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ava i l ab l e a t www.sc i enced i rec t . com

www.e l sev i e r. com/ l oca te /eco l econ

ANALYSIS

Differences and similarities between ecological and economicmodels for biodiversity conservation

Martin Drechslera,⁎, Volker Grimma, Jaroslav Mys ̌iakb, Frank Wätzoldc

aUFZ Centre for Environmental Research Leipzig-Halle GmbH, Department of Ecological Modelling, GermanybFondazione Eni Enrico Mattei, Palazzo Querini Stampalia, Campo S. Maria Formosa, Castello 5252, 30122 Venezia FEEM, ItalycUFZ Centre for Environmental Research Leipzig-Halle GmbH, Department of Economics, Germany

A R T I C L E I N F O

⁎ Corresponding author. Permoserstr. 15, 0431E-mail address: martin.drechsler@ufz.de (M

0921-8009/$ - see front matter © 2006 Elsevidoi:10.1016/j.ecolecon.2006.03.026

A B S T R A C T

Article history:Received 14 March 2005Received in revised form14 March 2006Accepted 15 March 2006Available online 27 June 2006

In this paper we investigate an important obstacle which substantially complicates co-operation between ecologists and economists but which has received little attention so far:differences between the modelling approaches in economics and ecology. To understandthese differences, 60 models addressing issues relevant to biodiversity conservation havebeen selected randomly from eight international economic and ecological journals. Themodels have been compared according to a number of criteria including themodels' level ofgenerality; the mathematical techniques employed for formulation and solution of themodels; the level of complexity and the way time, space and uncertainty are taken intoaccount. The economic models sampled are formulated and analysed analytically, tend tobe relatively simple and aremostly used to investigate general questions. Furthermore, theyoften ignore space, dynamics and uncertainty. Although some ecological models havesimilar properties, there is also a substantial number of another type of ecological modelsthat are relatively complex and analysed by simulation. These models tend to be ratherspecific and often explicitly consider dynamics, space and uncertainty. The integratedecological–economic models are observed to lie “in the middle” between ecological andeconomic models. An unexpected result is that they are not more complex than ecologicaland economic models (as one could have expected from a simple “merger” of models fromboth disciplines), but have an intermediate complexity.

© 2006 Elsevier B.V. All rights reserved.

Keywords:Ecological–economic modellingModellingBiodiversityConservation

JEL classification:B40,C60,Q57

1. Introduction

Over the past two decades, models have become importanttools for aiding decisions related to the conservation ofbiodiversity. Ecological models are frequently used to predictand assess the outcomes of conservation measures andecosystem management strategies (cf. for example Burgmanet al., 1993; Beissinger and Westphal, 1998; Jeltsch et al., 1999;

8 Leipzig, Germany.. Drechsler).

er B.V. All rights reserved

Frank and Wissel, 2002; Leslie et al., 2003). These efforts havebeen greatly facilitated by advances in computer technology,allowing models to be developed with sufficient complexity toanalyse how measures and management strategies affect thespatiotemporal dynamics of ecosystems. Despite theseadvancements, however, the practical use of ecologicalmodels for evaluating and improving conservation policieshas often been limited as they tend to neglect the economic,

.

1 Please note that models in theoretical and applied ecology aredifferent and that we have chosen journals that focus on appliedecology.2 Ecological Economics is as a transdisciplinary journal rather than

a purely economic one. It was nevertheless chosen because icontains a large number of economic models related to biodi-versity conservation.

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institutional and political dimensions related to conservation.This is the realm of economic models which are today alsoquite often used to analyse biodiversity conservation pro-blems (cf. for example Swanson, 1994; Skonhoft, 1998; Smithand Shogren, 2002; Bulte and Horan, 2003). However, just asecological models ignore or oversimplify the economic,institutional and political dimension of conservation, eco-nomic models often use oversimplified assumptions regard-ing the ecological effects of conservation measures or, aspointed out by Sanchirico and Wilen (1999), assumptions thatare outdated from the point of view of ecological theory.

