<oological Journal of the Linnean Society (1982), 74: 197-206
Criteria for the determination of the
direction of character state changes
M. J. BISHOP
University Museum of ,zbology, Downing Street, Cambridge
Accepted for publication June 1981
Phylogenetic reconstructions cannot be adequately assessed except in terms of probability models
which represent the processes of change. An evolutionary tree model of bifurcating splits, together with
a Brownian motion model of genetic drift have been shown to allow successful reconstruction of
phylogeny from data relating to gene frequencies of blood groups from human populations. Changes in
state cannot be dealt with by the Brownian motion model, and no adequate models have been
proposed for character state changes from the many possible sources. So, while the evolutionary tree
model is applicable to these problems too, only heuristic methods of analysis of the state data are
available, and these are known to be unsatisfactory under certain conditions. The concepts of
homology, polarity and homoplasy have been developed out of the attempt to describe the nature of
morphological state data, which is unpredictably related to genetic state data. The experimental study
of comparative functional morphology, at any developmental stage of an organism, is considered to be
the only valid tool for investigating the resulting character state tree hypothesis. However, the
speculative nature of such investigations is admitted.
KEY WORDS:-Phylogenetics
-
models of evolution - polarity - homology.
CONTENTS
Theory building in historical science . . . .
A model of evolution based on genotype frequencies .
The problem of discontinuities . . . . . .
The evolutionary tree model . . . . . .
Lack of a suitable model for character state change .
Homologyt polarity and homoplasy . . . . .
The direction of character state changes. . . .
Polarity from commonality? . . . . . .
Polarity from functional morphology? . . . .
Polarity from ontogeny? . . . . . . .
Polarity from geographical distribution?. . . .
Polarity from stratigraphy? . . . . . . .
Acknowledgements. . . . . . . . .
References. . . . . . . . . . .
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THEORY BUILDING I N HISTORICAL SCIENCE
The scientific basis for our knowledge of the properties of individual biological
populations lies in genetics, Genetics explains the apparently contradictory
observation that sexually reproducing organisms both resemble their parents and
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0 1982 The Linnean Society of London
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M. J. BISHOP
differ from their parents. There is a single theory, elaborated down to the
molecular level, which explains both this constancy of inheritance and its variation
(Dobzhansky, 1970; \+‘right, 1978).
Time dependent changes within a population may be observed by studying the
state of a population now and in the future. Evolution is then characterized by the
laws which enable us to predict the state of t h e population at a future time, or in
the past. Theory building is the interaction between the construction of laws, and
the finding of the appropriate set of descriptions of states which enable the laws to
be constructed (Lewontin, 1974). \Ye have to find a model for the evolutionary
process which we believe represents a process which is going on. The model must
be such that its parameters may be estimated to allow discrimination between
alternative hypotheses. I n population genetics, the first essential in erecting such a
model is a knowledge of the distribution of genotype frequencies.
A MODEL OF EVOLCTIOS BASED ON GENOTYPE FREQUENCIES
Cavalli-Sforza 8r Edwards (1967) proposed a model of evolution for purposes of
phylogenetic reconstruction to be used with data on genotype frequencies from
living populations. They suggested that two basic sorts of assumptions are necessary for phylogenetic reconstruction: (1) assumptionsabout the biological integrity of
the samples to be used; and (2) assumptions about the topology of gene flow
between the samples. X method is then needed to decide which of the possible
hypotheses for the topology of gene flow is most likely in accord with the data.
Cavalli-Sforza & Edwards (1967) stated “Evolution can only be described in
terms of the characters which are changing, and it is convenient to represent such
changes in a multidimensional character space in which each population occupies
a position determined by the values of the characters which it exhibits. . . . If a
time dimension, everywhere normal to the character space, is added, the course of
evolution (were it but known) could be seen as a tree, whose branches split as
populations diverge, unite as they hybridize and end as they become extinct. . . .
Data . . . will be represented by points in the space-time and the problem of tracing
evolutionary history will be that of fitting a suitable tree to these points . . .”
