Chapter 2Systematics as Problem-Solving

2.1 The Problem

Systematics is primarily concerned with problem solving. This might seem anobvious statement, yet the majority of those interested in systematics and phylogenyapproach the subject as being concerned with “inferences ”, “reconstructions”, or“estimations”, as captured in the title of the most comprehensive systematics textavailable, Inferring Phylogenies (Felsenstein 2004). To treat systematics as address-ing a problem or set of problems, rather than an exercise in “reconstruction” or“inference”, admits to the possibly of testable solutions and offers a way to eval-uate data such that they can be considered either relevant or irrelevant. It admitsto the possibility of discovering taxonomic or geographic relationships rather thanimposing them. The general problem may be phrased as follows: “What are theinterrelationships among organisms?"

2.2 The Solutions

For any particular problem, the number of terminal taxa (a collection of organismsgrouped together, either species or groups of species) is specified from the outset;and it is their interrelationships that are to be discovered. For any specified numberof terminal taxa, there are a finite number of possible solutions when results arepresented as hierarchical branching diagrams or classifications. That a hierarchicalbranching diagram is utilised has significance only inasmuch as it is the graphicrepresentation of a specific relation or set of relationships, which is one way ofdepicting the Cladistic Parameter. Any solution will suggest that, among the taxabeing considered, some are more closely related to each other than they are to theremainder, thus creating new taxa corresponding to the newly discovered node unit-ing them. For example, among four taxa the total number of possible solutions is 26(Table 2.1). Of those 26, 15 are fully resolved (all inter-relationships are solved—two nodes are identified), 10 partially resolved (only some inter-relationships aresolved—one node is identified), and 1 completely unresolved (no inter-relationshipsare solved—which is not really a solution) (Table 2.1). Consider the first solution

21

22 2 Systematics as Problem-Solving

Table 2.1 All 26 solutions (cladograms) for a four-taxon (A–D) problem: 15 two-node solutions,10 one-node solutions, and one unresolved “solution”

Two-NodeCladograms

One-Node Cladograms UnresolvedCladogram

A(B(CD)) AB(CD) A(BCD) ABCDA(D(BC)) AC(BD) B(ACD)A(C(BD)) AD(BC) C(ABD)B(D(AC)) BC(AD) D(ABC)B(A(CD)) BD(AC)B(C(AD)) CD(AB)C(D(AB))C(B(AD))C(A(BD))D(C(AB))D(B(AC))D(A(BC))(CD)(AB)(AC)(BD)(AD)(BC)

in column 1, Table 2.1: A(B(CD)). The notation A(B(CD)) can be represented asa branching diagram (Figure 2.1). The diagram has two nodes, one uniting C andD (Figure 2.1a, node 2), the other uniting B, C, and D (Figure 2.1a, node 1). Eachnode might be named in a taxonomic hierarchy, such that BCD is a genus and CDa subgenus. Reference below to branching diagrams, hierarchical classifications,solutions, or cladograms all share the same meaning as a summary of relationships.

For a four-taxon problem, any of the solutions in Table 2.1 are possible, inas-much as the nodes from each union receive support from relevant data. In the

Fig. 2.1 a–c: Cladograms offour taxa. (a) A–D with twonodes, BCD and CD; (b) A–Dwith one node, BCD; (c) A–Dwith one node, CD

A

B

C

D

2

1

A

B

C

D

1

A

B

C

D

2

a

b

c

2.2 The Solutions 23

case of a four-taxon problem (A–D), if all available data support only groups CDand BCD, then the problem is relatively trivial (Figure 2.1a)—the only creditablesolution being A(B(CD)). Finding solutions becomes more complex when data con-flict rather than simply accumulate—that is, when data support alternative solutions(see Chapter 11). Mere accumulation of data—no matter how large that accumu-lation might be—is insignificant if it all points to the same solution. We discussconflicting data in more detail below, but at present we focus only on non-conflictingdata.

Some cladograms in Table 2.1 might be considered partially resolved (Table 2.1,columns 2 and 3). For example, cladogram A(BCD) has one node resolved, leavingthe possibility of further resolution (Figure 2.1b, node 1). The addition of morenon-conflicting data may result in a second node being resolved. There are threepossibilities:

A(BCD)

1 A(B(CD))2 A(C(BD))3 A(D(BC))

These possibilities are achieved by finding support for the extra node containedwithin BCD; that is, any of the three smaller groups CD, BD, and BC. These smallergroups nest within the larger group, BCD.

