全 文 ：Journal of Systematics and Evolution 46 (2): 109–129 (2008) doi: 10.3724/SP.J.1002.2008.07166
(formerly Acta Phytotaxonomica Sinica) http://www.plantsystematics.com

Fifty years of character compatibility concepts at work
George F. ESTABROOK*
(Department of Ecology and Evolutionary Biology, The University of Michigan, Ann Arbor, MI 4809-1048, USA)
Abstract In the mid 19th century, systematic biologists realized that observable similarities and differences
among a group of related species could be the basis for hypotheses about the evolutionary relationships among the
species and their ancestors. Such hypotheses can be expressed as characters. A character is comprised of two or
more character states of species considered to be similar with respect to a basis for comparison. The states of a
character may also be arranged into a character state tree to hypothesize speciation events associated with changes
from one character state to another. In the mid 20th century, some systematists realized that sometimes pairs of
characters (or character state trees) could be incompatible as hypotheses, i.e., they could not both be true. Through
the 1950s, ’60s and ’70s, tests for, and ways to resolve, incompatibilities were used to estimate an ancestor rela-
tion based on mutually compatible characters. An estimate was often shown as a diagram connecting ancestors to
their immediate descendants (not quite correctly) called a phylogenetic tree. More recently, other applications of
compatibility concepts have been developed, including: identify characters that appear to be random in the context
of their data set; combine estimates of ancestor relations for subsets of taxa in a larger collection into a single
estimate (a so-called supertree) for the whole collection; and interpret geographic patterns in an evolutionary
context.
Key words biogeography, character compatibility, character evaluation, convex groups, phylogenetic trees,
reciprocal illumination, speciation, supertrees
This review begins with a discussion of character
state change, which distinguishes between changes
that occur within species, often in similar ways within
several related species, and changes that occur when a
new species evolves from its ancestral species. The
former changes are sometimes modeled as a random
process; the latter are often used to describe or iden-
tify species or higher taxa. A challenge faced by a
systematist working near the species level is to dis-
tinguish the former from the latter kind of change.
Although we prefer the latter for describing species
and studying their evolutionary relationships, changes
stably associated with the evolution of new species
may remain difficult to distinguish. Some changes
become more clearly associated with evolutionary
events when taxa above the species level, such as
species complexes, sections, or genera, are compared.
Generally, throughout this review, I will speak of the
evolutionary unit, EU, as if it were a species, and of
the process by which one EU evolves from its imme-
diate ancestral EU as speciation. However, compati-
bility concepts apply above the species level, and in
the view of many systematists are more appropriately
applied above the species level. In any case, to under-
stand correctly the concepts and applications of
character compatibility theory, it is important to
realize that characters and character state trees should
be based on changes stably associated with speciation
(or its analog among higher taxa).
How character state trees express hypotheses of
speciation associated with character state change and
how true character state trees can be combined are the
subjects of sections 1, 2, and 3. Character state trees
are partial estimates of the ancestor relation, which
indicates which species evolved from which ancestors.
Character state trees, as hypotheses, are either true or
false. If two character state trees are true, then they
can be added (combined) to make a single character
state tree that refines the partial estimates of each. Of
course we do not know which character state trees are
true as hypotheses, but we can attempt to apply this
addition process to any two character state trees; the
process will fail to produce a new character state tree
if and only if the two character state trees are incom-
patible as hypotheses. The explanations and examples
of these three sections are important to a basic under-
standing of character compatibility concepts, but they
can be skimmed by readers more interested in history.
Section 4 recognizes authors writing in the 1960s
and ’70s who became aware that characters could be
incompatible. Soon it was realized that incompatibility
could result from the particular arrangement of the

———————————
Received: 19 December 2007 Accepted: 4 March 2008
* E-mail: gfe@umich.edu; Tel.: 1-734-764- 6219; Fax: 1-734-763-0544.
Journal of Systematics and Evolution Vol. 46 No. 2 2008

110
states into character state trees, so that re-arrange-
ments of the states could resolve incompatibility.
However, the membership of EUs in the states them-
selves could also cause incompatibility. Tests to
reveal the various causes of incompatibility were
discovered and described. By the early 1980s, these
concepts were in place and their properties elucidated.
Section 5 examines how incompatibilities were
resolved to produce mutually compatible characters
from which an estimate of the ancestor relation could
be easily constructed. When Hennig’s manuscript was
translated from German into English and published in
1966, it provided many early career systematists in the
non-German speaking world with some very specific
guidelines for resolving incompatibilities. Although
Hennig held radically new views of what constitutes a
higher taxon, for many early career systematists his
Teutonic explicitness was a refreshing alternative to
the very subjective approaches of the well established
evolutionary systematists, who were making it diffi-
cult for other than their favored apprentices to access
professional opportunities. Predating DNA sequence
data, Hennig’s approach advocated the use of almost
anything known about natural history of organisms to
resolve incompatibilities. Soon a new, powerful and
doctrinaire school of thought (Cladism) became
established, nominally recognizing Hennig as their
guide but largely forgetting his advocacy, adopting
instead an automatic criterion (parsimony, proposed
by others in the 1960s) for resolving incompatibilities
that could be applied by computers to DNA sequence
data without the participation (intervention, responsi-
bility) of the systematist. Fortunately, the power of
Cladism over young minds in our field has largely
dissipated.
The application of probability to compatibility
concepts is the subject of section 6. Through the
1970s and ’80s, population geneticists used probabil-
ity concepts applied to changes that they construed as
happening at random to study evolution below the
species level, using maximum likelihood to estimate
“phylogenetic” tree branching patterns. Although
systematists using compatibility concepts would seek
to avoid random changes as the basis for characters
used to estimate the ancestor relation, maximum
likelihood estimates were used by some systematists,
especially those relying primarily on DNA sequence
data, because it too enabled an automatic computer
estimate of the ancestor relation. In the 1990s, prob-
ability concepts were used with character compatibil-
ity to recognize characters whose state composition
could not be distinguished from random, in the con-
text of their data set. This is especially important for
DNA sequence data in which some sites may repre-
sent bases for comparison more appropriate for analy-
sis by random models, such as maximum likelihood.
Preliminary evidence suggests that elimination of such
sites may clarify estimates based on distance or par-
simony methods.
Section 7 discusses other applications of com-
patibility, which include elucidating biogeographical
patterns, suggesting hybridization events in the evolu-
tionary history of a study group, incorporating strati-
graphic information into the estimation of the ancestor
relation, and constructing supertrees. The relationships
among compatibility, monophyly and classification
are discussed in the final section 8.
1 Concepts of character state change
For centuries, people have recognized groups of
organisms that are similar, and arranged them hierar-
chically into larger, increasingly less similar, groups.
In the late 19th century, the theory of evolution pro-
vided systematists with a mechanism to explain
similarities and differences among kinds or organisms,
but it had very little impact at that time on our view of
relationships reflected in the higher taxa traditionally
recognized. Students of evolution developed an
understanding of speciation and change, well ex-
plained by the great writers of the mid 20th century,
such as Stebbins (1950), Mayr (1963) and Grant
(1963). More recently, the mechanisms and conse-
quences of speciation are discussed by many authors
in Otte and Endler (1989). At the individual and
population level, genetic changes occur “at random”
by mutation, or by chromosomal rearrangement from
one generation to the next. Within a breeding popula-
tion, over generations these changes may be lost or
they may spread to many other individuals (by natural
selection); or they may be irrelevant to survival and
reproduction and so drift at random. When popula-
tions become genetically isolated (spatially, tempo-
rally, behaviorally, etc.), it is no longer possible for
changes in one to be spread to the other. Over time,
this may result in the accumulation of sufficient
differences that it is no longer genetically possible for
members of one population to breed with members of
the other; speciation has occurred.
Thus, systematic biologists looked for observable
expressions of the changes associated with speciation
to recognize and describe distinct species. They are
confounded in their task by many natural phenomena

