UINIVLRSITY OF ILLINOIS LIBRARY URBANA -CHAMPAIGN BIOLOGY r FIELDIANA: ZOOLOGY A Continuation of the ZOOLOGICAL SERIES of FIELD MUSEUM OF NATURAL HISTORY VOLUME 72 FEB131979 FIELD MUSEUM OF NATURAL HISTORY CHICAGO, U.S.A. TABLE OF CONTENTS 1. The Differentiation of Character State Relationships by Binary Coding and the Monothetic Subset Method. By Hymen Marx, George B. Rabb, and Harold K. Voris 1 2. Amphisbaena medemi, an Interesting New Species from Colombia (Amphis- baenia, Reptilia), with a Key to the Amphisbaenians of the Americas. By Carl Cans and Sandra Mathers 21 3. Trachelyichthys exilis, a New Species of Catfish (Pisces: Auchenipteridae) from Peru. By David W. Greenfield and Garrett S. Glodek 47 4. The Status of Hybalicus Berlese, 1913 and Oehserchestes Jacot, 1939 (Acari: Acariformes, Endeostigmata). By John B. Kethley 59 5. A New Species of Allactaga (Rodentia, Dipodidae) from Iran. By Daniel R. Womochel 65 6. A New Helogeneid Catfish from Eastern Ecuador (Pisces, Siluriformes, Helogeneidae). By Garrett S. Glodek and H. Jacque Carter 75 7. Differential Epibiont Fouling in Relation to Grooming Behavior in Palae- monetes kadiakensis. By Bruce E. Felgenhauer and Frederick R. Schram 83 2- 1 FIELDIANA Zoology Published by Field Museum of Natural History Volume 12, No. 1 October 21, 1977 The Differentiation of Character State Relationships by Binary Coding and the Monothetic Subset Method HYMEN MARX ^HJKM fflSTfW SBWD CURATOR, DIVISION OF AMPHIBIANS AND REPTILES FIELD MUSEUM OF NATURAL HISTORY KlfiW 1 7 1977 GEORGE B. RABB DIRECTOR, CHICAGO ZOOLOGICAL PARK LIBRARY AND RESEARCH ASSOCIATE, DIVISION OF AMPHIBIANS AND REPTILES FIELD MUSEUM OF NATURAL HISTORY AND HAROLD K. VORIS ASSISTANT CURATOR, DIVISION OF AMPHIBIANS AND REPTILES FIELD MUSEUM OF NATURAL HISTORY The monothetic subset method devised by Sharrock and Felsen- stein (1975) is a powerful tool for analysis of relationships among biological organisms. It was referred to in the literature prior to 1975 as the Combinatorial Method (Wake and Ozeti, 1969; Liem, 1970; Inger, 1972; Heyer, 1974; Zehren, 1974). These authors applied the method to generate phyletic summaries of various animal groups, using the now-standard character state tree format, equivalent to the character state transformation series of Maslin (1952) and Hennig (1966). The method also has applications, not yet exploited, as an organizational tool in other disciplines. The purpose of this paper is to introduce methods for treating a variety of character state relationships for use in phenetic and phyletic studies. The monothetic subset method is well adapted to this task because it uses binary data. Application of these treat- ments to data on viperid snakes is in a forthcoming paper. US ISSN 0015-0754 Library of Congress Catalog Card No.: 77-087734 Publication !269 1 ^^ ^^ 1Q1BURRILLHAU NQV 2 8 2 FIELDIANA: ZOOLOGY, VOLUME 72 MONOTHETIC SUBSET METHOD The monothetic subset method has two main characteristics with respect to ordinary taxonomic materials. First, it is a reductionist method of organizing data that makes no assumptions beyond those inherent in the character state relationships provided. In this re- gard, it is very distinct from assumption-bound phyletic methods, such as that of Camin and Sokal (1965) and others. Secondly, the method maintains lists of character states for all monothetic sub- sets generated and thus it is always possible to refer directly to shared states for any subset. With data in such a form, it is possible to trace the character state relationships of individual taxa and/or groups of taxa at any given level of shared states. In addition, character state correlations within and between combinations can be traced or extracted. The measure of similarity of taxa in the output from the Sharrock and Felsenstein monothetic subset method is not a similarity coefficient. Rather it specifies the actual number of the same charac- ter states held in common by all taxa in a group. These groups of taxa are called the non-redundant, monothetic subsets. Specifically, a non-redundant monothetic subset is the largest group of taxa sharing a given