Given that both ecologists and economists use models withapparent limitations complementary to each other, it seemsreasonable to combine them into integrated ecological–econo-mic models which are able to overcome the respective dis-ciplinary limitations (Perrings, 2002). Indeed, over the past fewyears, the number of ecological–economic models addressingissues relevant for biodiversity conservation has increasedconsiderably (cf. for example, Ando et al., 1998; Richards et al.,1999; Johst et al., 2002; Baumgärtner, 2004; Holden and Shiferaw,2004; Perrings and Walker, 2004; Wätzold and Drechsler, 2005).

Although its benefits are well recognised, ecological–eco-nomicmodelling is still far frombeing anestablishedapproach.A possible reason may be general barriers complicatinginterdisciplinary environmental research (e.g., that disciplinaryresearch is generally more rewarding in terms of careerprospects than interdisciplinary research). Suchanexplanationis certainly plausible but does not consider an intricacyinherent to ecological–economic modelling which substantial-ly complicates the co-operation between ecologists andeconomists and has received little attention so far: differencesin modelling approaches between economics and ecology.

Since mathematical models are a common tool of researchin both disciplines, it is often implicitly assumed that they caneasily be combined. Such an assumption, however, neglectsthat differentmodels andmodelling approaches exist and thatsuch differences may make a combination difficult or evenimpossible. Models may differ in various ways including levelof generality, mathematical technique that is employed forthe formulation and solution of the model, and considerationof real world phenomena such as time, space and uncertainty.

The aim of this paper is to identify possible differences andsimilarities between ecological and economic modellingapproaches. By making the differences between economic andecological models explicit we aim to reduce communicationproblems thatmay arise if economists and ecologists talk about“models” and believe they mean the same but in fact think ofsomething different. Furthermore, making differences explicitmay also facilitate the search of economists and ecologists formodelling approaches suitable for an integrated analysis.

To enhance our understanding of modelling approaches inecology and economics we carried out a literature survey andcompared 60models that address issues relevant to biodiversityconservation. All models were selected randomly from eightinternational journals from both disciplines and classified aseither “ecological” or economic” or “ecological–economic”. Themodels were evaluated according to a number of criteria thatwere chosen to capture essential differences inmodel purpose,structure, designand analysis, and, finally, the outcomes for thethree mentioned classifications were compared.

The paper is structured as follows: Section 2 explains howmodels were selected and classified and presents the criteriachosen to evaluate and compare the models. Section 3 pre-sents the results including a comparison of the classifiedmodels by the various criteria and an analysis of possible rela-tionships between the criteria to better understandwhymodelsin a particular category have particular properties. The paperconcludes with a summary and discussion of the results inSection 4.

2. Methods

2.1. The data base

In ecology, the following four leadingconservation journalswereselected: Biological Conservation, Conservation Biology, EcologicalApplications, and Journal of Applied Ecology.1 All papers from theyears 1998 to 2003 containing the words ‘model’ or ‘model(l)ing’in either the title, abstract or keyword listwere filtered. Fromtheresulting papers, 30 were selected randomly for detailedevaluation (see Appendix A1). Papers presenting descriptive,statistical models were not selected because similarities instatistical methods might mask differences between ecologicalandeconomicalmodels. Statistics is auniversally applicable toolfor data analysis accepted in ecology and economics (as well asnumerous other disciplines like medicine or astronomy) and,hence, similarities between statistical models do not tell muchabout the modelling attitudes in the individual disciplines. Ofthe economic journals, Environmental and Resource Economics,Journal of Environmental Economics andManagement, LandEconomicsand Ecological Economics2 were chosen. All papers from the years1998 to 2003 quoting biodiversity, conservation, nature protec-tion or species in the abstract or title and applying amathemat-ical modelling approach were identified and — as with theecological journals— 30 papers were selected at random, againignoring statistical and econometric models (see Appendix A2).