ESTABROOK: Character compatibility concepts


111
that produce observable differences between individ-
ual organisms that are NOT changes associated with
speciation, such as juvenile and adult forms, sexual
dimorphism, developmental anomalies caused by
damage or disease, facultative response to environ-
ment, clinal variation over space, and of course the
within population genetic variation described above.
In the early 20th century, common gardens, experi-
mental breeding, and larger numbers of specimens to
study have helped systematists recognize more accu-
rately changes associated with speciation (Briggs &
Walters, 1969). Although changes associated with
speciation provide potentially relevant data with
which to estimate the history of speciation, it was not
until the middle of the 20th century that some sys-
tematists began to carefully consider concepts that
would enable them to use changes associated with
speciation to estimate evolutionary relationships
among species, and use those estimates to recognize
higher taxa.
One concept construes changes associated with
speciation to differ from changes that occur “at ran-
dom” in individuals and that are sometimes spread
over generations through breeding populations; spe-
cies changes have the same origin, but after speciation
they usually can no longer be spread by breeding
between members of different species. Changes
associated with speciation interrupt phyletic continuity
over time (Estabrook, 1972). This concept gives rise
to a historical-biological species concept in which a
species evolves at a time in the past, usually in a
somewhat restricted geographic area, persists through
time possibly dispersing to other geographic areas,
and ultimately goes extinct (a few still extant species
have not gone extinct yet). During the life of a species,
a population may become isolated and independently
evolve enough genetic difference so that its members
can no longer breed with members of the species from
which it was isolated, as described above. In this way,
one species becomes the immediate ancestor of an-
other that evolved from it. This process may happen
repeatedly, so that one species may come to be the
immediate ancestor of several distinct species. In this
way, the study of evolutionary relationships among
extant species implicates ancestral species that existed
over past time, and has for one of it principal objec-
tives an estimate of the ancestor relation among
related species, past and present. This view of speci-
ation and systematics has come to be called evolu-
tionary systematics and is represented by Simpson
(1961) and Mayr (1969) among many others over the
past 40 years, including more recently Skelton (1993).
2 Characters and character state trees
We rarely know for sure the branching pattern of
phyletic lines leading up through time to the extant
species under study, but to illustrate the concepts, we
consider a hypothetical case in which we do. Suppose
that we are studying a group S of six extant species (a,
b, c, d, e, f) whose phyletic lines branch upward
through time as shown on the left in Fig. 1. Whenever
a phyletic line branches, one branch represents a new
species and the other represents the continuation of the
ancestral species. Arrows identify speciation events
and point to the branch created by changes that pro-
duced a new species. The diagram on the right of Fig.
1, shows the ancestor relation that results from these
speciation events; a line is drawn upward from an
ancestral species to any immediate descendant spe-
cies. Thus, each line in the diagram represents a
speciation event on the phylogenetic tree. We say that
species x is an ancestor of species y if there is a series
of one or more upward lines leading from x to y.



Fig. 1. Hypothetical branching of phyletic lines leading to 7 species
(a, b, c, d, e, f, g) on which speciation events are indicated by arrows.
The diagram of the corresponding ancestor relation is shown on the
right.

On the same hypothetically true branching pat-
tern of phyletic lines, the speciation events could have
occurred at different times and places. Figure 2 shows
an example. You can see from the diagram of the
resulting ancestor relation that it is quite different
from the ancestor relation of Fig. 1. This example
should make it clear that there is not a one-to-one
relationship between phyletic branching patterns
(phylogenetic trees) and ancestor relations, because
the latter are a result of the historical speciation events
that created the species we study. Although it is
possible to have extinct species represented in S, some
ancestral species may not be represented in S because
of extinction. Figure 3 shows the same speciation
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Fig. 2. The same phyletic lines as in Fig. 1, but with speciation events
in different places. The diagram of the corresponding ancestor
relation is shown on the right. This illustrates how different ancestor
relations can be even when the branching of the phyletic lines is the
same.




Fig. 3. The same phyletic lines as in Fig. 1 with the addition of an
extinct species, x. The diagram of the corresponding ancestor relation
is shown on the right.


events as Fig. 2 together with an additional speciation,
indicated with *, after which the ancestral species, x,
goes extinct and so is not found among the species in
S; the resulting ancestor diagram is shown on the
right. You can imagine the variety of speciations and
extinctions that could occur on a phylogenetic tree and
the resulting variety of ancestor relations.
One of the tasks of systematics is to use the
similarities and differences that can be observed
among the species in a group under study to estimate
their ancestor relation. To examine more explicitly
how these concepts relate to this task, it is appropriate
to define some terms. If one can observe a given
structure for each species in a collection S of species
under study, and recognize distinct variations, then the
species can be placed into groups so that those in the
same group look the same with respect to that basis
for comparison, but those in different groups look
different. Such a basis for comparison is called a
character, and the groups that result are called its
character states. For a character to be relevant to the
ancestor relation, its states should be based on changes
associated with some of the speciation events that
created the species in S, as discussed above. Of
course, not all speciation events need be associated
with a change in the structure defining a given char-
acter, but when that structure did change, it should
have been in association with a speciation event. Such
a character can be used as the basis for a hypothesis
about the ancestor relation. This hypothesis is ex-
pressed as an ancestor relation diagram in which the
character states play the role of individual species, and
as before, a line leading up from one state to another
represents a speciation event on the phylogenetic tree,
as shown in Fig. 4.



Fig. 4. The same phyletic lines as in Fig. 1, but with only two
speciation events indicated. The corresponding character state tree is
shown on the right.


The character state tree (CST) shown on the right
represents the two speciation events shown by arrows
near the phylogenetic tree on the left. The speciation
indicated by the lower arrow changed a structure from
the form exhibited by species f and g to the form
exhibited by species c, d and e; the speciation indi-
cated by the upper arrow changed that form to the one
exhibited by species a and b. If the phylogenetic tree
and the speciation events shown on the left of Fig. 4
are historically correct, then we would say that the
hypothesis of the CST is true (or simply that the CST
is true) because it corresponds to speciations on the
true phylogenetic tree (Estabrook et al., 1975).
If two CSTs are true, then by considering all the
speciation events that correspond to one or the other
or both of them, another true CST (called the sum of
the first two) is determined, as shown in Fig. 5. The
“sum” CST is a refinement of either of the two CSTs
that were added, because it represents all the
ESTABROOK: Character compatibility concepts


113
speciation events of either. In the same way, another
true CST could be added to this sum to create an even
more refined CST, as shown in Fig. 6. The two
changes distinguishing state (d, e) represented by
CSTs iii and iv may have been associated with the
same speciation event, or with different speciation
events suggesting the possibility of an extinct ances-
tral species represented by the dotted circle. However,
the most ancestral state contains only extinct ancestors
because of speciation events on both branches of the
phyletic lines leading up to the extant taxa. A mo-
ment’s consideration should make it clear that if
enough true CSTs are added, then the sum CST
becomes the diagram of the ancestor relation itself, in
which will be shown, in their historical place, ances-
tors not represented in S. Thus, an ancestor relation is
a CST sufficiently refined so that each state has at
most one species.



Fig. 5. The sum of two character state trees, with corresponding
speciation events indicated on the phyletic lines of Fig. 1 at the right.



Fig. 6. A third character state tree is added to the sum shown in Fig.
5.

3 Compatible character state trees
Of course, not all CSTs are true; there are three
basic ways in which they can be false, as shown in
Fig. 7. On the right of Fig. 7 we again see our hypo-
thetically true phylogeny, and on the left three false
CSTs. They are false because there is no possible way
that speciations could have occurred on this true
phylogenetic tree so that they would correspond to the
lines in the CSTs. The leftmost misrepresents the
direction (trend) of the changes, because changing the
direction of change so that state (f, g) is primitive does
make it possible to put speciation events on the phy-
logenetic tree so that this CST would be true. The
middle CST connects pairs of states that cannot all be
next to each other and still represent speciation events
on the phylogenetic tree; redirecting these proximity
relations cannot make a CST whose speciation events
can be placed on the true phylogenetic tree. However,
attaching state (c) to state (d, e) instead of to state (a,
b) does make this possible. For the rightmost CST,
there is no way to place a speciation on the phyloge-
netic tree so that even its states would result.