The cladogram AB(CD) also has one node resolved, leaving the possibility offurther resolution (Figure 2.1c, node 2). Addition of more non-conflicting data mayresult in another node being resolved. There are three possibilities:

AB(CD)

1 A(B(CD))2 B(A(CD))3 (AB)(CD)

This does not exhaust all possible solutions. The CD group may be retained butcan include within either A or B providing a further four solutions:

AB(CD)

4 A(C(BD))5 A(D(BC))6 B(C(AD))7 B(D(AC))

To allow for these possibilities requires some flexibility. If the cladogram AB(CD)is considered to be two separate statements of relationship, rather than a group, thenit remains possible that only one is found to be true. The two separate statements ofrelationships are A(CD) and B(CD). If both A(CD) and B(CD) are indeed true—thatis, receive support from further non-conflicting data, then the only possible overallsolution is AB(CD). If only A(CD) is found to be true, five further solutions arepossible:

24 2 Systematics as Problem-Solving

A(CD)

1 A(B(CD))2 B(A(CD))3 (AB)(CD)4 A(C(BD))5 A(D(BC))

If only B(CD) is found to be true, five further solutions are possible:

B(CD)

1 A(B(CD))2 B(A(CD))3 (AB)(CD)6 B(C(AD))7 B(D(AC))

As solutions 1–3 are common to each series, there is a total of seven possiblesolutions (Table 2.2). In Table 2.2, cladograms 1–3 correspond to what Nelson &Platnick (1980) call Interpretation 1, based on the interpretation that C and D aremore closely related to each other than either is to A or B (Nelson & Platnick 1980).That is, C + D remain each other’s closest relatives. Interpretation 1 is analogousto Assumption 1 in biogeographical problems (Platnick 1981, Nelson & Platnick1981, Humphries & Parenti 1999). Cladograms 1–7 correspond to what Nelson &Platnick (1980) called Interpretation 2, based on the assumption that C and D aremore closely related to each other than either of them is to A and/or B (Nelson& Platnick 1980). Interpretation 2 is analogous to Assumption 2 in biogeographicproblems (Platnick 1981, Nelson & Platnick 1981, Humphries & Parenti 1999).

2.3 Discovering Solutions

Taxonomic problems change as data accumulate and additional terminal taxa be-come relevant. In spite of arguments to the contrary (e.g., Graybeal 1998), increasingthe number of taxa simply changes the nature of the problem (Platnick 1977b: 440).For example, with one additional taxon, a four-taxon problem with 26 possible solu-tions becomes a five-taxon problem with 236 possible solutions. With more terminaltaxa, the number of solutions increases at an alarming rate (Table 2.3). 1

If increasing the number of taxa changes only the magnitude of the problem, thenprogress in systematics is limited to three options:

1. The acquisition of new data (characters)2. Re-examination of data (characters) already studied3. Consideration of data (characters) representation

1 The mathematical formula for this progression is given in Felsenstein (1978).

2.3 Discovering Solutions 25

Table 2.2 All possible cladograms for four taxa relative to the cladogram AB(CD). Solutions 1–7can be found with more non-conflicting data.

Character AB(CD)

All possible cladogramsfor four taxa

Solution of Nelson & Platnick(1980)

Two-node trees

1.B(A(CD)) Interpretations 1 & 22.A(B(CD)) Interpretations 1 & 23.(AB)(CD) Interpretations 1 & 24.A(D(BC)) Interpretation 25.A(C(BD)) Interpretation 26.B(C(AD)) Interpretation 27.B(D(AC)) Interpretation 28.C(D(AB))9.C(B(AD))10.C(A(BD))11.D(C(AB))12.D(B(AC))13.D(A(BC))14.(AC)(BD)15.(AD)(BC)

One-node trees

16.A(BCD)17.B(ACD)18.C(ABD)19.D(ABC)20.AB(CD) Original Character21.CD(AB)22.BD(AC)23.BC(AD)24.AD(BC)25.AC(BD)26.(ABCD)

Table 2.3 Relationship between numbers of terminal taxa (T) and numbers of possible cladograms(solutions). Figures given for T = 3 to T = 10

T Cladograms

3 44 265 2366 2,7527 39,2088 660,0329 1,281,89210 282,137,824

26 2 Systematics as Problem-Solving

These three options exhaust all possibilities (Platnick 1977b, Patterson 1981a).The first option is straightforward. In the last two decades, for example, the primarysource of new data has been DNA nucleotides, having a profound effect on studies inphylogeny and classification (Cracraft & Donoghue 2004). Yet systematists workingon a wide range of organisms continue to find new and unknown non-molecularcharacter systems (e.g., Smith & Stockley 2005). Regardless of their source, newdata are always welcome.