Full and mathematically satisfactory phylogenetic analyses using this model
were later performed by Thompson (1975). T h e data were derived from human
populations, within which it was assumed that mutation was small compared with
other pressures, and that the amount of migration was small and did not cause
extensive hybridization. Random genetic drift was successfully represented (after
transformation) by a process of Brownian motion in multidimensional space. This
i5 the simplest available adequate model for a process which is known to be taking
place. The Brownian motion model does not hold for changes of state to produce
new alleles within the course of evolution.
-4selection model cannot be refiited, since by postulating the required selection
coefficients, any pattern of gene frequency variation may be explained. Therefore,
to measure selection, historical data are required. It has to be assumed that such
selection as has occurred may be incorporated in the Brownian motion.
X model for the process of splitting of populations may be erected, but leads to
difficulties and is unnecessary. .411 that need be assumed is that there existed a
single common ancestor of all populations, and that the course of evolution may be
represented by a tree formed by a series of bifurcating splits.
CHARACTER STATE CHANGES
1 99
Thompson (1975) analysed the problem by the method of maximum likelihood
estimation (Edwards, 1972). The likelihood of a particular hypothesis is
proportional to the probability of obtaining the observed data if the hypothesis is
true. In the evolutionary problem there are many competing hypotheses, framed
in terms of parameters which have an associated probability distribution, and only
one set of data. The relative merits of two hypotheses in explaining the same data
may then be compared as a ratio of likelihoods, and the solution obtained by
finding the values of the parameters which maximize the likelihood of the
observations.
THE PROBLEM OF DISCONTINUITIES
The maximum likelihood solution of problems in the evolution of human
populations has been very successfully applied by Thompson (1975). It would be
desirable to apply analogous procedures to the analysis of the phylogeny of species,
but there are a number of unsolved (and perhaps insoluble) difficulties. Even for
the reconstruction of the tree linking populations of a single species, the genetic
model cannot deal with alleles at a locus unless they are shared by at least 3% of
each population under consideration. It is immediately apparent that this inability
to deal with changes of states of alleles during the course of evolution prohibits the
reconstruction of species phylogeny. Many other problems arise when attempts to
find a suitable model are pursued.
There is a lack of an adequate description of biological species and of the laws
governing the processes and mechanisms by which they are transformed during
evolution. Hypotheses about the formation of new species are not supported by
observation, but are based upon extrapolation from observed features of
population genetics which it is considered would produce species phylogeny on a
longer time scale (Lewontin, 1974), on karyological studies (White, 1973), and on
patterns of behaviour or geographical distribution of organisms in nature which
are believed to be the result of recent speciations (Dobzhansky, 1970).
The ultimate need is for a dynamically sufficient description of biological species
which not only allows the present states to be established, but which also allows the
laws of transformation to be found. No satisfactory solution is known at present,
but the properties of many kinds of data are being investigated.
THE EVOLUTIONARY TREE MODEL
The nature of the data available has tended to exert an undue influence upon
thinking on the evolutionary tree problem. Workers on morphological data have
developed ideas in parallel to those of the population geneticists.
Nelson (1970) outlined a theory of comparative biology, without reference to the
formulation of Cavalli-Sforza & Edwards (1967). According to Nelson (1970 : 377)
“Three sorts of assumptions seem necessary for comparative studies. These concern
( 1) biological species, (2) relationships, and (3) homologies”. Nelson pointed out
that the individuals of a sample must be attributed to a group of biological and
historical integrity. This group might be called a species, subspecies, variety, race
or population. The integrity of the group might have to be assumed rather than
demonstrated. O n the subject of relationships Nelson states “Given two or more
species represented by samples, either fossil or Recent, one may assume they share
200
M. J. BISHOP
one of two sorts of biological relationships: (1 ) a relationship of common ancestry,
and (2) an ancestor-descendant relationship.” T h e problems of homology belong
to the data definition phase, rather than to the evolutionary tree model itself.
