Comment

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Conservation Biology, Pages 904–906Volume 14, No. 3, June 2000

Expert Systems, Fuzzy Logic, and Coral Reef Development under Environmental Stress

RAYMOND J. O’CONNOR

Department of Wildlife Ecology, University of Maine, Orono, ME 04469–5755, U.S.A.,email oconnor@umenfa.maine.edu

Introduction

Meesters et al. (1998) offer a fuzzy logic model withwhich to predict the development of coral reefs undervarious levels of environmental stress. Their paper bringsseveral innovative elements to the conservation manage-ment of coral reefs but needs to be considered with cau-tion on two grounds. First, although they describe a so-phisticated and innovative implementation of an expertsystem, they misleadingly portray the system as a predic-tive model, with the implication of corresponding capa-bilities. Second, they fail to specify a critical componentof the fuzzy logic process, namely the method used toreach a “crisp” decision when multiple fuzzy rules aretriggered, and this precludes independent repetition ofthe work. Their approach is more likely to find practicalapplications if it is correctly described, with all criticalinformation provided.

Fuzzy Logic Elements

Meesters et al. (1998) were concerned with the predic-tion 10 years hence of two aspects of coral reef condi-tion: the extent of living cover of hard corals and thespecies richness of the reef. These two output or re-sponse variables were known or suspected to be influ-enced by seven predictor or independent variables,namely suspended particulate matter, dissolved inor-ganic nitrogen, soluble reactive phosphorus, availablesubstratum, and current coral colony size, cover, and di-versity. Predictions for such complex systems are typi-cally made via multiple linear regression or response sur-face analysis (Cressie 1991) in which response variablesare modeled as functions of all of the seven predictorvariables and their interactions, possibly with higher-

order terms (such as quadratic or cubic functions) forsome or all of the predictors present. Because each pre-dictor variable is typically continuous, such models areextremely demanding of data. Meesters et al. (1998) of-fer two innovations with which to address this issue.Their first insight was to recognize that predictions ade-quate for management decisions might well be reachedwith coarser data, obtained by “binning” each predic-tor’s values into a small number of interval bins. Binninghas recently emerged as a valuable aid to modeling com-plex systems, especially spatially explicit ones (Carr etal. 1992). For example, if one considers just a bivariatedependence of the response variable, then binning eachof the predictor variables

x

1

and

x

2

into just three inter-vals (low, L; medium, M; high, H) allows only nine com-binations (LL, ML, HL, LM, MM, HM, LH, MH, HH, wherethe bin values are for

x

1

and

x

2

in that order), and esti-mating the appropriate response value for each of thesenine bins is less demanding of data than estimating theparameters to fit a fully elaborated function in

x

1

and

x

2

and their higher powers and interactions. This simplicitycomes, however, at the price of the simplification of re-lationships to the low-medium-high triplets. With eachadditional variable, the number of bins needing esti-mates trebles, to 27, 81, and so forth, with a total of 3

7

5

2187 for the seven variables of the coral reef model.Meesters et al.’s (1998) second insight was to recog-

nize that although values for each variable could be as-signed to one of three bins on the basis of two arbitrarilychosen cut-points for the variable, analysts often differas to choice of cut-points depending on whether theyare focused on the low, medium, or high category. InMeesters et al.’s study, for example, when the “low” cat-egory was defined, colony size had to be

,

0.1 m

2

to bejudged unequivocally “low” in size and had to be

.

0.5m

2

to be unequivocally “not low,” yet when the me-dium category was defined, colony size had to be

,

0.3 m

2

to be judged definitely “not medium” in size.Hence, a colony of 0.4 m

2

was too small to be unequivo-cally “not low” and too large to be unequivocally “not

Paper submitted February 26, 1999; revised manuscript acceptedSeptember 1, 1999.

Conservation BiologyVolume 14, No. 3, June 2000

O’Connor Expert Systems, Fuzzy Logic, and Coral Reefs

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medium.” Meesters et al. (1998) therefore resorted tofuzzy logic to resolve such uncertainties of judgement.Fuzzy logic recognizes that a colony of size 0.4 m

2

, forexample, has a finite chance of being judged as low insize but also a finite chance of being judged medium insize. Where binning is required, however, the 0.4 m

2

value must be assigned to one or another of the low andmedium bins. Fuzzy logic provides formal proceduresfor deciding which to use. Several different fuzzy logicalgorithms are available with which to make such deci-sions; in general they yield different results (Kosko1992), so it is essential to know which method was em-ployed. Meesters et al. (1998), however, omit the criticalinformation about which method they used.