Each of the obtained 60 models was assigned into one ofthe three categories “predominantly ecological”, “predomi-nantly economic”, and “ecological–economic”. Such an as-signment is not easy, because it is generally difficult to draw aline between a ‘disciplinary’ model and an ‘ecological–eco-nomic’ model. Various papers that were reviewed are clearlydominated by one discipline but also contain elements fromthe other (e.g. an ecological paper which contains a cost anal-ysis as a sub-component of an otherwise ecological model).However, classifying such a model as ‘ecological–economic’would be inappropriate as knowledge from the non-dominantdiscipline is only taken into account to a very limited extent.Instead of a clear distinction between disciplinary and ecol-ogical–economic models, there is evidently a continuum andan arbitrary line has to be drawn somewhere. Bearing this in

t

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mind, we chose a two step approach to distinguish between thedifferent categories ofmodels. In the first step,wedifferentiatedbetween purely disciplinary models which do not contain anyknowledge from the other discipline and other models. For thesecond step, we screened the papers containing models of thelatter type and categorised those as ecological–economic whenthe paper included references to journals from both disciplines.The choice for such references as an indicator for ecological–economic models was motivated by the assumption thatbuilding ecological–economic models requires in-depth knowl-edge from both disciplines and that such knowledge is usuallyacquired through a careful reading of the disciplinary literature.We excluded references to more general journals that containeconomic as well as ecological and integrated papers, such asScience, Nature and Ecological Economics.

The classification led to 30 ecological, 12 economic and 18ecological–economic models which form the data base of theanalyses. As it is the purpose of this paper to identify generaltrends rather than to provide exact statistical results the sizeand structure of the data base are sufficient. The models arenow evaluated with regard to a number of criteria.

2.2. Purpose of the model

The considered criteria are

• General model = {yes or no}• Specific model (case study) = {yes or no}

Models may have different purposes. We distinguish be-tween models that try to explain general phenomena andmodels designed for specific situations. We classify the mo-dels by the kind of data used in them. General models may becompletely hypothetical or use observations and data to ex-clude unrealistic settings, but the models are not parame-terised for specific cases; in contrast, specific models use datarelated to specific situations. Both of these criteria are eval-uated independently, because some of the general modelsare parameterised for a specific situation. These models arecounted as general and as specific.

2.3. Criteria describing model formulation, solution andcomplexity

The considered criteria are

• Model formulation = {analytical or algorithmic}• Model solution = {analytical or numerical or by simulation}• Number of model parameters

Models are characterised by the way they are formulatedand how results are obtained. We make the followingdistinctions: the formulation may be analytical (the model iscompletely described by equations), or algorithmic (flowcharts or if-then rules are needed to describe the model).The results of analytical models are obtained either analyti-cally (e.g. by solving equations for equilibrium solutions), nu-merically (e.g. by determining eigenvalues in a matrix model),or through simulation (e.g. by simulating the dynamics of apopulation time step by time step); algorithmic models are

always run on a computer, i.e. they are solved throughsimulation. Numerical methods are distinguished from simu-lations by the fact that simulations try to mimic a real processwhereas numericalmethods approximate analytical solutionsof analytical models.

Modelling approaches may differ in terms of the model'scomplexity. An obvious indicator of model complexity is thenumber of parameters. For the purpose of the present analysiswe consider a parameter a numbermediating the relationshipbetween state variables. State variables measure or character-ise the state of the system modelled, such as the size of apopulation. A parameter here may be the growth rate of thepopulation that determines how the population size changesfrom this year to the next. Parameters are constant during therun of a model or for the analysis of a certain model scenario.Sometimes parameters are not known with certainty and tocope with this uncertainty frequency distributions are used.Or, relationships between state variablesmay be described notby single numbers but graphically by curves. The properdescription of the shape of such frequency distributions orcurves may require more than one parameter. For simplicity,we generally assume a number of two parameters in thesecases (representing, e.g., mean and variance of a frequencydistribution, or slope and offset of a straight line).

2.4. Consideration of uncertainty, time and space

The considered criteria are

• Uncertainty is considered = {yes or no}• Model is dynamic = {no, or yes with continuous time, or yes withdiscrete time}

• Model considers space = {no, or yes being spatially differenti-ated, or yes being spatially explicit, or yes being both spatiallydifferentiated and explicit}

In modelling one often has to deal with uncertainties ofvarious types which are included, e.g., through stochasticdifferential equations, probability density functions, sensitiv-ity analysis, etc. (see, e.g., Brown, 2004). While a detailedreview and comparison of these approaches is beyond thescope of the present paper, we simply record whetheruncertainty is taken into account or not.

