Inlernalionol Journal/or Parasilo/og.y, Vol. 26, No. 6, pp. 589417, 1996
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INVITED REVIEW
Phylogenetic Tree-building
DAVID
Molecular Parasitology
A. MORRISON
Unit, University of Technology Sydney, Westbourne Street,
Gore Hill, NS W 2065, Australia
(Received
13 October
1995;
accepted
3 March
1996)
Abstract-Morrison
D. A. 1996. Phylogenetic
tree-building.
Iniernationul
Journal fir Parasitology
26:
589-617.
Cladistic
analysis is an approach
to phylogeny
reconstruction
that groups taxa in such a way that
those with historically
more-recent
ancestors
form groups nested within groups of taxa with moredistant
ancestors.
This nested set of taxa can be represented
as a branching
diagram or tree (a cladogram),
which is
an hypothesis
of the evolutionary
history of the taxa. The analysis is performed
by searching
for nested groups
of shared derived character
states. These shared derived character
states dehne monophyletic
groups of taxa
(clades), which include all of the descendants
of the most recent common ancestor.
If all of the characters
for
a set of taxa are congruent,
then reconstructing
the phylogenetic
tree is unproblematic.
However,
most real
data sets contain incongruent
characters,
and consequently
a wide range of tree-building
methods has been
developed.
These methods differ in a variety of characteristics,
and they may produce topologically
distinct
trees for a single data set. None of the currently-available
methods are simultaneously
efficient,
powerful,
consistent
and robust, and thus there is no single ideal method. However,
many of them appear to perform well
under a wide range of conditions,
with the exception
of the UPGMA
method and the fnvariants
method.
Copyright
0 1996 Australian
Society for Parasitology.
Published
by Elsevier Science Ltd.
Key
words:
Phylogeny;
evolution;
cladistics;
cladograms.
English of Hennig (1966). These methods are now
usually referred to as “cladistics”,
and the evolutionary diagrams they produce “cladograms”,
to distinguish them from all prior phylogenetic studies, many
of which were neither explicit nor repeatable (note
that I am using the word cladistics to include a wide
class of explicit and repeatable phylogenetic analyses,
which may be a broader definition
than would
be accepted by many phylogeneticists,
who would
restrict the term to the more strictly Hennigian
methods). The current interest in cladistic analyses
has inevitably led to a proliferation
of data analysis
techniques; and the apparent plethora of methods for
phylogenetic
analysis is typical of a young science
still coming to terms with both its aspirations and its
constraints.
It is therefore important for practitioners to understand the limitations
of the available techniques as
well as to appreciate their capabilities
(Felsenstein,
1982). Unfortunately,
the current wide choice among
possible phylogenetic methods seems to be daunting
INTRODUCTION
If we accept
the proposition
that evolution exists,
then meaningful comparisons among organisms must
ultimately include a phylogenetic
context (Maddison
& Maddison,
1992). This is because the evolutionary
relationships
among a group of taxa constrain any
other possible relationships that might exist. It is thus
not surprising that in biology there has been a long
history of attempts to deal with the reconstruction
of
genealogical history (Nelson & Platnick, 1981; Mayr,
1982; Stevens, 1994), notwithstanding
the difficulties
associated with producing testable hypotheses about
historically unique events.
It is, however, only in the last 30 years that
widespread attempts have been made by systematists
to produce
explicit and repeatable
methods for
the construction
of phylogenetic
trees (Felsenstein,
1982), notably with the translation from German into
Tel: +61-2-3304159;
Fax: +61-2-3304003;
E-mail: [email protected].
589
590
D. A. Morrison
for many people, and they thus acquire little knowledge of the relative advantages and disadvantages of
the various methods. This is unfortunate,
because the
choice of data-analysis methods should be based on
their apparent appropriateness
for the data at hand,
rather than on the local availability
of computer
programs or on historical inertia (Hillis, Allard &
Miyamoto,
1993). It is my purpose here to review the
phylogenetic
inference methods that are currently
available, and to indicate what is currently known
about their strengths and weaknesses. This will allow
a more informed decision to be made when assessing
which of the methods might be appropriate
for a
particular data set.
Along the way, I will attempt to make clear some
of the aspects of phylogenetic
analysis that are obviously misunderstood
by non-specialists, and to dispel
a few widely-held misconceptions.
My discussion will
focus on molecular sequence data (particularly
DNA
and RNA), since trees derived from this source are
increasingly
those with which parasitologists
are
working (e.g., Nadler, 1990), there being a limit to
the usefulness of phenotypic
characteristics
for
constructing
phylogenetic
trees for most parasites.
Indeed, it is the proliferation
of molecular data sets
that is introducing
many people from outside of
systematics to the science of phylogeny (Miyamoto &
Cracraft, 1991; Hillis, Huelsenbeck & Cunningham,
1994a); and it is for this reason that phylogenetic
principles
need to be clearly introduced
to nonexperts. Furthermore,
many of the recent advances in
cladistics have been motivated by attempts to deal
with problems that are specific to molecular
data
(Penny et al., 1990), and the similarities and differences between traditional
and molecular phylogeny
thus need to be emphasized.
I do not intend to describe the tree-building
techniques in any great detail, partly because most
of them are covered in the excellent review by
Swofford & Olsen (1990) and in the books by Nei
(1987) and Li & Graur (1991), and partly because
nothing is more intimidating
to most biologists than
mathematics.
I concentrate
much more on those
aspects of phylogenetic
analysis that are likely to be
of most practical and theoretical
interest to nonexperts. I start by summarizing
the principles
of
cladistic analysis, before proceeding
to a review of
the alternative
methods
for constructing
cladograms. A number of introductory
reviews covering
similar topics, but from different perspectives, include those of Felsenstein
(1988), Olsen (1988)
Sneath (1989), Beanland
& Howe (1992), Hillis
et al. (1993) and Stewart (1993); and there is also
the worthwhile
introductory
book by Forey et al.
(1992).
PHYLOGENETIC
ANALYSIS
Cladistics
The study of evolutionary
processes has often been
considered to be unscientific because it deals with
historically
unique events (Popper, 1957). Hypotheses concerning these events are thus not universal (in
either space or time) and, therefore, they are considered to be untestable in the contemporary
world. The
sociological
development
of phylogenetic
analysis
has consequently been based largely on the erection
of what have been called “evolutionary
scenarios”
describing
the presumed
genealogical
history of
the organisms under study. The number of such
scenarios that may be created is, of course, limited
solely by the imagination
of the researcher, and none
of the scenarios are likely to be open to falsification.
Cladistic analysis can thus be seen as an attempt to
base phylogenetic analysis on a more objective footing, where the phylogenetic hypotheses are explicitly
stated, along with the evidence supporting (and contradicting) them, and are then subjected to quantitative testing. Its practitioners
therefore claim that
cladistics is designed to make phylogenetic
analysis
into an hypothetico-deductive
science, where explicit
hypotheses are subjected to repeatable attempts at
falsification.
Note that the claimed advantages
of cladistic
analysis are not intended to denigrate pre-cladistic
biologists, nor is there any suggestion that these
biologists did not apply their minds to phylogenetic
questions. However, it is clear that pre-cladistic phylogenetic analyses were not necessarily based on
repeatable methods that produced explicit hypotheses of evolutionary
relationship
which could be
subjected to falsification (Nelson & Platnick, 1981).
Furthermore,
the taxonomic
groups produced
by
pre-cladistic
biologists were not necessarily monophyletic (see below), and therefore did not always
reflect evolutionary
history. Post-Darwinian
biologists have had the unenviable
task of producing
taxonomic
schemes that should, in theory, reflect
evolutionary
history, without any theoretical framework for how they should go about discovering what
the evolutionary
history actually was (Stevens, 1994).
Cladistics is an attempt to provide this theoretical
framework.
Cladistic analysis as an approach to phylogeny
attempts to group taxa on the basis of their ancestry.
In the analysis, taxa are grouped in such a way that
those with historically
more-recent
ancestors form
groups nested within groups of taxa with moredistant
ancestors.
The analytical
technique
is
based on a widely-held
view of the mode of the
evolutionary
process: species are lineages undergoing
Invited Review
divergent
evolution
with modification
of their
intrinsic attributes, the attributes being transformed
through time from ancestral to derived states. Thus,
if a species is a group of populations,
then if 1 group
of populations
acquires a new (derived, advanced or
apomorphic)
character state while the rest do not (i.e.
they retain the ancestral, primitive or plesiomorphic
state) then these populations constitute a new species.
This new species then forms a separate historical
lineage that diverges from the other populations,
and
maintains
its own historical
tendencies and fate.
Evolution
can thus be thought of as a branching
sequence of historical lineages, and indeed the only
diagram in Darwin (1859) represents precisely such a
branching sequence.
When a character changes from an ancestral state
to a derived state in a lineage it is historically unique
(a novelty), and it will be passed on to all of the
descendants of that lineage (even if the character is
later modified into something else). Therefore, the
branching sequence of evolution can be deduced by
searching for nested groups of shared derived character states (synapomorphies)
among the taxa being
analysed. So, if a derived character state is observed
in 2 or more taxa, then we can hypothesize that they
share this apomorphy
because they are descended
from a common ancestor, and that they inherited the
apomorphy
from that ancestor. The possession of a
shared ancestral state (a symplesiomorphy)
tells us
nothing about the phylogeny of the taxa, since this
state was inherited from an ancestor that is also held
in common with those taxa possessing the derived
state. Thus, cladistic analysis is simply the search for
nested sets (a hierarchy) of synapomorphies
among
the taxa. Each synapomorphy
represents an ancestral
lineage that has diverged from its related lineages,
thus being contemporary
evidence for a prior
evolutionary
event (Table
1). Clearly, the only
characters that are of use for a cladistic analysis of a
group of contemporary
taxa are those features that
reflect their evolutionary
history. There is, of course,
no simple method for determining
which features
these are, but at least the method forces the practitioner to be explicit about the characters that have
been chosen for the analysis.
Homology
For this analytical technique to work, homologous
rather than analogous character states must be compared across the taxa (Hall, 1994). That is, for all of
the taxa we must compare like with like, particularly
with reference to the evolutionary
origin of the
attribuies. Characters and their states are thus hypotheses of evolutionary
homology. As an example,
591
for Character 16 in Table 1 possession of denticles,
dermal scales, epidermal scales, feathers and hair are
all considered to be homologous character states of a
single character. In practice, characters and their
states are postulated as homologous
on the basis of
their structural,
positional,
ontogenetic,
compositional and/or functional correspondences;
and they
are postulated between different taxa so as to maximize the number of one-to-one correspondences
of
their parts (Stevens, 1984). The choice of characters
to be included in a cladistic analysis may be somewhat arbitrary,
but can include intrinsic attributes
such as morphology,
anatomy, embryology,
behaviour, physiology, ultrastructure,
cytology, biochemistry, immunology,
ecology and even geography. The
important points are that the characters used in the
analysis are hypothesized to reflect the evolutionary
history of the taxa, and that the character states of a
single character are hypothesized to have a unique
evolutionary
origin.
