Syst. Biol. 49(3):480–500, 2000
Taxic Homology and Three-Taxon Statement Analysis
R OBERT W. S COTLAND
Department of Plant Sciences, University of Oxford, South Parks Road, Oxford OX1 3RB, United Kingdom;
E-mail: [email protected]
Abstract.—Three-taxon statement analysis (3TA) and standard cladistic analysis (SCA) were evaluated
relative to propositions of taxic homology. There are deŽnite distinctions between complement relation
homologs and paired homologs. The complement relation is discussed, relative to rooting, parsimony,
and taxic propositions of homology. The complement relation, as implemented in SCA, makes sense
only because SCA is a simple evolutionary model of character-state transformation. 3TA is a method for
implementing complement relation data from a taxic perspective. The standard approach to cladistic
analysis distinguishes taxa by rooting a tree, which means that that approach is incompatible with
taxic propositions of homology, because a taxic homology is a hypothesis of relationship between
taxa that possess a homolog relative to taxa that lack a homolog. It is not necessary to treat paired
homologs from a transformational perspective to distinguish informative from uninformative data.
3TA yields results markedly different from those of SCA. SCA, which seeks to minimize tree length,
may not maximize the relation of homology (congruence) relative to a tree. [Cladistics; taxic homology;
three-taxon statement analysis.]
Three-taxon statement analysis (3TA) is a
parsimony-based tree building method that
utilizes items of information (three-taxon
statements) implied by homology propositions (Nelson and Platnick, 1991) to elucidate relationships between taxa. Standard
cladistic analysis (SCA) is a parsimony-based
tree building method that seeks to construct the most-parsimonious network of
character-state changes. Standard cladistic
analysis and 3TA are discussed and evaluated relative to two classes of taxic homology propositions distinguished by Patterson
(1982): Žrst, homology propositions of the
type termed complement relation, that is,
the presence of a structure relative to its absence, and second, homology propositions,
termed paired homologs, which are different
structures that share topographic correspondence. The complement relation describes a
topographically corresponding structure, a
homolog, shared by some taxa but absent
from others at a particular hierarchical level
(Patterson, 1982:48). For example, presence
and absence of a carpel at the level of seed
plants constitutes a complement relation homolog. Paired homologs are topographically
corresponding structures present in different
forms in taxa at a particular hierarchical level.
For example, hyomandibula and stapes are
paired homologs at the level of gnathostomes
(Patterson, 1982:53).
From the perspective of taxic homology,
“the force of a hypothesis of homology is that
the inclusive group is monophyletic by virtue
of the homology” (Patterson, 1982:34) and
“every hypothesis of homology is a hypothesis of monophyletic grouping” (Patterson,
1982:33). Patterson’s taxic view of homology is that of a relation between taxa that
possess a homolog relative to taxa that lack
the homolog. From this perspective, complement relation homologs and paired homologs have different implications for understanding relationships between taxa. This
is because complement relation homologs
result in a single proposition of taxic homology, whereas paired homologs result in
two propositions of taxic homology. The two
types of relation are not distinguished in SCA
because the coding method assumes transformation between character states. Thus
complement relation homologs are characterized by a transformation between absence
and presence, and paired homologs are characterized by a transformation between two
or more alternative character states. This approach has been criticized because the homology between character states is never
questioned in SCA (Pleijel, 1995); rather, a
transformational relationship between the
character states is simply assumed (Nelson,
1994; Pleijel, 1995; Carine and Scotland,
1999). In the context of other data, SCA
merely minimizes the number of times a
transformation occurs, but the transformational relationship between the character
states is never tested.
The view that the absence part of a complement relation homolog cannot constitute
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a hypothesis of homology (Nelson, 1978;
Patterson, 1982) is at odds with the implementation of SCA and the vast majority of published SCA data matrices. At the
stage of data matrix construction, SCA is
agnostic to any particular explanation of
absence until the tree is rooted. Coding
absence as a character state makes sense
within the context of character transformation that seeks to view all character states
through the lens of plesiomorphy, synapomorphy, and homoplasy to be optimized
within the most-parsimonious reconstruction of character-state changes. For this reason, SCA implements a model of character evolution, albeit a simple one. Treating
absence as a character state within an explicit model of character evolution also assumes homology (Hennig’s auxilliary principle) within those taxa that lack a particular
homolog. Although groups in any analysis
are given by rooting the tree, taxa that lack
a feature are partitioned together on the unrooted tree because they share the lack of a
structure. Alternatively, Carine and Scotland
(1999) argue that for seed plants, for example, the possession of a carpel is a hypothesis of a group (angiosperms) relative to other
seed plants, whereas the absence of a carpel
is not (gymnosperms). Possession of a carpel
is thus a homolog that applies to certain taxa
but is inapplicable for other taxa that lack a
carpel. Advocates of this approach argue that
it makes no sense, at the level of all organisms, to partition taxa together on the basis
that they lack a carpel, because this adds to
the possibility that those taxa will be recognized as a group, albeit such a result is dependent on the position of the root. Coding
absence of a carpel makes sense only for tree
building methods that seek to explain all data
and the lack of it in the context of character
evolution.
Paired homologs treated as transformations have also been challenged from advocates of 3TA on the basis that character
states are treated as ancestral. Nelson (1994)
stated that although ancestral taxa have no
place in a systematic analysis because all
taxa are treated as terminals, ancestral characters retain a central role in SCA. The importance and primary role of a transformational view of cladistic characters are linked
directly to how characters are coded in a
matrix. Published studies present a spectrum of opinions as to what counts as trans-
481
formations, albeit unordered, for the same
structures and taxa. For example, compare
the data matrices and coding protocols of
Crane (1985), Doyle and Donoghue (1986,
1992), Loconte and Stevenson (1990), and
Nixon et al. (1994) for seed plants. Other studies (Pleijel and Dahlgren, 1998) ignore any
notion of paired homologs and all character
states are coded in absence/presence format.
In still other studies (for review, see Hawkins,
2000), analyses consist of a mixture of characters, some coded as transformations and others coded in absence/presence format, often
without discussion or justiŽcation. Given the
plethora of coding protocols utilized in standard cladistic matrices, it is difŽcult to argue that a transformational view of cladistic
characters is central to the method because
these are subordinate to and determined by
the coding protocol.
