Phenetics and Numerical Taxonomy Applied to Systematic Nematology T

Phenetics and Numerical Taxonomy Applied to Systematic Nematology t

W. WAYNE Moss AND W. A. WEBSTER ~

Numerical taxonomy and the phenetic modified by speculation on their evolutionary approach to classification have aroused history. Essentially, a phenetic study at- considerable interest and debate among tax- tempts to recognize groups based on data, onomists in recent years. It will not be rather than on inferences from data. The possible here to examine the controversy in desired product of a phenetic study is a any depth, but a few comments on certain "natural" classification (16), a set of group- aspects of theory and methodology may be ings based on a maximum of shared char- helpful in considering their relevance to sys- acters. Such classifications are generally tematic hematology. References to pertinent assumed to possess both a maximum in- articles dealing with these and additional formation content and a higher predictability aspects are included in the bibliography (8, than classifications based on fewer, heavily- 12, 13, 14, 16, 19, 23, 27, 33, 50, 51, 52, weighted characters deemed to have evolu- 53). tionary significance, although there are PHENETICS reasons for suggesting that this assumption The phenetic approach to the classifica- need not always hold true, as discussed tion of a set of organisms or objects involves below. the establishment of inter-object similarities The phenetic approach is nothing new; based on all available data from the objects, taxonomists have been processing their ma- with resultant groupings purposely left un- terial phenetically for centuries, by intuitively grouping together individuals sharing a ma- Received for publication 5 September 1969. jority of characteristics in common. The 1 Project initiated jointly in the Department of Entomology congruence between many of the newer classi- of The University of Kansas, Lawrence, and the Animal Diseases Research Institute, Hull, Canada; continued at fications obtained by computerized methods the Academy of Natural Sciences, Philadelphia with help with earlier classifications obtained conven- from NSF Research Grant GB-6851; and completed in the Division of Entomology, University of California, Berke- tionally is therefore not surprising, as phe- ley. Special thanks are due the Miller Institute for Basic Research in Science of the University of California, netics is a major component of most orthodox Berkeley, for support in the form of a postdoctoral re- classifications. Since the time of Darwin, search fellowship to W. W. Moss. Computer time was provided by the Computation Center of the University of however, it has been considered desirable to Kansas (Project 0729), and by the Computer Centers of the University of Pennsylvania (Projects 086446 and describe the results of biological classifica- 4025) and the University of California (Projects 8639 and tions in an evolutionary context. 708"/). Photographs were taken by the Bin-Graphic Unit, Research Branch, Canada Department of Agriculture. In contrast to cladistic methods that at- The manuscript benefitted greatly from a critical reading by J. H. Camin, Department of Entomology, University tempt to classify on the basis of presumed o[ Kansas, Lawrence. u Postdoctoral Research Fellow, Division of Entomology, common ancestry (regardless of phenetic University of California, Berkeley 94"/20; on leave from similarity or dissimilarity) (9, 24, 26), and Academy of Natural Sciences, 19th and Parkway, Phila- delphia, Pa. 19103 and Animal Diseases Research Institute, phyletic ("evolutionary") approaches that Canada Department of Agriculture, P. O. Box 1400, Hull, Quebec. combine a vaguely-defined mixture of phe- 16 SYMPOSIUM: PHENETICS AND NUMERICAL TAXONOMY • Moss, Webster 17