Concepts of homology are often intuitively
obvious when dealing with, for example, morphological
data, and these concepts can be put into practice
through
a detailed study of ontogeny
(e.g., the
homologies
postulated in Table 1 are thus mostly
unproblematic);
and the alignment
of molecular
sequences is the direct equivalent of these homology
assessments (Mindell,
1991). The concepts of homology in molecular and morphological
studies are
thus fundamentally
the same (de Pinna,
1991;
1993). So, alignment
of molecular
Williams,
sequences involves a series of hypotheses of homology among the taxa, with 1 hypothesis of homology
for each position (nucleotide or amino acid) in the
sequence. It is important
to recognize this, because
it is clear that often very little attention is paid
by molecular
biologists
to this point to a
morphologist
the assessment of homology
is an
important (and time-consuming)
component of phylogenetic analysis, but to a molecular biologist the
assessment of homology is apparently often an afterthought. The correct formulation
of hypotheses of
homology is just as important for molecular data as it
is for morphological
data; and it is clear from the
literature
that many of the so-called controversies
about the phylogeny of particular
groups of parasites are based as much on disagreements
about
sequence alignment as on disagreements about actual
evolutionary
events (e.g., Ellis & Morrison,
1995).
Unfortunately,
for molecular
data
there is
little possibility
of further investigations
(such as
ontogeny) to assess homology,
and so in practice
homology assessment is very different for molecular
studies (Mindell,
1991). Positional
homology
can
be represented by either identical character states
none
no
no
no
no
no
no
scale-less
16 Body covering
Em al
denticles
no
no
no
no
no
no
none
no
no
no
no
no
yes
yes
Sharks
no
no
no
no
no
none
no
no
no
no
no
no
dermal
scales
yes
yes
yes
yes
yes
Ermal
scales
no
no
no
no
no
smooth
epidermis
II0
no
none
yes
yes
yes
yes
no
no
no
none
no
no
no
no
no
yes
yes
Frogs
yes
yes
yes
Teleosts Lungfish
no
none
no
no
no
no
no
no
smooth
epidermis
yes
yes
yes
Yes
yes
yes
yes
Salamanders
no
yes
none
no
no
no
no
no
no
epidermal
scales
yes
yes
yes
yes
yes
yes
Turtles
no
yes
two
yes
yes
no
no
no
no
epidermal
scales
yes
yes
yes
yes
yes
yes
Lizards
no
yes
two
yes
yes
no
no
no
no
epidermal
scales
yes
yes
yes
yes
yes
yes
Snakes
no
yes
two
no
no
yes
Yes
yes
no
epidermal
yes
yes
yes
yes
yes
Crocodiles
phenotypic data for extant vertebrates that might be useful for reconstructing their evolutionary history
no
yes
one
no
no
no
no
no
yes
hair
feathers
yes
yes
yes
yes
yes
yes
Mammals
no
yes
two
no
no
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
Birds
These 16 characters each have at least 2 character states that are hypothesized to be homologous, one of which is postulated to be ancestral (the states “no”, “none”, and
“scale-less”). The other (one or more) states are postulated to be derived from this ancestral state, and the taxa that share these derived states are then hypothesized to have
inherited these states from a common ancestor. These shared derived character states (synapomorphies) thus group the taxa into sets that reflect their evolutionary history. Note
that Character I has only I state in this data set, because the derived state has been inherited by all of these taxa, and it thus forms a synapomorphy for the group (vertebrates)
as a whole. Furthermore, Characters 9 and I6 have more than 2 homologous states, thus implying that the ancestral state has been modified more than once during the
evolutionary history of these taxa; each of these derived states forms its own set of taxa. A possible cladogram derived from these data is shown in Fig. I. The data are from
Romer (1971) and Maddison & Maddison (1992). Note that this non-parasitological example has been chosen because the homology assessmentsand the resulting cladogram
are not controversial, which is something that cannot be said for any parasitological example known to me.
IlO
no
no
no
no
no
no
yes
Lampreys
1 Internal skeleton
2 Jaws
3 Ossified skeleton
4 Internal nostrils
5 Atria1 septum
6 Four limbs
7 Teeth pedicillate
8 Amniotic egg
9 Temporal fenestrae
IO Hemipenes
11 Suspensorium streptosylous
I2 Antorbital fenestrae
13 Lateral fenestrae ossified
I4 Gizzard
I5 Homeothermy
Character
Table I-Some
Invited
(nucleotides or amino acids) in all sequences, substitutions in 1 or more sequences (representing
point
mutations),
or insertions/deletions
(indels) in 1 or
more sequences. The most problematic
aspect of
sequence alignment is the positioning
of indels, and
this problem becomes more acute for more divergent
sequences. It is worthwhile
in this context to distinguish between gaps, which are introduced
into
the sequences by the alignment
procedure,
and
indels, which are actual mutation
events (Olsen,
1988); clearly, the objective is to introduce into the
sequences only gaps that truly represent indels.
There are 3 possible scenarios for the degree of
difficulty of sequence alignment. Firstly, there may be
relatively few indels, in which case a robust sequence
alignment can usually be produced by hand. Such a
situation is shown, for example, by protein-coding
parts of mtDNA (Miyamoto
& Cracraft, 1991) and
the plant rbcL gene (Chase et al., 1993). Secondly, the
sequence may represent a molecule for which there is
an a priori biological model of secondary structure in
which certain active sites must be maintained;
the
alignment is then constrained by the base-pairing of
the model (Olsen, 1988). Such a situation is shown,
for example, by the 5s (Specht, Wolters & Erdman,
1990), 12s (Gutell et al., 1985) and 18s (Van de Peer
et a/., 1994) rRNA genes.
Thirdly, there may be many indels and no a priori
structure model. Under these circumstances
it is
usual to use a mathematical
algorithm to produce the
alignment. These algorithms all attempt to produce a
sequence alignment that optimizes some chosen criterion of match between the individual
sequences
(cost). That is, the sequences are compared using a
pattern-matching
process that searches for correspondence between the elements of the sequences,
introducing
gaps into the sequences as required to
maximize some criterion for optimality
of the correspondence. There are many algorithms
currently
available
(see Waterman,
1989; Doolittle,
1990;
Chan, Wong & Chiu, 1992; and McClure, Vasi &
Fitch, 1994), which optimize a variety of mathematical functions measuring the overall alignment cost.
When there are more than 2 sequences, most of these
algorithms
use exact procedures
(see below for a
definition)
to align the sequences pair-wise, but then
use heuristic procedures (see below for a definition)
to braid these alignments into a multiple alignment.
Thus, these procedures do not guarantee to produce
the globally optimal alignment; nor do they guarantee that the optimal alignment (even if they could find
it) represents the true alignment (Thorne & Kishino,
1992).
I am not going to discuss these various algorithms
here, because this is an area of active research and
Review
593
very little is known about their theoretical or practical limitations
(Thorne & Kishino,
1992; McClure
et al., 1994). However, 1 important
generalization
may be made: the differences between the alignments
produced by the various algorithms is often less than
the differences
produced
by varying
the “gap
weights”. These weights refer to the relative cost of
inserting a new gap into a sequence or extending
an already-existing
gap, and there is no way of determining analytically
what these weights should be
(Rinsma-Melchert,
1993). Most of the computer programs that implement the alignment algorithms have
default values for the weights that are designed to
produce “biologically
interesting”
results, and very
few molecular biologists seem to be willing to deviate
from these default choices. It is, however, clear that
to simply report that a particular computer program
was used to align the sequences is meaningless (since
the work cannot be verified) unless the weight values
are also reported (Wheeler, 1995).
In dealing with the problematic nature of sequence
alignment, molecular biologists often delete parts of
their sequences from the cladistic analysis. The
rationale for this is that those parts of the sequences
that cannot be aligned reliably should be excluded
from the estimation of the phylogeny (Olsen, 1988).
This is probably
very sensible (Smith, 1994), but
unfortunately
there is often no objective criterion
given for deciding which parts of the alignment are
ambiguous,
the decisions usually being made by
“visual
inspection”.
Gatesy, DeSalle & Wheeler
(1993) have suggested that those parts of the alignment that are sensitive to the gap weights (i.e. where
the alignment
varies significantly
when the gap
weights are changed)
may constitute
unreliable
hypotheses of homology and may therefore be candidates for exclusion; and Ellis & Morrison
(1995)
have shown that for some organisms it is the doublestranded parts of rRNA that may contain most of the
phylogenetic
information
when the sequences are
aligned according to secondary structure. Thus, there
is considerable
room for further research into the
problems of sequence alignment.
It is also important to recognize that there is also
a more general level of homology
assessment for
molecular data. The sequences being compared must
themselves be homologous
rather than analogous
(Fitch, 1970). Thus, only orthologous
sequences will
reflect the historical relationships
of species, while
paralogous
sequences (e.g., the 2 sequences that
result from a gene duplication)
will reflect only
gene history, xenologous
sequences (e.g., recentlyincorporated
sequences such as result from horizontal gene transfer) will only partly reflect gene history,
and plerology (e.g., the inter-mixture
of exons and
594
D. A. Morrison
introns) will only reconstruct a composite gene
history (Patterson, 1988; Williams, 1993). All
molecular studies thus rely on the assumption that
the sequences from the taxa being compared are
orthologous, and this may be a dubious assumption
for distantly related taxa (Sneath, 1989). Any
sequence for which orthology has not been established should be omitted from the analysis (Olsen,
1988).
Furthermore, for orthologous sequences there is
the implicit assumption that the sequences being
compared are actually from the organisms being
studied, rather than from some other co-habiting
organism. For example, it is now recognized for the
ITS gene that many of the published sequences
purporting to be from conifers and ferns are actually
those of fungi, while the published Mimulus
(monkey-flower) sequences are actually those of
green algae (P. Weston, personal communication).
As a tinal observation on molecular data, it is
worth emphasizing the distinction between species
trees and gene trees. The result of cladistic analysis of
molecular data is a gene tree (provided that the entire
gene has been sequenced), hypothesizing relationships among the genes or genomes that have been
sampled, whereas a species tree reflects the actual
evolutionary pathways (Pamilo & Nei, 1988). The
gene tree may be fundamentally incongruent with
the true species phylogeny, with the genome tree,
and with other gene trees (e.g., Cao et al., 1994;
Cummings, Otto & Wakeley, 1995), due to various
phenomena such as allelic polymorphism, introgression, lineage sorting, unequal rates of speciation
and gene mutation, lateral transfer, hybridization, or
mistaken orthology (Pamilo & Nei, 1988; Penny
et al., 1990; Doyle, 1992; de Queiroz, Donoghue &
Kim, 1995). Thus, for the reconstruction of phylogenetic history, a single gene may be, in practice, no
more useful than a single morphological character
(Doyle, 1992). It may, therefore, be unwise to assume
tacitly in molecular studies that the number of
characters being used to reconstruct a phylogeny
is equivalent to the number of positions in the
sequence. Furthermore, a living organism is an
integrated functioning whole, not just a collection of
unrelated genetic attributes. Thus, an organism is a
collection of interactions between genes, and between
genes and their environment (i.e. a phenotypic
whole), and it is the organism as a whole that takes
part in the evolutionary process. Consequently, there
is no more reason for genetics to reflect phylogeny
than for anything else to do so (de Queiroz et al.,
1995). In fact, morphological characters may be a
better reflection, because they integrate many genetic
and phenotypic characters.