Treating character states as ancestral and
as part of transformations has also been discussed from the perspective of orthology and
paralogy in molecular systematics by Nelson
(1994). With reference to a Žgure from Li
and Graur (1991:152, their Fig. 8) illustrating the evolution of human globin genes,
where individual genes are viewed as terminals rather than any gene as ancestral, Nelson
(1994) argues that gene trees are the equivalent of character-state trees. Characters (gene
family) or their states (gene) need not be
treated as ancestral to understand their relationships relative to a tree. Nelson’s logic has
similarly been applied to homologs (Nelson
and Platnick, 1991), which can be treated as
properties of terminal taxa for the purpose
of estimating the systematic hierarchy. A homolog can therefore be evaluated relative to
all possible trees and other data, by expressing a given homolog in the form of its smallest constituent units, which are three-taxon
statements. Figure 1a demonstrates that a
homolog shared by all taxa is uninformative. Figure 1b demonstrates the relation of
homology, which is a relation between taxa
that share a homolog relative to taxa that
lack a homolog. The information content of
a hypothesis of homology can be expressed
in the form of three-taxon (item) statements
(Fig. 1c). For the purposes of analysis, a given
three-taxon statement coded (11)0 is accommodated or not, relative to a tree as evidence
of relationship. An evolutionary tree is a hierarchy of relationships between taxa and has
been described as a hierarchy of homology
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FIGURE 1. Homologs, homology, and three-taxon statements. (a) A homolog shared among four taxa is uninformative. (b) A homolog shared among four taxa but absent from two taxa results in a hypothesis of homology.
(c) Homology (ABCD)EF can be expressed in the form of 12 three-taxon statements.
(Rieppel, 1988). 3TA utilizes the relation of
homology in an attempt to estimate taxa
(taxic homology). In contrast, SCA seeks to
minimize tree length of character-state transformations (Farris, 1983). SCA treats characters and their states as ancestor–descendent
character-state changes.
Sattler (1984, 1994) has also taken issue
with a transformational view of morphological characters and their states. Sattler
(1984) argued that the proposed transformation not only is unobserved, it is usually, in principle, unobservable, because no
direct material transformation of structures
ever occurred (for discussion, see Weston,
2000). Sattler (1994:459) stated that “In each
generation, organisms are (re)constructed
(Goodwin, 1984:114; Oyama, 1988, 1989), and
in this (re)construction more or less similar or
different character states may appear,” and
(1984:385) that “a ower does not give rise to
another ower.” Sattler (1994) agreed with
Hay and Mabberley’s (1994) view that the
concept of character-state transformation involves a category error; because characters
and their states are hypotheses, that is, ideas,
they cannot be said to have participated in
phylogenetic transformation, a real process
(Weston, 2000).
Here, I explore 3TA in the context of
complement relation homologs and paired
homologs. The structure of the paper is as
follows. First, I discuss complement relation homologs in the context of taxic homology and SCA. Second, I discuss hypotheses of taxic and transformational homology
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483
in the context of character polarity. Third,
I introduce 3TA. Fourth, I discuss an example, analyzed by using SCA and 3TA,
demonstrating that minimizing tree length
of character-state transformations does not
maximize the relation of homology relative
to a tree.
T HE COMPLEMENT R ELATION
The Complement Relation
and Character Coding
The complement relation is a hypothesis
of taxic homology at a particular hierarchical level where some taxa possess a structure (present) and other taxa do not (absent). Patterson (1982) rightly characterized
the complement relation as including a part
(absence) of a homology proposition that
failed his similarity test because absence contains no similarity or topographic correspondence. Consider four terminal taxa (ABCD),
two of which (AB) share a homolog (present)
and two of which (CD) lack the homolog
(absent). These data are compatible with only
one of the three possible unrooted trees for
four taxa that pairs (AB) relative to (CD) and
pairs (CD) relative to (AB) (Fig. 2). Part of
Figure 2 pairs A and B relative to C and D
based on a homolog possessed by (AB) but
lacking in C and D. The unrooted tree also
recognizes a second component that pairs
(CD) relative to A and B. The (CD) component differs from the (AB) component in
that it is not supported by any data. The
taxic representation of these data is Figure 3,
which recognizes (AB) by the shared homolog but treats C and D, both of which
lack the homolog, separately from (AB) and
also independently from each other. The relational aspect of these data imply two conclusions relative to a tree: (AB) share a node
FIGURE 2. The most-parsimonious unrooted tree for
one complement relation homolog, present in AB and
absent in CD.
FIGURE 3. One complement relation homolog shared
among four taxa from the perspective of taxic homology, demonstrating that only the presence part of the
homolog is informative.
relative to C and (AB) share a node relative
to D (Fig. 3). When constructing a data matrix for analysis with current parsimony programs, characters of the complement relation
kind are usually coded in binary format and
treated as unrooted transformations. In these
situations the absence of a homolog has equal
status to the presence of a homolog.
The Complement Relation and Rooting
Complement relation homologs are routinely coded in standard binary notation, assigning either a 0 to denote the presence of
a homolog and a 1 for the lack of the homolog (Fig. 4a), or a 0 for absence and a
1 for presence (Fig. 4b). Whether presence
or absence is assigned 1 or 0 is immaterial,
because both character states will be treated
as equivalent. Consider six taxa (ABCDEF)
with three homologs of the complement
FIGURE 4. Complement homologs coded in binary
form. (a) 0 = presence; 1 = absence. (b) 0 = absence; 1 =
presence.
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TABLE 1. Data matrix of three complement relation
homologs shared among six taxa and the implied components based on absence and presence.
Homologs
Taxon
1
2
3
A
B
C
D
E
F
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1 = present; 0 = absent.
Present components
AB1
ABE2
ACF3
Absent components
CDEF1
CDF2
BDE3
Superscript number = homolog number.
relation type. In Table 1, these data are coded
in binary notation (and the components they
imply), using a 1 to denote possession of a
homolog and 0 to denote absence of a homolog. Table 1 also illustrates how components based on absence can accumulate in a
data matrix when characters are of the complement relation type: Taxa sharing the absence part of the complement relation are
partitioned together because existing parsimony programs distinguish components
based on a numerical code but cannot distinguish components based on possession of
a homolog from those based on absence of a
homolog. Figure 5a, the most-parsimonious
unrooted tree for these data, shows that all
internal branches of the tree are supported
by character-state changes. However, if the
tree is rooted on the internal branch between
(AB) and (CDEF), as shown in Figure 5b, two
of the original components that are based
on absence (CDEF) and (DCF) are now part
of the fully resolved topology and are supported by apparent synapomorphic absence
characters. Consider taxon D, which shares
no homolog with any other taxon but has become incorporated into the tree (Fig. 5b). Secondary losses (homoplasies), such as characters 1 and 2 (Fig. 5b), are derived from coding
absence of a homolog as a character state and
from the choice of root for the tree. Homoplasies such as characters 1 and 2 do not require ad hoc hypotheses (extra steps) on the
tree. For SCA, such an approach makes sense
within the context of coding secondary loss
as a possibility relative to a simple model of
character-state transformation.
FIGURE 5. Trees from the data in Table 1. (a) Mostparsimonious unrooted tree. Arrows indicate the direction in which the possession of a homolog is present.
(b) Rooted tree, showing that clades CDF and CDEF are
not supported by the possession of a homolog.
From a taxic perspective the complement
relation homologs from Table 1a can be
depicted in relation form as in Figure 6a.