netics and cladistics (32), phenetics is a groupings recognized are natural, phenetic relatively straightforward, "here-and-now" assemblages. sort of approach aimed at determining To a person engaged in a phenetic study, present-day similarities, regardless of how the fact that a character may be present in they might have come about. The fact that three recognizable character states, A, B the organisms to be classified are the prod- and C, is certainly of interest, and his aim ucts of a process of organic evolution is will be to group together those objects with certainly of interest, but the /act of evolu- identical character states. The fact that state tion's occurrence need be neither pertinent A might be considered "primitive" or "an- nor useful in the determination of phenetic cestral" or "plesiomorphic" by a phyletic similarities (2). Evolution is without argu- worker (and the same state very likely ment a central, unifying concept of biology. "specialized" or "derived" or "apomorphic" However, although it is true that a knowl- by another) is a consideration outside the edge of evolutionary processes and pathways defined scope of a phenetic taxonomy. De- can be gained through analysis of phenetic spite the fact that many phenetic workers data, it is also true that the actual course are interested in aspects of evolution as they followed by evolution will be known with pertain to areas outside of taxonomy, it has certainty for a vanishingly small number of been suggested that pheneticists are opposed biological groups to be classified; and this to inferences on evolutionary processes be- statement is particularly true for the Nema- cause of their refusal to attempt to classify toda. The unravelling of possible or probable in an evolutionary context (30). This criti- evolutionary pathways in this context is a cism is analogous to saying that a man is stimulating intellectual exercise, but it can be anti-water because he drinks water, but re- little more than that. A classification that fuses to try to walk on it! reflects presumed evolutionary pathways is a theory (31 ), but a theory that is not testable NUMERICAL TAXONOMY other than in terms of itself (2). There is Numerical taxonomic studies attempt to no observer of the entire phylogeny of a recognize similarities and establish classi- group to whom we can turn and say, "Does fications by means of operationally-defined, our classification correctly express the phy- numerically-oriented procedures (56). Most logeny of this group?". Accordingly, even numerical studies are purely phenetic, al- with a moderately complete fossil record, any though some attempts have been made to evolutionary classification is based on spec- carry out phyletic studies operationally and ulation from phenetic data, and cannot be numerically (9, 10, 22, 29, 58, 60, 61). objectively confirmed ( 13 ). We may be able Some of the most bitter disagreements in to predict that additional, as yet undis- the history of systematic biology have accom- covered, taxa will fit into the categories that panied the introduction and application of we have erected, and that additional characters will be found to show trends con- numerical taxonomy (NT), as recent issues of cordant with characters used previously. pertinent journals such as Systematic Zoology However, the fact that such (phenetically) and Taxon will witness. Heralded as a agreeable taxa and characters may indeed be panacea by its proponents, NT has been found proves nothing about the congruence condemned as an abomination by its critics. of the classification with the actual phy- It appears likely that both sides have an logeny, although it may indicate that the element of truth. There is no doubt that 18 Journal of Nematology, Vol. 2, No. 1, January 1970

many existing, conventionally-derived taxon- conventional taxonomy. As an example of omies have a significant content of valuable a double-edged criticism, NT has been con- information, and will not be swept away by demned (32) for not being able to separate the application of numerical approaches. At phena (sample[s] of phenotypically similar the same time, there are ways in which NT specimens; or, more usually, groups recog- can considerably clarify taxonomic situations nized in a phenetic study) from taxa ("tax- muddled by conflicting phyletic opinions onomic group[s] sufficiently distinct to be based on different, heavily-weighted char- worthy of being distinguished by name and acter complexes, as well as by variations in to be ranked in a definite category"); and descriptive technique. In addition, NT offers this is quite true. The fact that several a variety of stimulating, new ways of attack- individuals form a distinctive, phenetic group ing systematic problems and of visualizing in a numerical study provides few clues as their results. to whether or not the group is an intraspecific In view of the controversy surrounding population, a species, a genus, etc. Such a NT, its admitted drawbacks in some areas, decision must be left to the taxonomist carry- and the fact that the field is still in a con- ing out the study. This weakness would seem siderable state of flux, a reasonable question a formidable deficit of numerical phenetics; for a nematode taxonomist to ask with ref- yet is the conventional taxonomist in any erence to NT is: "Why bother?"; and there better position? In fact, he is not. In recog- is no easy answer to this question. There nizing groups above and below the species are both theoretical and practical objections, level, the conventional taxonomist must rely as well as advantages, to the undertaking of predominantly (or entirely) on phenetic a phenetic, numerical study, and the potential data, usually morphologic; at the species worker should be aware of these before com- level the conventional taxonomist may have mitting himself. recourse to the biological species concept, if THEORETICAL CONSIDERATIONS: Oil the he can apply it to the preserved material theoretical level, NT has been roundly that serves as the basis of classificatory con- criticized by respected workers with consider- clusions in most groups of organisms (e.g., able taxonomic experience (6, 30, 45, 47, Nematoda), but in most cases he finds him- 48), and a prospective numerical worker self in the same position as a pheneticist. In should be aware that he is risking "an excur- a way he may be even worse off, since he is sion into futility" (46). However, a careful very likely recognizing his groups pheneti- reading will show that the majority of such cally, but non-operationally, and while claim- criticisms can be consigned to three cate- ing to be using unspecified, evolutionary gories: the semantic, the emotional, and the criteria. double-edged. Semantic quibbling and emo- Nevertheless, it is quite true that a method- tional, dogmatic outbursts against the use of ology as much in its infancy as NT has flaws, computers and the intrusion of operational, and a prospective user should not expect to mathematically-oriented procedures into the receive the final answers to his problems "art" of taxonomy are sometimes amusing along with output from the computer. Some- and frequently frustrating, but certainly do times problems only begin at this stage! little to advance the cause of systematics; PRACTICAL CONSIDERATIONS: If one can Gilmartin (23) discusses this in some detail. overcome his qualms about the theoretical In addition, many criticisms of NT, though bases of NT, additional, practical hurdles lie valid, are as much or more applicable to ahead. First and foremost, the methods of SYMPOSIUM; PHENETICS AND NUMERICAL TAXONOMY ° Moss, Webster 19