Polarity
Having determined the homology of the character
states, the key to cladistic analysis is the distinction
between derived character states and ancestral states
(character polarity). It is important to note that this
is a local concept that applies only to a particular
set of taxa. By this I mean that a character state
is only considered to be derived relative to a specified ancestral state, and it may well be the ancestral
state for a further derived state. As an example,
for Character 16 in Table 1 possession of epiderma1 scales is a derived state relative to possession
of dermal scales, but is an ancestral state relative to possession of either feathers or hair.
Thus, possession of epidermal scales is a synapomorphy for Turtles+Lizards+Snakes+Crocodiles+
Birds+Mammals, while possession of feathers is a
synapomorphy for Birds and possession of hair is a
synapomorphy for Mammals; this character does not
supply a synapomorphy for the grouping only of
Turtles+Lizards+Snakes+Crocodiles. Possession of
epidermal scales is thus a synapomorphy at a more
general level than is possession of either feathers
or hair. There is thus a hierarchical relationship
between ancestral and derived character states,
and recognizing synapomorphies therefore involves
determining the correct level of generality of
homologies.
Clearly then, the success of a cladistic analysis
rests on the correct determination of the relative
apomorphy of the character states, and numerous
criteria have been proposed for doing this (Crisci &
Stuessy, 1980; Stevens, 1980; Bryant, 1992; Nixon &
Carpenter, 1993). Most of these criteria rely on
illogical arguments or on assumptions that are either
false or untestable; and it is worthwhile recognizing
only 2 objective possibilities: the direct method;
and outgroup analysis. These are complementary
methods, and both may thus be used in any 1 data
set. For the direct method, the hierarchical relationship between ancestral and derived character states is
observed directly, and it does not require any preexisting hypotheses of character polarity. On the
other hand, the outgroup analysis method does not
directly observe character polarity, and it relies upon
an hypothesis of the relationship of the taxa under
study to their near relatives.
The direct method (Weston, 1988) states that: if 1
character state is possessedby all of the taxa that also
possess the alternative state, and in addition it is
possessedby some taxa that do not possessthe other
state, then it is postulated to be the ancestral state.
For example, open gill slits are possessed by all
chordates in at least the embryonic stage, but in
tetrapod chordates these close early in development;
Invited
Review
595
Fig. 1. A phylogenetic
tree derived from the character
data shown in Table 1. Almost
all of the characters
shown in Table
1 have derived states that are congruent
with this cladogram;
that is, the synapomorphies
form a perfect series of nested sets.
For example,
Characters
10 and 11 form a set consisting
of the Lizards+Snakes,
while Characters
12-14 form a set of the
Birds+Crocodiles;
these characters
are plotted
on the branch
referring
to the hypothesized
ancestor
where the derived
character
state arose (and the other characters
can be plotted in similar fashion).
The only exception
to this congruence
concerns
Character
15, for which 2 evolutionary
origins of the derived state must be postulated
(i.e. it appears twice on the
cladogram):
that is, there is an apparent
convergence
on this cladogram,
where the derived state is postulated
to have arisen
in 2 separate
ancestors.
This implies a mistaken
hypothesis
of homology
(a homoplasy)
for homeothermy
in Birds and
Mammals.
Other cladograms
could be constructed
in which this convergence
does not occur (i.e. in which Character
15 is
a synapomorphy
uniting
Birds+Mammals),
but in all of these cases at least 2 of the other characters
must then be
homoplasious.
thus, all chordates possess open gill slits but only
some possess both open gill slits (early in development) and closed gill slits (later in development).
Consequently,
possession of closed gill slits is
hypothesized to be derived relative to possession of
open gill slits. This type of argumentation
can be
applied to many types of characters (Nelson, 1978;
Weston, 1988, 1994), but it is probably
of limited
utility for molecular data. However, Weston (1994)
has successfully applied the direct method to gene
duplications
(paralogy) to polarize the a and b subunits of ATPase based on taxa from the archaebacteria, eubacteria and eukaryotes, thus providing
a
“root” for the tree of life.
The outgroup
analysis
(or indirect)
method
(Watrous & Wheeler, 1981) states that: if a character
state is found in both the ingroup (the group of taxa
under study) and also in the outgroup
(the sister
group of taxa), then it is postulated
to be the
ancestral state. For this method to provide unequivocal evidence of character
polarity,
the outgroup
should consist of at least 2 sequential sister groups
(Maddison,
Donoghue
& Maddison,
1984). For
example in Fig. 1, if we were interested in the
phylogeny
of the tetrapods
(the ingroup
thus
consisting of Frogs+Salamanders+Turtles+Lizards+
Snakes+Crocodiles+Birds+Mammals),
then
the
relevant sister groups (the outgroup)
would
be
at least the Lunglish
and the Teleosts. Thus for
Character 8 in Table 1, possession of an amniotic egg
is hypothesized
to be apomorphous
relative to the
lack of such an egg because all members of the
outgroup and some members of the ingroup lack it,
while only some members of the ingroup possess it.
This type of argumentation
relies on the existence of
a corroborated
higher level phylogeny for the taxa
being studied, because we need a priori knowledge of
the sister groups of the ingroup. Such higher level
phylogenies
in turn may rely on other outgroup
comparisons, and so on in a regress back to the origin
of life. Ultimately, we must rely on the direct method
for at least some of the characters in some of the
analyses.
Outgroup
analysis is the most common type of
argumentation
in cladistic analysis, but it is now
usually implemented
in a different way from its
original
formulation,
particularly
when analysing
molecular data (Smith, 1994). Instead of first determining character state polarity and then producing
the cladogram, it is now more common to produce an
596
D. A. Morrison
unrooted
cladogram
(a network) based on simultaneous analysis of all of the characters of both the
ingroup and the outgroup and then to determine the
root of the tree using the position where the outgroup
joins the ingroup (see below). This type of method
was first described by Farris (1972), and Nixon &
Carpenter (1993) provide a recent detailed summary.
In this method, there are no guarantees that any
particular
number of outgroups
or any particular
choice of outgroups will ensure that the cladogram
accurately reflects the evolutionary
history (Li et al.,
1987; Smith, 1994; Adachi & Hasegawa, 1995). In
practice, the phylogenetic
inferences will be more
robust if more outgroup taxa are chosen rather than
fewer, and the more closely-related
these taxa are to
the ingroup (Hendy & Penny, 1989; Wheeler, 1990;
Nixon & Carpenter,
1993). For molecular data, a
distantly-related
outgroup
may have surpassed the
point of saturation of base substitutions,
and there
will thus be a loss of phylogenetic
signal through
evolutionary
time as a result of random sequence
noise (Smith, 1994). The outgroup
may thus, in
effect, be random, and as such it will simply join the
rest of the cladogram on the longest internal branch
in the ingroup and will itself have a long terminal
branch (Wheeler, 1990). The best strategy may be for
the outgroup to consist of several taxa from the sister
group to the ingroup (Smith, 1994).
Conclusion
Ideally, all hypotheses of homology and relative
apomorphy will be congruent with one another. That
is, the sets of synapomorphies
for a group of taxa will
form a perfect nested hierarchy, and the polarization
of the character states provides a root for the tree.
The construction
of a cladogram
from the data
would then be unproblematic
(Fig. 1); and it was
indeed under these circumstances that Hennig (1966)
introduced his phylogenetic method. In most of the
real world, there are, however, always characters that
are incongruent with each other (homoplasies). These
incongruent
characters are postulated to result from
either reversals, where a derived character state reverts to the ancestral state, parallelisms,
where the
same derived character
state arises in separate
evolutionary
lineages, or convergences, where superficially similar character states have arisen in separate
lineages. Homoplasies are thus mistaken hypotheses
of homology.
In order to deal with the common existence of
homoplasies, a range of tree-building
techniques has
been developed in cladistics. Each technique implements a different stratagem for how homoplasies are
to be treated, and each technique may thus produce a
different hypothesis of phylogenetic
history for the
taxa being analysed. If a data set is perfectly congruent (i.e. all of the characters reflect the same
speciation and phylesis events), then all of the techniques will produce the same cladogram, which will
be the cladogram produced by the original method of
Hennig (1966). However, apparent
incongruences
almost always exist in the real world, and therefore a
range of methods has been developed to try to detect
the phylogenetic pattern that underlies the apparent
contradictions.
Cladistics is basically axiomatic, in the sense that if
the assumptions (the axioms) are accepted then the
rest (the corollaries)
follows directly from them.
Thus, like all axiomatic propositions,
if one or more
of the assumptions are invalid, then the rest of the
edifice falls with them. The key assumption is that
evolution is mainly a divergent process. Homoplasies
are thus assumed to represent “errors”,
rather than
evidence in favor of some form of alternative
evolutionary
process (i.e. that does not produce a
tree-like set of relationships),
such as hybridization,
endosymbiosis,
recombination,
gene duplication
(producing
pseudogenes),
or lateral transfer. You
might like to keep this in mind when you next
attempt to interpret an apparently
fully-bifurcating
cladogram, as such alternative evolutionary processes
are increasingly
being recognized
as relatively
common.
Phylogenetic trees
For the purposes of cladistics, it is assumed that
the phylogenetic pattern of evolutionary
history can
be represented as a branching diagram like a tree (a
cladogram),
with the terminal branches (or leaves)
linking the taxa being analysed and the internal
branches (or internodes) linking hypothesized ancestral taxa (nodes) (Fig. 1). The cladogram is thus
usually constructed
purely from a knowledge
of
contemporary
taxa, but it implies the existence of
ancestors with particular
characteristics. Traditionally, the descendants of an ancestor on a cladogram
are called daughters,
while the siblings after a
speciation event are called sisters (so a descendant is
a daughter relative to its ancestor and a sister relative
to its other sibling). Note that if either of the daughters undergoes further speciation then the sister to a
particular
contemporary
taxon may actually be a
group of contemporary
taxa (i.e. all of the descendants of its sister); thus the sister to the Turtles in
Fig. 1 is the group formed by the Lizards+Snakes+
Crocodiles+Birds+Mammals.
Two types of evolutionary
information
can be
represented on a cladogram. Firstly, the speciation
Invited
Review
591
Fig. 2. The same phylogenetic
tree as shown in Fig. I, but with the branch lengths drawn proportional
to the number of
characters
being transformed
from an ancestral
to a derived state along that branch (the number
of character
state changes
is also marked
on each branch).
This cladogram
thus shows both the phylesis and the speciation implied by the data in
Table I.
events in evolutionary
history are represented by the
branching sequence of the tree. Secondly, the phylesis
events may be represented by the relative length of
the branches on the tree (in which case it is sometimes
referred to as a phylogram).