Fig. 7. Three character state trees each false for a different reason.


Two CSTs do not have to be both true for it to be
possible to add them; they can be added so long as
there is some phylogenetic tree (true or not) on which
all their speciations can be simultaneously placed.
Then from the placement of these speciations on this
phylogenetic tree the sum CST can be constructed.
But how can we find such a phylogenetic tree? Es-
tabrook and McMorris (1980) demonstrated that we
do not need to. They showed that there is a one-to-one
correspondence between CSTs and trees of subsets of
S. A collection of subsets of S is called a tree of
subsets of S if it satisfies two properties: S itself is one
of the subsets, and any two subsets either have no
species in common or one contains all the species that
are in the other. Each character state in a CST has a
subset in its tree of subsets consisting of all the spe-
cies in that state plus all the species in any descendant
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114
state. Thus, the most primitive state has for its subset
S, the entire study collection of species. States with no
descendant states have for their subset only the species
that they contain themselves. The correspondence is
shown in Fig. 8, where below each CST is shown its
tree of subsets, arranged so that derived states are
above their ancestors. The sum is determined by
combining the subsets from both trees of subsets; if
the result is itself a tree of subsets, then the sum is the
corresponding CST. In Fig. 8, the trees of subsets of
the two CSTs to be added are combined to make the
tree of subsets in the lower right; finally the CST
above is constructed using the principles described
above. This CST is the sum of the first two.



Fig. 8. The sum of two character state trees determined by their
respective trees of subsets.


Two CSTs do not have to be true for one to be a
refinement of the other. We can readily see from the
sum of two CSTs that if the tree of subsets of one CST
contains all the subsets in the tree of subsets of an-
other CST, then the first is a refinement of the second.
The diagram of the relation “is a refinement of”
among CSTs makes a semi-lattice. A diagram of this
semi-lattice for the simple case in which S contains
only 3 species is shown in Fig. 9. The refinement
relation has been studied theoretically by Estabrook
and McMorris (1980), McMorris and Zaslavsky
(1981), and Janowitz (1984).
Not every pair of CSTs can be added. When the
union of their two trees of subsets is NOT a tree of
subsets, as shown in Fig. 10, then there is no phy-
logenetic tree on which to place speciations that
correspond to the lines in both CSTs. Typically we do
not know the true phylogenetic tree so we can not test
a CST to discover whether it is true or not. However,
if two CSTs cannot be added, then they cannot both be
true; they are incompatible as hypotheses about the
ancestor relation among the species and their ances-
tors under study (Estabrook, 1984). Two CSTs that
can be added are compatible as hypotheses about the
ancestor relation. This concept of character compati-
bility, and others related to it, form the basis of a
variety of compatibility methods developed and used
over the past 50 years.
4 Early history of compatibility concepts
In the mid 1960s several workers independently
became aware that it may be the case that a feature of
some (but not all) species in a group under study
cannot be associated with a single speciation event on
a phylogenetic tree if another feature is. If the histori-
cal branching pattern of phyletic lines leading upward
to extant species does in fact form a tree, then the two
hypotheses that they each can be so associated are
incompatible. Wilson (1965) pointed out that if the
group of species with one feature were either distinct
from, or entirely contained in, the group with the
other, then the hypotheses were compatible, but if the
groups partially overlapped then they were not. You
can see that, in the case of two-state CSTs, this test is
identical to addition of CSTs by trees of subsets.
Hennig (1966, page 121 and Fig. 36) describes, if
more prolix, the same basic test. He (or his translators)
calls incompatible features “incongruous”, and points
out that one of two incongruous features must have
been wrongly interpreted, i.e., false. Of course they
both may have been “wrongly interpreted”. Camin and
Sokal (1965) consider several possible exclusive
states of the same homologous structure arranged in a
sequence to hypothesize the order in which they
evolved to produce a linear, multi-state CST. They
recognized that such CSTs could be contradictory
under the assumption that the branching pattern of the
phyletic lines leading to the extant species under study
forms a tree.
Once aware of these contradictory hypotheses,
the question of how to resolve them needed to be
addressed. Some of the contradictions may be a
consequence of errors in direction of evolution, i.e., a
feature may have been lost instead of gained, in which
case the group of species not exhibiting the feature
should be the one participating in the tests. One
approach to this problem is to hypothesize different
directions in an attempt to resolve contradictions.
Another approach is to eliminate direction from the
hypothesis by considering CSTs undirected. Le-
Quesne (1969) proposed a compatibility test for
ESTABROOK: Character compatibility concepts


115


Fig. 9. The lower semi-lattice of the refinement relation among all possible ancestor relations for a study collection of three species. The original
figure was drawn by C. A. Meacham in 1989 as class notes for his students at the University of California at Berkeley, CA, USA.


undirected two-state CSTs; if all four possible combi-
nations of present and absent for two features are
represented among the species in a study collection,
then the two-state CSTs associated with those features
are incompatible. Estabrook and Meacham (1979)
presented a test for undirected multi-state CSTs. They
proved that in a CST there is always a state that can be
designated as the most primitive so that the number of
species in any state x immediately derived from it,
plus the sum of the number of species in all the states
derived from state x, is never more than half the
number of species in S. A CST directed with such a
state most primitive is said to be directed “common
equal primitive”. They then proved that if two com-
mon equal primitive CSTs are incompatible, then they
will remain so directed in any other way. Thus if
CSTs are directed common equal primitive a compati-
bility test by trees of subsets will also test them as
undirected hypotheses. Estabrook (1977) suggested
that systematists might be tempted to believe that
common equal primitive because directing change that
way eliminates conflicts due to direction alone.
Meacham (1984a) made the then controversial sug-
gestion that the role of hypothesizing direction of
evolutionary change before estimating the ancestor
relation among species under study could be reduced,
or even eliminated, by reasoning with undirected
CSTs, especially in cases with little or no a priori
evidence to identify a primitive condition. Donoghue
and Maddison (1986) objected on philosophical
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116


Fig. 10. The incompatibility of two character state trees, discovered
using their respective trees of subsets.


grounds that were later shown to be irrelevant to
modern methods.
With two-state CSTs, there are no incompatibili-
ties that can be resolved by changing proximities of
states in CSTs because there is only one proximity.
However, with more general CSTs, we can ask for
two incompatible CSTs whether there are any other
CSTs with the same respective states that are com-
patible. This is especially relevant when the data
source provides predominantly multi-state characters.
In the 1970s protein sequencing became more com-
mon. Species could be compared based on which
amino acid appeared in any given position of a se-
quenced protein. The resulting characters often had
more than two states, and could have as many as 20
states. Multi-state characters continued to be relevant
through the 1980s as DNA sequencing became more
available. Here nucleotide bases represent character
states.
A character consisting of just its character states,
with no hypothesized state proximities or direction of
evolutionary change, is called a qualitative taxonomic
character (QTC). Without a CST for its states, a QTC
does not represent an explicit hypothesis about speci-
ation events on the true phylogenetic tree. However,
we can hypothesize that there are speciation events on
the true phylogenetic tree that produce a CST with the
same states as a QTC. In this way, a QTC represents a
hypothesis about speciation events; it is weaker than
the hypothesis associated with a CST and asserts
nothing about direction of change. Two QTCs are
potentially compatible if there are two compatible
CSTs with the same states respectively. Those CSTs
realize that potential. A character state is convex if the
unique path of (ancestor, immediate descendant) pairs
connecting any two species in that state contains only
species in that state. This mathematical term general-
izes a convex lens inside of which any two points
determine a line that lies entirely within the lens. A
true QTC will have states that are “convex” on the
diagram of the true ancestor relation. If two QTCs are
potentially compatible, then there exists some ancestor
relation (not necessarily true) for which all the states
of both are convex. Thus, all true QTCs are necessar-
ily potentially compatible with each other. Often,
when working within a context of only QTCs, poten-
tially compatible QTCs are called simply compatible.
In the mid 1970s, Fitch (1975), Sneath et al.
(1975) and Estabrook and Landrum (1975) independ-
ently suggested essentially the same way to test
whether two QTCs were potentially compatible, i.e.,
there existed compatible CSTs with their respective
states. Estabrook and McMorris (1977) mathemati-
cally proved the validity of the test of Estabrook and
Landrum (1975). To make the test, EUs are entered in
the cells of a matrix: states of the first character label
the rows, and states of the second character label the
columns; each EU is placed in the cell whose row and
column labels are the states to which it belongs, as
shown in Fig. 11. Moving only from one occupied cell
to another in a straight line horizontally or vertically
but never retracing a path already taken, if you can
return to an occupied cell you have already visited
then the two characters are incompatible, as for I and
III, otherwise the two characters are potentially com-
patible, as for I and II. In Fig. 11, possible moves are
shown with dashed lines. To discover two CSTs that
realize potential compatibility, first connect with
horizontal or vertical lines any cell or cell group not
yet connected to other cells in any way that does not
close a loop, and then designate as primitive any cell
in the connected network. Thus, for QTCs I and II in
Fig. 11, you could connect cell (IG IIT) containing (d,
f) to the empty cell (IC IIT) on the path between cell
(IC IIA) containing (b) and cell (IC IIC) containing (e,
g); then designate cell (IC IIT) primitive. The result-
ing CST for I has state C primitive with states A and
ESTABROOK: Character compatibility concepts