Estabrook (1972), while aware of the work of Cavalli-Sforza & Edwards, used
the language of set theory to describe an evolutionary tree model: “. . . the
assertion that evolutionary units have cladistic histories, which can be represented
as tree diagrams, will be taken as a necessary defining condition on the concept
euolutionay unit itself. . , . Consider a complete system of evolutionary units defined
to include its own common most recent common ancestor, and all evolutionary
units arising from it. Let us call this collection S’ to distinguish it from S, which is
the collection of known units in S‘. . . .\Ye are especially interested in the
relationship A, ’ is the ancestor of ’, defined for S’. . . for any units a, b, c in S’: 1.
aAa is always true; 2. if aAb and b.4a are both true, then a and b are the same
unit: 3. if aAb and bA4care true, then aAc is true also.”
According to Cracraft ( 1974), having made assumptions about the biological
and historical integrity of the taxonomic units, all models of phylogeny might
contain three basic components: “A statement about the nature of kinship
relationships to be accepted among taxonomic units. . . . A statement about the
origination and diversification of taxonomic units into lineages. . . . A statement
about the methods used to cluster lineages of taxonomic units”. Thus, Cracraft
would include a model for the process ofsplitting, though it is very hard to see how
this may be specified in the present state of knowledge.
Xone of these proposals offer any advance over the evolutionary tree model of
Cavalli-Sforza & Edwards, which is a clear and simple statement of the problem.
The difficulty arises in finding an empirically and dynamically sufficient
description of the character state data, which is the only data available for the
reconstruction of species phylogeny. Though character state data is available from
many sources, no satisfactory probabilistic model has been proposed to describe
any of the sorts of changes involved. Thus, in spite of claims of objectivity, no
means exist of assessing the validity of phylogenetic reconstructions made from
character state data, unless it be under a specific model.
I..4CK OF A SUITABLE MODEL FOR CHARACTER STATE CHANGE
No satisfactory model for character state change has been proposed. The best
that can be done is to investigate the properties of various mathematically
tractable models, as these give insight into the workings of the various heuristic
methods which have been proposed for the reconstruction of phylogeny from
character state data.
Felsenstein [ 1973) has used a Poisson model for character state change, and has
shown that the Camin and Sokal parsimony method does not give the maximum
likelihood i M L ) solution for the data investigated. This likelihood estimation
assumes that the state of all characters at the root is zero. Felsenstein (1973)
suggested that a different likelihood, in which the state at the root is uncertain, is
more appropriate. This likelihood was called Felsenstein likelihood (FL) by
Thompson (19751. .4ccording to my calculations, under FL the best solution for
the data of Felsenstein is not the parsimony solution. T h e maximum likelihood for
the big-bang tree (BB) is remarkably close in value to the overall maximum for
CHARACTER STATE CHANGES
20 1
either ML or FL (Table 1 ) . The difference in support S(ML) -S(BB) provides a
measure of the amount of information in the data, and for the data investigated is
seen to be extremely small. It is unrealistic to expect to be able to estimate a true
tree for any data set. Many solutions may not differ significantly when the
information content of the data is low, though others may be confidently rejected.
Felsenstein (1978) investigated an even simpler model, under which the
conditions for failure of the minimum length Wagner and the character
compatibility parsimony methods could be determined analytically. The
parsimony methods were shown to lack the property of statistical consistency.
Table 1. Maximum likelihood estimates under a Poisson model for the data of
Felsenstein (1973) - four living species, three characters: 2200, 0022, 3030
Times
Tree
Likelihood
Support
-
0.12494~
0.13437 x lo-’
-0.0728
0.0
-
-
-1.62
-1.42
-1.33
-
0.26865 x
0.31026 x
0.321 18 x
0.30386 x
4
4
t7
-1.17
-1.00
-1.14
-1.60
-1.24
-1.34
-1.33
Maximum likelihood (ML)
1234 (BB)
(13) 24
Felsenstein likelihood (FL)
1234 (BB)
(13) 24
(13) (24)
(12) (34) parsimony
-1.81
-1.80
-0.179
-0.0346
0.0
-0.0554
HOMOLOGY, POLARITY AND HOMOPLASY
Each source of character state data has a peculiar set of difficulties of
interpretation associated with it. Two contrasting sources are molecular sequence
data and morphology.
The amino-acids of proteins can be identified by chemical means, and their
sequence established. Homologies may then be established, not without some
difficulty, by matching sequences of similar proteins from different organisms.