Thus there is an explicit
distinction
between those evolutionary
events that
modify a taxon without causing new taxa to originate
(phylesis) and those evolutionary
events that do lead
to the origin of new taxa (speciation). Both of these
events are involved in evolutionary
divergence among
taxa. However, only the branching
sequence (the
topology) is essential to a cladogram, and indeed this
is the only information
shown in Fig. 1; the equivalent tree showing both speciation and phylesis is
shown in Fig. 2. This is not to say that the phylesis
events are not of interest, but merely that their
pattern is not an essential part of the interpretation
of
the tree; and indeed only some of the phylesis can be
shown on the tree (i.e. only for those characters being
used) while all of the speciation may be included.
Interestingly,
the book of Darwin (1859) is basically
about phylesis (the transformation
of 1 species into
another) rather than about speciation (the formation
of 2 daughter species from 1 ancestral species), in
spite of its title.
The branching sequence of a cladogram organizes
taxa into monophyletic
groups (clades), and the best
way to discuss the evolutionary
pattern represented
by a cladogram
is in terms of which taxa form
monophyletic
groups on the tree. A monophyletic
group is: a group of taxa descended from a single
ancestor and which includes all of the taxa descended
from this ancestor. Groups that do not include all of
the descendants of their most recent common ancestor are called paraphyletic
groups. Thus in Fig. 1
Crocodiles+Birds
form a monophyletic
group, as
do Lizards+Snakes+Crocodiles+Birds,
and also
Lizards+Snakes+CrocodiIes+Birds+Mammals,
but
Lizards+Snakes+Crocodiles
form a paraphyletic
group (because their most recent common ancestor
also has Birds as a descendant); the Class Reptilia as
usually defined is thus not a monophyletic
group (it
would have to include all of the members of the
traditional
Class Aves and Class Mammalia as well).
Simple though it may seem, it is my impression that
the recognition
of monophyletic
groups, and thus
the description and interpretation
of the evolutionary pattern shown by a cladogram, appears to be
one of the more difficult aspects of cladistics for
non-experts (see also the specific examples discussed
by Penny et al., 1990 and Brooks & McLennan,
1992).
It should also be recognized that any 1 cladogram can actually be drawn as a tree in many
different ways (Fig. 3). This is because the cladogram
only specifies the temporal order of the branching
D. A. Morrison
Fig. 3. Several ways of presenting
the same rooted
phylogenetic
tree. (A) Shows a cladogram
of the hypothetical
relationships
among 5 taxa; (B) is the same tree as in A but with 1 of the branches
(marked)
rotated;
(C) is the same tree
as in (B), but with another one of the branches
also rotated;
(D) is the same tree as in (C) but with another 2 of the branches
rotated.
All 4 of these trees represent
exactly the same evolutionary
history for the 5 taxa involved
- that is, they specify
exactly the same cladistic
relationships
among the taxa (e.g. Taxonl
is shown as the sister to Taxon
in all of the trees, and
Taxon
is the sister to this pair). There are a further
11 ways of drawing
exactly this same tree, as well.
sequence
daughter
ancestor
from
the
is drawn
root
to the tips,
on the tree to the
and
left
which
of the
and which is drawn to the right has no
evolutionary
meaning. Consequently, the taxa can be
rotated around each internal branch on the tree
without in any way affecting the meaning of the
cladogram. The best analogy here is to think of a
mobile hanging from the ceiling, and to think about
the way in which its parts can rotate freely. The
mobile does not change its basic form no matter how
much the parts are rotated, and similarly the phylogenetic information
in the cladogram
does not
change no matter which way we rotate the branches.
It is thus very easy for non-experts to think that 2
trees are different, when in fact the cladogram still
specifies exactly the same evolutionary
relationship
among the taxa (Fig. 3).
The distinction between rooted and unrooted trees
is very important
(Fig. 4), but it is also often problematical for non-experts. As noted above, the most
common method of cladistic analysis (particularly
for
sequence data) involves producing an unrooted tree
and then rooting the tree using the outgroup. This
rooting of the tree then indicates the direction of
evolutionary
change on the cladogram;
and this
allows hypotheses of relative character-state polarity
(ancestral vs derived) to be produced, and also allows
inferences about the composition
of monophyletic
groups to made. So, unrooted trees do not indicate
character polarity, nor do they unequivocally
show
monophyletic
groups. This is because a group that
appears to be monophyletic
on an unrooted tree will
be paraphyletic if the tree is rooted within this group.
For example, in Fig. 4 the group Taxonl+Taxon2+
Taxon is only indicated as monophyletic
in Tree E,
because this is the only tree of those shown in which
the root lies outside of this group. Any specified
unrooted
tree can actually be rooted on any of
its branches (Fig. 4), which is why it is important to
have an objective criterion (such as an outgroup, or
some characters polarized by the direct method) for
determining the position of the root.
Invited
Review
599
A
B
C
Fig. 4. Several of the rooted phylogenetic
trees that can be derived from a single unrooted
phylogenetic
tree. (A) Shows
an unrooted
cladogram
of the hypothetical
relationships
among 5 taxa; (B) is the rooted cladogram
that results from rooting
the tree in (A) on the terminal
branch leading to Taxonl;
(C) is the rooted cladogram
that results from rooting
the tree in
(A) on the internal
branch connecting
Taxonl+TaxonZ
with the other taxa; (D) is the rooted cladogram
that results from
rooting
the tree in (A) on the terminal
branch
leading to Taxon3;
(E) is the rooted cladogram
that results from rooting the
tree in (A) on the terminal
branch leading to Taxon5.
The unrooted
tree in (A) could also be rooted on the terminal
branch
leading to Taxon2,
on the terminal
branch leading to Taxon4,
and on the internal
branch connecting
Taxon4+TaxonS
with
the other taxa. There are thus as many possible rooting
points on an unrooted
tree as there are branches
on the tree. Note
that the unrooted
tree does not specify the direction
of evolutionary
change, while each of the rooted trees specifies a
different
direction
of evolutionary
change.
It is worthwhile
pointing
out here that, in spite of
its limitations,
an unrooted
tree is, in itself,
still a
valuable
phylogenetic
commodity.
This is because it
limits
the possible
cladograms
(rooted
trees) that are
supported by the data. For example, for 5 taxa there
are 105 possible rooted trees, and yet the unrooted
tree shown in Fig. 4 supports only 7 of these possible trees (i.e. we have rejected 98 possibilities).
Furthermore,
it will be possible to answer many
phylogenetic
questions using only the unrooted tree.
For example, none of the rooted trees that can be
derived from the unrooted tree shown in Fig. 4 has
Taxonl+Taxon3
as a monophyletic
group (since
Taxon
must also be included). Therefore, if this
grouping was one of the hypotheses of interest, then
we can test it adequately without ever needing to
600
D. A. Morrison
Table
2-Some
characteristics
of commonly-used
tree-building
methods
Method
Procedure”
Datab
Taxa’
Data*
1 Unweighted
pair-group
2 Neighbor-joining
3 Neighborliness
4 Minimum-evolution
5 Distance-Wagner
6 Least-squares
7 Maximum-parsimony
8 Weighted-parsimony
9 Compatibility
10 Maximum-likelihood
11 Invariants
12 Spectral
analysis
ak
ak
ak
opt
opt
opt
opt
opt
opt
opt
opt
opt
dist
dist
dist
dist
dist
dist
orig
orig
orig
orig
orig
orig
all
all
quart
all
all
all
all
all
all
all
quart
all
morph
morph
morph
morph
morph
morph
morph
morph
morph
molec
molec
molec
“Method
chooses
uses an algorithm
bMethod
analyses
taxa (dist).
‘Method
performs
dMethod
suitable
studies (molec).
a tree based on an optimality
criterion
(opt) (i.e. a search method)
or simply
(alg) (i.e. a constructive
method).
the original data (orig) or data that have been converted
to distances
between
calculations
on all taxa (all) or only
for both morphological
and molecular
on subsets of taxa (quart).
studies (morph)
or only for molecular
determine the root of the tree. Consequently, the
production of an unrooted tree is a very big step
towards the goal of producing a cladogram.
Finally, it is worthwhile remembering that a cladogram represents a set of hypotheses concerning
evolutionary history. There are hypotheses about:
character homology; character polarity; and phylogenetic relationships of taxa. All of these hypotheses
are stated explicitly by the cladogram itself, irrespective of whether they have actually been shown on
the diagram. The cladogram does not constitute an
experimental test of the evolutionary history of the
taxa, but it is a test of hypotheses of possible phylogenetic patterns. Becausethese hypotheses of pattern
are stated explicitly, they are open to objective tests
of their robustness. Furthermore, the hypotheses of
pattern are open to further objective testing through
cladistic analyses of other data setsfor the same set of
taxa. This may be as close as we will ever get to a
the data matrix directly, while others require that the
data have been converted to distances between taxa
before the analysis (i.e. a matrix of all possible
pair-wise distances between the taxa is calculated).
Furthermore, some of the methods that use an
optimality criterion evaluate that criterion over all
taxa, while some methods evaluate the criterion on
subsets of the taxa (usually 4 taxa, called quartets).
Some methods have been developed specifically for
sequence data, while others may be applied to any
type of data. The more commonly-used methods
(Huelsenbeck, 1995a) and their characteristics are
summarized in Table 2 , and are discussed below.
For those methods that have an optimality criterion, it is important to recognize that they are based
on a double-level optimization, where first the optimality criterion is optimized for a given tree topology, and then the tree that optimizes these optimal
values is selected (i.e. first you make each tree as
hypothetico-deductive
good
Methods for constructing
science
of phylogeny.
trees
Tree building. The tree-building methods that have
been developed vary in many properties (Swofford &
Olsen, 1990; Penny, Hendy & Steel, 1992). Some
methods choose the tree from among all of those
possible that either maximizes or minimizes some
optimality criterion (search methods), while other
methods merely follow an algorithm (a pre-defined
sequence of operations) to produce a single tree
(constructive methods). Some of the methods analyse
as you
can,
and
then
you
find
the
tree
that
is
the best). Methods thus need to be known that
accomplish the optimization for a specified tree, and
then methods need to be known for searching among
the trees for the optimal one. The first class of
methods will be unique for each tree-building procedure, but the second class of methods is more
general.
There are several strategies for finding the optimal
tree (or trees). Exact methods are those that guarantee to find the optimal solution, while heuristic
methods are computationally-efficient strategies that
should produce a solution that is at least close to the
Invited Review
optimal one even if it does not find the optimum. The
most efficient (see below) of the exact methods involve the use of the branch-and-bound
strategy
(Hendy & Penny, 1982). The need for heuristic
methods is simply one of practicality - the number
of possible trees to be tested by the exact methods
increases exponentially
with increasing numbers of
taxa (Felsenstein, 1978a). Heuristic search strategies
first try to find a tree that is a good estimate of the
final solution, usually by sequentially adding the taxa
to the growing tree, adding each taxon in the optimal
place on the tree. Most heuristic strategies then
search through those trees that are similar to this
initial tree in order to find a better solution, usually
using branch swapping (Swofford & Olsen, 1990).
