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THE PURPOSE AND JUDGEMENTS OF BIOLOGICAL CLASSIFICATIONS W. GRANT INGLIS Abstract Inglis, W. Grant (South Australia Museum, Adelaide, Australia) 1970. The purpose and judgements of biological classifications. Syst. Zool., 19:240-250.—Biological classifications are judged by assessing their predictive value against the co-variance of character-states in organisms not previously studied or against the classification of some character-states not previously studied in the organisms classified. As a corollary, taxonomists, judging by their published work, aim to produce that classification which maximises the concordance of the classifications of single characters or, put another equivalent way, which maximises the character correlations of the organisms being classified. Such classifications are then assumed to be inductive and, therefore, predictive and this predictive content is tested. It is argued that the sole operational aim of taxonomy is the production of maximally concordant, and so predictive, classifications which can be explained by the fact of evolution. The reversal of this explanatory role wherein it is claimed that phylogenies can be studied by erecting such classifications has obscured rather than clarified discussion of classification. It is further argued that because all the characters in a given organism are not correlated some weighting of characters is inevitable in producing general classifications and that the taxi- metric approach has obscured the discussion of classification by erecting a series of axioms which make the testing of any classification depend upon the method by which it was constructed rather than upon the form of the classification itself. It is frequently argued that any classifica- tion must have a purpose while Mayr (1966) has made the point that some way of judg- ing the "goodness" of biological classifica- tions is needed. Both these points are well taken but deal with the same question since it is only possible to judge one classification relative to another if the aims or purposes of the classifications are known, and if they are known to be the same. To dismiss one classification as less phylogenetic, or phene- tic or natural than another (even if the other is only implied) is not satisfactory because it converts to an argument on method and underlying philosophy which becomes cir- cular. Thus, classification x is better than classification y because it was obtained by using method z which we know is a better method than any other method because it produced classification x which is obviously better than classification y because it was obtained by using the method z. Thus the argument is that the method tests the re- sult: the result does not test the method. Nevertheless, in practice, some way of judging classifications must exist since they are continually being altered and changed. In some cases the changes are considered retrograde, but this implies a judgement, while others are generally accepted as an improvement. Therefore taxonomists not only judge classifications but are frequently in agreement about the result of the judge- ment. The very fact that such judgements are made, and that there can be agreement with the verdicts, further implies that there is not only some aim in producing classifica- tions but that that aim is well known, or at least widely accepted. In addition to this is the known fact, frequently commented on, that it is usually impossible to tell by inspecting a classifica- tion to which school of methodology, or philosophy its constructor adheres. As a corollary, it can be said that the same clas- sification appears irrespective of the claimed beliefs of its constructor which suggests that classifications are produced in the same way although the methods are described in dif- ferent ways. Thus the two great revolutions in biological classification, the post-Dar- winian phase and the New Systematics, have had little practical result (Heywood, 1964) while, in spite of vociferous claims 240 at Russian Archive on December 22, 2013 http://sysbio.oxfordjournals.org/ Downloaded from

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THE PURPOSE AND JUDGEMENTS OFBIOLOGICAL CLASSIFICATIONS

W. GRANT INGLIS

AbstractInglis, W. Grant (South Australia Museum, Adelaide, Australia) 1970. The purpose and

judgements of biological classifications. Syst. Zool., 19:240-250.—Biological classificationsare judged by assessing their predictive value against the co-variance of character-states inorganisms not previously studied or against the classification of some character-states notpreviously studied in the organisms classified. As a corollary, taxonomists, judging by theirpublished work, aim to produce that classification which maximises the concordance of theclassifications of single characters or, put another equivalent way, which maximises thecharacter correlations of the organisms being classified. Such classifications are then assumedto be inductive and, therefore, predictive and this predictive content is tested. It is arguedthat the sole operational aim of taxonomy is the production of maximally concordant, andso predictive, classifications which can be explained by the fact of evolution. The reversalof this explanatory role wherein it is claimed that phylogenies can be studied by erectingsuch classifications has obscured rather than clarified discussion of classification. It isfurther argued that because all the characters in a given organism are not correlated someweighting of characters is inevitable in producing general classifications and that the taxi-metric approach has obscured the discussion of classification by erecting a series of axiomswhich make the testing of any classification depend upon the method by which it wasconstructed rather than upon the form of the classification itself.

It is frequently argued that any classifica-tion must have a purpose while Mayr (1966)has made the point that some way of judg-ing the "goodness" of biological classifica-tions is needed. Both these points are welltaken but deal with the same question sinceit is only possible to judge one classificationrelative to another if the aims or purposesof the classifications are known, and if theyare known to be the same. To dismiss oneclassification as less phylogenetic, or phene-tic or natural than another (even if the otheris only implied) is not satisfactory becauseit converts to an argument on method andunderlying philosophy which becomes cir-cular. Thus, classification x is better thanclassification y because it was obtained byusing method z which we know is a bettermethod than any other method because itproduced classification x which is obviouslybetter than classification y because it wasobtained by using the method z. Thus theargument is that the method tests the re-sult: the result does not test the method.