117



Fig. 11. Illustration of a test for the potential compatibility of two qualitative taxonomic characters, using seven species and three sites. A closed
loop in the coincidence matrix, shown lower right, indicates that the pair of sites is not potentially compatible.


G separately derived from it. The resulting CST for II
has state T primitive with states C and A separately
derived from it and state G derived from state A.
Some characters are inappropriate no matter what
their compatibility relations are with other characters,
for example, random changes within populations not
ultimately associated with speciation events, as dis-
cussed at the beginning of this essay. Characters based
on such changes are likely to be incompatible with
more appropriate characters. Another cause of inap-
propriate characters is mistaken homology, i.e., com-
paring non-comparable structures. A structure in one
species is homologous to a structure in another species
if each structure evolved from the same structure in
the most recent common ancestor of those two spe-
cies. This concept of homology is idealized because
virtually never can we make observations to tell for
sure whether these conditions have been met. We have
to guess based on things we can observe. This con-
cept, together with some ideas about how to guess
whether structures are homologous, is very old
(Owen, 1848; Lankester, 1870). Operational ap-
proaches to estimating homologies were discussed by
Inglis (1966), Jardine (1967, 1969), and more recently
Estabrook (1997, Figs. 21–24). Characters inappropri-
ate for these reasons are likely to be incompatible with
true characters. Incompatibilities with such inappro-
priate characters are best resolved by simply eliminat-
ing such inappropriate characters from further consid-
eration, if more plausible homologies cannot be
estimated.
Estimating homology is essential before protein
amino acid, or DNA base, sequence data can be used
as characters for any kind of analysis (including and
especially by computers). An estimate of homology
takes the form of sequence alignment. Sometimes
short sub-sequences that are identical in all taxa occur
in about the same place in the full sequence. These are
useful to aid in estimating homology of positions
(alignment), but once sequences are aligned with their
help, these positions become useless for estimating
relationships because they do not vary. Variable sites
can be used to estimate relationships provided that
variation accurately reflects relationship. But, espe-
cially if evolution has created gaps in aligned se-
quences, variable sites are more difficult to align.
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118
Needleman and Wunsch (1970) were one of the first
to suggest an operational procedure for alignment, and
increasingly sophisticated criteria and algorithms to
estimate homology among DNA base sequences have
been devised and discussed over the past few decades
by Waterman (1984), Thompson et al. (1994), Day
and McMorris (1994) and Kumar et al. (2004), to
name a few. The possibility of errors in homology still
remains for characters based on aligned DNA base
sequences. Discovering and eliminating sites whose
alignment is questionable should improve estimates of
relationship.
By the late 1970s, all the basic concepts for test-
ing the compatibility of hypotheses of speciation
events on a phylogenetic tree, based on comparative
observations of species in a group under study, had
been developed. Contemporary reviews are available
from McMorris (1975), Estabrook (1978, 1984),
Cartmill (1981), LeQuesne (1982), Meacham and
Estabrook (1985), and more recently Xu (1994)
described for the Chinese speaking world compatibil-
ity for the special case of characters with unbranched
CSTs.
5 Resolution of incompatibility to estimate
an ancestor relation
Construed as they are here, the more useful and
reliable characters are based on observable changes
associated with speciation events, in which a descen-
dant species becomes different in some respects from
its ancestral species. Characters based on random and
often reversible changes that occur within species,
especially if they occur within several less closely
related species, are less likely to compatibly reflect
much about the history of the speciation process.
Thus, as we attempt to reason with the patterns of
compatibility among groups of more reliable charac-
ters, what we can estimate is an ancestor relation,
commonly expressed as a directed diagram with an
arrow from any ancestor to each of its immediate
descendants, or as an undirected diagram that can
represent an estimate of the ancestor relation after its
most primitive place (root) is estimated. In particular,
we cannot directly estimate with characters, construed
as we have, the branching pattern of phylogenetic
lines. As we have seen from Figs. 2, 3, the same
branching pattern of phyletic lines can give rise to
strikingly different ancestor relations, depending
where the speciation events take place. With this in
mind, we examine some of the early approaches to
using compatibility of pairs of characters to estimate
the ancestor relation.
Early workers proposed three basic approaches.
(1) Make considerations of the development, adaptive
functions, parasites, diseases, biogeography, natural
history, etc. of the species under study to modify (if
possible) one or both CSTs in any incompatible pair to
resolve their incompatibility, until enough CSTs could
be added together to produce an estimate of the an-
cestor relation for the species under study. This proc-
ess has been called “reciprocal illumination” because
when some natural, biological factors suggest ways to
resolve some incompatibilities, the relationships
suggested by the sum of now more compatible char-
acters invite consideration of other natural, biological
factors with which to resolve other incompatibilities.
CSTs whose incompatibilities could not be resolved
by this process were set aside, as less reliable or
problematic. (2) Leave characters as originally con-
structed, but apply some operational (often quantita-
tive) criterion to choose one character (or a compatible
group) to make an initial partial estimate. Then, within
the context of subsets of S that are convex on this
partial estimate, apply the criterion again, until the
ancestor relation is resolved to the satisfaction of the
investigator. This approach is operationally possible
because of the mathematical fact that if two CSTs or
two QTCs are compatible in the context of S, then
they will remain compatible in the context of any
subset of S; but some pairs of CSTs or QTCs incom-
patible in the context of S may become compatible in
the context of only a subset of S. (3) Sub-divide
character states without consideration of the develop-
ment, form, adaptive functions, parasites, diseases,
biogeography, natural history, etc. of the group under
study, to create new characters with more, smaller
states, that are all mutually compatible. This approach
is operationally possible because of the mathematical
fact that if two CSTs or two QTCs are compatible,
there is always a way to subdivide any state (with two
or more species) of either to produce CSTs or QTCs
that are still compatible; and for any two incompatible
CSTs or QTCs, it is always possible to sub-divide
states enough to create two new compatible charac-
ters. In fact, there are in general very many ways to do
this, especially if S is large. For this reason, this
approach imposes the additional criterion that as few
as possible new character states should be created to
resolve all the incompatibilities among the characters.
Among practitioners of the first approach, one
of the most influential in his time was Hennig (1966).
This book is a translation into English by D.D. Davis
and R. Zangerl of an unpublished MS composed by
ESTABROOK: Character compatibility concepts