The important point to note is that heuristic searches
do not necessarily find the optimal solution, nor
do they necessarily get particularly
close to it. It
is therefore important
to accurately describe any
heuristic procedures used in an analysis, so that the
likely success of the method can be assessed.
There are many methods
for calculating
the
distances for those methods
that require them.
Distances specify a relationship
between pairs of
taxa, with taxa that have identical states for all of the
characters having zero distance between them, and
taxa that have no character states in common having
an arbitrarily
large distance. Some data that are
useful for cladistic purposes, such as those from
immunology,
nucleic acid hybridization
and breeding
experiments, are automatically
expressed as pair-wise
distances (West & Faith, 1990); but most character
data need to be mathematically
transformed
into
distances. The basic assumption when analysing distances is that the distances used provide an estimate
of the evolutionary
divergence among the taxa.
The wide array of possible general measures of
inter-taxon relationship
is summarized by Clifford &
Stephenson (1975). The most commonly used direct
distance measures are the manhattan
(sum of the
character-state
differences for all of the characters)
and euclidean (square-root
of the sum of the squared
differences) distances, although the former may have
more biological meaning (West & Faith, 1990). For
data with a mixture of multi-state
characters (i.e.
where different characters have different numbers of
states) it will be necessary to standardize the data
first, and the most popular standardized
distance is
the gower (range-standardized
manhattan)
distance.
It is also possible to convert measures of similarity
into distances (Swofford & Olsen, 1990), and there
are many published
versions of such measures
(Hubalek, 1982).
For DNA/RNA
sequence data, the distance between taxa can be estimated by the total number of
601
nucleotide
differences
between them (Gojobori,
Moriyama
& Kimura,
1990). However, rather than
just count the number of observed differences in
nucleotides between 2 taxa, it is usual to recognize
that there are likely to have been many superimposed
substitution/indel
events through evolutionary
time
(e.g., multiple
substitutions
at any one nucleotide
position), and that these superimposed events cannot
be observed
in the contemporary
taxa. Many
methods have thus been proposed to try to correctly
estimate
sequence
divergence
from
observed
nucleotide
differences (see Gojobori
et al., 1990;
Pollock & Goldstein,
1995; Rzhetsky & Nei, 1995),
based on models of nucleotide evolution that vary
from very simple to quite sophisticated.
These
methods work by estimating the expected amount
of nucleotide
divergence
between the sequences,
assuming some specified probability
that nucleotide
changes will occur during an evolutionary
timeperiod (such as that the number of changes follows a
Poisson frequency distribution),
usually by diIIerentially weighting the various transitions and transversions that are possible among the 4 nucleotide
character-states
(A, C, G, T/U) to reflect their
relative probability
of occurrence. The differences
observed between the taxa are thus “corrected”
for
unobserved multiple
substitutioniindel
events, and
the distances derived from these corrected data
should provide a better estimate of the evolutionary
divergence among the taxa.
The studies to date indicate that the simplest of the
various models of nucleotide evolution that is likely
to apply to real data sets is the 2-parameter model
of Kimura (1980), but that it may not be applicable
when the sequences are distantly related and/or the
total number
of nucleotides
examined
is large
(Rzhetsky & Nei, 1995). Part of the problem here
is that the rate of nucleotide
substitution
varies
within evolutionary
hneages (Li er al., 1987) as well
as among sites within a sequence (Olsen, 1987;
Shoemaker & Fitch, 1989). Consequently, the nucleotide evolution models may be better if the variance of
the estimates is reduced (Pollock & Goldstein, 1993,
and if they assume that the rate of nucleotide
substitution
varies from site to site according to a
gamma frequency distribution
(Jin & Nei, 1990).
Many other methods have also been proposed
specifically for calculating
distances from proteincoding DNA sequences, based on comparing codons
rather than nucleotides. They recognize the distinction between non-synonymous
and synonymous
nucleotide substitutions (i.e. those that do and do not
result in changes in the amino acid coded for), and
include both weighted and unweighted
pathways
methods (Gojobori et al., 1990). Distances may also
602
D. A. Morrison
be calculated directly from amino acid sequences
(Ota & Nei, 1994). Furthermore,
a number
of
methods have been proposed specifically for converting frequency data (such as allelic or genotypic
frequencies) to distances, based on different genetic
models (Rogers, 1991), and also for calculating
distances from restriction endonuclease data (Nei &
Li, 1979).
Tree-building methods. Here, I provide only a brief
introduction
to the procedures
employed
by the
various tree-building
methods. More details of most
of these methods, along with worked examples, are
provided
by Swofford
& Olsen
(1990),
and
Charleston,
Hendy & Penny (1994) provide a brief
mathematical
exposition.
The
Unweighted
pair-group
method
using
arithmetic
average (UPGMA)
is an algorithmic
method that analyses distance data (Michener
&
Sokal, 1957; Sokal & Michener, 1958). It groups the
taxa based on increasing distances between the taxa,
starting by grouping the 2 taxa with the smallest
distance, and then progressively adding more-distant
taxa to the group or to new groups. It assumes that
the data are ultrametric;
that is, a tree can be
constructed so that the observed distance between
any 2 taxa (i.e. in the original data matrix) is equal to
the sum of the branch lengths joining them (i.e. the
distance as measured along the branches connecting
the 2 taxa on the tree), and that the tree is rooted so
that all of the taxa are equidistant from the root.
Neighbor-joining
(Saitou & Nei, 1987; Studier &
Keppler, 1988) is another algorithmic
method that
analyses distance data. It is similar to UPGMA
in
that it starts by grouping the 2 taxa with the smallest
distance, and then progressively
adds more-distant
taxa to the group or to new groups. However, it
differs in modifying the distance matrix at each step,
so that each pair of groups is adjusted on the basis of
their average divergence from all other groups. The
method thus relaxes the ultrametric assumption, and
assumes only that the data are additive; that is, a tree
can be constructed
so that the observed distance
between any 2 taxa (i.e. in the original distance
matrix) is equal to the sum of the branch lengths
connecting them on the tree (patristic distance or
pathlength).
The Neighborliness
procedure (Sattath & Tversky,
1977; Fitch, 1981) is the final algorithmic
method
discussed that analyses distance data. It is based
on evaluating the 4-point metric (Dobson, 1974), a
relaxed definition of additivity for a set of 4 taxa. It
specifies the conditions for clustering 4 taxa into 2
pairs, based on the relative ranking of the patristic
distances between all possible pairs of the taxa.
Neighborliness
is thus a quartet method, evaluating
the 4-point metric for all possible subsets of 4 taxa
(quartets) to decide how the 4 taxa should be clustered, and then building clusters of the taxa that are
consistent with the largest fraction of the quartets
(i.e. the tree is the one for which the 4-point metric is
satisfied the largest number of times).
Other algorithmic
methods that analyse distance
data have been described
by Farris
(1977),
Chakraborty
(1977), Klotz & Blanken (1981), Li
(1981), Tateno, Nei & Tajima (1982), Hasegawa,
Kishino & Yano (1985), and Charleston et al. (1994);
but none of these has been widely used.
The Minimum-evolution
procedure (Edwards &
Cavalli-Sforza,
1964) analyses distance data using
an optimality
criterion. The tree chosen is the one
that minimizes the sum of the lengths of all of the
branches on the tree, these branch lengths being
estimated using linear algebra on the observed distances (i.e. from the original distance matrix) between
3 taxa inter-connected
by a common node. Rzhetsky
& Nei (1993) provide an exact method for optimizing
each tree; and Rzhetsky & Nei (1992) have suggested
an heuristic method for finding the optimal tree by
pointing out that the neighbor-joining
algorithm
is
guaranteed to find the Minimum-evolution
tree for 4
taxa.
The Distance-Wagner
method (Farris, 1972) also
analyses distance data using an optimality criterion.
The optimality
criterion
is the same as for the
Minimum-evolution
procedure:
the desired tree is
the one that minimizes the sum of all of the branch
lengths on the tree. However, in this case all of the
patristic distances (along the tree branches) connecting any 2 taxa are constrained to be greater than the
observed distances between these taxa, whereas the
Minimum evolution procedure assumes that some of
the patristic distances will be greater and some
smaller than the observed distances. Exact methods
for optimizing
each tree have been described
(Beyer et aZ., 1974; Waterman
et al., 1977), and
heuristic procedures for tinding the optimal tree are
usually used (Farris, 1972; Swofford,
1981; Faith,
1985).
The
Weighted
least-squares
(Fitch
&
Margoliash,
1967) and the Unweighted least-squares
(Cavalli-Sforza
& Edwards,
1967) are related
methods that analyse distance data using an optimality criterion.
They both choose the tree that
minimizes the error (i.e. the measured discrepancy)
between the observed distances between the taxa (i.e.
the original distance matrix) and the patristic distances connecting the taxa on the tree (pathlength).
So, for each possible tree they compare the sum of all
of the squared differences between the distances in
Invited Review
the original matrix and those on the tree, and they
then choose the tree that minimizes this sum. The 2
methods differ in the formula they actually use to
measure the discrepancy between the observed and
patristic distances, the unweighted method assuming
that all of the distance estimates have the same
absolute error and the weighted method assuming
that they are have the same percentage error. Exact
methods for optimizing each tree have been described
(Kidd & Sgaramella-Zonta,
1971; Beyer et aZ., 1974;
Waterman PZ al, 1977), and heuristic procedures for
finding the optimal tree are usually used.
The Maximum-parsimony
method (Farris, 1970;
Fitch, 1971) is the first method to be discussed that
analyses the original data matrix using an optimality
criterion. It is probably
the most popular method
among cladists, and indeed many cladists restrict the
definition of cladistics to include this method alone.
The optimal tree is the one that has the minimum
number of inferred character state changes (i.e. shortest tree length or fewest evolutionary
steps). Exact
methods for optimizing each tree have been described
(Fitch, 1971; Swofford & Maddison,
1987). Exact
methods for finding the optimal
tree include an
exhaustive search (i.e. testing every possible tree
topology)
and branch-and-bound
methods,
but
heuristic methods must be used for analyses with
more than about 20 taxa (Swofford & Olsen, 1990).
Special methods have been developed for frequency
data, such as allelic
or genotypic
frequencies
(Swofford & Berlocher, 1987).
The Weighted-parsimony
method (Farris, 1969;
Sankoff, 1975) is a generalization
of the Maximumparsimony
method that allows the characters and
character states to be weighted so that they contribute unequally
to the calculation
of optimality
(note that character weighting
and character-state
weighting
are separate ideas; Williams
& Fitch,
1989). The optimal
tree is the one that has the
minimum sum of the weights. The rationale for this is
that the unequal weights reflect unequal probabilities
of change in the characters (Felsenstein, 1981 b), the
weighting usually being applied so that evolutionarily
conservative characters or states can contribute more
to the reconstruction
of the phylogeny (Olsen, 1987).
The magnitude of the weights to be applied can be
decided either a priori (i.e. decided before the analysis) or a posteriori
(i.e. calculated after an initial
cladogram
has been constructed)
(Neff,
1986).