Figure 6a shows the three-taxon statements
implied by these data. Figure 6b is the
minimal tree for these data that maximizes
the relational aspect of all three homology
propositions relative to a tree. Figure 6b
accommodates 16 statements as evidence
of relationship, whereas 6 statements are
not accommodated and are not evidence of
relationship (nonhomology).
The Complement Relation and Parsimony
in the Context of Transformation
Consider the data matrix in Table 2 for
Žve taxa (ABCDE) and Žve homologs of the
complement relation type, with the 1 representing presence and the 0 representing
absence. Analysis of this matrix with SCA
result in two most-parsimonious unrooted
trees of six steps (Fig. 7). Comparing both
trees with the components based on presence versus those based on absence (Table 2)
shows that both trees are supported by the
presence of three homologs that display no
homoplasy on the trees (Fig. 7). Figure 7a
is supported by homologs 1, 2, and 3, and
Figure 7b is supported by homologs 2, 3,
and 4. For Figure 7a, homologs 2 and 3 support (ABD) and homolog 1 supports (AB).
The three homologs specify the same pattern, which is the unrooted tree (Fig. 7a). For
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FIGURE 6. The data from Table 1 represented as homology propositions relative to the minimal tree. (a) Three
complement relation homologs as hypotheses of homology and the implied three-taxon statements. (b) The minimal
tree for these data, incorporating 16 three-taxon statements and not accommodating 6 statements.
TABLE 2. Data matrix of Žve complement relation homologs shared among Žve taxa and the implied components based on absence and presence.
Homologs
Taxon
1
2
3
4
5
A
B
C
D
E
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1 = present; 0 = absent.
Present components
AB
ABD2
ABD3
ACE4
1
Superscript number = homolog number.
Absent components
CDE1
CE2
CE3
BD4
ABCD5
Figure 7b, homologs 2 and 3 support (ABD)
and homolog 4 supports (ACE). A group consisting of (ACE), which is supported by homolog 4, is, however, contradicted by (ABD),
which is supported by homologs 2 and 3.
Figure 7b thus seems problematic, because
the position of taxon A is contradicted by
homologs 2 and 3 relative to homolog 4.
However, Figure 7b is made possible because all character-state changes are treated
as equivalent; the contradictory nature of
(ACE), supported by homolog 4, and (ABD),
supported by homologs 2 and 3, cannot be
distinguished from (ABD), supported by homologs 2 and 3, and (BD), supported by the
absence of homolog 4. Absence of homolog 4
deŽnes (BD); moreover, this is treated as
a character-state change nested within homologs 2 and 3, which support (ABD). In this
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However, for topographically corresponding
homologs such as hyomandibula and stapes
at the level of gnathostomes, the situation is
rather different, as explored in the next section. To distinguish between complement relation homologs and paired homologs may
not always be straightforward. For example,
at the level of the angiosperm carpel, other
nonangiosperm taxa simply lack a carpel.
In other situations, greatly reduced modiŽcations (snake legs) are easily reconciled as
modiŽed and not absent. At the DNA level,
the absence of a length of sequence (deletion) is given by the topographically corresponding identity of the alignment and
so is not comparable with the situation of
simply lacking a carpel. The distinction between complement relation homologs and
paired homologs demands rigorous anatomical investigation, as is true for any homolog,
to rule against the matrix as a black box
(Patterson and Johnson, 1997).
FIGURE 7. Two most-parsimonious unrooted trees
for SCA for the data from Table 2. Arrows indicate the
direction in which a homolog is present. (a) Topology
supported by homologs 1 (AB), 2 (ABD), 3 (ABD), and
4 (CE). (b) Topology supported by homologs 2 (ABD),
3 (ABD), and 4 (ACE), which specify a contradictory
pattern.
example, treating absence as a character state
has resulted in a solution not validly supported by taxic homology. Absences such as
these are not discovered by cladistic analysis
but are imposed on an unrooted tree by an
algorithm that treats absence as a character
state, equivalent to all other entries in the
matrix.
Cladistic matrices that treat the complement relation in this way are treating the absence of data as equivalent to the presence of
data within the context of a particular model
of character evolution. The Žve complement
relation homologs from Table 2 are depicted
in Figure 8a, which shows each homolog as a
relation of homology and the implied threetaxon statements. Figure 8b is the minimal
tree for these data, maximizing homology
in the form of accommodated three-taxon
statements. From a taxic perspective, complement relation homologs provide unambiguous data that result in a hypothesis of
relationship between taxa that possess a homolog relative to taxa that lack the homolog.
In a sense, character polarity is given in such
data because only the shared possession of a
homolog provides evidence of relationship.
TAXIC AND TRANS FORMATIONAL
HOMOLOGY
Patterson (1982) distinguished two approaches to the study of homologies, which
he called taxic and transformational homology, terms derived from the taxic and transformational approaches to evolutionary theory described by Eldridge (1979). According
to Patterson (1982:34), “The taxic approach
[to the study of homology] is concerned
with monophyly of groups. The transformational approach is concerned with change,
which need not imply grouping.” Taxic homology has been discussed in a cladistic context from two very different points of view.
Rieppel (1994:90) stated that “homology is
not a transformation of an ancestral to a descendent character state. Instead homology
is a unique and deviant condition of form,
diagnostic of the particular taxon in question.” In contrast, de Pinna (1991:376) held
that “the proposal that a structure in one organism or taxon is a transformation of one
in another is essentially taxic.” For four taxa
(ABCD) in which taxa A and B share character state x and taxa C and D share character state x 0 , initially, two groups (AB) and
(CD) are hypothesized from a taxic perspective (Patterson, 1982:52). From a transformational perspective, however, no groups are
hypothesized until the tree is rooted; rather,
the data imply only a transformation x $ x 0 .
Consider, four taxa (ABCD), wherein (AB)
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487
FIGURE 8. The data from Table 2 represented as homology propositions relative to the minimal tree. (a) Five
complement relation homologs as hypotheses of homology and the implied three-taxon statements. (b) The minimal
tree for these data, incorporating 17 three-taxon statements and not accommodating 4 statements.
possess x (e.g., Žns) and (CD) possess x 0 (e.g.,
forelimbs) and that (x + x 0 ) = y (e.g., paired
appendages). A salient difference in the approaches of Rieppel (1994) and de Pinna
(1991) is whether the two character states x
and x 0 are represented as x + x 0 = y or x $ x 0 ,
respectively. Adopting Rieppel’s taxic view,
to consider the homology between x and x 0 as
equaling homolog y is uninformative at the
level of ABCD because all of those taxa have
paired appendages. Instead, within ABCD
are two putatively informative homologs,
x and x 0 , which are to be tested by analysis. Adopting de Pinna’s (1991) view within
the context of SCA, a transformation between x $ x 0 is postulated and termed primary homology sensu de Pinna (1991). Subsequent analysis of the transformation x $ x 0
in the context of SCA tests how many times
(once or more than once) the transformation occurs but never questions the transformational relationship between x and x 0 .