Nevertheless, in practice, some way ofjudging classifications must exist since theyare continually being altered and changed.

In some cases the changes are consideredretrograde, but this implies a judgement,while others are generally accepted as animprovement. Therefore taxonomists notonly judge classifications but are frequentlyin agreement about the result of the judge-ment. The very fact that such judgementsare made, and that there can be agreementwith the verdicts, further implies that thereis not only some aim in producing classifica-tions but that that aim is well known, or atleast widely accepted.

In addition to this is the known fact,frequently commented on, that it is usuallyimpossible to tell by inspecting a classifica-tion to which school of methodology, orphilosophy its constructor adheres. As acorollary, it can be said that the same clas-sification appears irrespective of the claimedbeliefs of its constructor which suggests thatclassifications are produced in the same wayalthough the methods are described in dif-ferent ways. Thus the two great revolutionsin biological classification, the post-Dar-winian phase and the New Systematics,have had little practical result (Heywood,1964) while, in spite of vociferous claims

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to the contrary, it now appears that the thirdand latest great revolution, taximetrics, isnot going to live up to the expectations ofits early proponents.

Einstein's (1933) comment on physicists,which follows, applies equally to taxono-mists. "If you wish to learn from the theo-retical physicist anything about the methodswhich he uses, I would give you the follow-ing piece of advice: Don't listen to hiswords, examine his achievements. For tothe discoverer in that field, the constructionsof his imagination appear so necessary andso natural that he is apt to treat them not asthe creations of his thoughts but as givenrealities."

It seemed to me reasonable, therefore, toexpect that within the practical taxonomicliterature was concealed the key to the twinproblems, with what aim do taxonomistsclassify and how do they judge the resultingclassifications? It also seemed probable thatthey were all doing the same things, in thesame way, but describing them in differentWords.

Before considering these questions I shalldiscuss the processes involved in classifica-tion and shall show how the same result canbe obtained in different, but equivalent,ways. This discussion is somewhat long,and superficially simple, but this is, I think,a consequence of the basic simplicity of theprocesses involved in classification. Thediscussion and analysis of such apparentlysimple processes is notoriously difficult andlongwinded, apparently as a consequence oftheir procedural simplicity which leads totheir frequently being treated as axiomatic.

CLASSIFICATION AS A PROCESS

There are two distinct processes in clas-sification which are frequently carried outat the same time. These are the establish-ment of those features, of the objects to beclassified, which can be treated as equiva-lent and then the grouping of the objectsto be classified on the basis of these fea-tures. In biology the first process is calledestablishing homologies.

Homology.—The process of establishinghomologies is frequently carried out as partof the process of classification and in prac-tice, in my own experience, the two proc-esses are often carried out at the same time.The importance of the homologies recog-nised to the resultant classification and therole they play in the final form of a clas-sification is frequently overlooked, or under-stressed. I know that the stress I lay on thisis not fully apparent to many taxonomists,particularly those who study vertebrateanimals. I have worked almost wholly withnematodes and I can assure those who havenot had this experience that the recognitionof homologies in this poorly studied groupis of the very greatest importance. As aresult of this experience I know that therecognition of new or rejection of old ho-mologies has an immediate result on thegroupings proposed in a classification. Anytwo animals being studied will be inevitablyseparated in a classification if non-homologyof any structure or set of structures is estab-lished.

Elsewhere I have discussed the conse-quences of trying to argue why certainstructures are homologous (Inglis, 1966)and attempted to show there that any state-ment of homology implies a total compari-son of the organisms concerned. I will notdiscuss the question again here, in spite ofthe imperfections in that publication where,among other things, I did not discuss howto treat missing or lost structures. This ismainly because I still have not developedan argument which satisfies me. I wouldonly draw attention here to the role whichsequences of changing morphological formplay in establishing homologies since I referto it below.

I repeat and stress that without firstestablishing homologies (irrespective ofhow they are defined) classification is im-possible, and that this is not "probably true"(Blackwelder, 1967) but wholly true. Be-cause in some groups the homologies havebeen recognised for many years, and arenow wholly accepted, their importance is

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overlooked, and many arguments aboutclassification are more correctly argumentsabout the way(s) in which homologies arerecognised or disagreement as to whichstructures are homologous. To consideronly one example, Simpson (1945) contendsthat the classification of whales with mam-mals and not fish is a result of the recogni-tion of the role of evolution. This is notwholly true. The reason is that there arestructures in whales which cannot be homol-ogyzed with structures in fish but can behomologyzed with structures in mammals.