NT are time=consuming. Several conven- The basic steps involved in carrying out tional studies can usually be done in the an introductory study have been documented interval it takes to carry out a comparable elsewhere (56), but can be summarized here numerical study. There are indications that briefly as: the choice of a group of objects numerical studies are more repeatable (36), (OTUs: Operational Taxonomic Units) to but again this advantage must be weighed be classified; the selection of characters that against the time element. Progress toward differ among the OTUs and cannot be optical scanning is encouraging (44, 55), further subdivided logically; the standardiza- but in the absence of such equipment much tion of characters to assure equal character effort must be expended in searching for weighting; the computation of similarity characters, listing them, and in the recording coefficients between OTUs; and, finally, the and punching of data. On the other hand, grouping together of OTUs with high mutual the time spent defining and searching for similarities. characters can be most rewarding. It is only The group to be classified should be rather human nature to seize on the most obvious small in an initial study. Workers vary in the and reinforcing characters when assessing speed with which they grasp the funda- relationships, but by so doing one may un- mentals, but fewer OTUs tend to reduce any consciously overlook more cryptic sources of possible confusion factor. For an initial information that could provide entirely new study, a group of perhaps ten to twenty insights into taxonomic structure. This, of OTUs seems reasonable. Additional reasons course, is a major advantage to an approach for restricting the number of OTUs are given that both allows and forces one to look for below. as many characters as possible. In addition, The selection of characters and the number the preparation of tables and character lists of characters to use in a numerical study are provides a basis on which a colleague can matters still under debate. It is an axiom of constructively criticise one's results, a basis conventional taxonomy that some characters usually lacking in conventional approaches. are more important than others; unfortu- An additional hurdle is the problem of nately, the reasons why this should be so are where and how to process data. There are rarely explained in any detail, and opera- several alternatives: one can write his own tional methods for rejecting less important programs, convert programs obtained else- characters are rare. Initial recommendations where to local facilities, or take or send data for phenetic numerical studies assumed, in the absence of logically defensible schemes to a center of NT activity where up-to-date, for weighting, that all characters are of equal sophisticated program systems are available. value in recognizing relationships; therefore, From personal experience, the last alternative all characters should contribute equally in is by far the most preferable, unless one has the computation of similarities. Subsequent considerable programming experience or en- work (35, 40, 57) has shown that some joys working with computers. characters do seem to contribute less in- METHODOLOGY: Assuming that all wor- formation than others: they may vary ries about theory and practicality have been randomly, show high variability, be difficult laid to rest, the next obvious question to be to measure or completely correlated with asked by our novice NT worker is, of course: other characters, etc. Exclusion of some "How does one do a numerical taxonomic characters in favor of others can be justified study?". in a numerical study, but the worker should 20 Journal of Nematology, Vol. 2, No. 1, January 1970