119
Hennig shortly before that date as a major revision of
a less well known book he had published 15 years
earlier. In his preface, Zangerl himself warns us of the
linguistic difficulties of making such a translation,
especially while the original German revision remains
unavailable to most scholars. Indeed, many of the
terms in Hennig (1966) are taken from evolutionary
biologists writing in English, where their meanings
have been well understood for decades, but given
different meanings, either by Hennig or by his trans-
lator in an attempt to translate Hennig’s German.
Unfortunately, this resulted in some serious misunder-
standings during the 1970s and 1980s, which are only
now beginning to be resolved. Mayr (1974) and Sokal
(1975) discuss some of these issues in more detail.
Making allowances for the flagrant misuse of
established terms by Hennig (1966), pages 120 and
121 of this book clearly describe a test for the com-
patibility of two 2-state CSTs; incompatible CSTs are
there called “incongruent”. Much of the rest of the
book is devoted to techniques of “reciprocal illumina-
tion” to consider the development, form, adaptive
functions, parasites, diseases, biogeography, natural
history, etc. of the group under study to modify one or
both of the pairs of incompatible CSTs to resolve
incompatibilities. Examples of applications of these
techniques are shown as branching patterns of phy-
logenetic lines, with speciation events associated with
character state changes marked on them. Although for
its time, this concept was enlightened, I suspect that
Hennig (1966), similar to almost everyone else at that
time, did not realize that branching patterns of
phyletic lines could not be explicitly estimated with
character state trees, only ancestor relations. This went
on to confuse Hennig’s followers (of which there were
many) over the next three decades, and ramifications
of this confusion are still with us today.
Many others who did not consider themselves
followers of Hennig also considered natural, biologi-
cal criteria to restructure CSTs to provide a more
consistent estimates, with authors typically publishing
only the completely compatible CSTs and the result-
ing ancestor relation (or inappropriately, phylogenetic
tree). Such results appear internally very consistent,
but often, specifically how they were achieved re-
mained unspecified. Good examples of natural criteria
for estimating CSTs are given by Marx and Rabb
(1972), who discuss criteria for structuring and modi-
fying CSTs in this spirit, applying them in explicit
detail to structure 50 CSTs for the morphological
characters of snakes. Other examples are given by
DeMarco et al. (1985) presented in Table 2 of
Estabrook (2001), Stein et al. (1984), Gardner and
LaDuke (1979), and more recently Strasser and Del-
son (1987) and Chen (1994). Few investigators use
this approach today, in part because molecular data
have come to dominate as the basis for estimating
relationships, and it is not yet clear how to apply
considerations from the natural world explicitly to
restructure QTCs arising from molecular data. This
approach may become more useful again as macro-
molecular data, e.g., chromosomal rearrangements or
other large scale genetic changes, become more
widely implicated in the estimation of ancestor rela-
tions.
The second approach uses an operational crite-
rion to select some of the CSTs or QTCs to use com-
patibly to make a (possibly only partial) estimate of
the ancestor relation. LeQuesne (1969) considered
2-state CSTs, and described a test for their compati-
bility. He called true CSTs “uniquely derived”; an apt
term because it reminds us that if a character is true
then the observable quality shared by all the species in
any character state evolved only once when the most
recent common ancestor of all the species in that state
evolved. LeQuesne (1974) evaluates all possible
2-state undirected CSTs with criteria related to the
number of other CSTs with which they are compati-
ble, chooses one of these as a first division in an
hierarchical classification, and then iterates the proc-
ess to resolve a classification. It is not clear how this
classification relates to an estimate of the ancestor
relation. In the case of CSTs, directed or undirected,
Estabrook et al. (1976b) proved that if all pairs of
CSTs in a collection of CSTs are compatible, then the
entire collection is compatible, i.e., there are ancestor
relations (namely all refinements of their sum) that are
refinements of every CST in the collection. Thus, a
maximal collection of pairwise compatible CSTs
could be chosen as the basis for a first (usually only
partial) estimate of the ancestor relation. Discovering
such a collection is equivalent to discovering the
maximal cliques in an undirected graph, a computa-
tionally difficult (NP complete) problem as S becomes
large. Bron and Lerbosch (1973) published an algo-
rithm to discover the largest collections (cliques) of
pairwise compatible CSTs. In 1976, Kent Fiala used
this algorithm, among others, to write the computer
program CLINCH (CLadistic INference by Compati-
bility of Hypothesised CSTs) used by Estabrook et al.
(1977) to estimate an ancestor relation based on the
largest collection of pairwise compatible characters.
LaDuke and Crawford (1979), Duncan (1980), Vara-
darajan and Gilmartin (1983) and Crins (1990) have
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120
also used CLINCH. Warnow (1993, 1994) discussed
efficient ways to implement this criterion. There may
be two or more largest (in numbers of CSTs) collec-
tions of pairwise compatible characters, often with
many CSTs in common. Voss and Voss (1983) used
the intersection of the two largest cliques to estimate
the ancestor relation. Fitch (1984) suggested choosing
the maximal clique whose CSTs were compatible with
the most other CSTs. Estabrook and Anderson (1978)
chose the single CST compatible with the most other
CSTs as the first partially resolved estimate of the
ancestor relation; subsequent analyses of two subsets
of S, convex on this partially resolved estimate,
(so-called secondary analyses) resolved the estimate.
Strauch (1978) makes extensive use of secondary
analyses, and Strauch (1984) explains in more detail
some of the tactics of secondary analysis. As CLINCH
became more widely used, subsequent versions in-
corporated these and other criteria; Fiala (1984)
documents its sixth version.
Many investigators were not comfortable hy-
pothesizing CSTs. The observable states of a QTC
seemed to have more objective reality than a CST,
which includes a hypothesis about how those states
evolved from one another. A collection of QTCs for a
study collection S of species (or other evolutionary
units) can be tested for potential compatibility and
maximal groups of pairwise potentially compatible
QTCs discovered, but as we have pointed out above,
there may be no possible estimate of the ancestor
relation on which all the states of the QTCs in such a
group are convex, i.e., these QTCs may not be
group-wise potentially compatible. This poses an
interesting problem whose mathematical analog has
been studied by Gavril (1974) and McMorris et al.
(1994). Related to this, Benham et al. (1995) general-
ized the concept of characters and their compatibility.
Of course, for a group of pairwise compatible
QTCs there may be an ancestor relation on which all
or most of them have convex states. To look for it,
start with two QTCs, make their matrix of intersecting
states and connect them as illustrated in Fig. 11. Then
choose any occupied cell as primitive, and direct
evolutionary change from it along the lines connecting
the occupied cells, to make a CST of their sum. Use
other QTCs in the group to refine (if possible) this
CST. Boulter et al. (1979) in their study of amino acid
sequences of plastocyanin from flowering plants were
among the first to apply compatibility of QTCs to a
major study. Estabrook (1991) and Camacho et al.
(1997) provide later examples.
Especially with the advent of molecular data sets,
it became unclear how to hypothesize CSTs, or how to
take the first approach to resolve incompatibilities in
consideration of other natural data. Especially in data
sets with a large number of more distantly related
EUs, the second approach applied to CSTs or to the
potential compatibility of QTCs often resulted in
typically only a small fraction of the data participating
in estimates of the ancestor relation. In molecular data
sets, high levels of incompatibility may result from a
larger fraction of molecular data evolved as random
changes not associated with particular speciation
events. With other forms of data, high levels of in-
compatibility may result from adaptive syndromes
being selected repeatedly on different phyletic lines as
populations of less related species were subject to
similar selection pressures. In either case, especially
with larger data sets, the first two approaches were
difficult for many investigators to apply; an automatic
incompatibility resolving criterion was desired.
The third approach is to use an automatic in-
compatibility resolving procedure: subdivide some of
the states of the CSTs a minimum number of times so
that all CSTs become mutually compatible. This
criterion, suggested by Camin and Sokal (1965), has
been called “parsimony” because it minimizes the
number of times that an ad hoc character state change
had to be hypothesized to eliminate logical incom-
patibility among the CSTs. The parsimony criterion
can be easily modified to apply to QTCs (subdivide
states a minimum number of times to make them all
convex on an ancestor relation). This made parsimony
especially attractive to workers who wanted to avoid
hypothesizing CSTs. Discovering which ancestor
relations were parsimonious in the context of a collec-
tion of CSTs is a mathematically difficult problem.
Early workers took one of two basic approaches: (1)
Study this problem mathematically in an effort to
create algorithms, or (2) devise heuristics that might
make plausible guesses. Estabrook (1968) was one of
the first to address this problem mathematically.
Nastansky et al. (1974) continued his mathematical
approach to derive more powerful results. However,
this mathematical approach proved computationally
impractical except for small data sets; heuristic ap-
proaches, typically based on swapping branches to
look for more parsimonious trees, proved to be more
practical. Computer programs to implement these
parsimony heuristics were among a collection of
several, called PHYLIP, written by Felsenstein in the
1970s. Easy to use and readily accessible, PHYLIP
was revised periodically for the next two decades. Its
version 3.5 was published by Felsenstein (1993). Soon
ESTABROOK: Character compatibility concepts