In addition touncertainty, consideration of time and space isa decisive characteristic of a model. We differentiate betweendynamic and static models. In a dynamic model, time isexplicitly considered, whereas this is not the case in a staticmodel. Models that only investigate equilibria are counted asstatic, as the dynamics of the system are not consideredexplicitly. In order to classify a model as a dynamic model thestate variable(s) has/have to be calculated for different points intime in a single model run. Within the dynamic models wedistinguish betweenmodels that consider time in a continuousmanner and models that consider time in a discrete manner.

We distinguish between three classes of models that takeinto account physical space to varying degrees. For a model tobe considered as ‘spatially explicit’, state variables must existwhich explicitly refer to space, i.e. co-ordinates in thelandscape. This includes the explicit consideration of topo-logical relations (e.g. neighbourhood), direction, distances and

Fig. 1 –Percentage of reviewed economic, ecological andecological–economic models that address general or specificproblems. Note that a model may address both kinds ofproblems.

3 We are aware that computational models are increasinglyapplied in some fields of economics (e.g. Judd, 1997), but they aremuch less common than in ecology and are practically non-existent in the economic analysis of biodiversity conservation.

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distance-dependent interactions between state variables atdifferent locations. Typical examples are cellular automatawith, for example, next neighbour interaction. In a ‘spatiallydifferentiated’ model, parameters differ between patches ofland. However, the location of the patches is not considered.Examples include economic models with two or more regions,whose locations are irrelevant in the analysis, and in par-ticular, whose interactions are not distance-dependent. Mod-els that are both spatially differentiated and spatially explicitform the third class of spatial models. Models which arespatially explicit but not spatially differentiated consider ahomogeneous environment so that heterogeneities only canarise due to the interaction of model entities. An example isConway's famous ‘Game of Life’ (Gardner, 1970).

For each of the three model categories, ecological, eco-nomic and ecological–economic, the proportion of modelsfalling into a particular class (e.g., formulated analytically,being spatially explicit, etc.) is recorded. In a few cases modelsmay not be uniquely assigned to a particular criterion. Forinstance, a model may be solved partly analytically and partlynumerically. In this case it is counted both as analytical andnumerical. Alternatively, from the description of the model inthe paper it may be impossible to decide on a certain char-acteristic. For instance, it may be unclear whether themodel issolved numerically or through simulation. In such a case, themodel is counted half as numerical and half as simulation.

2.5. Relationships between criteria

To gain a deeper understanding of the differences between themodels, relationships between criteria are identified. Forinstance, models with many parameters might be more likelyto be spatially explicit thanmodels with few parameters. Suchinformation allows a further categorisation within the classi-fication into ecological, ecological–economic and economicmodels. To find these relationships between criteria weconsider the ecological, ecological–economic and economicmodels separately and for each set determine the correlationbetween the criteria.

In the present analysis we have a mixture of nominalscaled (e.g., the classification into dynamic or static) andordinal criteria (the characterisation of models by the numberof parameters). In such a case the ordinary correlationcoefficient cannot be applied. Instead we perform a contin-gency analysis (Clauβ and Ebner, 1978). Due to the presence ofan ordinal criterion such a contingency analysis leads tounique results only if all criteria are dichotomic, such that amodel either falls into a particular class (e.g., dynamic) or not.Therefore for the contingency analysis we reformulate allabove criteria into dichotomic ones (Table B1 in Appendix B).

Basically, the contingency analysis is a χ2 test, whichmeasures whether the observed relationship between twocriteria is significantly higher than what would be expected ifnumbers were distributed randomly (Appendix B).

A contingency analysis does not tell whether the relation-ship between two criteria is positive or negative. As our criteriaare dichotomic, the sign of the relationship can be identifiedeasily in another analysis: in the comparison of two criteria wecount the number of models that give the same result in bothcriteria (either true or false) and the number of models which

give opposite results (one is true and the other one is false). Ifthe former count is above/below the latter, there is a positive/negative relationship between the two criteria, which meansthat if a model fulfils one criterion it will be likely/unlikely tofulfil the other criterion, too.

3. Results

3.1. Model purpose

Nearly all economic models analysed (92%) are of a generalnature (Fig. 1). However, approximately one fourth of themodels (25%) are also specific. Here, some real world data areusually inserted in themodel and themodel is used to explain,predict or analyse a certain empirical phenomenon. In con-trast, only 40% of the ecological models analysed are general,whereas a largemajority (83%) has a specific character. On theother hand a large majority of ecological–economic modelshaveboth a general (89%) anda specific character (78%).We seethat the prevalent model purpose is different in the economicand ecological models of our sample and that the ecological–economic models tend to combine both approaches.