Classification.—Gilmour (1951) points out(implying a hypothetical metal) that if weclassify hot and hurt things and not-hot andnot-hurt things we have produced a dualgeneral classification which can be ex-trapolated to the inductive safety rule thatany hot thing will hurt. However experiencewith hot and hurting things shows that wecan have hot and hurt and red things con-trasted with not-hot and not-hurt and not-red things from which we can make thefurther inductive generalization that red-things are (probably) hot and will hurt. Inthis I am accepting temperature, pain-pro-duction and colour in each thing as homol-ogous characters: not-hot and hot, not-redand red, not-hurt and hurt are differentcharacter states of the characters tempera-ture, pain and colour.

Now the same groupings can be obtainedin two ways. First by constructing a matrixof the characterstates in a number of orga-nisms from which by inspection the constantassociation of one state of one characterwith one state of some other characters)can be established. In other words, onecharacter is covariant with another or others(i.e. if one character is in a given state theother character will always have a corre-sponding state). This leads, if we return tothe study of the hypothetical metal, to theconclusion that the character states red, hotand hurt always occur together in a singlething, while the states not-red, not-hot andnot-hurt always occur together in anothersingle thing. From this it is concluded that

the states are covariant and this is ex-pressed, as above, in the form: all redthings studied are hot and hurt. But inexpressing this as a classification an induc-tive element is assumed and the groupingis diagnosed in the form (implied at least):all red things are hot and hurt.

Such an association analysis is easy tocarry out with small numbers of charactersand even easier if they fall into clear cutgroups but becomes much more difficultif many characters are considered, or ifuncorrelated characters are considered.

However an exactly similar result can beobtained in a different way, by formingsingle character-state classifications andcomparing such classifications. In this waya series of character classifications areformed for hot:not-hot, red:not-red, hurt:not-hurt etc. things and the groups formedcompared. When these single characterclassifications are compared and the groupsformed in each are found to contain thesame individuals or specimens (i.e. theclassifications are concordant) the samegeneral classification can be produced aswith the matrix analysis.

Thus, the production of general classifica-tions can be carried out in two differentways. The first, or matrix method, is fre-quently described or implied in discussingthe production of biological classifications,and is usually called analysis of charactercorrelation or co-variance, while the second,or unified character classification methodhas rarely been referred to, although this iswhat Adanson describes. Further it is clear,by referring to published works by practis-ing taxonomists, that character classificationcomparison is frequently used in testing anygiven classification.

Thus, changes are proposed in a givenexisting generalized classification becausethe groups into which some new information(i.e. character states) can be arranged differfrom those of the generalized classification.In other words the first classification istested by comparing it against a classifica-tion of new information. If the classifica-

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tions do not agree changes are suggested inthe generalized classification to minimize,or eliminate, the discordances or else thenew characters are ignored as "not-good."

Thus, when the generalized classificationhot and hurt:not-hot and not-hurt things istested against the classification of red:not-red things it is considered to be reinforcedbecause the same individuals occur in thecorresponding groups in the classificationsof both characters. When however the unitcharacter classification of heavy:not-heavythings is compared with the hot and hurt:not-hot and not-hurt classifications the in-formation on which the "weight" classifica-tion is based will probably be discarded forthe purposes of the overall unified classifica-tion as consisting of bad characters, orconvergent, or parallel characters (to usebiological terminology) because the "weight"character classification would almost cer-tainly be discordant with the classificationbased on the other characters. On the otherhand the discordance could lead to a re-assessment of all the information previouslyused in an attempt to discover some reasonfor the discordance, such as an error inrecognizing homologies.

Let us revert to the characters tempera-ture, colour and pain and consider anotherfeature of such characters. The two statesrecognised for each character are extremesof a range so that on further analysis wecan have not-hot: warm: hot; subdividedfurther we can have not-hot -.warm: very-warm : almost-hot: hot. Similarly a parallelseries of not-hurt: hurt can be developedand also, not-red:red (admittedly this lastis less likely). We now have a third wayof considering the characters and theirstates in which sequences of changing statecan be developed which are concordant.When the analysis of these sequences orcharacter clines is carried far enough it can,of course, be argued that any division intocharacter states is arbitrary, and that allthree characters and their states reflect onlyone character, temperature, and should onlybe treated as one and no classification is

possible (i.e. no classes can be recognised).Therefore classifications, whether reachedby the matrix or character classificationmethods, rely upon the recognition of dis-tinct character states.