121
parsimony algorithms themselves became the subject
of mathematical study; Hendy and Penny (1982)
established branch and bound criteria, and this
mathematical study has continued (Argawala et al.,
1995, Ganapathy et al., 2003). Swofford (1991)
produced a powerful set of programs to implement
parsimony (and other criteria), which has been in-
tensely maintained, widely distributed, and remains
one of the principal technologies in use (Swofford,
2003).
When parsimony divides character states to re-
solve incompatibilities, the original CSTs are con-
verted to new CSTs, typically with more states.
Commonly in larger data sets, there are many different
ways to subdivide a minimum number of character
states to resolve incompatibilities. These ways result
in different collections of new CSTs. The same an-
cestor relation may refine all new CSTs in each of
these different collections, or some may be refined by
one ancestor relation, others by another, etc. Some-
times parsimony produces a very large number of
collections of new CSTs that resolve incompatibilities
equally parsimoniously, and suggest many, often quite
disparate ancestor relations.
Typically, parsimony heuristics evaluate only
“fully resolved” ancestor relations, in which none of
the species (or other EUs) in S have ever served as an
ancestor of any other, and no ancestral species has a
representative in S. The true ancestor relation is never
“fully resolved” whenever S contains EUs that have
served as ancestors for others. This is commonly the
case in paleontological studies; for examples see
Smith (1994). True ancestor relations that are not fully
resolved may also be the case with many studies of
extant taxa; for example Gates (1982) describes
Banisteriopsis campestris, a weedy shrub spread over
the aluminum-rich, laterite soils of the central savan-
nah of Brazil, and several other species of that genus
that occur uniquely on several geographically isolated
quartzite outcrops each not more than a few tens of
square kilometers in size. These species seem to have
evolved directly from B. campestris when populations
became isolated on these outcrops. If this were the
case, then the true ancestor relation would be unre-
solved; its diagram would be fan-shaped with B.
campestris primitive and the other species descended
directly from it.
Some variations of parsimony do not weight all
subdivisions of characters states equally. In one
variation, after a character state has been subdivided
once, further subdivisions are weighted less or not at
all. In another variation, after any state of a character
has been subdivided once, subdivisions of that state or
other states in that character are weighted less, or not
weighted at all, in which case (if the heuristic process
gets the right answer) the heuristic will discover an
ancestor relation for which the fewest number of
characters need to have any of their states subdivided;
such an ancestor relation is a refinement of every
character in a largest maximal clique of compatible
characters. In this way we can see that there is a
continuum of criteria from strict parsimony to esti-
mating an ancestor relation that refines all the charac-
ters in a largest clique of compatible characters.
Because the popular PHYLIP package contains a
program CLIQUE that finds an ancestor relation that
requires subdivision of states in a minimum number of
characters, many workers have used PHYLIP (and not
CLINCH) to discover an ancestor relation that is a
refinement of a largest clique of compatible charac-
ters. A recent example is given by Gupta and Sneath
(2007) who used PHYLIP to discover largest maximal
cliques of compatible 2-state characters in a very large
data set of DNA sequences comprising thousands of
sites for 24 species representing a wide diversity of
proteobacteria. The five major groups identified by
this compatibility method were the same as those
identified by more computationally intense and
mathematically sophisticated recent methods, and the
ancestor relations among these groups were all very
similar. The authors concluded from their results that
compatibility analysis is a useful new tool. This
conclusion is clearly wrong in one respect; compati-
bility analysis used in this way is an old tool.
Through the 1960s and ’70s, several other meth-
ods for estimating the ancestor relation from QTCs,
but not directly related to compatibility concepts, were
proposed. They are mostly outside the scope of this
review, but Felsenstein (2004) provides an excellent
review of some of them.
6 Probability of compatibility
Some mid 20th century investigators of evolu-
tionary history, especially those working below the
species level in human genetics, such as Edwards and
Cavelli-Sforza (1964), construed changes in gene
frequencies, DNA base pairs, or other indications of
evolution as random processes, not stably associated
with speciation events. Because populations within the
same species (especially human) are generally less
genetically isolated than distinct species, tree branch-
ing patterns may be inappropriate representations of
the historical evolutionary relationships among
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122
populations within a single species (Baum & Es-
tabrook, 1978; Ward et al., 1991). Nevertheless,
population geneticists used probability to model these
random processes as occurring along tree branching
patterns connecting populations. Once a particular
random process is hypothesized, maximum likelihood
methods can be used to estimate a (usually) undirected
tree branching pattern. Random models of character
state change and maximum likelihood estimation of
tree branching patterns of phyletic lines became more
widely used to estimate evolutionary relationships
among species as well. Felsenstein (1983) pointed out
that in some modeled cases, especially those including
a distantly related evolutionary unit, maximum likeli-
hood estimates differed from those made by compati-
bility or parsimony, and would continue to do so even
if more data were generated. From this he concluded
that in such cases the estimates made by compatibility
or parsimony were misleading. However, if many
changes are random, but some changes are stably
associated with speciation events, maximum likeli-
hood may get the “wrong” answer and compatibility
or parsimony do better, especially if random changes
are somehow recognized and removed before a com-
patibility or parsimony estimate is made. Qiu and
Estabrook (2008) observed that when the apparently
more random sites were removed parsimony estimates
became more stable with higher branch support while
maximum likelihood estimates produced a variety of
branching patterns with weaker branch support.
Recently, Kolaczkowski and Thornton (2004) have
clearly demonstrated this effect with simulation.
Probability concepts have been applied to com-
patibility to try to recognize, so to eliminate or un-
derweight, characters that seemed to be more random.
LeQuesne (1972), presented a formula to calculate the
probability that two 2-state characters would be
potentially compatible at random; he used this concept
to rank characters in order of “merit” to be considered
uniquely derived (true), or to select characters for
further consideration. Meacham (1981, 1984b) de-
fined clearly the concept of “at random” implicit in
LeQuesne (1972) and described mathematically how
to calculate the probability that two (or a group) of
CSTs (with any number of states) would be compati-
ble at random. It became clear that some kinds of
CSTs were more likely than others to be compatible at
random with others; CSTs with many large advanced
states were less likely to be compatible at random.
This suggested another criterion for choosing a collec-
tion of compatible characters for the initial estimate
(or subsequent secondary refinements) of the ancestor
relation; instead of choosing the largest clique, which
might have many CSTs likely to be compatible at
random, choose the clique of CSTs least likely to be
compatible at random. Meacham’s computer program
COMPROB enabled investigators to implement this
criterion accurately to identify maximal cliques least
likely to be cliques at random.
Especially in data sets with a large number of
taxa, the number of characters (CSTs or QTCs) in the
largest (or least likely) clique was often a small frac-
tion of the total number of characters. An immediate
consequence of this is that in many cases most char-
acters are false, because true characters always belong
to the same clique (but perhaps not always the largest
one). Flagrantly false characters, whose states would
have to be subdivided many times to become convex
on the true ancestor relation, might be as likely to be
compatible with other characters as a character to
whose states EUs were assigned at random. For a
given QTC in a collection describing the EUs in S, the
probabilities with which it would be compatible at
random with each other QTC in the collection could
be summed to give the number of other QTCs with
which it would be expected to be compatible at ran-
dom. This could be compared with the number with
which it was actually compatible; if this number were
not substantially more than would be expected at
random, then the character could be set aside as
indistinguishable from random. Remaining characters
could be dealt with in any of the three approaches
described above.
Meacham (1994) construed the number of other
characters with which a given character is compatible
as a random variable, and undertook to estimate its
distribution under the hypothesis that the given char-
acter was random. Because exact algorithms in the
style of Meacham (1981) become complicated and
computationally intractable for QTCs, or for CSTs for
data sets with a large number of EUs, Meacham
(1994) used simulation to make close approximations
to compatibility related probabilities. To estimate the
probability that a given character (QTC or CST)
would be compatible with at least as many other
characters as it actually was, under the hypothesis that
it was a random character, he chose with equal prob-
ability another character from among those with the
same number of EUs in each state as the given char-
acter, and counted the number of other characters in
the data set with which it was compatible, noting
whether this was at least as many as the given charac-
ter. This was repeated 1000 (or more) times. The
fraction of these random characters that were
ESTABROOK: Character compatibility concepts


