, the set of all the parameters which the

biologist decides to integrate in his model. The management of individuals, and correlatively their

physiological variations, enables the reﬁnement of the model to close reality with the detailed level

the user wants.

We think that the two last points are essential. Even if spatial diffusion processes can be modeled by partial

differential equations, it is indeed impossible to take into account spatial constraints and distant stochastic

interactions (propagation of cuttings, of seeds, of sparks hundreds of meters away and sometimes a few

kilometers away). For instance, Figure 29.5(b) presents the spreading of Caulerpa taxifolia in the harbor

of “Villefranche sur Mer,” France, this model will be presented in details in the next section. C. taxifolia is

a green alga of tropical origin introduced by mistake in the Mediterranean Sea (Meinesz and Hesse, 1991),

it is currently colonizing the North Mediterranean (Hill, 1997) and we quote this application here since

it will give a concrete example of the importance of spatial constraints in some ecological models. In this

Ecological Modeling and Simulation 29-11

(a) (b)

FIGURE 29.5 (a) Map provided by the simulation model coupled with a GIS; C =Caulerpa taxifolia;R=rocks;

M =harbor mud; S =sediment; P =Posidonia oceanica beds. Inside the harbor: C =C. taxifolia, it appears in a two

gray scale; light gray corresponds to densities higher than 80%. (b) Result of a spectral analysis with 255 replicates.

model, the individual behavior including the spreading of cuttings and the stolon growth are important

colonization factors. In Figure 29.5, inside the harbor, denoted by a “C,” C. taxifolia appears mainly in

light gray, and spotting outside the harbor correspond to the spreading of Caulerpa cuttings. To obtain

colonization maps, we have to use spatial constraints, including the shape of the harbor, the bathymetry,

the position of undersea substrates, which are key elements. Such constraints impose the coupling of an

individual-based discrete-event simulation with a Geographical Information System and also the design

of discrete geometry algorithms (Hill et al., 1998).

As opposed to what can be modeled with IBMs, Huston, DeAngelis, and Post (Huston et al., 1988) note

that when we use formal models we often combine many individual organisms to describe a single variable

and each individual is assumed to have an equal effect on every other individual. This kind of modeling

is often mandatory because of the mathematical tools used. The resulting problem is that it violates two

main biological principles:

1. Each individual of a given population is different, with regard to behavior and physiology.

2. Interactions between individuals are inherently local. Spatial aspects are often key factors in biology.

IBMs do not require the same level of simplifying assumptions used for state-variable models. This fact

mainly explains the rise of this modeling approach observed by Judson, Breckling, and Müller at the

beginning of the 1990s (Breckling and Müller, 1994; Judson, 1994). The object-oriented approach enables

us to describe individual organisms that change their inner states and their environment. In Figure 29.6 we

see again how an IBM model can take into account spatial constraints by coupling the simulation model

with a geographical information system (GIS). Figure 29.6 presents a modeling of herbivorous behavior

in the French “Massif Central.” GIS combined with GPS devices assigned to horses and cows were used to

obtain precious ﬁeld data (such as animal behavior, animal pasturing choices, and location).

In an IBM, individuals are able to react to their changing environmental state and to reproduce in

their “virtual” environment. This could sound like a deﬁnition of an “artiﬁcial life,” but the scientiﬁc

community studying “artiﬁcial life” has the following objective: they want to give access to the domain of

life-as-it-could-be by extending the limits of our current biology knowledge described as life-as-we-know-it.

For more details, the interested reader should consult the ofﬁcial Journal of the International Society of

Artiﬁcial Life edited by MIT Press. A common interest of both disciplines is the study of emergent

properties. With an IBM it is possible to understand how local interactions between individuals contribute

29-12 Handbook of Dynamic System Modeling

FIGURE 29.6 Modeling of herbivore followed by GPS devices (horses and cows).

to structural changes at higher levels (DeAngelis and Gross, 1992; Grimm and Railsback, 2005). In an IBM,

we try to set up a model where local interactions work as far as possible as they do in nature (according to

ﬁeld observation). Local interactions enable the emergence of properties observed in an ecological context

(Breckling et al., 2005). Scientists, working in Social Sciences, study the use of primitive rules assigned

to individuals to observe a more global behavior; they often use multiagent systems. As we said, we can

consider a multiagent system as an extension of an IBM in which social interactions have a signiﬁcant role

to explain the system behavior.