Maslin (1952) has proposed the termmorphocline to describe a sequence ofchange in the states of a single characterwhile he and Hennig (1966) (among others)consider that concordant or parallel charac-ter clines can be used to establish phy-logenies. Such character clines are, asstressed above, frequently used individuallyto establish, or justify the recognition ofhomologies and less rarely, as concordantsequencies, to form classifications. There-fore the claim that phylogenies are estab-lished independent of classification hassome justification, if it is accepted thatsuch character clines tell us somethingabout phylogeny. However the recognitionof character clines implies that differencesin character states are ignored and onlyseparate character clines can be used toform groups within a classification.

Thus, there are three ways of developingclassifications, depending on the initial ap-proach, of which two will produce the sameresult while the third, character clines, willnot and is more usually used to establishhomologies and phylogenies. All three rep-resent different conceptual models of theway in which various character states aregrouped to produce a classification.

The matrix method of developing a gen-eralized classification is probably the easiestto use when dealing with a large numberof characters and, possibly, character states.It is certainly the method most frequentlyreferred to in discussions of classificationby analysis of co-variance of characters.The major difficulty of using such a matrixmethod as a conceptual model from whichto discuss the processes of classification isthat it is then difficult to describe why somecharacters are dismissed as bad and whyweighting is inevitable.

The use of the comparison and unificationof single character classifications in an over-

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all classification, on the other hand, providesa better conceptual model in that it allowsmany features of biological classificationas a process to be explained. Thus, I un-expectedly note that in using this latterapproach we classify character states notorganisms. The organisms are then clas-sified by producing an overall summarizingclassification of the different characterclassifications. Using the matrix method onthe other hand we classify individuals anddeduce from this the character states diag-nostic of the groups formed.

JUDGEMENT OF A CLASSIFICATION

Biological classifications consist of cate-gories which are defined in terms of thecharacter states of the organisms whichthey contain, or which are referred to them.As argued above the character states ofthe characters used are selected becausethey are covariant and the categories aredefined in general terms which imply thatthe character state associations are constant.Biological classifications, in other words,represent general summaries of a largeamount of information within which, byimplication, it is assumed that the characterassociations are universal, and that theclassifications are inductive and, therefore,predictive. This assumption of an inductiveand predictive content leads to the way inwhich such classifications are, and havebeen, tested.

A change is proposed in an existing clas-sification for one of three major reasons.There can be disagreement on previouslyrecognized homologies. This is stressedabove and will not be considered further.More usually a change is proposed becauseof a failure in the inductive-predictive effi-ciency of the existing classification. Thiscan be the result, as referred to above, ofstudying some new character over a widerange of previously studied organisms. Thecharacter states of this new character aregrouped in a classification which is thenfound to be covariant or discordant withthe existing general classification. In this

way the predictive content of the generalclassification is tested and if the classifica-tions are concordant the general classifica-tion is reinforced. If, however, the characterand general classifications are discordantone or the other is considered to be faultyand both are reexamined. If no obviousreason for the discordance, in the sense ofan error, can be found some character willbe weighted to retain the best possiblegeneral classification.

A given general classification is judged inanother way by studying previously usedcharacters and their states in a previouslyunstudied organism. If the character statecorrelations are found to be discordant withthose predicted by the existing generalclassification that classification is reassessed.This position frequently arises when anorganism is found which "links" two taxa.

I conclude that taxonomists have an aim,an assumption, and a way of judging biolog-ical classifications. The AIM, which is im-plied by the judgement, is to produce thegeneral classification which best reflects thecorrelation of the characters, or the concor-dance of the unit character classifications,from which it is derived. The ASSUMP-TION is that such a general classificationwill be inductive and, therefore, predictive.The JUDGEMENT of such a general clas-sification is formed by comparing it againsta classification of some previously unstudiedcharacter and its states, or by comparing thecharacter correlations found in a previouslyunstudied organism to the character correla-tions in the previously studied organisms onwhich the general classification was built.

It is clear that this aim and judgementhave been and continue to be consistentlyapplied or implied by practising taxono-mists, irrespective of their proclaimedmethodology.

A POSTERIORI CONCORDANCE AND WEIGHTING

By using the conceptual model of theprocedures leading to a biological classifica-tion as being the production of classifica-tions for each character which are then

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compared to produce the final summarizinggeneral classification several things can beshown. (I hasten to add I am not recom-mending that this method is or should beused in practice.)

It is clear that existing biological classifi-cations are frequently changed because theydo not match a classification of some newinformation. I made this point above, but itexplains why information on a range ofcharacter states must be available beforeit is useful in classification. This is fre-quently described as enough new informa-tion to enable the character to be weighted.This means, on my model, that enoughinformation is needed to produce a singlecharacter classification which can be com-pared to the established classification. Thenif the established and single character clas-sifications do not agree the latter can beweighted (i.e. discarded or explained away)or can be incorporated with the former byrearranging the taxa (which may involvediscarding or explaining away some of thedata on which the established classificationwas erected). Equally, it gives a model forthe way in which dissimilar evidences canbe assimilated into one classification with-out raising the problem of their equivalence(i.e. inches of tail against colour of eyesagainst body temperature etc.).