123
compatible with at least as many other characters as
the given character estimates this probability.
Meacham (1994) called this probability Cf, the Fre-
quency of Compatibility Attainment. He applied this
to evaluate the 53 morphological characters of angio-
sperms published by Donoghue and Doyle (1989),
ranking them by their Cf, the probability that a ran-
dom character would be compatible with at least as
many other characters as observed. By this criterion,
25 characters were significantly non-random at the Cf
< 0.05 level. He then used parsimony to reconcile
incompatibilities among only the top ranked charac-
ters, which produced an estimate similar to, but less
ambiguous than, that of Donoghue and Doyle (1989).
Camacho et al. (1997) used the character evaluation
method of Meacham (1994) in conjunction with
potential compatibility of QTCs to estimate relation-
ships among species of a subterranean genus of Crus-
tacea. Qiu and Estabrook (2008) apply the character
evaluation method of Meacham (1994) to a large
molecular data set to choose the less apparently
random sites for further analysis with bootstrap par-
simony and maximum likelihood using PAUP. Pisani
(2004) applied the criterion of Meacham (1994) to
evaluate 866 DNA sites for 47 species chosen to
represent the diversity of Arthropoda. There were 172
sites with Cf > 0.5, i.e., can not reject at p = 0.05 the
hypothesis that the character is random based on the
number of other characters with which it is observed
to be compatible. These 172 sites were removed and
those remaining were subject to maximum likelihood
and neighbor joining analyses to estimate branching
pattern of phyletic lines. Pisani (2004) suggests that
removing characters with Cf > 0.5 may reduce the
effects of long branch attraction; he also observed that
when characters with Cf much lower than 0.5 were
also removed, results began to deteriorate. However
Qiu and Estabrook (2008) observed increased clarity
of parsimony estimates of relationships among key
groups of angiosperms when all characters with Cf >
0.2 were removed. Day et al. (1998) used the number
of compatible pairs of characters in a whole data set as
a random variable under the hypothesis that all the
characters in the data set were random in the sense of
Meacham (1994). They analyzed 102 published data
sets, of which 12 had fewer compatible pairs than
would be expected at random. In general, they ob-
served that inclusion of outgroups increased the
probability that compatibilities levels are random,
sometimes substantially so.
Salisbury (1999) suggested another way to use
probability to evaluate cliques of compatible charac-
ters, which he termed “strongest evidence”; where
Meacham (1994) calculates the probability that a
clique of compatible characters would be mutually
compatible if they were all random characters, i.e.,
that there is some ancestor relation with which they
are all compatible, Salisbury (1999) calculates the
probability that the characters in a clique of compati-
ble characters would be independently each compati-
ble at random with the ancestor relation that they
jointly determine, which is a stricter criterion with a
lower probability. Salisbury implemented strongest
evidence compatibility in a computer program, called
SECANT, which also contains most of the functions
of CLINCH.
7 Other applications
Compatibility concepts have been applied to sev-
eral other areas. Ringe et al. (2002) recognize the
parallel between the historical development of related
languages and the evolution of species to structure
features of related languages as characters, and find
maximal cliques of compatible characters as a basis
for estimating their historical relationships.
O’Keefe and Wagner (2001) used character
compatibility as a basis for testing hypotheses of
character independence. An advantage of their ap-
proach is that it does not require estimating an ances-
tor relation, which may itself assume character inde-
pendence. Characters with similar patterns of com-
patibility with the other characters in the data set are
candidates for dependence; simulation under the
hypothesis of independence estimates significance
levels. This is a second example, along with Meacham
(1994), of using compatibility concepts to evaluate
characters in a phylogenetic context without needing
to estimate an ancestor relation.
One way to resolve incompatibilities among
characters is to hypothesize explicitly reticulate events
(such as hybridization) in the evolution of the EUs
under study. Corti et al. (1986) hypothesized hybridi-
zation events, severely constrained by the meiotic
failure of certain chromosomal rearrangements, to
resolve incompatibilities. von Haeseler and Churchill
(1993), Bandelt (1994) and Jakobsen and Easteal
(1996) used compatibility concepts to describe phy-
logenetic networks more generally.
Nelson and Platnik (1981) explored the possibil-
ity, suggested earlier by Hennig (1966) and many
others, that there may be a link between the phyloge-
netic relationships among species, and the history of
the processes that have resulted in their occupancy of
Journal of Systematics and Evolution Vol. 46 No. 2 2008

124
particular geographic areas. Estabrook (1985) used
compatibility concepts to demonstrate the potential
tenuousness of this relationship. However, character
states convex on an undirected estimate of the ances-
tor relation may suggest a historical relationship
among geographic areas if species evolved either by
rare dispersal into geographically disjunct areas, or as
a consequence of those areas becoming disjunct
through the establishment of barriers to dispersal.
Estabrook (2001) gives an example of this, and con-
siders available natural history data to judge which of
these two processes seems most likely. Craw (1988)
has interpreted compatibility relations among “char-
acters”, construed as the presence or absence of
species in distinct geographic areas, to suggest his-
torical patterns. The simultaneous evolution of species
with the “evolution” of the isolated areas they occupy
is a fascinating phenomenon, especially because
conceptually it is analogous to parasitic species
evolving simultaneously with their hosts, or gene
duplications (like speciation for gene lineages) evolv-
ing simultaneously with the species of whose genomes
they are a part. It is possible that an estimate of an-
cestor relation for the areas (hosts, species) is incom-
patible with the ancestor relation implied for the area
(hosts, species) by an estimate of the ancestor relation
for the species (parasites, gene lineages). How to
resolve such incompatibilities is a difficult problem,
which was effectively addressed by Page (1994,
1996). Much progress to understand it more thor-
oughly has been made by a number of workers since,
but its discussion is beyond the scope of this review.
Rock strata containing fossils have been used to
estimate the interval of time from the evolution to the
extinction of species (or other higher taxon). These
estimates could place so-called stratigraphic con-
straints on estimates of the ancestor relation. For the
past two decades or more, the question of whether
such stratigraphic constraints should be imposed on
estimates made with comparative characters has been
hotly debated. Cladists, who believe that ancestral
species have ceased to exist, generally oppose strati-
graphic constraints, as do others who believe that such
stratigraphic estimates are generally too inaccurate to
impose constraints. Huelsenbeck (1991) presents
some of these issues in more detail. Estabrook and
McMorris (2006) examined the consequences of
stratigraphic constraints on the mathematical founda-
tions of character compatibility analysis established
by Estabrook et al. (1976a, b) and discovered that
these consequences can be quite severe.
Methods to estimate ancestor relations, such as
parsimony, often produce many different estimates, so
the question arises how to combine them into a single
estimate. Investigators may also want to combine
estimates based on different data sources, e.g., differ-
ent genes, or different members of the same gene
family, in which case the several estimates may not
involve exactly the same species. Many ways to
combine estimates have been suggested; the descrip-
tion of all is beyond the scope of this review, but one
way uses compatibility. An estimate is represented by
several 2-state CSTs; to each ancestor corresponds a
2-state CST with its advanced state containing that
ancestor and all its descendants. These CSTs are all
compatible and their sum reconstructs that estimate of
ancestor relation. All the CSTs of all the estimates to
be combined are analyzed for compatibility and a
maximal clique of compatible CSTs are added to
produce the combined estimate. Rodrigo (1996)
argues convincingly for the appropriateness of this
method, and suggests a way to combine estimates that
do not each involve every one of the species in S. His
suggestion becomes computationally unwieldy when
many estimates each missing many species are to be
combined. This problem is avoided by using a parsi-
mony hill climbing heuristic with the optimality
criterion that the number of characters for which any
state needs to be subdivided is minimized. Ross and
Rodrigo (2004) make a thorough assessment of this
compatibility method, and Wilkinson et al. (2005) test
this method, together with 13 others, to demonstrate
its consistency and stability.
Some forms of data distinguish a group of some
of the species under study; such a group might be a
plausible candidate for a character state convex on the
ancestor relation, but there may be no compelling
evidence to imagine that the remaining species will
also make a convex state. An example of this is the
presence of an endonuclease binding site which may
have evolved only once but may have been subse-
quently lost in descendant lineages; in this way the
group of species that do not posses the site would not
make a group convex on the ancestor relation.
McMorris (1977), Meacham (1983) and Templeton et
al. (1992) have grappled with such so-called partial
binary characters.
Instead of estimating an entire ancestor relation,
investigators may be primarily concerned to test the
credibility of specific hypotheses of monophyletic in
the context of a group of species under study for
which character data are available, especially when
those hypotheses are incompatible with each other.
Archie (1989) was among the first to suggest an
ESTABROOK: Character compatibility concepts