IBMs do also present many limits; most of them can be rapidly reached depending on our computing

capacity. The main limit is that IBMs do not scale well in space, they are best suited to study ecosystems at

a local or regional scale. In addition, the number of individuals and individual interactions is also limited

(linked computing capacity). This is not crucial when we work on the scale of an ecosystem (millions of

individuals can be simulated over a 100 years even on a desktop personal computer).

To work on different scales, we have to face the challenge of simulating scale transfers. The team

of scientists running the Earth Simulator supercomputer in Japan introduced what they called Holistic

Simulation to explore complex interdependencies between micro- and macroscale processes (Sato, 2003).

On such a supercomputer, it is possible to simulate a reasonable number of different scales with the major

interactions between the most signiﬁcant processes. Many scientists are trying to develop simulations

of the interactions between the main processes at different scales to help understanding the behavior of

complex systems (not only ecosystems). However, only Japan possesses a supercomputer dedicated to this

purpose, and it has been the World’s fastest public computer for two successive years (2003 and 2004).

Multiscale modeling methods are presented in this book by Mark Sheppard.

29.9 Applications

We will now give more details for a couple of linked applications where the development of an IBM was

necessary. The ﬁrst application was already brieﬂy introduced, it deals with the spreading of C. taxifolia

in the North Mediterranean. Posidonia oceanica, a protected Mediterranean species, and other more

common species are endangered by this colonization. The second application deals with the simulation of

C. taxifolia biocontrol using the Elysia subornata (a marine slug). This biocontrol simulation was achieved

using a multimodel embedding various models of different formalisms. A chapter of this book is devoted

to multimodeling (by Minho Park, Paul Fishwick, and Jinho Lee).

Ecological Modeling and Simulation 29-13

FIGURE 29.7 Simulation of C. taxifolia spreading around Monaco 12 years after its introduction. A spectral result

obtained for the same geographical site is also presented on the top left of the ﬁgure.

In 1984, the French coast of the Mediterranean Sea near Monaco was the initial site of the development

of C. taxifolia. Twelve years latter, this species had colonized several thousand hectares of the French and

Italian coasts and was detected in numerous places of the northwestern Mediterranean coast, from Croatia

(Adriatic sea) to the Balearic Islands (Spain). Figure 29.7 presents the simulated situation around Monaco

12 years after the alga introduction and a spectral result that will be discussed a few paragraphs later.

This development has locally induced an intense alteration of the coastal ecosystems both on endoge-

nous species distribution (alga, cnidaria, sponges, echinoderms, ﬁshes, etc.) as well as on the ecosystem

functioning. To predict the development of C. taxifolia, a simulation study was undertaken through an

interdisciplinary joint venture between marine ecologists, biologists, and computer scientists. An IBM

had been implemented to take into account spatial interactions and anthropic dispersion (dispersion by

people) or activities such as eradication. The attentive reader will recall that this model was based on a

coupling of a Geographical Information System with a stochastic discrete-event simulation, and was able

to deal with distant stochastic interactions. Even though the model had to cope with incomplete data

and sampling difﬁculties encountered in the hostile environment of the sea, interesting calibration and

validation procedures speciﬁed by oceanographers have been successfully achieved. The calibration has

been achieved on various sites and the model results matched a satisfying level of prediction at different

spatial scales (from a few centimeters to a few kilometers). Our calibration dealt with the local and spatial

patterns of expansion, the increase of C. taxifolia biomass, the increase in covered surfaces, and the invasive

behavior toward existing communities. The fact that we knew the initial settlements and that we had been

following the maps of Caulerpa evolution since 1988 was of great help in the calibration process. Indeed,

concrete evolution maps have been successfully compared with simulated maps obtained by a spectral

analysis of stochastic spatial results (Hill, 1997). Figure 29.5(b) presents on the right a spectral analysis of

simulation results over 5 years, using 255 replicates on Villefranche-sur-Mer harbor (La Darse) site. This

kind of result can be understood as a map of colonization probabilities; the darker the colors, the higher

the frequency of settlement. Spatial aspects in the spreading of cuttings did take into account geograph-

ical data available such as harbor walls, bathymetry, and different substrates. More details on how the

model determines whether or not a speciﬁc place was frequently or infrequently settled are given in Hill

et al. (1998).