set of character states. This fits the rule set forth by Sneath and Sokal ( 1973, p. 20), "... they are formed by rigid and successive logical divisions so that the possession of a unique set of features is both sufficient and necessary for membership in the group thus defined." The computer program developed by Sharrock and Felsenstein ( 1975) operates on a binary data matrix of taxa by character states. Each taxon is coded as having (1) or not having (0) each character state. An example will help clarify the procedure. Below, the distri- bution of eight states is recorded in binary form for three hypotheti- cal taxa. Taxon A B C 1 2 3 States 4 5 6 7 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Note that this array may represent data from one eight-state or as many as eight one-state characters, depending on the number of states per character. Members of Subset Number of Subset Subset Number Shared States Size (Taxa) 1 7 1 A 2 4 1 B 3 3 2 AB 4 3 2 AC 5 2 3 ABC MARX ET AL.: CHARACTER STATE RELATIONSHIPS 3 The computer output for these data would give the following in- formation: Identity of Shared Character States 2,3,4,5,6,7,8 1,6,7,8 6,7,8 5,7,8 7,8 In the output the non-redundant monothetic subsets are listed in descending order based on the number of shared character states. For each subset the total number of members is recorded, the in- dividual members are listed and the character states shared by all the members are given. The first subsets are usually single species with unique combinations of character states, as is the case for the first and second subsets here. The third subset in this example reveals that species A and B share three characters, numbers 6, 7, and 8. The fourth subset shows that species A and C also share three states (numbers 5, 7, and 8). The latter suite of character states overlaps, but is distinct from the suite of character states shared by species A and B. At the level of two shared states the three species form a subset sharing character states 7 and 8. Although the monothetic subset method does not incorporate cladistic or phylogenetic assumptions into its algorithm, the method can accept data organized in ways which can incorporate a wide variety of assumptions. It is to this significant feature of the method that we particularly wish to draw attention. The following sections delineate the general types of character state relationships and describe various treatments of character state data that may be of value in analysis of the nature of relationships of taxa. CHARACTER STATE RELATIONSHIPS The problem of defining characters for taxonomic work has been considered in many ways by taxonomists (see Estabrook and Rogers, 1966; Sneath and Sokal, 1973, p. 72 for a general discussion of unit characters). However, in the past decade it has become standard practice to use character state transformation series in 4 FIELDIANA: ZOOLOGY, VOLUME 72 nearly all phylogenetic or cladistic studies (see Szalay, 1977). Pro- cedures for deriving character state transformation series are discussed in numerous papers (e.g., Hennig, 1966; Marx and Rabb, 1970; 1972; Ross, 1974). All procedures result in a subjective, re- lative probability estimate of a character's evolution. However, most methods so far described which utilize transformation series require a complete transformation series. A more flexible system of handling character state relationships would have two significant advantages. First, a variety of character state relationships reflecting a range of levels of understanding of the characters could be accommodated, including those involving characters with incomplete or ambivalent information. Thus charac- ters for which a transformation series is not inferable or only par- tially inferable could still be incorporated into an analysis. Second, one may wish to look at relationships of taxa from a variety of per- spectives, utilizing different amounts of information on character state relationships. In this study we recognize that character information can be organized in four fundamental ways: 1) Characters may exist as single independent bits or states