It is also important to realize that once the decisionabout the boundary values to use has been made, fuzzylogic plays no further part in the model formulation: binboundaries have now been determined, and the only re-maining source of variation in the model is the values ofresponse variable to be assigned to any given combina-tion of bin values. That is, in the bivariate exampleabove, all observations of

x

1

and

x

2

must necessarily fallinto one of nine bins, and, because each bin has its ownassociated value of the response variable, there are justnine possible values of the response variable. Meesterset al. (1998) surveyed a range of affected and pristinereefs to determine the empirical ranges of each of theseven predictor variables and ensure the generality oftheir results. It is therefore arguable that the fuzzy limitsreported for each of these variables in their Table 1would have been better replaced with the crisp valueseventually computed. If the method used to obtain crispboundary values is not known, the data presented intheir Table 1 cannot be used to reproduce their “crisp”decisions. (They in fact used the centroid of the summedamplitudes of each fuzzy rule firing; E. Meesters, per-sonal communication).

An Expert System Perspective

According to Meesters et al. (1998), the response valuesattributed to each of the binned cells were set by an iter-ative process of expert judgement and case histories andsubsequent adjustment. For a bivariate case, this meansthat the values assigned to each of the nine bins wereadjusted until experts (and case history data, whereavailable) were in agreement. That is, the model is not apredictive model of the type typically generated by mul-tivariate analysis but is solely a device for organizingdata. For the bivariate case, such a model simply summa-rizes nine rules of the type “if variable

x

1

is low and vari-able

x

2

is high, then experts believe the response vari-able will take the value

Y

” (where

Y

is a number and thedefinitions of low and high have been reached via thefuzzy logic process). Such an organizing structure may

be valuable as a tool for management decisions, but it isill described as a “predictive model.” The distinction be-tween this management aid and a predictive model isblurred by three other elements of Meesters et al.’s(1998) presentation. One is their decision to presenttheir results as smoothed three-dimensional diagrams.The resolution of diagrams such as their Figs. 2–4(which plot a response variable on a vertical z-axisagainst two independent variables on x- and y-axes) canhave in reality at most three values (low, medium, high)on the x- and y-axes and at most nine values (becausethe other five independent variables are constant withinany given plot) on the vertical axes. The mesh overlaidby the smoothing, however, lends the appearance ofmuch greater resolution to the model than is appropri-ate. This practice has been heavily criticized in othercoarse-resolution modeling arenas (e.g., Claussen 1998)because it tends to give to the application predictionsgreater confidence than is warranted by the underlyingcoarse resolution. Second, Meesters et al. (1998:962)also describe their model as yielding “. . . a single exactvalue for each combination of (exact values of) inputvariables . . .,” which is strictly true even if “exact val-ues” are not equated with “crisp values” but which doesnot emphasize that the “single exact value” is the samefor wide ranges of each input value. Such language rein-forces the spurious confidence suggested by the plotspresented. Third, the authors describe the behavior ofthe model—and by implication the coral reef system—inthree paragraphs (beginning at the bottom of p. 962) inthe type of language typically used with statistical orprocess models. In their case, however, all these fea-tures of relationships between response variable and in-dependent variable are there because experts believedthat the system behaved that way. Although the use ofsome case histories goes beyond pure reliance on expertopinion, the model nonetheless does not predict in theusual scientific sense but rather encapsulates a wealth ofreal-world experience. It is, in effect, an expert system.These criticisms are not altered by the seven variable sit-uation needing 2187 combinations, although that com-plexity reinforces its value as an expert system.

In summary, Meesters et al.’s (1998) contribution ismisleadingly described by them as a fuzzy logic model ofcoral reef development. What they present is essentiallyan expert system for organizing knowledge about reefdevelopment under environmental stress. Their systemcontains two noteworthy features, the idea of binningthe input variables to limit the numerical complexityhandled and the clever idea of using fuzzy logic to re-solve uncertainty in how to bin borderline predictor val-ues (once the method of determining crisp values isstated). Their predicted values, however, come largelyfrom expert opinion and not from the empirical data ofa true statistical model. Developing and implementingthe use of such information as an expert system—and

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Expert Systems, Fuzzy Logic, and Coral Reefs O’Connor

Conservation BiologyVolume 14, No. 3, June 2000

especially one with that number of rules—is a signifi-cant contribution to conservation management. Expertsystems, should be recognized as such, however, andthe distinction from conventional ecological modelsshould be maintained if readers are not to be misled.

Acknowledgments

I thank E. Meesters and S. Westmacott for their help inclarifying points arising from their original manuscript. Iam grateful to E. Meesters and M. L. Hunter for review ofa draft of this manuscript.

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Cressie, N. 1991. Statistics for spatial data. Wiley, New York.Kosko, B. 1992. Neural networks and fuzzy systems. Prentice-Hall, En-

glewood Cliffs, New Jersey.Meesters, E. H., R. P. M. Bak, S. Westmacott, M. Ridgley, and S. Dollar.

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