make extremely clear the grounds on which formation plateau. On the basis of at least such exclusions took place; for example, three studies to date (21, 34, 41), a certain Bird and Mai (5) recommended the omis- amount of leeway exists with regard to char- sion of characters shown to have high acter sampling, as well as errors in recogniz- coefficients of variation and Farris (20) ing homologies and in the recording of data. suggested a method of assigning lower weight Put slightly differently, it would appear that to such characters. Of questionable value the basic data structure will tend to come are studies such as that of Kendrick and through once a certain minimum number of Weresub (28), who began an NT with both characters is attained; this structure will tend a large number of characters and firm con- to be maintained as additional characters are victions as to what their final groupings added, but may be affected somewhat ad- should be. When many characters did not versely by the addition of characters showing produce the desired groupings, the number random trends. of characters was gradually reduced until A computed table of OTU × OTU simi- only a selected few remained; these, fortui- larity coefficients is the closest approximation tously, gave exactly the results desired: a to the "truth" obtainable in an introductory classification based on a few, heavily- numerical study, in that this table represents weighted characters. The circularity involved similarities between all possible combinations in such a study is evident. of OTUs computed on the basis of all in- Some workers have introduced logical, cluded characters. Unfortunately, a table of operational schemes for character weighting numbers can be rather difficult to interpret, (20, 29, 38). In the absence of such and this difficulty tends to be compounded schemes, however, it remains an axiom of drastically as the number of OTUs increases. NT that characters should contribute equally. For this reason various techniques such as For this reason, character standardization is graphic and cluster analysis have been de- generally recommended as an integral part vised to aid in grouping together those OTUs of a numerical study. with high mutual similarities. It is difficult to recommend how many Graphic analysis (7, 34, 62) places the characters to use in a numerical study, al- OTUs on graphs, in positions relative to though attempts have been made to do this their similarity values, to produce a 2-dimen- (56). In groups with reduced morphology sional picture of relationships. Cluster anal- one may be hard pressed to find a dozen ysis, which is also a device for portraying characters, while in others one may be liter- relationships in two dimensions, generally ally overwhelmed. In time it may be possible starts by grouping OTUs with mutually high- to issue recommendations based on the group est similarities, and proceeds from there to to be studied, the number of OTUs and the add OTUs with somewhat lower similarity kinds and mix of available characters (quan- values. The manner in which unclustered titative vs. qualitative). It may be possible OTUs are added to existing pairs and groups to predict the number of characters needed varies according to the method. The results by means of sampling experiments, such as of cluster analysis are generally presented in those carried out by Rohlf (41), in which the form of a dendrogram of phenetic rela- random samples of characters might be tionships or phenogram (30, 52). Unfor- analysed to indicate how many additional tunately, phenograms are prey to numerous characters would be needed to reach an in- ills, including their resemblance to conven- SYMPOSIUM: PHENETICS AND NUMERICAL TAXONOMY ° Moss, Webster 21