De Pinna’s (1991) notion of primary homology is equivalent to a column in a cladistic data matrix that is plesiomorphic for all
taxa included in the matrix. Given the conjectural and hypothetical nature of homology propositions, assuming a transformation of character states is problematic because
homology between states is never tested.
De Pinna’s (1991) notion of primary homology is an untested hypothesis of characterstate transformation because the transformational relationship is always assumed.
The decision that two character states be
treated as a transformation is determined
by topographic correspondence, which is
equivalent to the similarity test of Patterson
(1982). Whether similarity can ever constitute a proper test has been much discussed
(Bock, 1977; Cracraft, 1981; Patterson, 1982;
Stevens, 1984; de Pinna, 1991), and similarity
has been described as a criterion rather than
a test (de Pinna, 1991). Despite the importance of topographic correspondence for the
determination of homologs, processes such
as homeosis (Sattler, 1984, 1994) and multiple substitution in DNA sequence data show
that transformation/substitution may not be
understood by simply assuming, on the basis
of similarity, the most-parsimonious transformation between extant character states.
For 3TA, all observations are tested during
analysis and either provide evidence of relationship or not.
Patterson (1982:52) provided three Venn
diagrams for exploring the possible relationship between two character states, termed
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FIGURE 9. Patterson’s (1982) view of paired homologs, before analysis, in relation to character polarity. (a) Homolog x 0 speciŽes a group and x does not.
(b) Homolog x speciŽes a group and x 0 does not. (c) Both
homologs x and x 0 specify groups.
paired homologs, x and x 0 , here reproduced
as Figure 9. In Figure 9a, x 0 is diagnostic of a
group and x is not; in Figure 9b, x is diagnostic of a group and x 0 is not; and in Figure 9c,
both x and x 0 are diagnostic of groups. A
crucial aspect of the three possible relations
between the two homologs, explored by
Scotland (2000), is that Figure 9c includes the
informative parts of both Figures 9a and 9b;
it effectively summarizes all possible informative homologs for these data at this hierarchical level. Therefore, the relation between the two homologs is explored in the
context of other data and relative to how
they diagnose groups on a tree. Characterstate distributions such as x in Figure 9a
and x 0 in Figure 9b are uninformative about
relationships within (ABCD). Homologs x
and x 0 are paired only in the sense of topographic correspondence—“an essentially
imprecise and subjective process” de Pinna,
(1991:377)—and in the sense that they may
together make up a homolog at a higher
taxonomic level (Patterson, 1982; Rieppel,
1988).
It is not necessary to treat paired homologs
from a transformational perspective to discover the informative parts of these data relative to a tree. For example, consider the tree
(A(B(CD))) given by other data; x is found in
(AB) and x 0 in (CD). Figure 10a is the SCA
explanation for these data in that x is treated
as plesiomorphic (uninformative) and x 0 is
viewed as a synapomorphy for the node
(CD). Figure 10b is the 3TA explanation that
accommodates two three-taxon statements
as evidence of relationship and a further two
that do not provide evidence of relationship
relative to the tree. SCA interprets paired
homologs from a transformational perspec-
FIGURE 10. Distribution of a paired homolog (x and
x 0 ) relative to a given tree. (a) Homolog x is uninformative about relationships in the context of SCA and would
be considered plesiomorphic. (b) Homolog x results in
two three-taxon statements that are not accommodated
on the tree.
tive relative to plesiomorphy and synapomorphy. 3TA seeks only to establish informative homologs (or parts thereof) as evidence
of relationship relative to all possible trees.
Adopting this approach of treating all
homologs as potentially informative means
that informative (homology) and uninformative (nonhomology) homologs emerge from
analysis of all data relative to all possible
trees. Relative to Figures 9 and 10 and the relations between taxa, character polarity comprises two distinct elements—an informative part (homology) and an uninformative
part (nonhomology)—which agrees with
Patterson’s (1982:21) assertion that synapomorphy and homology are the same.
For example, paired appendages (Žns +
forelimbs) constitute a homology at the level
of gnathostomes. Within gnathostomes, Žns
do not form a group and are therefore
nonhomology. Forelimbs diagnose a group
(tetrapods) and are homologous at the level
of tetrapods. At some hierarchical levels, polarity of some paired homologs is obvious
in that the ingroup (x and x 0 ) are hierarchically nested at a level in which all outgroup
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taxa have x. For example, at the level of
Acanthaceae, some taxa have retinacula
(modiŽed funiculus), whereas other taxa
have an unmodiŽed funiculus, which they
share with all other plant families. Polarity is straightforward and in these situations a paired homolog (x and x 0 ) within
Acanthaceae reduces to one informative homolog for analysis of Acanthaceae. However,
the assumption in such examples is that
the ingroup (Acanthaceae) is already established. In many situations, the polarity seems
straightforward in that ingroup taxa possess
(x and x 0 ) and outgroup taxa possess only
(x). For such a situation, x may be plesiomorphic at the level of ingroup plus outgroup,
and so remains uninformative at the level
of ingroup plus outgroup. The explanation
of x and x 0 for the ingroup will depend on
the relationships between ingroup taxa relative to a tree (see below and Fig. 11). However, polarity discussed with reference to
this type of example (high-burden homologs)
obfuscates the situation found in most studies. In many studies, a putative ingroup that
possesses (x and x 0 ) is nested within other
taxa that also possess x and x 0 . Such situations lead to the inŽnite regress of outgroup comparison (Colless, 1984) in the
attempt to optimize ancestral character transformations. For this reason, advocates of 3TA
have taken issue with the estimation of ancestral character states because it is optimization dependent (Platnick et al., 1996). Consider a paired homolog (x and x 0 ) shared
among Žve taxa (Fig. 11a), such that before
analysis, (AB) are putative outgroups. These
data are shown, relative to a given tree, in
SCA format (Fig. 11a) and 3TA (Fig. 11b)
format. Homolog x, which is possessed by
(ABE), is denoted x1 , x2 , and x3 , and homolog x 0 is denoted x10 and x20 to facilitate
discussion. Figures 11c–e, are three different SCA explanations of these data, which
explain x 0 as parallelism (Fig. 11c), apomorphic to a reversal (Fig. 11d), or plesiomorphic (Fig. 11e). All three explanations are
length two, involving one ad hoc hypothesis within the constraints of a transformation model of character evolution. For 3TA,
optimization is irrelevant to how data Žt a
tree. Homolog x 0 results in three three-taxon
statements (Fig. 11b). Homolog x results in
six statements (Fig. 11b). The tree accommodates four statements (Fig. 11f) as evidence
489
for a relationship among the homologs, taxa,
and the tree.
Figures 12a and 12b show two topographically corresponding homologs from the perspective of SCA (Fig. 12a) and 3TA (Fig. 12b).