However this argument leads to a furtherimportant consequence. The aim is toproduce concordant classifications and thefinal classification is specially constructedto do this after establishing the characterclassifications. In other words, the finalclassification is produced by establishing ana posteriori concordance of data in the sensethat concordance is not assumed to existbut is tested for and the classification isthen developed to reflect it or reinforce itand discordant character classifications arediscarded, that is such characters areweighted negatively.

The principle behind this argument is byno means new and is discussed in greatdetail by Hennig (1966) among many others(see particularly Hennig's discussion of the

"Criterion of Veracity" p. 129 et sec; but Iam not expressing agreement with him thatthis establishes anything about phylogeny).

One further consequence is that in at-tempting to produce and present an overallgeneralized classification some characterclassifications are almost inevitably discor-dant with the majority and must be (or willbe) ignored. It is therefore inevitable thatsome characters must be preferred to othersand this process is more usually calledweighting. In other words the attempt toproduce the best possible general classifica-tion by establishing an a posteriori concor-dance of character classifications involves aweighting of characters. I return to weight-ing below but would stress that it is insome cases, at least, a consequence of pro-ducing generally concordant classifications.

A PRIORI CONCORDANCE AND WEIGHTING

That classifications can be produced bymathematical methods is undoubted andthat the approach is valuable and importantis also, I think, true. Nevertheless there aresome logical difficulties in this approachwhich do not depend on circularity, weight-ing or phylogeny. Perhaps the apparentlynaive criticisms of classical methods, putforward by some taximetricians, are due tothe failure of the classical taxonomists tomake their methods and aims clear but thephilosophy or logic underlying taximetricsis also open to criticism.

The fundamental difference between thenumerical approach and the classical is thatnumerical taxonomy assumes covariance ofcharacters and does not attempt to establishit, as is done by the methods outlined above.In contrast to the a posteriori assessment ofconvarience, discussed above, with its asso-ciated weighting, taximetrics is based on ana priori assumption of covariance with itsassociated a priori non-weighting.

This is best demonstrated by consideringthree assumptions made by Sokal andSneath (1963), of which the first two areinterdependent: The Nexus Hypothesisand The Nonspecificity Hypothesis. The

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first of these, and I quote, is based on theassumption (Sokal and Sneath's word) that,". . . every taxonomic character is likely tobe affected by more than one genetic factorand that, conversely, most genes affect morethan one character," while the second hy-pothesis states that, ". . . we assume (myitalics) that there are no distinct largeclasses of genes affecting exclusively oneclass of characters such as morphological,physiological, or ethological, or affectingspecial regions of the organisms such ashead, skeleton, leaves."

The philosophy underlying these a prioriassumptions is unclear and their validity isopen to grave doubt. I feel that to viewbiological classification as an indirect wayof studying evolution is at least as reason-able, probably more reasonable, than to useit as an indirect study of genetics. Most ofthe argument advanced by Sokal and Sneathconcentrates on the second assumption andit is considered to be supported by hypo-thetical examples of classification congru-ence. That is, it is claimed that a classifi-cation based, for example, on structuralfeatures of the brain will be the same asthat based on characters of the intestinaltract. In other words it is an abstract argu-ment supporting an a priori assumption thatall characters are covariant or that all char-acter classifications must inevitably be con-cordant. This assumption has not beenconfirmed by any study and in my expe-rience is incorrect in many groups.

The reasons for introducing the Nexusand the Nonspecificity Hypotheses (orAssumptions), are not made clear by Sokaland Sneath, and at first sight they appearto be unrelated by taxonomy. However,what they effectively mean is that it isassumed that the characters in any group oforganisms being classified will be covariantand that any character classifications willbe concordant. This is the most marked,in fact fundamental, difference betweenso-called classical methods of taxonomy andnumerical taxonomy. The latter assumeswhat the former is trying to establish.

Such an a priori assumption of covarianceis likely to produce acceptable inductiveclassifications only so long as the mathe-matical analyses are applied to previouslywell analyzed or assessed homologies andcharacters. The mathematical methods, aswe already know, may then produce classi-fications in agreement with those producedby more old-fashioned methods. Unfor-tunately, because it would simplify classifi-cations, recent numerical studies of theNexus Assumption have shown that it isnot valid, a fact long known to classicaltaxonomists. If it did apply, any singlecharacter classification would be whollyinductive and predictive and no problemswould arise in constructing overall classifi-cations. In fact overall classifications wouldnot be necessary.