The second option above deals directly with the issue of re-investigating charac-ters already known—or characters assumed to be known—to verify or confirm theirinternal consistency. Thus, many comparative biologists are occupied with the samequestion: Is this identified “part” of one organism really the same as that “part” inanother organism? A recent example is the “parts” of turtles (Lee 1996, 1997, Riep-pel 1996, DeBraga & Rieppel 1997; see Vickaryous & Hall 2006). The pectoralgirdle of turtles is a highly derived structure among primitive reptiles and turtles.The endochondral shoulder girdle (scapulocoracoid) in primitive reptiles consists ofa scapula (lacking anterior processes) and two discrete coracoids, anterior and pos-terior (Figure 2.2). In Pareiasaurs the scapulocoracoid consists of a scapula with ananterior, acromion-like process, and two discrete corcoids (anterior and posterior).The acromion-like process has been interpreted as a “flange of scapula”. In turtles,there is a well-developed flange to the scapula. There are conflicting propositionsof “sameness” concerning the “flange of scapula”: Either the flange is understoodto be a modified anterior coracoid, hence the flange of the scapula in Pareiasaursis a unique character (an autapomorphy) (Lee 1998), or the anterior coracoid hasbeen lost in turtles and the flanges in Pareiasaurs and turtles are really the “same”(homologous and synapomorphic) (Rieppel 1996). Each interpretation may producedifferent relationships (Lee 1996, 1998, Rieppel 1996).

ba

Fig. 2.2 Two illustrations of the turtle shoulder girdle. (a) From Lee (1997: 234, Fig. 12); (b) fromDe Braga & Rieppel (1997: 303, Fig. 2), reproduced with permission of Blackwell Publishing.

2.3 Discovering Solutions 27

Identifying the shared “parts” of organisms remains very much a central task ofsystematic investigations.2 Resolution of such issues leads to a greater understand-ing of the organisms in question. The “parts”, when identified, are usually referredto as homologues. Comparison of various parts of organisms is often understoodas determining their homology. Below we develop the notion that the homologuetaken alone is the part, while homology is the relationship derived from the parts.This distinction, only recently appreciated, is of central significance. It is directlylinked to the third possibility above, that of data representation.

The notion that homology is discovered had led some systematists, primarilythose interested in numerical methods, to suggest a fourth option for progress:

4. Examination of the method to discover “congruent” distribution of characters

Here we might consider Felsenstein’s comment that “. . . statistical, computa-tional, and algorithmic work on them [phylogenetic trees] is barely 40 years old”(Felsenstein 2004: xix). Remarkably, that 40 years has not produced a consensus—nor even attempted to—or even found agreement concerning what might bestbe achieved from “statistical, computational, and algorithmic work”. Felsenstein’sbook is a good example, as he suggests no preference for the very many methodshe summarises, leaving the reader to ponder the general usefulness of these past 40years’ endeavour. Still, of methods there are plenty, spawning an industry that showsno sign of abating—again, the general idea seems to be that the more methods avail-able, the better the chance of discovering . . . well, discovering what? This questionis something we concern ourselves with below.

Homology is considered indispensable to systematic enquiry and is understoodas “. . . the most important principle in comparative biology” (Bock 1974: 386,Patterson 1982a: 22). Be that as it may, we believe that the following questionremains unanswered, or at least has not hitherto been fully articulated. Relative tothe Cladistic Parameter, is there a “unit” of classification or a “unit” of phylogeny,derivable from our understanding of homologues (the parts of organisms) and, ulti-mately, of homology (their relationship)?

The idea that there might be a basic “unit” for classification (and phylogeny)will be either appealing or irrelevant, depending on one’s point of view (cf. Jardine1969a: 44, Colless 1972). To offer some focus on the formation of this point ofview, we first provide a historical account of the archetype (Ebach 2005, Chapter 3),exploring a concept that has engendered much discussion but little clarity. We thendiscuss the development of the concept of homology to illustrate that, as we under-stand the issue, there always were two central concepts in comparative biology, oneregarding “homologues”, the other “homology”. That the two concepts have becomeinextricably intertwined with each other over the last 150 years is significant, as weshall demonstrate (Williams 2004).

2 A major source of concern in molecular systematics is their alignment, bringing the sequencesof nucleotides into line with each other. In one sense, this operation is the same as that whichmorphologists regularly use. Any two sequences, if there are mismatches, differ in certain areasand their alignment is not at all straightforward.