3.2. Model formulation, solution and complexity

The ways in which models of the three categories are for-mulated and solved are shown in Fig. 2. While all economicmodels of our sample are formulated analytically, a significantproportion (26%) of the ecological models is formulated algo-rithmically. This means that there is some common groundbetween ecology and economics in the form of analyticalmodelling, but that one approach — algorithmic modelling —that is quite common in the ecological models investigated isnon-existent in the set of economic models.3 Even larger

Fig. 2 –Percentage of reviewed ecological, economic andecological–economic models that have an analytical oralgorithmic formulation (a) and are solved analytically,numerically, or via simulation (b).

Fig. 3 –Percentage of papers of a certain type (ecological,economic, and ecological–economic models) that includemodels with a certain number of parameters.

Fig. 4 –Consideration of time in ecological, economic, andecological–economic models.

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differences exist regarding the solution techniques applied inthe two disciplines. All economic models reviewed are solvedanalytically, whereas only a comparatively small fraction ofthe ecological models (17%) choose this approach. The largemajority of the ecological models are solved either numeri-cally (30%) or through simulation (53%). The percentages forthe ecological–economic models lie quite well in the middlebetween those for the ecological and the economic models.

Model complexity was measured by the number of modelparameters and this was found to be on average higher inecological (16.5) than in ecological–economic (11.9) andeconomic (8.8) models (cf. Fig. 3).

The main reason for the different number of parametersbetween ecological and economic models is that next to asubstantial number of rather simple ecological models thesample contains some very complex models with a largenumber of parameters (7 out of the 30 ecological models havemore than 30 parameters and 5 more than 50 parameters,whereas none of the economic models has more than 15parameters). Ecological models tend to havemany parameterswhen they address communities of many different species(Köhler et al. 2002), or when they consider in detail manydifferent behaviours (Pettifor et al. 2000).

3.3. Consideration of uncertainty, time and space

Uncertainty is considered in 50% of the economic modelssampled. It is more frequently taken into account in theecological–economic models (66%) and in nearly all ecologicalmodels (97%).

Similarly, a substantial majority of the ecological (74%) andecological–economic models (85%) are dynamic while this istrue for only half of the economic models (Fig. 4). In all threecategories there are more models with discrete time stepsthan continuous models. The only difference (not shown inFig. 4) is that time-discrete economic models often use anabstract time (periods) while time-discrete ecological modelshave a physical time (mostly years, but also hours or decades).

Most of the economicmodels (75%) sampled donot explicitlyconsider space (Fig. 5). If space is considered, only spatiallydifferentiated models are applied. By contrast, a significantshareof theecologicalmodels (33%) is both spatially explicit and

Fig. 5 –Consideration of space in ecological, economic, andecological–economic models.

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differentiated. A smaller percentage is spatially differentiated(13%) while 53% of the models do not explicitly consider spatialaspects. The fact that none of the ecological models in oursample are spatially explicit but not differentiatedmeans that ifspace is considered explicitly then also a heterogeneous envi-ronment is considered. Similar to the ecological models, abouthalf of the ecological–economicmodels consider space and theydo so more or less equally distributed in a differentiated, ex-plicit, or differentiated and explicit manner. Here, a certainfraction of models (17%) exists which is spatially explicit butdoes not consider environmental heterogeneity.

3.4. Relationships between criteria

The above results indicate that the economic models in oursample form a relatively homogenous group: all of them areformulated and solved analytically, most of them are generaland not specific; they have a relatively small number ofparameters, mostly do not consider space, and only half ofthem are dynamic and consider uncertainty. In contrast, theecological and ecological–economic models in the sampleform a less homogenous group than the economic models.Therefore we take a closer look at these models.

Table B2 in Appendix B shows the signs of the significantcontingencies (“correlations”) between the criteria in the set of30 ecological models of our sample. Some of them are trivial,because the criteria are mutually exclusive (for instance, amodel that is formulated analytically cannot be formulatedalgorithmically at the same time). The significant non-trivialcontingencies are:

• Models formulated algorithmically (analytically) have more(less or equal) than 15 parameters and are (not) spatiallyexplicit.