The dangers and difficulties of this apriori assumption of covariance arise, or arelikely to appear, when either the mathe-matically produced classifications differamong themselves, for the same organisms,or are radically different from those de-veloped by more old-fashioned means. Theextreme condition would, of course, be ifthere were no nonmathematical classifica-tion available against which to judge dis-cordant mathematical classifications since,to date, virtually all numerical classifica-tions are tested against a nonmathematicalclassification.

The problem is once again that of judginga classification, which in turn implies someaim. This is answered by Sokal and Sneathwith an expression of axiomatic faith, "It isour belief (my italics) that when taxa areestablished on the basis of an adequaterepresentation of characters, the resultingclassification will be natural, in the senseof Gilmour."

"In the sense of Gilmour" refers to Gil-mour's (1951) argument (which I accept)that a suitably formed classification basedon much information is likely to be induc-tive over a wide range of data and is likelyto be more generally useful than one basedon little information (but note this is itself

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an inductive argument!). Such an inductivemulti-character classification Gilmour called"natural," a much abused term which I taketo mean "best." But this argument is re-versed when it is assumed that a betterclassification must inevitably result from theinclusion of more unassessed information.The whole strength of Gilmour's argumentis that inductive classifications are based onthe concordance found to exist betweencharacter classifications, not on the amountof crude information used.

We have, however, returned to the sameposition as with classical methods where itis argued that the way of testing a classifica-tion is to examine how it was constructed.This is as sterile an approach when appliedto numerical methods as when applied tophylogenetic, typological, or evolutionarymethods. In practice numerically producedclassifications are tested against a previousclassification; but, when numerical classifi-cations differ, it is impossible to know whythey differ.

A further consequence of the a prioriassumption of covariance of characters ap-pears when Sokal and Sneath (1963: p.210-215) discuss, "The incorporation ofadditional data into a classification (Inter-study coordination)." From this they con-clude that, "Adding new characters will bewarranted only if the new characters arequite numerous or if the earlier classifica-tion has been based on relatively few char-acters."

This argument is justified by reference toa third assumption expressed in yet anotherhypothesis, the Hypothesis of the MatchesAsymtote, which states, "The hypothesis,then, simply assumes (my italics) that, asthe number of characters sampled increases,the value of the similarity coefficient be-comes more stable; eventually a furtherincrease in the number of characters is notwarranted by the corresponding mild de-crease in the width of the confidence bandof the coefficient" (Sokal and Sneath, 1963,p. 114).

The only justification for this assumption

is that the previous two assumptions arecorrect and that the reversal of Gilmour'sargument is valid. But it simply states thesame test in another way, the judgement ofa classification is the amount of unassessedinformation put into it at the beginning andnot the results obtained at the end. Yetagain, methods test results, results do nottest methods.

It is instructive to note that the applica-tion of taximetrics, based on an a prioriassumption of covariance, leads to the posi-tion where it is suggested that new informa-tion should be ignored. This is completelyopposed to the classical approach in whichnew information is looked on as being ofthe greatest importance as a way of testingany existing classification.

The overwhelming danger of this seriesof axiomatic belief statements is that every-thing derives from them and there is notheoretical way of testing any classificationthey produce. The fact that such classifica-tions are in practice tested by comparisonwith other classifications is not justified bythe theoretical background. The series ofaxioms, expressed as hypotheses, leaves onlyone possible test, to repeat the analysis withmore data, since the axiom is that more datawill lead to a better classification. At nopoint is it suggested that the inductive orpredictive content of the classificationshould be looked at.

WEIGHTING OF CHARACTERS

Weighting, in discussions of taxonomicmethod, means that in producing a generalclassification one or more character classifi-cations are considered to override anotherdiscordant character classification, or clas-sifications. There are various reasons forthis stressing of one character classificationin preference to another, some of whichcan be a priori, others a posteriori. That is,in some cases it is decided that the classifi-cation, or classifications, of some characterstates will be used in preference to othersbefore any classifications have been formed{a priori). In other cases certain charac-

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ter state classifications are stressed becauseit has been established by previous studiesthat such classifications are covariant withthose of many other character states in thegroup of organisms under study (a pos-teriori).