of information. In these cases the character state is either present or absent and alternative states or conditions do not exist. Some biochemical features clearly belong to this level of organization (Sneath, 1957). Characters of this sort are binary characters by definition and no special coding procedures are needed. Therefore, no examples of this category are included here. 2) The majority of characters used by taxonomists are treated as a series of two or more mutually exclusive states. States are treated as if they were alternatives (alleles) in a single genetic complex (locus). In this case states are organized into dependent sets where the only restriction on the occurrence of a state is the mutual ex- clusion relationship with other states. Most phenetic studies use data sets of this sort. An example data set follows, with the charac- ter states in the body of the table. Character I II III IV Taxon L 1 1 etc. M 2 1 N 3 2 4 2 MARX ET AL.: CHARACTER STATE RELATIONSHIPS 5 These character state data are converted into a binary code by simply considering each state present (1) or absent (0), as in the procedure used by Kluge and Karris (1969). Below is the binary data matrix for this example. Character I II III Original char, state 1 2 3 4 1 2 Binary state 1 2 3 4 5 6 Taxon L 1 1 M 1 1 etc. N 1 1 1 1 It should be noted that although the character states now appear as they would if they represented independent characters, the states are still dependent variables (i.e., a taxon can only have one state per character). The maximum number of independent units of infor- mation is the number of characters. 3) It is possible to have series of mutually exclusive states that can be positionally related to each other. Not only are the character states thought to be associated through the same genetic system, but they are also thought to have a particular positional arrange- ment. Thus in an evolutionary sense some states may be separated from each other by intermediate states, which are assumed always to have been possessed by species making the shift between the two extreme states. An example follows. Each of the above states has a direct relationship to another state to which it is connected by a bond. Conceptually the bond indicates that either state can be directly changed to the other (i.e., the trans- formation can proceed in either direction). The states in the first character have the following equivalent relationships. 1 2 3 = l<->2<->3 = 1 >2 1< 2 >3 2< 3 i I 1 *- 44 4 6 FIELDIANA: ZOOLOGY, VOLUME 72 Under these circumstances states which are directly bound to more than one state have the potential of giving rise to more than one state and originating from more than one state; they are termed "focal" states. Below is a tally of the number of separate origins for each state and the number of states for which it can be a source. Character I states 1, 3, 4 each originate 1 time states 1, 3, 4 are each a source state 1 time state 2 originates 3 times state 2 is a source state 3 times A similar treatment for the second character is given below. Character II 1 - 2 = l<->2 = 1 >2 states 1, 2, each originate 1 time states 1, 2, are each a source state 1 time Because all relations are reciprocal, the number of states from which a state can originate is the same as the number of states to which it can give rise. Thus character I, state 2, can give rise to three states (1, 3, or 4). States 1, 3, and 4 each have only one inter- state relationship and are "terminal" states. The positional re- lationships are recognized in the binary code by weighting focal states (by multiple occurrence) according to the number of states to which they are directly related. A binary matrix which reflects these state relationships is given below. Character Character state Weighted state Binary state 1 1 1 2 2 2 2 3 I 2 4 3 3 5 4 4 6 II 1 1 7 2 2 8 Taxon L M N 1 1 1 1 1 1 1 1 1 1 4 ) Character states may be related to each other positionally and with respect to polarity (e. g., Marx and Rabb, 1972, p. 10). Here MARX ET AL.: CHARACTER STATE RELATIONSHIPS 7 both positional and directional information is given for a