Extreme difficulty is then encountered because of the many possible substitutions
of amino-acids at a single site, leading to character state ‘trees’ which are networks
with closed loops. Repetition of the same change in different lineages is to be
expected, and any model for the process of change must incorporate this fact.
The interpretation of morphological data is open to a large degree of subjectivity
from the outset. We have to assume, or demonstrate, that the phenotype is a
reliable reflection of the genotype. It is also assumed that significant morphological
features will be expressed in every species of a lineage, and cannot be carried as
redundant genetic information which can later reappear in the phenotype. The
hypotheses of homology are fundamental and crucial to phylogenetic
reconstruction based upon morphological data. But morphological homologies
cannot be established in the same way as gene frequencies.Jardine (1970) pointed
out that topographic homologies are the only sort that can be recognized, since to
make a homology between structures because two organisms are believed to be
related by common descent is circular if that belief is based upon morphology.
There is no guarantee that topographic homologies will also be phylogenetic
homologies. Sneath & Sokal (1973: 83-84) would favour a purely operational
M. J. BISHOP
202
definition of homology, standing as absolutely determined between two samples,
and unfalsifiable. This definition may be correct within its own frames of reference,
but is unhelpful for the purpose of phylogenetic reconstruction. The concept of
homology of Simpson (1975: 1G17) is that which is required. Dynamic processes
are believed to underlie the differences observed between structures, and putative
phylogenetic homology between two samples, supposed to be related by common
ancestry, may be falsified by examination of a third sample.
Having established such homologies and so defined the character complexes
which are supposed to be changing, the main task of the morphological method is
to establish character state trees which do not contain closed loops, that is to
eradicate all suggestions of homoplasy. Hecht's ( 1976) weighting classes may be
seen as an attempt to give a qualitative ordering of character complexes according
to the probability that homoplasy will remain undetected.
There is, therefore, a marked contrast between the attitude to molecular
sequence data, where homoplasy is an expected result of evolution, and the
morphological approach where homoplasy is an evil to be eradicated by careful
sifting and choice of characters. The character state tree hypothesis is seen to be a
\very complex aggregate hypothesis subject to numerous possible errors which are
summarized in Table 2. The hope of finding an adequate general probability
Table 2. Errors in the character state tree hypothesis
1 Errors of homology
la. Accepting a structure as homologous when i t is not.
lb. Rejecting a structure as not homologous when it is.
( 2 I Errors of tree topology
2a. Placing the states in an incorrect relationship on the tree.
2b. Assigning the wrong polarity to directions of change.
( 3 ) Errors of homoplasy
3a. Rejecting a structure as homoplastic when it is not.
3b. Accepting a structure as not homoplastic when it is.
I
model for the processes of morphological change seems remote, and no reliable
method of evaluation of the validity of phylogenetic reconstructions based upon
character state data is available at the present time.
THE DIRECTION OF CH.4R.4CTER STATE CHANGES
The foregoing discussion is intended to place the matter of polarity into
perspective, and it is doubtful if general rules can prove valid in the absence of a
specific model for change. Numerous criteria for the determination of polarity have
been proposed, and every proposal has been countered by the converse view that
the criterion in question is useless. Here I present some of these opposing views with
commentary.
Marx & Rabb (1970) listed ten criteria for determining the direction of
character state changes, but I believe they were largely mistaken, though it should
be pointed out that they were assuming that phylogeny was partially known. Their
criteria were:
1 I Uniqueness
j 2; Relative abundance
CHARACTER STATE CHANGES
203
(3) Correlation of derived states
(4)Morphological specialization
( 5 ) Ecological specialization
(6) Geographic restriction
(7) Closely related taxa
(8) Correlation of applied criteria
(9) Genetic structure
(10) Fossil record
Correlation of derived states and correlation of applied criteria belong to the
stage of reconstruction of the evolutionary tree and should not be used, in the first
instance at least, to assign polarity. The authors do not make explicit how they
would use genetic structure to determine polarity.
POLARITY FROM COMMONALITY?