A priori weighting can be used for severalreasons, and even for no obvious reasons:1, In many cases a priori weighting is usedbecause of the large number of diverseindividuals to be classified. It may then bedecided on previous experience of anothergroup of organisms or a hopeful guess thatsome character or suite of characters maybe more indicative of character covariancethan some others; 2, Some character may beselected, or simply studied, because of thepersonal interest of the student involved,which need not be primarily taxonomic; 3,It may be decided on some theoreticalground that some characters must be moreimportant to the organisms being classifiedand it is concluded that such importancewill produce the best classification; 4, Itmay be decided that some character is ofgreater importance than some other in indi-cating phylogenetic relationships; 5, It maybe that some character can be studied overa wide range of organisms more easily andrapidly than any other; 6, Expedient weight-ing. Much weighting is expedient and is aconsequence of the Law of Maximum Re-turn for Minimum Effort which controls somuch of taxonomy. The numbers of orga-nisms to be classified are so great, thenumbers of characters and associated char-acter states are so great, the clamour fortaxonomic results is so great, and the num-ber of taxonomists so small, that in manygroups it is only possible to survey a re-stricted range of characters and hope thatthe resultant classification will not collapsetoo quickly. This I call expedient weightingwhich is much more common than manynontaxonomists appreciate.

A posteriori or correlative weighting ofcharacters is generally accepted as moremeaningful than a priori weighting butraises difficulties perhaps as great as those

engendered by a priori weighting (I hastento add that I agree a priori weighting is tobe deprecated but is frequently expedientand sometimes inevitable.). When a pos-teriori weighting is considered to be due tofinding those features ". . . which . . . sep-arate previously recognised natural taxa."(Sokal and Sneath, 1963, p. 34) I think thatmost would accept this as a reasonabledefinition. Certainly I did, and still do inpart.

The implications of such a definition are:1, that students should concentrate on thestudy of such characters to the exclusion ofothers, and stress them in producing classifi-cations; or 2, that because such features areknown to be correlated with many othersthe others can be considered to have beenstudied when the former have been studied;or 3, that only such features need be usedin diagnosing taxa without mentioning anyothers. I am sure that a posteriori weightingis considered to justify any of these implica-tions or any combination of them. Howeverthis, and similar definitions does not stressor even imply, the negative aspect of weight-ing. That is, any form of weighting impliesignoring those features which contradictthose preferentially selected. Thus a pos-teriori weighting implies discarding thosefeatures which do not separate taxa orflatly contradict the taxa erected.

The most interesting feature of negativeweighting is that it is frequently neithera priori nor a posteriori. Let us consideran example to make this clear. It may bethat when the members of a group oforganisms are being classified it is foundthat there are several character classifica-tions which fall into two groups of concor-dant classifications. Within each of thesegroups the character classifications are con-cordant but the two overall classifications ofthe groups are discordant. Let us assumefurther that the first of the overall classifica-tions reflects more unit character classifica-tions than the other. Then on the principlethat the most general classification is thebest (this is certainly done in practice) the

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first generalized classification would beaccepted as the better classification and thesecond would be suppressed. In otherwords the characters from which the latterdiscordant classification was derived arenegatively weighted, and without such nega-tive weighting no general classification ispossible. It follows that the production ofa classification in such a case is dependentupon weighting and the weighting is neithera priori nor a posteriori but is best calledConcomitant Weighting since it is carriedout at the same time as the classification isproduced and no general classification ispossible without it.

It may be argued, reasonably, that insuch cases and in cases when the groups ofconcordant character classifications reflectroughly the same number of character clas-sifications, no general classification shouldbe, or could be, produced. This I wouldaccept and it appears that many argumentsabout "difficult groups" arise from just sucha position where there is no larger numberof concordant character classifications tojustify one overall classification in prefer-ence to another.

Finally the term weighting is frequentlymisapplied to cases which are due to therecognition or denial of homologies. Forexample, to return to Simpson's (1945)argument that the recognition of phylogenyled to whales being classified with mammalsrather than with fish, it could be arguedthat the fish-like characters of whales werenegatively weighted relative to their mam-mal-like characters. This would be an errorsince the weighting is only considered tohave occurred because of an earlier error(from the present point of view) correctedby the recognition that some structures inwhales could be homologyzed with struc-tures in mammals and could not be homol-ogyzed with structures in fish.

This may be looked on as setting up astraw man so I will give another case whichI heard presented at a meeting on taxonomy.It was pointed out to the meeting that agroup of flowering plants had recently been

split into two groups because of a weightingof flower structure against other characters.It turned out that the author concerned hadargued that in one group of plants certainstructures which had previously been con-sidered to be petals were sepals and he had,as a consequence, separated the membersof this group from the others with whichthey had previously been grouped. This isa clear case of a classification change whichsuperficially appeared to be due to a weight-ing process but which is in fact a conse-quence of the nonacceptance of previouslyaccepted homologies.

Taximetrics has an entirely differentbasis in that objectivity and repeatabilityare its aims and, apparently, its tests. Be-cause of the various axioms on which themethod is based any possibility of testingany classification by the methods outlinedabove is eliminated. The method willproduce maximally inductive classifications,is the claim, so that any failure in this re-spect must represent a methological errorin that insufficient characters were studied.