• Models solvedanalyticallyornumericallyhaveasmallnumberof parameters, are general, not specific and not dynamic.

• Models solved by simulation have a large number ofparameters, are specific and not general, are dynamic withdiscrete time and consider space.

• Models with less than five parameters have continuous time.

Similar to Table B2, Table B3 shows the correlations for the18 ecological–economic models in our sample. The significantnon-trivial correlations are

• Analytical models are general.• Algorithmic models are solved by simulation, are not

general and are spatially explicit.• Models with 5 or fewer parameters are solved analytically.• Simulation models are dynamic with discrete time.• Uncertainty isnotconsideredinmodelswithcontinuous time.• Models with relatively few parameters do not consider space.

From these observations we can classify each of the sets ofecological and ecological–economic models into two classes:the first class, termed “simple models” contains the analyticaland general models that have few parameters, are static orcontinuous in time, often deterministic, and do not considerspace; the models in the second class, termed “complexmodels” have many parameters, are not general but dynamicwith discrete time and explicit consideration of space.

This distinction is very similar to that derived from thecomparison between ecological and economic models. Alto-gether, we can observe “simple”models among the ecological,ecological–economic and economic models while the “com-plex models” are found among the ecological and ecological–economic models only. The proportion of complex models ishigher among the ecological models than among the ecolog-ical–economic models.

4. Discussion

We compared 60 ecological, economic and ecological–economicmodels related tobiodiversity conservationemployinga rangeofcriteria describing the models' purpose, design, structure andanalysis. While some common ground exists significant differ-ences are to be observed in themodelling approaches of the twodisciplines economics and ecology. Generally speaking, eco-nomicmodels tend to be general and are formulated and solvedanalyticallywhereas ecologicalmodels tend to be specific and—while the majority of models is formulated analytically — asignificant fraction is formulatedalgorithmically. Inaddition, theecological models that are formulated analytically are mostlysolved numerically or through simulation. Another importantdifference between the two disciplines is that ecological modelsexplicitly take into account time, uncertainty and space to amuch larger extent than economicmodels. Moreover, if they arespatial, economic models are usually spatially differentiated(e.g., two regions with different conditions) while ecologicalmodels are often spatially explicit (locations and sizes of regionsconsidered explicitly), an approach which does not exist in theeconomicmodels of our sample.

Since models are a common tool of research in economicsand ecology, it is often implicitly assumed that they can easilybe combined. By making the differences between economicand ecologicalmodels explicit we hope to have helped to avoidmiscommunication that may arise if economists and ecolo-gists talk about “models” and believe they mean the same butin fact think of something different. The question that arisesfrom the analysis of this paper is, of course: What are the

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reasons for the differences between economic and ecologicalmodels? Increased understanding would improve the abilityto determine the appropriate approach for ecological–eco-nomic models (Wätzold et al., in press). A thorough treatmentof this question is beyond the scope of this paper and shouldbe a matter of further research. We offer five possible reasonsas a starting point for this research:

(1) Different disciplinary traditions: The two disciplines haveevolved historically in a differentmanner.While in bothdisciplines analysis of real-world observations as wellas theoretical reasoning and mathematics play impor-tant roles, the former approach appears to have beenmore influential in the development of ecology whiletheoretical reasoning and mathematics were moreinfluential in economics.

(2) Differences in the systems analysed: Ecological and eco-nomic systems may be structured differently. It mightbe, for instance, that spatial heterogeneity has lessinfluence on the dynamics and the functioning of aneconomy than on the dynamics and the functioning ofan ecosystem. This implies that in ecology there is astronger tradition of taking into account spatial hetero-geneity than in economics.

(3) Differences in the perception of the system analysed: Ecolog-ical and economic systems might not be dissimilar instructure per se, but they might be perceived differentlyby the researchers or certain features are given differentdegrees of relevance. Economists might, e.g., view theirsystems as being usually in an equilibrium state thatonly occasionally changes due to some shocks. Ecolo-gists in contrast, might view their systems as constantlychanging (Walker et al., 2004).