Several general a priori weighting schemes have been
proposed,
such as Dollo-parsimony
(Le Quesne,
1974), where no parallelisms
or convergences are
permitted,
and Camin-Sokal-parsimony
(Camin &
Sokal, 1965), where no reversals are allowed, as well
as compatibility
weighting (Penny & Hendy, 1986;
603
Sharkey, 1989). However, many a priori weighting
schemes have also been developed specifically for
molecular sequences, where the genetic mechanisms
responsible for nucleotide substitutions make it seem
unreasonable
to assume equal weights for all
changes. Differential
weights can be applied to (see
Hillis et al., 1993): (1) different sequence positions
(character weighting),
thus emphasizing
functional
inequalities along the sequences (e.g., different codon
positions in translated genes, stems vs loops in structural RNAs, hypervariable
positions in mtDNA); or
(2) the same sequence positions
(character-state
weighting), thus emphasizing mutational biases (e.g.,
transitions
vs transversions,
relative substitution
frequencies,
base composition,
synonymous
vs
non-synonymous
changes). A posteriori
weighting
schemes include successive approximations
(Farris,
1969), quadratic
weighting
(Fitch & Yasunobu,
1975), transformation
series (Mickevich,
1982),
dynamic weighting
(Williams
& Fitch, 1989) and
homoplasy
weighting
(Goloboff,
1993). Exact
methods for optimizing each tree using weights have
been described (Sankoff & Cedergren, 1983).
The Compatibility
method (Le Quesne, 1969,
1982) also analyses the original data matrix using an
optimality criterion. The optimal tree is the one that
has the largest set (clique) of mutually compatible
characters (i.e. characters for which there is no
homoplasy
on the tree). The method proceeds by
testing the pair-wise
compatibility
of all of the
characters, and then examining all possible cliques of
characters. The method thus relies on the theorem
that a group of characters which are pair-wise compatible are jointly compatible. This is always true for
both polarized and unpolarized
2-state characters
(Estabrook & McMorris,
1980), but for unpolarized
multi-state characters it is possible for a collection of
pair-wise
compatible
characters not to have any
phylogeny for which they are all compatible (Fitch,
1975). Branch-and-bound
methods are available for
finding the maximal cliques.
The Maximum-likelihood
procedure (Felsenstein,
1973a,b) is another method that analyses the original
data matrix using an optimality
criterion.
So far,
practical
likelihood
methods
have only been
developed for analysing nucleotide
sequence data
(Felsenstein, 198la), protein sequence data (Kishino,
Miyata & Hasegawa, 1990), and restriction site data
(Felsenstein,
1992), with
restricted
maximumlikelihood
methods also available for continuous
characters (Felsenstein, 198lc). The optimal tree is
the one that maximizes the statistical likelihood
that the specified evolutionary
model produced the
observed data. For example, for a given model of
nucleotide evolution (the most commonly-used
one is
604
D.
A. Morrison
the generalized Kimura 2-parameter model described
by Kishino & Hasegawa, 1989), formulae are derived
that describe the probability
that an initial nucleotide
will be transformed into a specified nucleotide during
an evolutionary
time-period.
The likelihood for each
nucleotide position is then equal to the prior probability of finding the initial nucleotide at that position
multiplied
by the probability
of transformation.
The
likelihood of the divergence of 2 sequences during the
time-period
is then the product of the likelihoods at
each position, and the overall likelihood for a tree is
the product of the likelihoods along the branches. No
exact methods for optimizing
each tree have been
described, and iterative (“hill-climbing”)
methods are
used (Fukami & Tateno, 1989). Exact methods for
finding the optimal tree involve an exhaustive search
(since suitable branch-and-bound
methods are unknown),
and so heuristic
methods
(Felsenstein,
1981a) are usually used for analyses with more than
about 5 taxa.
The Invariants
(or Evolutionary
parsimony)
method (Lake, 1987; Cavender & Felsenstein, 1987)
also analyses the original data matrix using an optimality criterion, although it was developed specifically for analysing nucleotide
sequence data. It is
based on evaluating the number of operator invariants (linear for the method of Lake; quadratic for the
method of Cavender & Felsenstein) for 4 taxa, which
specifies the conditions for clustering the 4 taxa into 2
pairs, based on the relative number of transversions
on the internal branch of the unrooted tree to those
on the terminal branches. The use of Invariants is
thus a quartet method, evaluating the invariants for
all possible subsets of 4 taxa (quartets) to decide how
the 4 taxa should be clustered, and then building
clusters of the taxa that are consistent with the largest
fraction of the quartets (Lake, 1988). Exact methods
are used for the evaluation of the invariants.
Spectral analysis (Penny, Hendy & Henderson,
1987; Hendy & Penny, 1993) is the final procedure
that analyses the original data matrix using an optimality criterion.
It has been developed
only for
nucleotide
data, originally
with 2-state characters
(Hendy,
1989) and more recently with 4 states
(Hendy,
Steel & Penny, 1994). This procedure
first uses the hadamard
transformation
(Hendy &
Charleston, 1993) together with a model of sequence
evolution
(such as the 2-character-state
model
of Cavender,
1978a,b) to adjust (or correct) the
observed
data
for
unobserved
character-state
changes (e.g., multiple substitutions
at a sequence
position), thus producing
a matrix of expected data
(i.e. expected number
of character-state
changes
under the evolutionary
model adopted).
These
corrected data are then used to estimate the degree
of support for every possible subset of taxa, by
summing the number of the expected character-state
changes that are compatible with each subset. The
Closest-tree method (Hendy, 1991; Steel et d, 1992),
a compatibility-type
method based on minimizing
the sum-of-squares, is then used to select the optimal
tree as the one with the largest set of mutually
compatible subsets of taxa. Exact methods for finding the optimal
tree include branch-and-bound
methods (Hendy & Penny, 1989), with a limit of
about 20 taxa.
Characteristics. Clearly, it is impossible to compare
the many tree-building
methods based on their
relative ability to detect the phylogenetic
pattern
underlying
the apparent incongruences
in real data
sets, because the real phylogenetic pattern is almost
never known. Instead, many other criteria have been
proposed to assess the relative usefulness of the
various tree-building
methods, although
many of
these criteria have not yet been effectively evaluated
for most of the methods. Those criteria about which
we know the most are outlined here - no single
method meets all of the criteria (Penny et al., 1990,
1992).
The Computational Eficiency of a method refers to
the relative speed with which a solution is produced
(Penny et al., 1992). All of the algorithmic procedures
are relatively efficient, as the computation
time does
not increase dramatically
as the number of taxa is
increased. On the other hand, none of the optimality
methods is efficient, because the number of trees from
which the optimal one needs to be chosen (i.e. at the
second step in the double-optimization)
increases
exponentially
as the number
of taxa increases
(Felsenstein, 1978a). Finding the optimal tree using
exact methods is an example of the large class of
NP-complete
mathematical
problems
(Graham
&
Foulds, 1982), for which no efficient procedure is
known (or is expected ever to be known). So, for
large data sets (both in terms of number of taxa and
number of characters) heuristic methods must be
used for all of the optimality methods if a solution is
to be produced within a reasonable time. This means
that finding the optimal solution cannot be guaranteed for the analysis of large data sets - just how
large “large” is depends on the computing
power
(both software and hardware) available for the analysis and the patience of the cladist. This situation is
compounded
for data sets with a relatively
low
phylogenetic
signal (see below), which are likely to
have multiple optimal trees that are structurally quite
different (Maddison,
1991) -these
“islands” of trees
may not easily be found by heuristic techniques
(Page, 1993).
Invited Review
605
The Maximum-likelihood method is even more quartet methods ignore that part of the information
inefficient than all of the other methods that use that comes from the incompatibilities among the
optimality criteria. For Maximum-likelihood, the quartets, while Compatibility analysis assumes that
first step in the double-optimization (i.e. optimizing
incompatible characters have no phylogenetic
each tree topology) has no simple analytical solution information at all (Hill, 1975). Furthermore, the
(Fukami & Tateno, 1989), unlike all of the other Parsimony and Compatibility methods do not use
methods, and so computationally-intensive iterative characters that have constant states across all of the
procedures must be used. This problem is exacer- taxa, nor characters where only 1 of the states
bated by the fact that there may be more than 1 way occurs in more than 1 taxon (autapomorphies); and
of optimizing a particular tree topology (Steel, 1994). these may form a large proportion of sequence data
These problems are then compounded by the lack of (for example, I looked at an arbitrary selection of
a branch-and-bound algorithm for the second step in 20 molecular studies published in 1994, and found
the double-optimization; and so there is a severelimit that on average 84% of the nucleotide positions
to the sizeof the data set that it is practical to analyse were uninformative for Parsimony/Compatibility
by the Maximum-likelihood method.
analysis using these 2 criteria). The MaximumThe Power of a method refers to the response of likelihood, Invariants and Spectral-analysis methods
the method to increasing amounts of data (Olsen, ignore characters with missing character-state data
1988) - with an increasing number of characters in for any of the taxa, including indels for sequence
the original data matrix we expect a method to data, which may also constitute a sizable proconverge to a single tree (i.e. a limit is reached portion of the original data matrix. The Invariants
beyond which further increases in the data do not method is also based entirely on transversion substichange the tree produced by the method) (Penny & tutions, and there may not be enough in a data set
Hendy, 1986). A powerful method is one in which the to effectively infer the branching pattern, or the
convergence occurs with a relatively small number of frequency of transitions may confound the pattern
characters (Hillis, Huelsenbeck & Swofford, 1994b). (Jin & Nei, 1990; West & Faith, 1990); it thus
appears to have very low power (Hillis et al.,
Power is also related to the amount of information
in the original data matrix that is actually used to 1994a,b).
construct the tree (Penny et al., 1992, 1993) - all of
The Consistencyof a tree-building method refers to
the tree-building methods omit some of the character its ability to converge to the correct tree (Felsenstein,
information, and so the power of these methods may 1988). That is, with an increasing number of characbe reduced. However, it is important to note that not ters in the data matrix a consistent method converges
all of the character information is necessary for the to the single correct tree, and a method is inconsistent
reconstruction of an evolutionary tree, and that if there are any possible situations where it converges
therefore it is not loss per se but loss of relevant to the wrong tree (i.e. there are systematic or noninformation that is important (Shoemaker & Fitch, random errors). Consistency is related to the assump1989; Penny et al., 1993).
tions (e.g., the evolutionary model) made by the
Compared with the character-based methods, all tree-building method - if the assumptions are not
of the distance methods involve a very large loss of met for a particular data set then consistency cannot
information in converting the original data into be expected.
distances. This is because there will be multiple
There are fundamental assumptions underlying all
character data sets that produce exactly the same of the tree-building methods, such as that evolution
distance matrix (Felsenstein, 1982; Penny, 1982), and proceeds as a continuous-time markov process
this problem becomes worse for increasing numbers (Beanland & Howe, 1992), whether they are explicit
of taxa and characters (Steel, Hendy & Penny, 1988). or not for a particular type of data (e.g Rodriguez
Moreover, for sequence data it is not clear how to et aZ., 1990). The most notable assumption is that
calculate distances when the aligned sequences con- character-state changes are independent and identitain terminal length variations, indels or ambiguous cally distributed (Cavender, 1978a; Olsen, 1987;
nucleotides (since the models of nucleotide evolution
Shoemaker & Fitch, 1989; Sanderson, 1995); which
are based on estimating rates of transitions and means that no character-state change affects any
transversions only) - including or excluding these other character-state change, and that all characterfeatures in the calculations can produce differ- state changes are equally likely. If evolution has
ent distance estimates (Swofford & Olsen, 1990; occurred then this assumption is generally not true,
Beanland & Howe, 1992).
because of the common history of the taxa during
The character-based methods also do not use all at least some evolutionary period. The distance
of the data (Penny et aZ., 1990). For example, the methods will be particularly sensitive to this problem
606
D. A. Morrison
(Felsenstein, 1988), although all of the methods suffer
from it (Felsenstein, 1982).