Figures 12c–g show Žve possibilities for these
data. The maximum length for these data
within the context of SCA is two (i.e., two
transformations: Figs. 12f and 12g). In this
context, parsimony is applied within the constraint of assumed character-state transformation. Figures 12f and 12g could be interpreted as evidence that x 6 = x, x 0 6 = x 0 and that
x and x 0 are separate characters that do not
provide evidence of relationship at any hierarchical level (Fig. 12k). This explanation is
precluded by SCA because the transformation x = x 0 is simply assumed (Figs. 12c–g)
and SCA can only discover x 6 = x (Fig. 12g) or
x 0 6 = x 0 (Fig. 12f). Elsewhere, I have demonstrated (Scotland, 2000) that any homolog,
despite its distribution among taxa, can be
accommodated at the base of a tree with no
extra steps. In the context of parsimony and
assumed transformation of character states,
plesiomorphic explanations for incongruent
homologs have no competitors. Figure 12b
shows the four three-taxon statements that
result from these data. Figures 12h–k show
four possibilities in the context of other
data and illustrate a decreasing number of
accommodated three-taxon statements relative to whether the data provide evidence
of relationships between taxa. In contrast,
Figures 12c–g demonstrate that a relationship between character states is always assumed in the context of SCA. However,
assuming untested character-state transformations has a profound effect on to what extent data provide evidence for nodes on a
tree. This is explored in the next section.
T HREE-TAXON S TATEMENT ANALYSIS
Nelson and Platnick (1991) proposed a
new method of systematics termed threetaxon statement analysis (3TA). Judging by a
number of sceptical rebuttals (Harvey, 1992;
Kluge, 1993, 1994; Farris et al., 1995; De
Laet and Smets, 1998; Farris and Kluge,
1998) and the paucity of 3TA in the published literature (Nelson and Ladiges, 1994;
Nelson, 1996; Udovicic et al., 1995; Williams,
1996; Carine and Scotland, 1999; Scotland,
2000), the method has not yet met with any
490
S YSTEMATIC BIOLOGY
VOL. 49
FIGURE 11. The distribution of a paired homolog (x and x 0 ) on a tree of Žve taxa, as given by other data relative
to SCA and 3TA. (a) Homolog x shared by ABE and homolog x 0 shared by CD represent a transformation between
character states in the context of SCA. (b) 3TA view of these data and nine implied three-taxon statements. (c) SCA
view of x0 as a parallelism . (d) SCA view of x 0 as apomorphic. (e) SCA view of x 0 as plesiomorphic. (f) Four threetaxon statements are accommodated on the tree as evidence for relationship among the homologs, taxa, and the
tree. Homolog x is denoted x1 , x2 , and x3 for taxa A, B, and E, respectively. Homolog x0 is denoted x10 and x20 , for
taxa C and D, respectively.
substantial amount of support. Nelson and
Platnick (1991) did not distinguish between
complement relation homologs and paired
homologs, which left unclear exactly what
their matrices represented in terms of homology propositions. Here I report my analysis
of matrix 19 from Nelson and Platnick (1991),
which effectively demonstrates that minimizing tree length of character-state trans-
formations (Farris, 1983) and maximizing the
relation of homology yield markedly different results.
Three-Taxon Statement Matrices
For 3TA, the relationship between data
and a tree is straightforward. To analyze
data, all homologs are converted into implied
2000
S COTLAND—TAXIC HOMOLOGY
491
FIGURE 12. Paired homologs shared among four taxa explored in the context of SCA and 3TA. (a) Paired homologs, x and x 0 , in the context of SCA. (b) Paired homologs, x and x 0 , and the resulting four three-taxon statements.
(c) One-step change in the context of SCA, given by an ambiguous optimization at the base of the tree. Nonetheless,
the transformation between x and x 0 is one step. (d) One-step change in the context of SCA in which x is treated
as plesiomorphic. (e) One-step change in the context of SCA in which x 0 is treated as plesiomorphic. (f ) Two-step
change in the context of SCA in which x is treated as plesiomorphic. (g) Two-step change in the context of SCA in
which x0 is treated as plesiomorphic. (h) Tree accommodates four three-taxon statements. (i) Tree accommodates
two three-taxon statements. (j) Tree accommodates two three-taxon statements. (k) Tree does not accommodate any
three-taxon statements.
three-taxon statements. All three-taxon statements are then evaluated relative to all rooted
trees, and the minimal tree is the one that
accommodates the maximum amount of homology. As yet, no speciŽc 3TA computer
program exists to implement the method.
However, Nelson and Platnick (1991) realized that existing parsimony programs can
implement 3TA by simply coding with a
question mark (?) all taxa, to which a particular statement coded (11)0 does not apply (Nelson and Ladiges, 1993). Several early
critiques of 3TA have focused on this issue
(Harvey, 1992; Kluge, 1993). Consider the
data shown in Table 3 for one complement
relation homolog shared by taxa C and D
(coded as 1) and absent from A and B (coded
as 0). The homolog implies two three-taxon
statements: (CD)A, wherein C and D share
a homolog that is absent from A, and (CD)B,
wherein C and D share a homolog that is absent from B. This is coded as (11)0 for each
statement and all other taxa are coded with
?. The coding of each three-taxon statement
492
TABLE 3. One complement relation homolog shared
among four taxa coded in standard binary and threetaxon statement formats.
Taxon
All zero outgroup
A
B
C
D
VOL. 49
S YSTEMATIC BIOLOGY
Homolog 1
SCA coding
Absent
Absent
Present
Present
N/A
0
0
1
1
3TA coding
0
0
?
1
1
0
?
0
1
1
1 = present; 0 = absence; ? = inapplicable.
with (11)0 and all other taxa with ? implies
that each column in the matrix contains
one item of information, that is, that the
two 1s share a relationship relative to the
taxon coded 0. A given three-taxon statement is accommodated on a tree with length
1 or is not accommodated with length 2.
In an analysis of 20 three-taxon statements, wherein 10 are accommodated and
10 are not accommodated, the tree will be
length 30 for these 20 statements. Analyses
are performed by using existing parsimony
programs in conjunction with an all-zero
outgroup which serves as a device to orientate all three-taxon statements relative to
all possible rooted trees. Question mark entries can, however, result in overresolution
(nodes not supported by statements), but if
the strict consensus tree of all trees is the same
length, it is minimal. If the strict consensus
tree is longer than all potentially overly resolved trees it may be necessary to manually check all output trees to identify minimal trees. Table 4 contains Žve columns, each
representing a complement relation homolog
present (1) and absent (0) in various taxa.
Table 5 describes the strict consensus trees
that results from analyzing the three-taxon
equivalent matrix for each homolog sepaTABLE 4. Five complement relation homologs shared
among seven taxa.
Complement homologs
Taxon
1
2
3
4
5
All zero outgroup
A
B
C
D
E
F
G
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1 = presence; 0 = absence.