series of dependent states. Character I Each state is related to other states unidirectionally. The unidi- rectional information is incorporated into the binary data matrix by positing that taxa have not only the state they actually possess, but also all states that lie in the path of this state from its origin. Thus in Character I: Taxa possessing state 1 are coded as having state 1 " 2 " " 2&1 " 3 " 3&2&1 " 4 " 4&2&1 and in Character II : Taxa possessing state 1 are coded as having state 1 " 2 " " 2&1 This information is converted into the binary code directly for each taxon. Thus in the matrix below taxon M which possesses state 2 of character I is coded as having both states 1 and 2 because state 2 arose from state 1. Character I II Orig. character state 1 2 3 4 1 2 Binary state 1 2 3 4 5 6 Taxon L 1 1 M 1 1 1 N 1 1 1 1 1 1 1 1 1 1 It can be seen from the above that the binary code, which is a technical necessity for the computer program of the monothetic subset method, has the added advantage of allowing a high degree 8 FIELDIANA: ZOOLOGY, VOLUME 72 of flexibility in character state coding. Using the binary code, character states can be related to each other in a variety of ways. TREATMENTS OF SPECIFIC CHARACTER STATE RELATIONSHIPS Within the framework of the four fundamental types of character state relationships presented above are several treatments which may be applied to reflect various approaches and considerations. To illustrate, we start with a hypothetical set of states' for four taxa in Table 1 and a corresponding set of standard character state transformation series in Figure 1. Where mutually exclusive states of characters are recognized but no connecting relationship among states is known, states are coded independently. Each state becomes an independent binary character. This is conceptually represented for the hypothetical data set in Figure 2a, and the binary code is in Table 2a. This is strictly a phenetic treatment equivalent to the unit character desig- nations of Sneath and Sokal (1973, p. 72). This treatment is appropriate when one wishes to weight states equally or where in- formation on connectedness and polarity is unavailable. The same approach may be applied to derivative states only ( fig. 2b, table 2b) to provide the phenetics of derivative states only. This is appropriate when one wishes to eliminate primitive states from consideration, yet provide for differentiation of taxa with the mini- mum of character state information, which is unweighted. Figure 2c shows a relationship where only connectedness of states is used. The example binary data are in Table 2c. This treatment is appropriate when one wishes to recognize the positional affinity of states but not polarity, and is useful where primitive states are not inferable or where ambidirectional changes are likely (i.e., evolu- tionary reversals). 'In dealing with even modest sets of real data, the computer program available to us for the monothetic subset method generates a vast quantity of combinations of taxa with their shared character states. Objective and repeatable criteria for select- ing combinations are necessary to summarize these large arrays of combinations (Voris, 1977, p. 100). With the program we now have the number of taxa is limiting and one may be required to select taxa from the total data set. We have been in- formed by J. S. Farris of a more efficient computer program for combinatorial methods. With such a program it may be possible to scrutinize large groups of taxa with large numbers of characteristics for phyletic patterns and courses of change in suites of characters. MARX ET AL.: CHARACTER STATE RELATIONSHIPS I II III IV CHARACTERS FIG. 1. Transformation series for the four characters presented in Table 1. The primitive state is circled. Arrows indicate the direction of transformation. Figure 2d illustrates a treatment where direction relationships of all states are known. The binary Table 2d shows the primitive state is included here. This treatment is appropriate when one wishes to incorporate entire transformation series, with consequent weighting of derived states relative