The commonality principle (uniqueness, relative abundance, closely related
taxa) has been the major method applied by some workers. Strauch (1978: 2 7 6 7 )
stated: “The principal method used in this study is that of ground plan or
correlation. . . . It is assumed that primitive characters are more likely to be
distributed throughout other groups similar to, and supposedly related to, the
group under study (outgroups), are more likely to be widespread within the group
under study than any derived state, and are therefore more likely to be associated
in the same evolutionary units with the primitive states of other characters.”
In the same year, Van Valen (1978: 296) stated that he considered the method
fallacious: “One other criterion commonly applied deserves consideration because
I think it provides no information whatever in itself, despite being easy to use and
broadly available. This criterion is how common the character state is in the group
under consideration. It is superficially plausible, I think probably for two related
reasons. First, it should usually give the same result as the criterion of minimally
discordant phylogenies from different characters. Secondly, if an ancestor is
randomly chosen from among 99 species with state A and 1 with state B, the
probability is 0.99 that the ancestor will have A. Consider mammalian
reproduction. Six of 4200 or so recent species of mammals are oviparous. By the
criterion of commonality the probability of oviparity being primitive as 1 in 700.
Yet it is primitive. . . . One could just as well (perhaps better) choose randomly
among 2 character states as among 100 species. The discordance of the results here
indicates that the method is fallacious, the reference set (characters or species :
which?) is not defined.”
And of course if we consider amniotes, oviparity becomes common. Phylogenetic
analysis should not be dependent on the sample from which the characters are
drawn. There should be criteria which may be investigated independent of such
considerations, or else circularity may be so readily introduced.
POLARITY FROM FUNCTIONAL MORPHOLOGY?
Such a criterion might be the evidence from functional morphology
(morphological specialization, ecological specialization) where meaning may be
given to the nature of morphological change during evolution. Kluge & Farris
(1969: 2) find such speculations too dangerous: “Several methods for prior
204
M. J. BISHOP
selection of ‘good’ taxonomic characters have been suggested, but not all are
equally well suited to quantitative analysis. Among the criteria that are the most
subjective are those that depend upon weighting characters according to the
individual taxonomists’ opinions (presumably formed before any taxonomic
analysis had been performed) concerning the functional importance of characters,
the significance of the biological roles of characters, the implications of functional
relationships between characters, and the ‘most logical’ direction of evolution for
characters. We regard this type as too conjectural to be of any importance in
taxonomic procedure. That such methods depend on an individual’s
understanding of a phenomenon immediately opens up the possibility of endless
argument between different taxonomists with different understandings of the same
situation. . . . Serious taxonomic errors may be produced directly by the
taxonomist’s speculation in biological phenomena. . . . We believe that ‘biological’
and ‘functional’ evidence for inferring importance and direction of evolution of
characters should be excluded from objective taxonomic studies, at least until such
evidence can be interpreted in a more rigorous way than is generally possible.”
Schaeffer, Hecht & Eldredge (1972: 35-6) held just the opposite opinion: “The
most interesting and potentially useful characters, at least in vertebrates, are those
which can be studied in relation to some major function - feeding, locomotion,
reproduction, perception - primarily because they give meaning to any
consideration of adaptation. The form of the skeleton is clearly related to the first
two functions, and it may provide some information about the last two. Muscle
scars on trilobite glabellae . . , and hinge lines on pelecypod shells are also subject
to functional interpretation and may be treated in the same way. However the
functional meaning of the dermal skull pattern of fishes, in the centra of
amphibians and in the coiling of gastropods, still defy understanding. They are,
nevertheless, empirically useful for purposes of comparison and classification.”
It is this author’s position that attempts to reconstruct phylogeny from
morphological data are very poorly founded from the theoretical point of view.
The whole exercise would be hollow and futile if it were not for the fact that studies
of functional morphology can be made, and this is the only part of the
reconstruction open to experimental investigation. The fact that apparently
competent authorities do not agree is not a disadvantage: there is nevertheless a
correct interpretation to be found.
POL.4RITY FROM ONTOGENY?