TABLE 5. Results of analysis for Žve complement relation homologs from Table 4 coded in 3TA format. The
strict consensus tree indicates that the homolog partitions the taxa into those that possess the homolog
relative to those that lack the homolog. The number of
three-taxon statements and the fractional weight of each
individual statement are also shown.
Homolog
Strict consensus
No. of
statements
Fractional
weight
1
2
3
4
5
OA(BCDEFG)
OAB(CDEFG)
OABC(DEFG)
OABCD(EFG)
OABCDE(FG)
15
20
18
12
5
0.33
0.4
0.5
0.66
1
O = outgroup.
rately. The strict consensus of these data is
that those taxa possessing a homolog form
a group in which the taxa that lack the homolog do not belong. Table 5 also contains
the number of statements implied for each
column and the fractional weight of each of
those statements. Fractional weighting can
be applied to a given homolog that contains
logically dependent three-taxon statements
(Nelson and Ladiges, 1992a). For instance,
a homology distributed as (ABC)D speciŽes three three-taxon statements—(AB)D,
(AC)D, and (BC)D—any two of which logically imply the third. Fractional weighting
corrects for this logical dependency (but see
De Laet and Smets, 1998). For the example discussed below, fractionally weighted
analyses and equally weighted analyses are
reported. Three-taxon matrices were generated from TAS and TAX (Nelson and Ladiges,
1992b). Implementation of 3TA, in the context of various critiques, is usefully discussed
in Willams and Siebert (2000).
M ATRIX 19: T HE CLADISTIC CONTENT
OF A D ATA M ATRIX
The Matrix
Matrix 19 of Nelson and Platnick (1991)
effectively highlights the difference between
SCA and 3TA and is shown here as Table 6
and Figure 13a. Figure 13a contains 14 binary
characters that are taken here to represent
a mixture of complement relation homologs
and paired homologs. For SCA, all homologs
are treated as paired, whether they represent
complement relation or paired homologs.
For SCA, the data from Figure 13a can be
coded in binary form (Table 6). For 3TA,
which distinguishes complement relation
2000
493
S COTLAND—TAXIC HOMOLOGY
TABLE 6. Matrix 19 of Nelson and Platnick (1991). These data represent paired homologs coded 0 and 1.
Homologs
Taxon
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
D
E
F
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1 = present; 0 = present.
and paired homologs, Figure 13a reduces to
Figure 13b because homologs 3a, 6a, 7a, and
10a represent absence. The 3TA matrix, is
shown in Table 7. Inspection of Figure 13a
shows that, for SCA, the distribution of
the Žrst three characters (1–3) is repeated
(characters 4–6). Similarly, characters 7–9 are
repeated (characters 10–12). Characters 1–
6 (Fig. 13a) include six character states—
(CDEF), (BDEF), (ADEF), (CDEF), (BDEF),
and (ADEF)—that are all possessed by
taxa D–F and to a lesser extent by taxa A, B,
FIGURE 13. Data from Table 6. (a) SCA treats these data as 14 paired homologs. (b) The 3TA view of these data
omitts the homologs 3a, 6a, 7a, and 10a because they represent no data.
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VOL. 49
S YSTEMATIC BIOLOGY
TABLE 7. Three-taxon statement matrix for Figure 13b.
Homologs
Taxa
Homologs
Homologs
Homologs
1a
1b
2a
2b
3a
3b
4a
4b
A
B
C
D
E
F
1111
1111
0???
?0??
??0?
???0
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
????11??1111
??11??11??11
11????1111??
111111??????
1111
0???
1111
?0??
??0?
???0
?0?0?0?0?0? 0
????11??1111
0?0?0?0?0?0 ?
??11??11??11
11????1111 ??
111111????? ?
—
—
—
—
—
—
????11??1111
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
??11??11??11
11????1111??
111111??????
1111
1111
0???
?0??
??0?
???0
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
????11??1111
??11??11??11
11????1111??
111111??????
5a
5b
6a
6b
7a
7b
8a
8b
A
B
C
D
E
F
1111
0???
1111
?0??
??0?
???0
?0?0?0?0?0? 0
????11??1111
0?0?0?0?0?0 ?
??11??11??11
11????1111??
111111??????
—
—
—
—
—
—
????11??1111
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
??11??11??11
11????1111 ??
111111????? ?
—
—
—
—
—
—
????11??1111
??11??11??11
11????1111??
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
111111??????
0???
?0??
??0?
???0
1111
1111
????11??1111
??11??11??11
11????1111??
111111??????
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
9a
9b
10a
10b
11a
11b
12a
12b
0???
?0??
??0?
1111
???0
1111
????11??1111
??11??11??11
11????1111??
?0?0?0?0?0? 0
111111??????
0?0?0?0?0?0 ?
—
—
—
—
—
—
????11??1111
??11??11??11
11????1111 ??
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
111111????? ?
0???
?0??
??0?
???0
1111
1111
????11??1111
??11??11??11
11????1111??
111111??????
?0?0?0?0?0? 0
0?0?0?0?0?0 ?
0???
?0??
??0?
1111
???0
1111
????11??1111
??11??11??11
11????1111??
?0?0?0?0?0? 0
111111??????
0?0?0?0?0?0 ?
13a
13b
14a
14b
?0?0?0?0?0? 0
????11??1111
??11??11??11
11????1111??
111111??????
0?0?0?0?0?0 ?
1111
???0
??0?
?0??
0???
1111
1111
???0
??0?
?0??
0???
1111
?0?0?0?0?0? 0
????11??1111
??11??11??11
11????1111 ??
111111????? ?
0?0?0?0?0?0 ?
A
B
C
D
E
F
A
B
C
D
E
F
and C. Similarly, characters 7–12 include six
character states—(ABCF), (ABCD), (ABCE),
(ABCF), (ABCD), and (ABCE)—that are all
possessed by taxa A–C and to a lesser extent by taxa D, E, and F. Characters 13 and
14 include (AF) and (BCDE). Nelson and
Platnick (1991) pointed out that even when
characters 1–12 are multiplied any number of times relative to characters 13 and
14, SCA fails to recover clades (ABC) or
(DEF), whether polarity is determined before
the analysis or not.
Character Conict
Matrix 19 contains character conict. An
important question is, how much? Character conict (homoplasy) is often wrongly
depicted as a hindrance for systematics
(Patterson, 1982). Recent studies (Hillis, 1996;
Albert et al., 1997) have demonstrated that
homoplasy can provide much of the evidence for a tree in the context of adequate
sampling of taxa. Carine and Scotland (in
press) made the same point for a morpho-
logical data set, in that all characters were
homoplastic but analysis resulted in a tree
with 70% resolution. This suggests that homoplasy is homology at a more restricted
hierarchical level, despite claims that homoplasy is distinct from homology (Sanderson
and Hufford, 1996:329). Apparently some homologs have an exact Žt to a tree, and most
tree building methods are successful with
this type of data. Other homologs have an inexact Žt relative to a tree but can provide evidence at more restricted hierarchical levels of
systematic relationship (Hillis, 1996; Carine
and Scotland, in press). Issues in relation to
character constancy and inconstancy are not
new. In his section on weighting homologies,
Patterson (1982:44) wrote:
Yet there are homologies which appeal to us of high
weight. A few examples from vertebrates include the
eye, eye muscles, semi-circular canals, amnion, mammalian ear ossicles, feathers, ural centra of teleosts,
claspers and placoid scales of chrondrichthyans. Have
we weighted these homologies, and if so, how?