tional phyletic trees, and their tendency to SOME RECENT APPLICATIONS accumulate distortions as one progresses Few numerical taxonomic studies have from tips to base (43). Methods have been been attempted on helminths, so it would be developed to aid in detecting phenogram unwise to draw too many conclusions from distortions (34, 54), but their application the existing literature. However, results ob- can be time-consuming and they do not al- tained so far seem encouraging. ways work as well as they might (15, 37). Ukoli (59) used NT to analyse morpholog- Suffice it to say that the relationships pictured ical relationships among fifteen species of the in a phenogram should not be accepted at genus ADharyngostrigea Ciurea, 1927, and face value, but should be analysed carefully found several distinct groups. Pertinent for their correspondence with relationships changes in nomenclature were proposed as present in the original matrix of similarity a result. values. Bird (3, 4) and Bird and Mat (5) ob- Additional methods of portraying OTU tained satisfactory results from numerical, relationships have been suggested. Barra- phenetic studies of twenty-four species in the clough and Blackith (1) computed discrimi- genus Trichodorus Cobb, 1913, as well as a nant functions and generalized distances detailed analysis of various populations, geo- among ten groups of eelworms (Ditylenchus), graphic and ecologic, within T. chrbtiei Al- including males and females of D. mycelio- len, 1957. In order to obtain a good phe- phagus Goodey and larvae, males and fe- netic sample of a taxon, they recommended males of three races of D. dipsaci (Kiihn). wide sampling of living populations from Relationships were illustrated in the form of different geographic and ecologic situations, a 2-dimensional projection of a 3-dimen- with analysis of morphometric and allometric sional model. characters for degree of variation. Quite recently, workers such as Rohlf (42, Moss and Webster (37) in a preliminary 43), Hendrickson and Sokal (25) and study of a group of selected strongylates Oxnard (39) have applied rather sophisti- examined representatives of seven species in cated techniques of principal components, five nominate genera. Two studies were centroid factor analysis, and canonical anal- carried out, involving individual character ysis to the study of taxonomic relationships. readings (27 OTUs) and average character Their methods produce various kinds of out- readings (70TUs). Distance and correla- put, including 3-dimensional models, and tion coefficients gave very similar results in represent some of the most intriguing ap- these studies. Cluster analysis produced proaches to taxonomy ever devised. Rohlf phenograms that were extremely accurate in (43) has shown that while cluster analysis their presentation of results initially present of similarity values provides a clearer picture in the similarity tables, and which showed of relationships at high levels of similarity, exceptionally good definition of groups. Our i.e., within phenetic groups, factor analysis groupings tended generally to be close to and related techniques provide a better those recognized earlier in conventional picture of relationships at lower levels of studies by Dougherty (17, 18), and the im- similarity, i.e., between phenetic groups. Ac- plications of this are discussed elsewhere cordingly, the application of both approaches (37). can provide complementary results and a Findings of more general interest arising more balanced analysis of taxonomic struc- from the strongylate study included further ture than either method applied by itself. evidence for the inapplicability of the phenon 22 Journal of Nematology, Vol. 2, No. 1, January 1970

FIG. 1. Centroid factor projection model of 27-OTU strongylate study. A. viewed along first factor axis; B. viewed along second factor axis. OTU number codes as follows; 1-5 : Crenosoma canadensis; 6 : Metastrongylus pudendotectus; 7-11 ~--- Skrjabingylus magnus; 12 : Pneumostrongylus tenuis; 13-17 : Dictyocaulus viviparous; 18-22 : C. vulpis; 23-27 : M. aWL

line (a line drawn at right angles across a original set of distances on which our pheno- phenogram for the purpose of recognizing gram was based, and the set of distances taxa), and indications of the suitability of computed directly from the model of the using either individual character readings or OTUs in 3-space was 0.863. It is interesting average character values for each OTU. The to note that three dimensions were needed to problem of whether to recognize an aberrant separate the Crenosoma replicates from those OTU as a distinct taxon, as opposed to plac- of Dictyocaulus, and the Metastrongylus ing the OTU with its closest phenetic rela- replicates from those of Skrjabingylus. The tive, was encountered and discussed, but not meanings assignable to the three factor dimen- solved, indicating a need for more operational sions are uncertain, but it is unlikely that expressions of relatedness in taxonomy. any dimension represents size, as in a similar Further work on the strongylate material, study (34); all measurements in the present using centroid factor analysis and the projec- study were expressed as ratios (37). tion technique of Rohlf (42) on 27 OTUs If formal groupings were to be assigned resulted in the construction of a 3-dimen- as a result of the centroid study, our con- sional model (Fig. 1) and stereogram (Fig. clusions would likely differ from those of 2). Groupings shown in these figures are Dougherty (17, 18), Skrjabin et al. (49) most closely comparable to those of the dis- and Chabaud (11 ). The close approxima- tance phenogram obtained by Moss and tion of Dictyocaulus and Crenosoma in the Webster (37); the correlation between the factor projection model is certainly not con- SYMPOSIUM: PHENETICS AND NUMERICAL TAXONOMY ° Moss, Webster 23