The distance methods will also be inconsistent if
the data are not additive (Felsenstein, 1988), as there
is no exact solution for estimating the tree under
these circumstances
(Swofford
& Olsen, 1990).
Additivity
of taxonomic
data is unlikely because
the distances are only estimates of evolutionary
divergence,
and are therefore
expected to vary
randomly around the true divergence value (i.e. the
data will be additive only if there is no homoplasy).
One of the consequences of this is that trees with
negative branch lengths are theoretically
possible
when
using
the Neighbor-joining,
Minimumevolution
and Least-squares methods (Swofford
&
Olsen, 1990). UPGMA
adds the further constraint
that the data are ultrametric; that is, that evolutionary divergence among the taxa occurs at a uniform
rate through time (such as occurs with a molecular
clock). This is also unrealistic.
All of the methods will also be inconsistent if the
amount of homoplasy is large, because homoplasy
makes unrelated taxa appear to be more similar
(Olsen, 1987; Swofford & Olsen, 1990). This will be a
particular
problem
if the frequency of characterstates varies between taxa (Penny et al., 1990); for
example, for sequence data similar GC-content often
unites unwanted branches on a tree (Sidow & Wilson,
1990, 1991; Lockhart
et al., 1992; Marshall, 1992;
Hasegawa & Hashimoto,
1993) and all tree-building
methods are sensitive to this (Lockhart
e? al., 1992,
1994).
Methods may also be inconsistent when there are
juxtaposed long and short branches on the tree (e.g.,
unequal rates of phylesis or speciation),
as these
branches will tend to join together (often referred to
as “long branches attracting”).
This has long been
recognized as a particular problem for the Parsimony
and Compatibility
methods
(Cavender,
1978a;
Felsenstein, 1978b; Hendy & Penny, 1989; Zharkikh
& Li, 1993; Takezaki & Nei, 1994), but we now
recognize that it also applies to all of the distance
methods as well as to the Invariants and Closest-tree
methods (Jin & Nei, 1990; Penny et al., 1990; de Bry,
1992; Huelsenbeck & Hillis, 1993; Steel, Hendy &
Penny, 1993; Zharkikh
& Li, 1993; Hillis et al.,
1994b). The Maximum-likelihood
method appears to
suffer least from this problem (Hillis et al., 1994b).
The Robustness of a tree-building
method refers to
how much the assumptions of the method can be
violated before the method becomes inconsistent
(Penny et al., 1990). This may be the most important
criterion,
because the idealized assumptions of the
methods are likely to be violated by real data sets
(Huelsenbeck,
1995a,b). Many of the consistency
problems listed above may thus not necessarily preclude use of the various methods if they are robust.
The distance methods, for example, may be quite
robust to the problem
of non-additivity
if the
distance
estimates
are corrected
for multiple
character-state changes and the problems of negative
branch-lengths
are addressed (Felsenstein, 1988); and
even UPGMA does not require perfectly ultrametric
data (Colless, 1970). The consistency
problems
associated with homoplasy can also potentially
be
solved (i.e. the methods can be made robust) by any
method that provides a framework for making corrections for multiple character-state changes (Penny
er al., 1993), such as the use of transformations
and
corrected
distances (e.g., for unequal nucleotide
composition,
use of the LogDet
transformation,
Lockhart et al., 1994; compositional
statistics, Sidow
& Wilson,
1990, 1991; or character
weighting,
Marshall,
1992). Consistency can often be restored
(i.e. the methods made robust) when there are juxtaposed long and short branches by adding taxa to the
analysis that join the tree on the long branches
(Hendy & Penny, 1989; Penny et al., 1990; Lento
et al., 1995), or by using character weighting schemes
that shorten the branches (Swofford & Olsen, 1990;
Hillis et al., 1993). However, the preferred method
is to make corrections for multiple character-state
changes using transformations
(Jin & Nei, 1990; de
Bry, 1992; Steel et al., 1993; Huelsenbeck,
1995a).
Note that the attempts to improve the consistency of
the tree-building
methods by using corrections and
transformations
apply only to molecular data, because it is possible to use a consistent model of
character-state
changes that will apply to all of the
characters in any 1 data set. It is not obvious how to
appropriately
correct or transform
other types of
data, since each character will have its own model of
character-state change.
A popular approach to studying the robustness of
the various methods is by using simulated data,
where the original tree and the characteristics of the
data are known, and the behavior of the tree-building
methods under these conditions
is evaluated (e.g.,
Tateno et al., 1982; Li et a!., 1987; Sourdis &
Krimbas,
1987; Kim & Burgman,
1988; Saitou &
Imanishi, 1989; Jin & Nei, 1990; Rohlf et al., 1990;
Nei, 1991; Sidow & Wilson,
1991; Hasegawa &
Fujiwara,
1993; Huelsenbeck
& Hillis,
1993;
Charleston et al., 1994; Hillis et al., 1994a,b; Kuhner
& Felsenstein, 1994; Tateno, Takezaki & Nei, 1994;
Gaut & Lewis, 1995; Huelsenbeck, 1995a,b; Tillier &
Collins, 1995; Yang, 1995). There is clearly a large
conceptual gap between simulated data and real data
(Miyamoto
& Cracraft, 1991; Hillis et al., 1994a),
and most of the simulations
apply only to the
Invited Review
branching
order of a limited number of taxa under
specific evolutionary
models. The jury is still out on
the results (cf. Felsenstein, 1988), but these studies
show that many of the tree-building
methods are
actually quite effective (i.e. robust) over a wide range
of evolutionary
conditions. The most robust of the
methods appears to be the Maximum-likelihood
procedure, with UPGMA
and the Invariants method
being the least robust. The robustness of the other
methods seems to depend very much on the ability
to correctly
utilize transformations
for multiple
character-state
changes or to appropriately
apply
character or character-state
weighting;
clearly this
requires a priori knowledge about the evolutionary
process in the taxa being studied that is unlikely to be
available. It is unfortunate
that Spectral analysis has
not been incorporated
into most of the simulation
studies to date, in order to test whether its theoretical
advantages are met in practice.
Finally,
there are methodological
and philosophical considerations
that are often used to compare the techniques (Miyamoto
& Cracraft, 1991).
In particular,
the algorithmic
procedures are often
criticized because they provide no method for ranking alternative
tree topologies
(i.e. there is no
criterion to compare trees and decide how “good”
any of them are as estimates of phylogeny) (Swofford
& Olsen, 1990). This is a serious limitation if we treat
a cladogram as being an attempt to estimate the true
phylogeny, because we are using incomplete information and there is thus a degree of uncertainty about
the correctness of our estimate (Felsenstein, 1988). It
is thus always a good idea to assess how much better
the optimal tree is than the next-most-optimal
tree
(or set of trees) (Swofford, 1991), especially as these
trees may not be independent
of each other (Penny
et al., 1995).
After tree construction. We can never know
whether our cladogram actually represents the true
phylogenetic
history of the taxa concerned. Therefore, there are 3 further issues that need to be dealt
with once a phylogenetic
tree has been constructed
using 1 or more of the methods outlined
above:
assessing the magnitude of the phylogenetic signal in
the cladogram; assessing the robustness of the monophyletic groups represented on the cladogram; and
comparing the structure of multiple cladograms from
the same set of taxa. Although
these issues are
extremely important
for cladistic analysis, they are
only briefly introduced
here because a full coverage
would require a separate (although shorter) review.
Even randomly-generated
data will lead to the
construction
of a cladogram
if any of the treebuilding techniques is applied to them. It is therefore
607
important
to quantitatively
assess the magnitude of
the phylogenetic signal (i.e. that part of the character
variation
that is potentially
informative
about the
evolutionary
history) in a set of data - is the support
for a particular
tree any better than would be
expected from a random data set? Quantifying
this
information
also allows cladograms to be compared
effectively with each other - a cladogram with a
stronger phylogenetic signal is to be preferred. Four
classes of techniques have been developed: optimality
measurements (for those methods that use an optimality criterion), such as consistency and homoplasy
indices (Archie, 1989; Farris, 1989, 1991) for the
Parsimony
methods,
likelihood
values for the
Maximum-likelihood
methods, and sums-of-squares
for the Least-squares
methods; skewness indices
(Huelsenbeck,
1991; Hillis & Huelsenbeck,
1992);
analytical statistical tests (Felsenstein,
1988; Li &
Gouy, 1991; Li & Zharkikh,
1995); and randomization (or permutation)
statistical tests (Goloboff, 1991;
KBllersjij et aZ., 1992; Ahoy, 1994; Faith & Ballard,
1994).
A cladogram is interpreted in terms of the monophyletic groups of taxa that it hypothesizes.
It
is therefore important
to quantitatively
assess the
robustness of all of the groups indicated by the
branching sequence of a cladogram (i.e. the degree of
support for each branch in the tree) - is the support
for a particular
group any better than would be
expected from a random data set? Many classes of
techniques have been developed, including: analytical
procedures, such as confidence limits, branch-length
variances and likelihood-ratio
tests (Li & Gouy,
1991; Li & Zharkikh,
1995); resampling procedures,
such as the bootstrap (Li & Zharkikh,
1994, 1995;
Sanderson,
1995), the jacknife (Felsenstein,
1988)
and topology-dependent
permutation
(Faith, 1991);
and non-statistical
procedures,
such as the decay
index (Bremer, 1994), clade stability (Davis, 1993),
and spectral signals (Hendy & Penny, 1993).
It is unlikely that different tree-building
methods
will always produce identical trees for the same data
set, given their different underlying assumptions, and
it is also possible for multiple optimal trees to be
produced by a single tree-building
method. Furthermore, we may wish to compare cladograms produced
using different sets of characters (since congruence
among data sets may constitute the strongest achievable evidence for the true phylogeny;
Penny &
Hendy, 1986), and these may differ as a result of
sampling error, different stochastic processes, or different branching histories (de Queiroz et al., 1995). It
is therefore usually necessary to quantitatively
compare the structure of multiple trees from the same set
of taxa. For example, which monophyletic
groups
608
D. A. Morrison
are supported by (congruent among) which set of
trees? - monophyletic groups that are supported
by several trees are to be preferred. Several classesof
techniques have been developed (most of them reviewed by Swofford, 1991): consensus trees; largest
common pruned trees; consensus indices; tree
comparison metrics; partition tests (Farris et al.,
1995); and randomization tests (Rodrigo et aZ., 1993).