Complexity is not the answer, for placoid scales and
ural centra are simple enough. Constancy is one
2000
495
S COTLAND—TAXIC HOMOLOGY
answer: we might weight these homologies highly because they are reliable in large numbers of species, and
inferred loss is unknown, or rare and easily resolved.
But constancy is only to say that the homology remains uncontradicted. Then the real criterion is lack
of contradiction, which is, in turn, only to say that
these characters are repeatedly corroborated as homologies by others which are congruent with them.
I suggest that when we weight homologies highly,
it is not because of complexity, or functional importance, but because the groups they form are congruent with those formed by many other characters,
and are contradicted by few or none. In short we do
not need to weight homologies: they weight themselves, by associations which are beyond the bounds
of chance.
Patterson (1982:45) discussed
(1979) concept of burden:
Riedl’s
Reidl argues that burden is correlated with Žxation
and constancy; with age position (e.g., central versus
peripheral in the nervous system or circularity system); with taxomonic rank (i.e., with position in the hierarchy); with low variability, or inferred resistance to
change; and negatively correlated with convergence
(the higher the burden, the less likely is convergence).
All these features, except position in an organ system,
are characteristic of the examples of high-weight homologies: it is not something we assign. To repeat,
homologies weight, or burden themselves.
Patterson (1982:45) concluded that
“Reidl’s positive correlation of burden with
hierarchic rank and constancy, and negative
correlation with convergence (incongruence), explains why systematics is more
difŽcult at low taxonomic levels than at
high.” Much of the debate that surrounds
systematic method is, in part, concerned
with how to deal with incongruent data
or homologs that have an inexact Žt to a
given solution. Characters such as eye color,
stamen number, nucleotides, leaf shape,
plumage color, and so on, can be highly
variable, so much so that often terminals
in analyses are coded polymorphic for a
feature. These types of characters are often
forced into particular transformational
hypotheses. For example in a recent phylogenetic analysis of gulls, Chu (1998:5)
wrote:
In a minority of multistate characters, the states could
be unambiguously arranged in a sequence that passes
from one condition through one or more intermediate conditions to another condition . . . . for example
among the study taxa I hypothesized that brown eyes
are intermediate between red and yellow eyes, because some specimens have red-brown eyes and others have yellow-brown or mixed brown and yellow
eyes, whereas none have orange eyes.
In relation to diploid, multiallelic organisms, it is perhaps not surprising that the
expression patterns of some features seem
to be highly variable within a particular set
of taxa. To repeat, Sattler (1994:459) stated
that “In each generation, organisms are
(re)constructed (Goodwin, 1984:114; Oyama,
1988, 1989), and in this (re)construction more
or less similar or different character states
may appear.” All that I emphasize here is
that some features are highly variable within
particular systematic problems and that SCA
and 3TA have very different ways of dealing
with this type of character distribution. SCA
seeks to optimize paired (shared) homologs
as ancestor–descendent character transformations. 3TA seeks to explore whether a particular homolog, or parts thereof, can be accommodated relative to all data and a tree
as evidence of relationship. In this sense,
a tree (classiŽcation, taxonomic rank, phylogenetic context) determines the burden of
a character.
Results
Analysis of the SCA matrix from Table 6
results in one most-parsimonious unrooted tree of length 22 (Figs. 14a and 14b).
Figure 14b, the result of SCA, demonstrates
that paired homologs 3, 6, 7, 10, 13, and
14 are unique (one-step) transformations on
the unrooted tree that provide structure for
the unrooted topology (Fig. 14b). Figure 14c
is an arbitrary rooted tree of 22 characterstate changes for Figure 14b, rooted between
(AF) and (BCDE). Figure 14c demonstrates
that 6 from the total of 28 homologs provide evidence of relationship between the
taxa for this solution. From a transformational perspective the particular topology of
the unrooted tree (Fig. 14b) is determined by
six unrooted character transformations (homologs 3a and 3b, 6a and 6b, 7a and 7b, 10a
and 10b, 13a and 13b, and 14a and 14b). Relative to the rooted tree (Fig. 14c), characters 3a,
6a, 7a, and 10a represent secondary losses
that require no additional steps on the tree.
The 3TA matrix (Table 7) for these data
yields a total of 208 three-taxon statements.
The statistics for fractionally weighted and
equally weighted trees are presented in
Table 8. Equal weighting results in nine
minimal trees (Figs. 15a–i), and fractionally
weighted analysis yields four trees (Figs. 15b,
15c, 15e, 15f). One hundred four three-taxon
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S YSTEMATIC BIOLOGY
sume for the comparison that absence has
equal status to presence, for both 3TA and
SCA, and that the character polarity is determined with reference to outgroup taxa,
as is usual in most studies. Therefore, the
matrix (Table 6) can be represented for SCA
and 3TA as in Table 9. For this comparison,
SCA yields Figure 16a, which is simply a
rooted version of Figure 14b. Fractionally
weighted and equally weighted 3TA yields
one minimal tree (Fig. 16b). For these data
any of the taxa (A–H) can be used as functional outgroups, and SCA fails to yield
(ABC) or (DEF), whereas 3TA yields ABC
or DEF for all possible functional outgroups (A–F). There is, however, one SCA
analysis that yields (ABC) and (DEF). If all
14 homologs (Fig. 13a) are treated from a
nontransformational perspective—that is, all
28 homologs (Fig. 13a) are coded 1 and 0 is
used to root the tree with reference to an allzero outgroup (Table 10)—SCA yields one
most-parsimonious tree (Fig. 16c).
DIS CUSS ION
FIGURE 14. SCA analysis of data from Figure 13a and
Table 6. (a) Unrooted tree of length 22. (b) Unrooted tree
showing character transformations. (c) One rooted tree
of 22 character-state changes.
statements are accommodated on all minimal trees (Fig. 15a–i). In other words, 50% of
the total number of statements provide evidence of relationship between the taxa.