125
approach to this, and a variety of other approaches,
whose description is beyond the scope of this review,
have since been proposed by several investigators.
One of those approaches uses compatibility concepts.
For each competing hypothesis, the probability that it
would be compatible at random with each character
with which it is compatible is transformed to its
negative logarithm and summed. This provides a test
statistic whose realized significance is estimated by
simulating the hypothesis that the monophyletic group
in question could have been any collection of EUs the
same size with equal probability. Competing hy-
potheses of monophyly can be compared using the
significance with which each rejects the hypothesis
that they seem random in the context of the data. A
computer program, MEAWILK, (Frohlich & Es-
tabrook, 2000) performs this analysis. Qiu et al.
(2006) used MEAWILK to test competing hypotheses
about the deepest divergences in land plants.
8 Compatibility, monophyly and higher
taxa
Not all systematists of the mid 20th century, in
attempting to formulate well defined concepts with
which to study evolutionary relationships among
species, embraced the concept that distinct species
evolve from their ancestral species, which may con-
tinue to have an independent existence through time
until their extinction. Cladists did not recognize an
ancestor relation among species, but considered an
ancestral species to be “identical with all the species
that have arisen from it” (Hennig, 1966, Fig. 18).
Hennig (1966) clearly describes incompatible CSTs
and discusses a wide variety of ways to consider
additional data to resolve incompatibilities, but con-
trary to the claims of his followers, this work does not
advocate automatic criteria, such as parsimony, for
resolving incompatibilities. Fundamental to Hennig’s
explanations of the methods he describes are the two
concepts: synapomorphy (shared derived character
states), and monophyly (group contains all the de-
scendants of its most recent common ancestor). Both
of these concepts depend on the direction of evolu-
tionary change. The relevance of these concepts to
estimating branching pattern of phylogenetic lines was
defended at the time by some very respected systema-
tists, such as Donoghue and Maddison (1986). As I
have shown above, Meacham (1984a) pointed out that
branching patterns can be estimated independent of
estimates of direction of evolutionary change, and
because this involves fewer a priori hypotheses, many
argue that they should be. Virtually all modern “com-
puter” methods to estimate phylogenetic relationships,
such as parsimony, maximum likelihood, neighbor
joining, etc., make their estimates with no considera-
tion of the direction of evolutionary change. Direction
is estimated after branching pattern has been esti-
mated, often by choosing a primitive place in the
undirected branching pattern. The dangers of includ-
ing a distantly related species as a surrogate for this
place were pointed out by Baum and Estabrook (1996)
and evidenced by the results of Day et al. (1998). If
direction of evolutionary change plays no role in the
estimation of branching pattern of phyletic lines, then
neither do synapomorphies nor monophyly. However
convex characters states, a fundamental concept of
compatibility, remain convex no matter how an undi-
rected branching pattern may be directed.
Many cladists became strong advocates of mo-
nophyly (defined above) as the only legitimate basis
for the recognition of higher taxa, partly, or perhaps
even mostly, as a consequence of denying the contin-
ued existence of ancestral species. Monophyly can be
lost with the evolution of new species, even when
there is no change in the ancestral taxon, e.g., reptiles
may have been a monophyletic taxon until birds
evolved from them, but then (according to cladists)
the existence of birds invalidated reptiles as a natural
taxon, even though reptiles themselves did not change.
The requirement to constrain the recognition of higher
taxa by requiring strict monophyly with respect to an
estimate of the ancestor relation is much more strin-
gent than the constraint long recognized by evolution-
ary systematists, who require only that a system of
higher taxa be compatible (as a CST) with a generally
accepted estimate of the ancestor relation. An early
but very clear example is provided by Hall (1928) Fig.
27, which is the diagram of an ancestor relation of the
species in a (convex but not monophyletic) section of
the genus Haplopappus (Poaceae). Some more recent,
but equally clear, examples are given by Michener
(1977) and Varadarajan and Gilmartin (1983). Es-
tabrook (1986) presented a computer program CON-
PHEN to evaluate possible classifications into higher
taxa constrained to be compatible with a given ances-
tor relation. Meacham and Duncan (1987) point out
several problems with monophyly as an overly strict
criterion for higher taxa. When this monophyly crite-
rion results in the destruction of a convex, phenotypi-
cally distinct and long recognized genus or family, it
makes scientific nomenclature unstable and interferes
with access to older name-based publications. Another
methodological problem is becoming apparent; when
Journal of Systematics and Evolution Vol. 46 No. 2 2008

126
workers are trying to clarify relationships near the root
of a phylogenetic tree, they are often reluctant to
remove members of well established monophyletic
groups far from the root, even though the inclusion of
these less related taxa are likely to confound their
analysis. Sometimes this reluctance stems from a
belief that it is illegitimate to analyze a convex, but
not monophyletic, group. More progress will be made
when we learn to focus taxon sampling near the area
in question and avoid the inclusion of distantly related
taxa, even if they are descendants of some of the
ancestors in question.
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Availability of computer programs
Many computer programs related to the concepts discussed here are available from the authors of the publications cited. In addition,
many are available to be freely downloaded from my own web site: www-Personal.umich.edu/~gfe/. These include:
* SECANT by Ben Salisbury. Accepts character data, implements strongest evidence compatibility, and also incorporates many of
the functions of CLINCH by Kent Fiala.
* MEACHAM accepts sequence data and applies the character evaluation criterion of Meacham (1994), then selects sites with Cf less
than a specified threshold, and writes them to a file for subsequent analysis.
* CONPHEN accepts an ancestor relation and distance matrix, discovers close groups convex on that ancestor relation.
* MEAWILK accepts sequence data and hypotheses of monophyly, evaluates hypotheses using compatibility criteria, as well as some
others.
* ADQUARC4 accepts area x taxon presence/absence data, evaluates compatibility of “taxa” , finds cliques and reveals the
“ancestor” relation they determine.
* STRATCOM accepts character data and a stratigraphic range for each taxon, evaluates character compatibility in a stratigraphic
context.