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FIG. 2. Stereodiagram of relationships obtained by centroid factor analysis (Rholf's method). The first factor axis runs across the width of the page, the second from top to bottom. The third axis is at right angles to the plane of the page and the positions of the 27 OTUs along this axis become visible when the two views are superimposed by means of a stereo viewer. OTUs coded as follows: small, solid dots = Dictyocaulus viviparous; large, solid circles = Crenosoma canadensis; large, solid circles with vertical bars ~ C. vulpis; small, open circles = Skrjabingylus magnus; large, open circle = Pneumo- strongylus tenuis; rectangles with longer axis running across page = Metastrongylus apri; rectangle with longer axis running length of page ~ M. pudendotectus. sistent with the separation of Dictyocaulus the incorporation of additional, more "typi- into a superfamily distinct from that contain- cal" trichostrongylid material might appreci- ing the remaining genera ( 11, 49), nor is the ably affect the degree of relationship between separation of Pneumostrongylus and Meta- Dictyocaulus and Crenosorna shown in the strongylus and the close approximation of present study (cf. similar results in Moss, the latter genus and Skrjabingylus in our 35). study consistent with the recognition of the We believe that the discreteness of the families Metastrongylidae (containing Pneu- groupings recognized by numerical ap- mostrongylus and Metastro.ngylus) and proaches in this and our earlier study (37) Trichostrongylidae (including Crenosoma, is quite promising in terms of subsequent Dictyocaulus and Skr/abingylus) (17, 18). characterization of taxonomic units within However, in view of the fact that ours was a the Nematoda. preliminary study with limited representa- CONCLUSION tion, intended primarily to test the ap- It should be clear from the above that plicability of the method to systematic there are no uncluttered avenues of escape nematology, we are not at this time overly from taxonomic problems via numerical, concerned with the congruence, or lack of phenetic approaches; their use requires a congruence, of our results with existing sys- knowledge of where the problems lie, an in- tems. For this reason we have likewise telligent input of data, and a careful analysis refrained from the formal recognition of of results. The few nematological studies taxonomic groups. It is our hope to carry attempted so far have been encouraging, but out an expanded strongylate study, using have also raised questions pertinent to theory representatives of additional nominate taxa, and methodology; this is, of course, as it in order to obtain a broader picture of rela- should be. A worker with experience in con- tionships. For example, it is possible that ventional taxonomy will certainly find it ex- 24 Journal o[ Nematology, Vol. 2, No. 1, January 1970