Matrix 19 can be further explored in the
context of imposed character polarity, relative to outgroup taxa. Assume for the comparison that taxon A is outgroup to B–F and
is used as a functional outgroup to polarize characters and determine plesiomorphy
from synapomorphy for the B–F ingroup. As-
Matrix 19 demonstrates that data matrices
with moderate amounts of character conict
may not be best accommodated as transformations within a simple model of character
transformation. Matrix 19 demonstrates that
low-burden homologs can contain a large
element of congruent data expressed in relationship relative to a tree. The example
demonstrates that treating such data from the
perspective of ancestor–descendent character transformations can have a profound effect on how many data provide evidence for
a tree. It may be folly to assume that all systematic problems will yield in the light of increased data. There are » 100 genera of plants
that contain >400 species. These genera constitute » 22% of all angiosperms. These taxa
are notoriously difŽcult to classify because
the variation is that of the low-burden homolog type, wherein expression patterns of
homologs may not be most appropriately
recovered relative to a model of ancestor–
descendent character-state transformations.
It is useful to distinguish complement relation and paired homolog data for the implementation of a taxic view of homology sensu
Patterson (1982). This is because complement
relation homologs result in a single proposition of taxic homology, whereas paired homologs result in two propositions of taxic
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S COTLAND—TAXIC HOMOLOGY
497
FIGURE 15. Minimal trees for 3TA analysis of Figure 13b and Table 7. (a–i) Nine minimal trees with equal
weighting. Fractional weighting results in four trees: b, c, e, and f. (j) Strict consensus tree of all minimal trees.
TABLE 8. Tree statistics for 3TA analysis of Figure 13b
and Table 7.
No. trees
Total statements
Nonaccommodated statements
Accommodated statements
Length
Fractional
weight
Equal
weight
4
208
104
104
312
9
208
104
104
182
homology. Elsewhere (Scotland, 2000) I have
shown that, for example, DNA sequence
data contains a maximum of four shared
homologs (ACGT) for any given site in
aligned sequences, and that these data need
not be treated as transformation series. 3TA
can equally be implemented for sequence
data and for other multistate data (Nelson
and Ladiges, 1994; Scotland, 2000).
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S YSTEMATIC BIOLOGY
TABLE 9. Matrix 19 coded 0 representing the uninformative plesiomorphic state with reference to taxon A, which
is treated as a functional outgroup.
Homologs
Taxon
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
D
E
F
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0 = plesiomorphic state; 1 = apomorphic state.
TABLE 10. Matrix 19 from Figure 13a, coded with all 28 homologs in binary form.
Homologs
Taxa
1
2
3
4
5
6
7
8
9
10
11
12
13
14
OG
A
B
C
D
E
F
00
01
01
10
10
10
10
00
01
10
01
10
10
10
00
10
01
01
10
10
10
00
01
01
10
10
10
10
00
01
10
01
10
10
10
00
10
01
01
10
10
10
00
10
10
10
01
01
10
00
10
10
10
10
01
01
00
10
10
10
01
10
01
00
10
10
10
01
01
10
00
10
10
10
10
01
01
00
10
10
10
01
10
01
00
01
10
10
10
10
01
00
01
10
10
10
10
01
OG, outgroup; 1 = presence; 0 = absence.
FIGURE 16. (a) Most-parsimonious tree for SCA for
the data from Table 9, treating taxon A as a functional
outgroup. (b) Minimal tree for 3TA for the data from Table 9, treating taxon A as a functional outgroup. (c) Mostparsimonious tree for SCA for the data from Table 10,
treating all 28 homologs separately.
It is necessary to distinguish propositions
of taxic homology sensu Patterson (1982)
from Patterson’s (1982) congruence test of
taxic homology, which has been discussed as
a form of compatibility analysis (Patterson,
1988; de Pinna, 1991; Scotland, 2000) but remains to be accurately described. Here, I accept Patterson’s (1982) taxic view of homology propositions, wherein the possession of
a homolog leads to a hypothesis of a group
relative to taxa which lack the homolog. I
view 3TA as a method of implementing taxic
propositions of homology wherein the homology content of a given homolog can be
expressed in the form of three-taxon state-
ments (Fig. 1) that are accommodated or not
on a given tree as evidence of relationship.
In the context of SCA, parsimony provides a limited test because the transformational relationship between character states
of a character are never tested and parsimony tests only whether the transformation
is unique (one step) or homoplastic (more
than one step). Character-state changes become the salient feature of a parsimony analysis (de Queiroz, 1985; Brower, 2000) when
characters and their states are viewed as
transformations and parsimony is used to
minimize tree length. Given the plethora
of coding protocols utilized in SCA studies
(Hawkins, 2000), exact criteria for postulating transformations remain elusive. Furthermore, in numerous studies, homologs and
their topographically corresponding counterparts are not coded as transformations
(Hawkins, 2000).
The term relationship in systematics has
been shown to be meaningful only with reference to a tree. A is more closely related
to B than to C, if, and only if, (AB) share a
closer relationship (node) relative to C. This
approach has led to trees being the preferred
method for expressing systematic relationships at the expense of attempts to depict relationships as ancestor–descendent lineages.
Statements such as A and B are closely related
2000
S COTLAND—TAXIC HOMOLOGY
are inexact, because any statement of relationship demands a conditional phrase, relative to what? The same logic can be applied to
parts of organisms (homologs) whether they
be leaves or genes. Such an approach is based
on the relation of homology and acceptance
that models of evolution and estimating ancestral character states are “superuous to
homology analysis” (Patterson, 1982:57).
Evolutionary theory predicts that species
give rise to other species. Nevertheless, it is
customary to treat all species as terminal taxa
in a systematic study because no satisfactory
criteria exist for the estimation of ancestral
taxa, and all taxa are viewed in terms of sister group relations. Ancestors remain hypothetical relative to a tree of terminal taxa.
However, ancestral characters remain central to SCA, which treats homologs from the
perspective of transformations. As Nelson
(1994:128) stated,
Cladistis do not write of mother-, daughter-, and
sister-, characters (homologues). The burden of metaphor aside, cladistis might yet do so to advantage,
and treat characters of organisms (as they do taxa)
as terminal entities, and, for example, remedy afictions of transformation series analysis (e.g., Mikevitch
and Lipscomb, 1991; Lipscomb, 1992). One recalls
Patterson’s remark that “this view—nonterminal
branches of the evolutionary tree as hypothesis—was
one cause of the dispute over cladistics.” Perhaps
cladists are fated to repeat the dispute, this time over
characters rather than taxa, as if science after all moves
gradually, but one pace at a time.
ACKNOWLEDGMENTS
I thank Richard Bateman, Jonathan Bennett, Mark
Carine, Colin Hughes, Chris Humphries, Elizabeth
Moylan, Gary Nelson, Toby Pennington, Olivier
Rieppel, Andrew Smith, and David Williams for comments and encouragement. I thank Norman Platnick and
Mark Wilkinson for helpful reviews and Rod Page for
a helpful suggestion on the bottom line. This manuscript would not have been written without the help
of Gary Nelson (HELP, Inchon, particle of truth), Mark
Carine, and David Williams and the discussions I had as
a graduate student with the late, great Colin Patterson.
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Received 23 October 1998; accepted 29 September 1999
Associate Editor: R. Page