to their degree of derivative- ness. Figure 2e (binary Table 2e) shows a similar treatment with the most primitive state removed. This treatment corresponds to the standard character state transformation series where the primitive states are not used (Hennig, 1966). A modification which weights the primitive and focal states is an inversion of the transformation series (fig. 2f, table 2f). This is applicable when one wishes to emphasize the major relationships, rather than the differentiation of taxa contributed by the most derived states. One approach to equalizing characters is also presented here. All characters can be adjusted to have the same number of states with the insertion of hypothetical states in the transformation series (fig. 2g, table 2g). The actual positions of hypothetical states may be determined by various criteria, such as comparisons of the relationships of terminal and intermediate states in an outgroup. This treatment is applicable when one wishes to consider characters as if they were equivalent in terms of the weight given the terminal CHARACTERS III IV a 1 1 1 1 3 PHENETICS OF ALL STATES 2 2 3 2 3 2 4 b 1 1 1 1 3 PHENETICS OF DERIVED STATES 2 2 3 2 3 2 4 C 3 1 *? -i q i o q 1 /^ CONNECTED STATES o 1 w X4 d CONNECTION 2 j 2 3 3 2 3 4 1 AND POLARITY f f ALL STATES 2 iT pp T PP OP e 2 2 3 \4 3 t 3 4 \ / CONNECTION / 2 \ 2 / AND POLARITY / t t DERIVED STATES 1 1 1 f y > - x y WEIGHTING OF 2 i / \ 2 3 f XX t \ / PRIMITIVE STATES I \ / | X. f m h h m 2 2 3 3 3 4 g \ 1 "*^ s* h b 2 h EQUIVALENT t 1 4 I CHARACTERS h h h 2 4 1 1 t it 1 1 h CHARACTER 'i > 4 STATE LAYERS : im IK THIRD LAYER \ / SECOND LAYER \ / 2232 2 T \ / I I FIRST LAYER \ / 1 1 1 FIG. 2a-h. Different conceptual configurations of characters I through IV (see table 1, fig. 1 ). The primitive state is circled. Shaded states do not vary in the binary data set and thus they do not either register or differentiate. A line indicates con- nectedness, and arrows indicate direction of change (polarity). The designation "pp" refers to the pre-primitive state. This is the hypothetical condition from which the most primitive state in the study arose (Throckmorton, 1968; Voris, 1977, p. 99). This is operationally necessary in the binary coding to incorporate the primitive state into the transformation series, "h" refers to other hypothetical states. 10 MARX ET AL.: CHARACTER STATE RELATIONSHIPS 11 states. Where characters are very similar by all criteria except num- ber of states this method is especially appropriate. Another approach treats each layer of a transformation series independently (fig. 2h, table 2h). Thus primitive states are treated together as a group, as are secondary states (i.e., those states directly derived from the primitive states) and other levels, in- cluding the most derived level (Voris, 1977). Where data sets are very large this approach may be in order or when one wishes to compare or associate taxa simply on the basis of relative differen- tiation (e.g., Rabb and Marx, 1973). FIG. 3. An illustration of various character state relationships within one charac- ter (Character IV of table I). See Table 3 for the binary translation and compare to Tables 2a-f . The variety of character state relationships in this paper are presented as options. There are intermediate arrangements possible which allow maximal use of available information, including that from incomplete transformation series (fig. 3, table 3). We do not recommend the wholesale application of each treatment to all data sets. Particular treatments are recommended only where needed and appropriate. In a sequel to this paper, we will apply and analyze these treatments using several real data sets, in order to demon- strate what can and cannot be learned from these different "win- dows" into taxon relationships. Character state treatments of the kinds described above give an array of taxon relationships reflecting the limitations and emphases built into the data coding. The schematic illustrations of taxon relationships (fig. 4) from the characters processed above suggest the contrasts, but not the potential complexity in results from real data sets. SUMMARY The fundamental relationships possible among character states within characters extend from the case where the character and 1 T- o o> co r- to CM T-O FIG. 4. (see opposite). 