(4) Varying personal preferences of researchers: Various ecolo-gists have chosen their discipline, because they love thediversity and complexity of nature, animals and plantsand want to understand it. Such a personal backgroundmay lead to the desire of including all this richness ofecological systems in amodel. Economists may be ratherinterested in the general understanding of economicsystems. Furthermore,manyeconomists seemtohaveanaffinity to mathematics. They might then prefer thoseresearch questions that can be expressed as mathemat-ical problems and solved with mathematical methods.

(5) Models serve different purposes: In the philosophy ofscience a number of modelling purposes have beenidentified such as making predictions, learning about aphenomenon, and communicating a preconceivedmessage. Ecologists might use models more often forpredictions whereas economists might use them moreoften for learning or communication.

Whatever the reason behind the differences between eco-logical and economic models, presently the answer to ecologistHall's (1988) question “What constitutes a good model and bywho's criteria?” is likely to be different among economists andecologists: in economics, themajority ofmodellers prefer simplemodels which are analytically tractable; specific data, details ofspace, dynamics and uncertainty are sacrificed to the overallaim of analytical tractability. Thus, most economists probably

would rank a simulation model with more than 10 parametersand with reference to specific systems rather low. In contrast,many ecologists would be very sceptical of a simple modeladdressing real systems; yet, they would accept simple modelsas a tool to address general problems and concepts.

The general lesson from this is that economists who startthinking about developing ecological–economic models haveto be prepared that they might be involved in complexmodelling not typical and possibly less respected in econom-ics. On the other hand, ecologists starting collaborations withmodellers from economics have to be aware that in economicsanalytical tractability is much higher valued and simplemodels are more dominant than in ecology.

The considerable share of ecological–economic models inour sample is encouraging, as it indicates that the integrationof ecology and economics through modelling is possible.Regardingmost criteria that we evaluated, existing ecological–economic models lie in between the ecological and economicmodels. In particular, the complexity of ecological–economicmodels is not higher than that of disciplinary models (as onecould have expected from a naïve “merger” of models), but liesin between that of ecological and economic models. Thisshows that richer models, combining the two disciplines, canbe built without excessively increasing model complexity.Another remarkable observation is that in ecological–eco-nomic modelling, simple and complex models coexist to asimilar extent as in ecology. This is a promising finding,because most ecologists to date agree that the coexistence ofsimple and complex models is productive (Grimm and Rails-back, 2005, chapter 11).

Acknowledgments

Wewould like to thank Stefan Baumgärtner, Flemming SkovandNickHanley for valuable comments on themanuscript, andHans–Hermann Thulke for advice regarding the statistics.

Appendix A. Papers reviewed

A.1. Papers analysed from ecological journalsAanes, S., Engen, S., Sæther, B.-E., Willebrand, T., Marcström,V. (2002) Sustainable harvesting strategies of Willow Ptarmi-gan in a fluctuating environment. Ecological Applications 12/1,281–290.

Baron, J.S., Hartman, T.G., Kittel, T.G.F., Band, L.E., Ojima,D.S., Lammers, R.B. Effects of land cover, water redistribution,and temperature on ecosystem processes in the South PlatteBasin. Ecological Applications 8/4, 1037–1051.

Baillie, S.R., Sutherland, W.J., Freeman, S.N., Gregory, R.D.,Paradis, E. (2000) Consequences of large-scale processes forthe conservation of bird populations. Journal of AppliedEcology 37 (Suppl. 1), 88–102.

Cabeza, M., Moilanen, A. (2003) Site-selection algorithmsand habitat loss. Conservation Biology 17/5, 1402–1413.

Carpenter, S.R., Ludwig, D., Brock, W.A. (1999) Managementof eutrophication for lakes subject to potentially irreversiblechange. Ecological Applications 9/3, 751–771.

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Clark, M.E., Rose, K.A., Levine, D.A., Hargrove, W.W. (2001)Predicting climate change effects on Appalachian trout:combining GIS and individual-based modelling. EcologicalApplications 11/1, 161–178.

Couvet, D. (2002) Deleterious effects of restricted gene flowin fragmented population. Conservation Biology 16/2 369–376.