Studies of morptiogenesis have long held a very special position in attempts to
reconstruct phylogeny. Nelson ( 1973 : 88-9) has gone as far as to suggest that this is
the only valid technique: “But I would propose another possibility, one which, in
my opionion, has already played an important role in the history of phylogenetic
systematics, and has been, perhaps, of crucial importance in the development of
commonly used higher-level phylogenies of groups such as the Vertebrata. This
possibility is the only valid ‘direct technique’ of character phylogeny of which I
am aware; it involves, specifically, the study of ontogenetic character
transformations.”
According to Van Valen (1978: 295-6), this is merely one of several fallible
methods: “Estimating the polarity of characters is the first step in constructing a
phylogeny in the absence of a gradational series of fossils. It is also the most
CHARACTER STATE CHANGES
205
awkward step. There are several suitable if fallible methods, but they can’t always
be applied and are usually supplemented with fallacious ones. . . . Ontogeny
recapitulates phylogeny often enough that it can help determine polarity; the
effect occurs of course because a change earlier in a branching developmental
program has a greater likelihood of disrupting other processes. Loss of terminal
parts of a developmental program is similarly easy.”
It may be noted that a developing animal has to function as an individual as
much as does the adult. Parallel adaptations to embryonic life are just as likely to
be found as they are in other systems. The study of ontogeny is better seen as a
particular branch of the study of the functional morphology of living organisms.
POLARITY FROM GEOGRAPHICAL DISTRIBUTION?
Geographic restriction was suggested as a criterion by Marx & Rabb (1970), but
most would rather work out phylogeny independently of distributional data and
then try to erect some biogeographical hypotheses to explain distribution. I reject
geographical distribution as a criterion for polarity as it is not directly related to
gene flow, which underlies the evolutionary tree model.
POLARITY FROM STRATIGRAPHY?
This is the most controversial of the proposed criteria, often because the explicit
assumptions underlying a particular view are not made clear. I have to reject this
criterion as not being directly related to gene flow which is necessary for the
evolutionary tree model. If the prior assumption is made that the samples laid out
before one do indeed represent a continuity of gene flow in the single lineage of an
ancestor-descendent sequence, then one can indeed trace the fate of populations
through time.
This is the view of Gingerich (in Chivers & Joysey, 1978: 303) : “If we could
build up phylogeny from the fossil record, then we could actually see that in fact
some particular lineage went from a free ectotympanic ring to the ring being fused
with the bulla, or whatever. But as long as we go on manipulating these characters
to make some parsimonious arrangement that pleases us, we will never really know
what happened. It’s not sound procedure to labour over functional or ecological
explanations for changes that are merely hypothetical to begin with.”
But for Schaeffer et al. (1972 : 33-5) the sequence of fossils in rocks may not offer
a true picture of polarity. “Much of what we know about the evolutionary process
indicates that it proceeds within limits imposed by the ancestral genotype,
morphogenetic canalization and selection pressure. . . . In spite of some
apparently excellent fossil records that seem to show well-defined ancestraldescendent lineages at the species level (as seen in horses), it is probable the
detailed phylogenetic sequence and ramifications for most groups of organisms can
never be worked out from the fossil record. . . . Relatively low diversity groups
that have lived for a long interval in one geographical area and have a good fossil
record will provide the closest approximation of a phylogeny - not because we
know the temporal sequence in which the fossils occur, but because we have a
relative abundance of morphological characters that may be used to set up a
hypothesis of relationships. The chronocline concept implies, wrongly, we believe,
206
M. J . BISHOP
that the temporal sequence is, in itself, meaningful in evaluating evolutionary
relationships.”
ACKNOWLEDGEMENTS
I am grateful to Professor J. Felsenstein for providing a computer program
written in Fortran for maximum likelihood estimation of phylogeny from character
state data under a Poisson model. I wish to thank Dr K. A. Joysey for encouraging
my interest in phylogenetic studies at both a theoretical and a practical level. Dr
A. E. Friday pointed out to me the relevance of likelihood to phylogenetic
reconstruction, and patiently answered many of my questions relating to material
included in this paper. I am, of course, solely responsible for the errors.
.4 recent publication regarding botanical evidence, not available when this
manuscript was prepared, stresses the probabilistic nature of phylogenetic
reconstruction and expresses views similar to my own (Stevens, 1980).
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