29-14 Handbook of Dynamic System Modeling

Uses ⬎

Implements ⬎

Consults ⬎

Requests ⬎

Updates ⬎

Stochastic

discrete-event

simulation

multimodel

Slug death/

Birth model

Leslie

matrix

⬍⬍Interface⬎⬎

(Temperature array)

Temperature

model

Difference

equations

GIS

maps

Cellular

automata

Spatial

model

FIGURE 29.8 Excerpt of the UML class diagram for the biocontrol multimodel.

After an intensive use of this ﬁrst model, we developed at the end of the 1990s a multimodeling

simulation to assess the potential of a biocontrol of the alga C. taxifolia by means of a small marine slug

of tropical origin: Elysia subornata. Biological and ecological parameters were considered as key factors

related to the behavior of E. subornata toward C. taxifolia and toward the Mediterranean conditions. To

this end, growth, survival, reproduction, feeding on C. taxifolia, and foraging of E. subornata were studied

through laboratory experiments, details are given in Coquillard et al. (2000). Simulations, taking into

account spatial effects, were in agreement with the laboratory experiments, the results demonstrated that

the greatest impacts on Caulerpa were obtained using either just some adults or mixing adults and juvenile

slugs. In any case, better results were obtained by a scattering of slugs on isolated spots rather than on

clusters (with constant surfaces). Lastly, the choice of a suitable date for scattering increases the weak

consumption of Caulerpa resulting from the scattering of juvenile slugs. To set up experiments in large

mesocosm, an E.E.C. agreement is now necessary. Figure 29.8 presents a metamodel of this simulation

application using the UML (uniﬁed modeling language). The metamodel describes the multimodel used

for this biocontrol application; it integrates submodels of different formalisms, and can still be considered

as an IBM, since at its main level we do consider individual differences and local interactions between

individuals.

Many other applications can be found in which IBM or multiagent simulations are of greatest interest.

For instance, the simulation of spatial interactions was essential in the modeling of the reproduction of the

ﬁne-scale horizontal heterogeneity of a pure grass sward with its dynamics (Lafarge et al., 2005). We also

tried other formalisms like the metamodeling approach using artiﬁcial neural networks (ANN) trained

by the simulation results (Aussem and Hill, 1999). After a long training, this approach was able to give a

rough prediction of surface colonization but it was impossible to obtain colonization maps. More formal

approaches have also been studied though they are still using discrete-event simulation. In a recent paper,

we show how initial ideas and work proposed by Vasconcelos and Zeigler (1993) for ﬁre spreading and

simulation can beneﬁt from the recent advances in the theory of modeling and simulation (Muzy et al.,

2005). The last point we would like to highlight before ending this application section is the impact of

visualization tools. In the domain of ecological modeling or environmental modeling these tools are often

necessary for communication between specialists. Not only do they provide substantial gains in model

validation, but as in many other domains, the involvement of decision makers will also depend on the kind

Ecological Modeling and Simulation 29-15

FIGURE 29.9 Snapshot of the postprocessed visualization tool designed for a coupling with an IBM model of forest

ﬁre simulations.

and variety of presented results. A snapshot of a visualization tool we developed for ﬁre simulation is given

in Figure 29.9. Decision makers should, however, be warned that visualization can lead to wrong decisions

(either intentionally or unintentionally). In the case of stochastic simulations under spatial constraints,

end users have to be aware that the animation of simulation results they are watching is only a very small

sample of what could really occur. However, maps presenting spectral results do integrate a sufﬁcient

number of replications and are thus a better tool for decision-making.