12 MARX ET AL.: CHARACTER STATE RELATIONSHIPS 13 LAYERS 2 2. w x w w X,Y 2h FIG. 4. Simplified graphs relating taxa W-Z drawn from Tables 2a-h, showing only levels of maximum shared states. The graphs reflect the treatments of the same original data set (table 1) following the character state relationships in Figure 2. The binary data (Tables 2a-h) were literally used to provide these diagrams. More complex relationships in such data sets can be shown in a flow-chart format (e.g., Voris, 1977, p. 103, fig. 5). character state are synonymous, consisting of a single independent unit of information, to complex cases, including connectedness and polarity. The binary coding system is exceedingly flexible and use- ful in expressing these character state relationships and weighting them suitably. The monothetic subset method of Sharrock and Felsenstein uses binary data and provides a tabular array of com- binations of taxa with their shared character states. We propose that because this combinatorial method is itself free of assump- tions, it is ideal for examining relationships of taxa from the per- spective of the variety of phenetic and phyletic assumptions that can be incorporated in binary data sets as expressions of assumed character state relationships. A listing of the monothetic subset method in Fortran for the CDC6400 is available from Joseph Felsenstein, Department of 14 FIELDIANA: ZOOLOGY, VOLUME 72 Genetics, University of Washington, Seattle, Washington 98195. This version of the method lists the subsets in four different ways. Our thanks to Joseph Felsenstein, Ronald Heyer and Eric Lom- bard for their helpful comments on this manuscript. We are grateful for the financial support of the Chicago Zoological Park. TABLE 1. Character states of four characters for four taxa, W - Z. Character I II III IV Taxon W 2 3 3 4 X 2 2 2 4 Y 1 1 2 3 Z 1 1 1 2 TABLE 2a-h. Binary coded data tables representing various character state relation- ships for the characters in Table 1. a, all states are used phenetically; b, derived states only are used phenetically; c, all states are related by connectedness only; d, polarity for all states with successive derivativeness weighted; e, polarity with primitive states deleted and successive derivativeness weighted; f, reversed trans- formation series weighting the more primitive states; g, equal weighting of charac- ters by giving all characters the same number of states; h, treating character states in groups according to level of derivativeness. Note that in 2b a non-registering column for the primitive state is included for comparison with 2a although it never varies in the binary coding. In 2d and 2e, columns for the preprimitive and primitive states, respectively, register but con- tribute not at all to differentiation. Table 2a character [ II III IV original char, state 1 2 1 2 3 1 2 3 1 2 3 4 binary state 1 2 3 4 5 6 7 8 9 10 11 12 taxon W 1 1 1 1 X 1 1 1 1 Y 1 1 1 1 Z 1 1 1 1 -H O O O O i-H O O O O O O r-l i-H O O O O O O X Jx N co co |r; CO 3 CO Q) J^l 5|'8 I Hi * -c ' .5 -H I O O O O c O O O O I-H O O O -H O O O O i O O O O I rl O O ^H i O i O O O O ^H O O O O i-H i-H X 15 co i .i o O O O I-H O CN 3 i-H i-H i-H _ CO CO O O O O ,c O CD 'S | C CD t72 3 CO a -UJ 0, CM i 1 r- 1 i 1 I 1 i^ 0) C 0) C a -i o T3 '-3 j= 1 ^ CO be "crt CO II <-< o o o <2 _C E ^C CU b 2 CO ' 4J CN 2 i i i i i i o co _C CD CN C CO , , c J3 CO CO CD HH .-i ai I-H bjj 4_J 'O U CD 'S , "0 Jl 2 J CO co i> i i O O O el) E a 1 '3 cr CO IV ^ ? CD "co CO *5 c ^ JS CO S o o o> CJ CD CN CO ^H r-H 'C 3 CO - i-H CN a CD O O i I i 1 r] CD 4J CO s "3 CO CD CO 'w LH O, i ,_, ,_, ,_, 1 _ | ^ co CD a .-^ (V a L CO CO CO CO >. g _c a "3 CO CO l-c CD !