Cuarón, A.D. (1999) Effects of land-cover changes onmammals in a neotropical region: a modelling approach.Conservation Biology 14/4, 1676–1692.

Drechsler, M., Wissel, C. (1998) Trade-offs between localand regional scale management of metapopulations. Biolog-ical Conservation 83/1, 31–41.

Fenton, A., Gwynn, R.L., Gupta, A, Norman, R., Fairbairn, J.P.,Hudson, J. (2002) Optimal application strategies for entomo-pathogenic nematodes: integrating theoretical and empiricalapproaches. Journal of Applied Ecology 39, 481–492.

Foley, J.E., Foley, P., Pedersen, N.C. (1999) The persistence ofa SIS disease in a metapopulation. Journal of Applied Ecology36, 555–563.

Harding, E.K. (2002) Modelling the influence of seasonalinter-habitat movements by an ecotone rodent. BiologicalConservation 104, 227–237.

Haydon, D.T., Laurenson, M.K., Sillero-Zubiri, C. (2001)Integrating epidemiology into population viability analysis:managing the risk posed by rabies and canine distemper to theEthiopian wolf. Conservation Biology 16, 5, 1372–1385.

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240 E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 2 3 2 – 2 4 1

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Appendix B. The contingency analysis

To obtain the χ2 for the relationship between two criteria,e.g., between “the model is general”, and “the model isdynamic”, it is counted how many models of the set fulfilboth criteria (true/true), how many fulfil only the formercriterion (true/false), how many fulfil only the latter (false/true), and how many fulfil none of them (false/false). Thesecounts may be denoted as t11, t10, t01, and t00, respectively.Let z0= t00+ t01, z1= t10+ t11, s0= t00+ t10, and s1= t01+ t11, ands= t11+ t10+ t01+ t00. With f11=z1s1/s, f10=z1s0/s, f01=z0s1/s andf00=z0s0/s we obtain

v2 ¼X

i;j¼0;1

ðtij−fijÞ2fij

which measures the deviation of the tij from random values.To be statistically significant, the calculated (empirical) valueof χ2 has to exceed χcrit2 which in our case amounts to 3.8 (χ2

for 1 degree of freedom, α=5%).The strength of the correlation is strictly monotonically

related to χ2 and given by [(χ2 / (χ2+n)]1/2 where n is the numberof elements in the set (Clauβ and Ebner, 1978). For n=30 (18),the critical χcrit2 =3.8 corresponds to a correlation of 0.34 (0.42)on a scale between zero and one.

Table B1: List of 17 dichotomic criteria which for eachmodel are either true or false

No.

Dichotomic criterion

1

Model is formulated analytically 2 Model is formulated algorithmically 3 Model is solved analytically 4 Model is solved numerically 5 Model is solved by simulation 6 Model considers uncertainty 7 Number of parameters is ≤5 8 Number of parameters is ≤10 9 Number of parameters is ≤15 10 Model is general 11 Model is specific 12 Model is dynamic 13 Model is dynamic with discrete time 14 Model is dynamic with continuous time 15 Model considers space 16 Model is spatially differentiated 17 Model is spatially explicit (according to above definition)

Note that clearly not all criteria are statistically independent, whichhowever is not a problem in the pair-wise analysis of contingencies.

Table B2: The signs of the contingencies between the 17criteria of Table B1 which are significant at the 5% level

2 3

4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 − + − 2 − + 3 − + + 4 − + + + − − − 5 − − − + + + + + + 6

Table B2 (continued)

241E C O L O G I C A L E C O N O M I C S 6 2 ( 2 0 0 7 ) 2 3 2 – 2 4 1

2 3

4 5 6 7 8 9 10 11 12 13 14 15 16 17 7 + + 8 + 9 − − − 10 − 11 + + 12 + 13 − + + 14 15 + + 16 +

The analysis is based on the set of all ecological models. Each rowand column represents one criterion.

Table B3: The signs of the contingencies between the 17criteria of Table B1 which are significant at the 5% level

2 3

4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 − + 2 + − + + 3 − 4 5 − + 6 − 7 8 + − − − 9 − 10 − 11 12 + 13 − 14 15 + + 16

Trivial/non-trivial correlations are represented by small/largesymbols. The analysis is based on the set of all ecological models.Each row and column represents one criterion.

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