29.10 Conclusion

In this chapter, we have exposed a short history of ecological modeling followed by a survey of current

modeling practices using the best journal for publications in this research ﬁeld. We have given some

general indications concerning methodological choices including the importance of stochastic modeling.

Design problems such as the selection of an organization level have also been discussed. We hope that the

reader has seen that ecological modeling could beneﬁt from many modeling formalisms, most of them

are presented in different chapters of this book. Among the various formalisms we wanted to explain

why more ecological modelers started to build IBMs. This choice was retained since this technique is not

presented in other chapters of this book and because IBMs are of great help when we want to study the

role of individual difference, space, and diversity. With such models, we use what computer scientist would

call a bottom-up approach, since the emergence of ecological properties can be observed from the activity

of individual behavior. Two concrete applications have been presented dealing with stochastic simulations

under spatial constraints (C. taxifolia spreading and biocontrol in the North Mediterranean). However, we

must also warn people that taking this approach, most IBMs rapidly lead to complex simulation programs

(Lorek and Sonnenschein, 1999) and they are only interesting for limited spatial scales (local and regional).

In addition, IBMs need a large amount of attention for the design, development, and debugging (model

veriﬁcation). Software programming and statistical analysis experience is required when dealing with

stochastic simulation programs; interesting tools are presented in Kleijnen and Groenendaal (1992). Lorek

and Sonnenschein present software frameworks designed to help the building of IBMs, most of the time

29-16 Handbook of Dynamic System Modeling

they are built on top of general purpose programming languages, some rely on simulation languages. IBMs

can be extended and linked with many other formalisms in a multimodel (Fishwick et al., 1998; Coquillard

et al., 2000). Whatever the modeling technique, it is important to remember that serious calibration, as a

ﬁrst stage of model validation, can be achieved only if we have collected enough ecological information,

often supposing an extensive ﬁeldwork.

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Ontology-Based

Simulation in Agriculture

and Natural Resources

Howard Beck

University of Florida

Rohit Badal

University of Florida

Yunchul Jung

University of Florida

30.1 Introduction..................................................................30-1

30.2 Ways in Which Ontologies can be Applied to

Simulation.....................................................................30-2

Model Base

•

System Structure (Logical and Physical)

•

Representing Equations and Symbols

•

Connecting

Models with Data Sources

•

Integrating Documentation

and Training Resources

•

Reasoning

30.3 How to Build an Ontology-Based Simulation—

Bioprocessing Example.................................................30-6

Collection of Relevant Documents

•

Deﬁne Model in

Terms of Elements

•

Identifying Classes, Individuals, and

Properties

•

Deﬁne Equations

•

Initial Values of State

Variables, Constants, and Database Access

•

Generating

Program Code for Implementing the Simulation

•

Simulation Execution

30.4 Tools for Ontology-Based Simulation.........................30-10

Ontology Editor

•

EquationEditor

•

SimulationEditor

30.5 Conclusions...................................................................30-12

30.1 Introduction

An ontology is a formal representation of concepts and relationships among concepts within a particular

domain. In this chapter, the domain is models of agricultural and natural resource processes. There are

a vast number of concepts in this domain including abstract entities such as energy, mass, organism,

and mathematical operators (addition and subtraction) and speciﬁc entities such as soil chemicals, plant

components, or a particular plant disease. There are many relationships among these concepts (plant–

water, pest–host). A formal representation is a data structure that describes a concept or relationship and

which is based on a well-deﬁned language. Many different languages have been developed for building

ontologies including the Web Ontology Language known as OWL (OWL, 2005), a W3 standard.

Ontologies languages are object-oriented languages, but they are not programming languages. Ontolo-

gies include objects called individuals that represent particular things in the world (e.g., a particular

soybean crop). Classes categorize similar individuals, and classes can be generalized to superclasses (i.e.,

soybean is a legume) creating a taxonomy of concepts. Individuals have properties that can be primitive

values such as numbers (a soybean crop that has a size of 35 acres) or relationships to other individuals

(the soybean crop is host to several pests).

Because of the formal nature of ontology languages such as OWL, reasoners can be built that perform

inferences over the concepts in an ontology. Such inferences include automatically determining what class

30-1