> ^ ^H 03 co >> ^H CD 'CD M IS co CD = CO 3 CO c c 3 -4J 4J "2 CO fe T) CM 3 CS character original char, binary state O -S 1 1 3 CD 43 O S5 O CO "co CO 3 derivative st of 2d were US- V CO o> example beloi CO co " G T3 CO C J3 cfl ^ co 5S co C 0) _O T3 CO Cfl g-rf .2 CN C8 U B ?S Iff J c c s ca O r*- 1 C C D. co cc 16 CO ^ rvi O r-H r-H O O O O --H O r-H OS r-H r-H co oo CN C- -H O O O M CS1 CM CD _/ "S S ^ "r^ f= Jf I -H O O O O r-l O O CN CN r-H r-H O O X CM 1-1 r-H o o o o -S3 O O r-H -C r-H o o O i ^ I-H r-l r-l o o ^ 2 r-H r-H O O CO ^ O O i O co 1^ O O 1 O (1 CO I 1 r-H M * 2 r 1 r-H r 1 O CN _, T}< ^^ r-H _ ,_ r-l r-l - 2 o o O r-H r-H O O O CN ^ O i *" H *""* co CD CN r-H r-H r-H a o a ,_( 11 ^ "! JM CD =! rU r-H r 1 r 1 O "3 ^ O J= 05 r-H r-H o CD CO S CD CO O> r-H O O O j| i oo O O ^ ^ . S CN 00 O rH O O CO H3 J3 t~ r-H r-H O O JS t> o o r-H r-H r* ^ -C CD r-H r-H CO a CO CD r-H O o o o tc r-H in r-H r-H r-H r-H O) CN m O r-H o o o, CO CN Tf r-H r-l O O CO JS * M r-H r-H _g J3 00 r-H r-H O O "CO S CO -C CN r-H r-H O O -s CO r-H CO r-H r-l -0 a CN CN CO r-H r-l j.. s ^ X JH N CO C J3 r-l r^ ,-H ~ ~ * c3 o X S &o ^ -g "CO -2 ^ CM 5 ' "so co 0) w 2 >-. aracter stat state X -u O 1 co c > S.& g ^ C -5 CJ O J2 _c J3 " C CO o o 17 co cu E C 1 H m "* | l I CO CO CO I-H O O 1 ^ CO CN o o o o g 1 1 CO i-H o o o o to 2 K^ CM T}< > i CN CO CM ^ CN CM ^J Tj* ^ C*^ 1 1 O O O ^H g u .S -H ^ ^ yj co i-i i O O O O I-H O o o -* o i i CN I-H I-H -I o o 'S > ^ i -^ C8 CN CO H O O O O "* O O O ^H O O O ^H 1 1 ^H CO I-H O O O i CU 1 """ O O r* i-H ^H CN O O ^H --H ^ I-H I-H i-H o o ^H ^H ,0 a ^ 5 - ^XJHN 1 x :* N co is in % ||l o >> 1 - S -^ 2 W CC S W X *3 ^ 2 -S ^ *** QJ *-< Kr CO J 1 1 f .S H ^S u o -o ffl be .SP w ^ 111 18 MARX ET AL.: CHARACTER STATE RELATIONSHIPS 19 REFERENCES CAMIN, J. H. and R. R. SOKAL 1965. A method for deducing branching sequences in phylogeny. Evolution, 19(3), pp. 311-326. ESTABROOK, G. F. and D. J. ROGERS 1966. A general method of taxonomic description for a computed similarity measure. Bioscience, 16, pp. 789-793. HENNIG, W. 1966. Phylogenetic systematics. Univ. 111. Press, Urbana, 111. 263 pp. HEYER, W. R. 1974. Relationships of the Marmora tus species group (Amphibia, Leptodactyli- dae) within the subfamily Leptodactylinae. Contr. Sci., Los Angeles County Mus. 253, pp. 1-46. INGER, R. F. 1972. Bufo of Eurasia, pp. 102-118. In Blair, W. F., ed., Evolution in the genus Bufo, Univ. Texas Press, Austin, Tex. KLUGE. A. G. 1967. Higher taxonomic categories of gekkonid lizards and their evolution. Bull. Amer. Mus. Nat. Hist., 135(1), pp. 1-60. KLUGE, A. G. and J. S. FARRIS 1969. Quantitative phyletics and the evolution of anurans. Syst. Zool., 18(1), pp. 1-32. LlEM, S. S. 1970. The morphology, systematics and evolution of the Old World tree frogs ( Rhacophoridae and Hyperoliidae). Fieldiana, Zool., 57, pp. 1-145. MARX, H. and G. B. RABB 1970. Character analysis: an empirical approach applied to advanced snakes. Jour. Zool., London., 161, pp. 525-548. 1972. Phyletic analysis of fifty characters of advanced snakes. Fieldiana: Zool., 63, pp. 1-321. MASLIN, T. PAUL 1952. Morphological criteria of phyletic relationships. Syst. Zool., 1, pp. 49-70. RABB, G. B. and H. MARX 1973. Major ecological and geographic patterns in the evolution of colubroid snakes. Evolution, 27(1), pp. 69-83. ROSS, H. H. 1974. Biological Systematics. Addison-Wesley, Reading, Mass. 345 pp. SHARROCK, G. and J. FELSENSTEIN 1975. Finding all monothetic subsets of a taxonomic group. Syst. Zool., 24(3), pp. 373-377. 20 FIELDIANA: ZOOLOGY, VOLUME 72 SNEATH, P. H. A. 1957. The application of computers to taxonomy. Jour. Gen. Microbiol., 17, pp. 201-226. SNEATH. P. H. A. and R. R. SOKAL 1973. Numerical taxonomy. W. H. Freeman and Co., San Francisco, Calif. 571 pp. SZALAY, F. S. 1977. Ancestors, descendants, sister groups and testing of phylogenetic hypo- theses. Syst. Zool., 26(1), pp. 12-18. THROCKMORTON, L. H. 1968. Concordance and discordance of taxonomic characters in Drosophila classification. Syst. Zool., 17(4), pp. 355-387. VORIS, H. K. 1977. A phylogeny of the sea snakes (Hydrophiidae). Fieldiana: Zool., 70(4), pp. 79-169. WAKE. D. and N. OZETI 1969. Evolutionary relationships in the family Salamandridae. Copeia, 1969(1), pp. 124-137. ZEHREN, S. J. 1974. The comparative osteology and phylogeny of the Beryciformes. Unpub. Univ. Chicago thesis, 458 pp.