tremely stimulating to examine his views on 734-1487. In P. Grass6 (Ed.) Trait6 de the basis and practice of classification in the Zoologie 3 & 4. 12. COLLESS, D.H. 1967. An examination of light of numerical phenetics. Definite bene- certain concepts in phenetic taxonomy. fits can accrue from attempting a numerical Syst. Zool. 16: 6-27. study and, as Gilmartin has noted (23), the 13. COLLESS, D. H. 1967. The phylogenetic fallacy. Syst. Zool. 16:289-295. worker who evaluates a method from the 14. COLLESS, D. H. 1969. The phylogenetic viewpoint of a participant can bring more fallacy revisited. Syst. Zool. 18: 115-126. of value with his comments than one who 15. CROVELLO,T.J. 1968. The effect of alter- ation of technique at two stages in a nu- merely criticizes from the sidelines. merical taxonomic study. Univ. Kans. Sci. Regardless of whether or not phenetics Bull. 47:761-786. and numerical taxonomy prove to be the 16. DAVlS, P. H., and V. H. HEYWOOD. 1963. Principles of Angiosperm Taxonomy. Oli- wave of the future, they have certainly con- ver and Boyd. Edinburgh and London. tributed greatly in recent years to a belated 556 p. verbalization of taxonomic principles and 17. DOUGHERTY,E.C. 1949. A list of the trichostrongylid lungworms (Phylum Nema- methodology, and should continue to gen- toda) and a key to the six genera. Para- erate interesting hypotheses for testing in sitology 39:218-221. the future. 18. DOUGHERTY, E. C. 1949. The phylogeny of the nematode subfamily Metastrongyl- LITERATURE CITED idae Leiper (1909), a correlation of host 1. BARRACLOUGH,R., and R. E. BLACKITH. 1962. and symbiote evolution. Parasitology 39: Morphometric relationships in the genus 222-234. Ditylenchus. Nematologica 8:51-58. 19. EriRLICH, P. R. 1964. Some axioms of 2. BIRCH, L. C., and P. R. EriRLICH. 1967. taxonomy. Syst. Zool. 13: 109-123. Evolutionary history and taxonomy. Syst. 20. FARRIS,J.S. 1966. Estimation of conserv- Zool. 16:282-285. atism of characters by consistency within 3. BIRD, (3. W. 1967. Population density, biological populations. Evolution 20:587- morphologic, morphometric, and allomet- 591. ric variations of Trichodorus Cobb, 1913 21. FISHER, D. R., and F. J. ROHLF. 1869. and Trichodorus christiei Allen, 1957. Robustness of numerical taxonomic meth- (Sect. B) Diss. Abstr. 28:14. ods and errors in homology. Syst. Zool. 4. BIRD, G. W. 1967. Numerical analysis of 18:33-36. the genus Trichodorus. Phytopathology 22. FITCH, W. M., and E. MARGOLIASH. 1967. 57: 804. Construction of phylogenetic trees. Science 5. BIRD, G. W., and W. F. HAl. 1967. Mor- 155:279-284. phometric and allometric variations of 23. GILMARTIN, A. J. 1967. Numerical tax- Trichodorus christiei. Nematologica 13: onomy--an eclectic viewpoint. Taxon 16: 617-632. 8-12. 6. BLACKWELDER, R. E. 1967. A critique of 24. HENDRICKSON,J.A. 1968 (1969). Cluster- numerical taxonomy. Syst. Zool. 16:64-72. ing in numerical cladistics: a minimum 7. BUSACKER, R. (3., and T. L. SAATY. 1965. length directed tree problem. Math. Biosci. Finite graphs and networks: an introduc- 3:371-381. tion with applications. Mc(Draw-Hill, New 25. HENDRICKSON,J. A., and R. R. SOKAL. 1968. York. 294 pp. A numerical taxonomic study of the genus 8. CAMIN, J. H. The significance of incon- Psorophora (Diptera: Culicidae) Ann. En- gruence between phenetic and cladistic tomol. Soc. Amer. 61:385-392. dendrograms. (MS in preparation.) 26. HENNIG,W. 1966. Phylogenetic Systematics. 9. CAMIN, J. H., and R. R. SOKAL. 1965. A Univ. of Illinois Press, Urbana, Ill. 263 p. method for deducing branching sequences 27. HEYWOOD, V. H., and J. MCNEILL (Eds.) in phylogeny. Evolution 19:311-326. 1964. Phenetic and Phylogenetic Classifi- 10. CAVALLI-SFORZA,L. L., and A. W. F. ED- cation. Syst. Ass. Publ. No. 6, London. WARDS. 1967. Phylogenetic analysis 164 p. models and estimation procedures. Amer. 28. KENDRICK,W. B., and L. K. WERESUB. 1966. J. Hum. (Denet. 19:233-257. Attempting neo-Adamsonian computer 11. CHABAUD, A. (3. 1965. Nrmathelminthes, taxonomy at the ordinal level in the Basid- Rotif~res, (Dastrotriches, Kinorhynques. p. iomycetes. Syst. Zool. 15:307-329. SYMPOSIUM: PHENETICS AND NUMERICAL TAXONOMY • Moss, Webster 25

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