Further, taximetric methods ignoreweighting of characters yet some weightingis inevitable and even the taximetric meth-ods must have some concealed weighting;the difficulty is to establish what has beenweighted.

INDUCTION AND CAUSE IN

BIOLOGICAL CLASSIFICATION

That biological classifications which areinductive over a wide range of data andindividual organisms can be erected is wellestablished. Such induction could not beexpected a priori and is explained by thetheory of evolution. However the sequenceof argument is then reversed so that theoriginal explanatory value of the theory ofevolution is forgotten and evolution isaccepted as a historical fact which is to bestudied. This reversal of the argument leadsto the production of classifications beingconsidered a way of studying their explana-tion, evolution.

This is what I think Simpson means whenhe says, ". . . individuals do not belong to

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the same taxon because they are similar, butthey are similar because they belong to thesame taxon" (Simpson, 1961, p. 69). ButSimpson doesn't tell us how to recognise thetaxon independent of similarity. Howeverif we accept that taxa are erected to produceas high an inductive content as possible thiseliminates any appeal to similarity, and thesimilarity then becomes a consequence ofthe concordance, and Simpson's reversalbecomes acceptable.

Thus to consider the production of bio-logical classifications as the comparison ofspecimens leads to difficulties inherent inthe word similar or similarity. To use theconcept of comparison of character classifi-cations eliminates the question of overallsimilarity and replaces it with one of overallconcordance of character classifications.Yet the two methods are procedurallyequivalent. In this sense Hennig's (1966)Criterion of Veracity is a strong conceptand enables him to deny that similarityimplies or says anything about ancestralrelationships. Nevertheless most of thearguments advanced by the evolutionary orphylogenetic schools do not escape fromthe difficulty that the terminology ofmethod is confused with that of theoreticalexplanation and that of aim.

This does not appear to me to have hadany practical importance since, in spite ofthe elaborate and confused terminologythey use, taxonomists have consistentlyproduced classifications with the same aimand have judged them by the same criteria.Classifications stand or fall on their induc-tive and predictive content.

It is unfortunate that Sokal and Sneath(1963), among many others, have acceptedwhat classical taxonomists have writtenabout their methods without studying theresults they have produced. As a conse-quence, in an attempt to obtain the induc-tive-predictive classification, always aimedat, they have followed a flawed sequence ofreasoning which culminates in assumingthat what they are trying to establish mustexist before they produce any classifications.

Nevertheless this also is only theoreticallyor semantically important since in prac-tice "numerical" classifications are judgedagainst other classifications. Even if noother classifications existed I am sure thata non-predictive "numerical" classificationwould be discarded as "bad."

Finally it is instructive to note that bothschools reverse an explanation in derivingtheir methodology. The numerical schoolreverses the empirical fact that broadlyinductive classifications are based on ananalysis of much information to the argu-ment that much information must producea widely inductive classification. The evolu-tionary school reverses the argument thatinductive classifications can be explained byevolution to the argument that evolutioncan be studied by erecting inductive clas-sifications.

REFERENCESBLACKWELDER, R. E. 1967. Taxonomy, a text

and reference book. John Wiley & Sons, Inc.,New York. 698 p.

EINSTEIN, A. 1933. The method of science. Onthe method of theoretical physics, p. 80-83. InE. H. Madden [ed.] The structure of scientificthought. An introduction to philosophy ofscience. Routledge & Kegan Paul Ltd., London.

GILMOUR, J. S. L. 1951. The development oftaxonomic theory since 1851. Nature, 168:400-402.

HENNIG, W. 1966. Phylogenetic systematics.Univ. of Illinois Press, Urbana. 263 p.

HEYWOOD, V. H. 1964. Introduction. I. Gen-eral principles, p. 1-4. In V. H. Heywood andJ. McNeill [eds.] Phenetic and phylogeneticclassification. The Systematics Assn., Publ. No.6. 164 p.

INGLIS, W. G. 1966. The observational basis ofhomology. Syst. Zool., 15:219-228.

MASLIN, T. P. 1952. Morphological criteria ofphyletic relationships. Syst. Zool., 1:49-70.

MAYR, E. 1965. Numerical phenetics and tax-onomic theory. Syst. Zool., 14:73-97.

SIMPSON, G. G. 1945. The principles of classifi-cation and a classification of mammals. Bull.Amer. Mus. Nat. Hist., 85:I-XVI, 1-350.

SIMPSON, G. G. 1961. Principles of animal tax-onomy. Columbia Univ. Press, New York. 247 p.

SOKAL, R. R., AND P. H. A. SNEATH. 1963. Prin-ciples of numerical taxonomy. W. H. Freeman& Co., San Francisco. 359 p.

The South Australia Museum, Adelaide,Australia.

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