A parasitological example. To explore the practical
consequences for phylogeny reconstruction of the
wide range of available tree-building methods, it
is worthwhile exploring a concrete example. This
parasitological example illustrates and emphasizes
many of the points made in earlier sections, as well as
providing a brief step-by-step guide to a cladistic
analysis.
Methods. First, we need to consider the background to the problem that we intend to address with
the cladistic analysis. The members of the genus
Sarcocystis are parasitic protozoans with heteroxenous life cycles, in which both hosts are mammals.
The sexual stage is in the definitive host (often a
predator species) and the asexual stage is in the
intermediate host (often a prey species), with the
sporocysts being passed in the faecesof the definitive
host and ingested by the intermediate host. Studies of
this genus may be of economic importance, because
some of the species are important pathogens of
livestock and humans.
The current classification of the phylum Apicomplexa (Sporozoa) is based largely on ultrastructural
analysis, on details of the life-cycles, and on the
location of developmental stages. The internal
arrangement of the phylum is currently rather unstable, at least partly because of a lack of knowledge
of the life-cycles for many taxa. Cox (1994) treats the
coccidial parasites as a class (the Coccidea), with
Sarcocystis in the order Eimeriida. The family
Sarcocystidae is often subdivided into 2 subfamilies,
the Sarcocystinae (3 genera, 100 species) and the
Toxoplasmatinae (2-3 genera, 15 species) (Levine,
1985).
However, the phylogenetic relationships within the
Sarcocystidae remain ambiguous, at least partly because of difficulties in assessing the homology of
phenotypic characters. It is possible that molecular
data might alleviate these problems, although there
has been little consistency among molecular studies
to date. While the family as a whole is generally
considered to be monophyletic, several analyses of
small-subunit ribosomal RNA (ssrRNA) sequences
have questioned the monophyly of Sarcocystis
itself (Barta, Jenkins & Danforth, 1991; Tenter,
Baverstock & Johnson, 1992; Ellis et al., 1994). In
particular, these studies suggest a strong correlation
between the parasite phylogeny and that of their
definitive hosts, with species of the Sarcocystidae
forming 2 clades based on the use of either canids or
felids as their definitive hosts. Thus Surcocystis(felid
or canid hosts) is only monophyletic if both
Toxoplasma (felid host) and Neospora (unknown
host) are included within it.
Second, we need to consider the data that are
available to tackle this problem (i.e. the ingroup).
There are currently complete ssrRNA sequences
available for 8 species of the Sarcocystidae
(Sarcocystis arieticanis, S. fusiformis, S. gigantea,
S. muris, S. neurona, S. tenella, Neospora caninum,
Toxoplasma gondii), which can be used to test the
monophyly of Surcocystis. Several published sequences are available for some of the species (9 for
T. gondii, 2 for N. caninum), and for the purposes of
this example consensus sequences were derived for
these species (after alignment; see below) using the
MacClade 3.04 computer program (Maddison &
Maddison, 1992). The standard IUPAC ambiguity
codes were used for those few nucleotide positions
with more than 1 possible character-state in the
sequence (1 for S. muris, 1 for N. caninum, 26 for
T. gondii). Thus, we have a representative sample of
the family (e.g., species with both felid and canid
hosts), and we have taken inter-individual variation
into account as far as possible.
Third, we need to consider how the cladogram will
be rooted (i.e. the outgroup), sincemonophyly can be
assessed only on a rooted tree. The members of
the Eimeriida that are most closely-related to the
Sarcocystidae (see Levine, 1985) are the members of
Eimeriu (family Eimeriidae), for which 7 species
have published ssrRNA sequences (E. acervulina, E.
brunetti, E. maxima, E. mitis, E. necatrix, E. praecox,
E. tenella). For the outgroup, a single consensus
sequence was derived from the sequencesfor these 7
Eimeria species(after alignment) using the MacClade
program, with the standard IUPAC ambiguity codes
being used for those 68 nucleotide positions
with more than 1 character-state in the consensus
sequence. These ambiguous character-states can be
dealt with effectively by some analysis techniques,
while others treat them as missing data. For this data
set this different treatment has very little effect,
because in almost all casesthe Sarcocystis sequences
are invariant for these characters (i.e. the variability
is only within the Eimeria phylogeny itself and it
thus does not influence the reconstruction of the
Sarcocystis phylogeny).
Fourth, we need to consider character homologies
(i.e. sequence alignment). There are 9 sequences in
Invited Review
the analysis, 8 for the ingroup and 1 for the outgroup. The ssrRNA sequences for all of these species
were aligned using the secondary structure model
of Van de Peer et al. (1994) - all of the sequences
were obtained from this computer database. For the
cladistic analysis, the single-stranded
regions were
omitted, as Ellis & Morrison
(1995) have indicated
that it is the double-stranded
region that contains
most of the phylogenetic
information
for these taxa.
There are thus 694 nucleotide positions in the analysis. This procedure effectively deals with both the
problems
associated with positions
of equivocal
alignment
(since there are very few indels in the
double-stranded
region), as well as those associated
with relative character weighting based on structural/
functional inequalities along the sequences.
Fifth,
we need to consider
the tree-building
methods. Four tree-building
methods were used (covering the full range of possibilities),
in order to test
the sensitivity of the analysis to this source of variability. Two of these were distance-based methods, 1
of them algorithmic (Neighbor-joining)
and the other
with an optimality
criterion
(Unweighted
leastsquares). The other 2 methods were character-based
with optimality
criteria, one developed specifically
for nucleotide sequences (Maximum-likelihood)
and
one not (Weighted-parsimony).
The Phylip 3.57 computer program
(Felsenstein,
1995) was used for
the first 3 methods, employing
the heuristic search
with global branch-swapping
for those methods
with an optimality
criterion. The PAUP 3.1.1 computer program (Swofford,
1993) was used for the
final method,
employing
the branch-and-bound
search. Note that in order to test the monophyly
of Surcocystis, the only part of the cladogram that
needs to be interpreted
is the branching order (not
the branch lengths), since we will be independently
assessing the degree of support for monophyly
(see
below).
Sixth, we need to consider the evolutionary
model
or models that we wish to employ. Two models of
character-state change were used, in order to test the
sensitivity of the analysis to this source of variability.
The first model assumed that all nucleotide changes
were equally probable at each sequence position,
while the second model assumed that transitions were
twice as likely as transversions (for the trees shown in
Fig. 5 the transition
: transversion ratio is about 1 S,
as determined by the MacClade program). For the
maximum-likelihood
method, the transition
: transversion ratio was set as part of the specified model.
For the distance-based methods, the Kimura distance
measure was used to estimate sequence divergence,
and the transition
: transversion
ratio was set to
either 1 or 2. For the Parsimony method, a step-
609
matrix was used, with transitions weighted as 1 and
transversions weighted as either 1 or 2. The nucleotide frequencies are approximately
equal for all of the
sequences, and so there is probably
no need to
correct for GC-bias (the GC content varies from 50
to 60% across the sequences).
Next, we need to consider the magnitude of the
phylogenetic signal in the data (i.e. the robustness of
the cladograms). For those methods with an optimality criterion,
permutation
tests were used. Twohundred permutations
of the data were produced for
each model and each tree-building
method, and the
percentage of these replicates that produced
trees
that were at least as optimal as the observed tree was
calculated. The Phylip program implements this option for its tree-building
methods. For the Parsimony
analyses, some of the permutations
were performed
using the RandomCladistics
3.0 computer program
(Siddall, 1994); for the remainder, the Phylip program was used to create the permuted replicates and
these were then individually
fed into the PAUP
program.
Finally, we need to decide how we are going to
assess the magnitude
of the support that the data
have for the monophyly
of Sarcocystis. Bootstrap
resampling was used, which is implemented
in both
the Phylip and PAUP programs. Two-hundred
bootstrap replicates were produced for each model and
each tree-building
method, and the percentage of the
trees derived from these replicates that indicated
monophyly
of Surcocystis was calculated.
Results. Three cladograms
resulted from the 8
analyses (Fig. 5), with each of the optimality methods
finding a single most-optimal
tree for each analysis.
The Neighbor-joining
and Maximum-likelihood
analyses produced
the same tree irrespective
of
the model used (Table 3), this tree supporting
monophyly
of Sarcocystis.
However, the Weighted-parsimony
method produced different trees for the 2 models (Table 3), both
supporting monophyly of Surcocystis, but differing in
the relative placement of S. muris and S. neurona.
However, for the model in which transitions
and
transversions were equally probable, the tree in Fig.
5A is only one step longer (i.e. one more characterstate change) than the tree in Fig. 5B, and so there is
actually very little conflict between the 2 methods.
This result emphasizes the importance of considering
sub-optimal
trees in a cladistic analysis.
The Unweighted
least-squares method produced
the same tree irrespective of the model used {Table
3), but this tree does not support monophyly
of
Surcocystis, as S. muris and S. neurona are removed
from the clade. The contradiction
of monophyly
in
610
D. A. Morrison
, Eimeria
T. gondii
gondii
N. caninum
caninum
S. murk
neurona
S. neurona
muris
S. gigantea
gigantea
S.
fusiformis
fusiformis
S. tenella
S. tenella
\/
S. arieticanis
C
/
\S.
arieticanis
Eimeria
S. muris
S. neurona
T. gondii
N. caninum
S. gigantea
S.
fusiformis
S. tenella
S. arieticanis
Fig. 5. The 3 phylogenetic trees produced from the cladistic analysis of Sarcocysfis
Sarcocystis
ssrRNA. Table 3 shows which analysis
produced which of these trees. Trees (A) and (B) support monophyly of Sarcocystis,
whereas tree (C) does not,
this cladogram is supported only by a branch with
negative length (i.e. the branch from the ancestor
of the ingroup
to the ancestor of T. gondii+
N. caninum+S
gigantea+S. fusiformis+S.
tenella+S.
arieticanis).
This situation is not realistic, and so
the tree cannot be considered seriously as a possible
representation
of the real evolutionary
history of
these taxa. If this tree-building
method is constrained
to use only positive branch lengths (which is an
option
in the Phylip program),
then the cladogram produced does indeed support monophyly
of
Sarcocystis using both models (they produce the
cladogram shown in Fig. 5A).
The permutation
tests indicate that there is very
strong phylogenetic
structure in these ssrRNA data,
as no permutations
were found that produced
trees that were anywhere near as optimal as those
produced by the original data set (Table 3). The
phylogeny
of Sarcocystis can thus be usefully
evaluated using this data set.
The bootstrap
resampling
indicates
relatively
strong
support
for the Sarcocystis
clade (i.e.
Sarcocystis is monophyletic
in more than 85% of the
replicates) for all of the methods in which it occurs
(Table 3). This support is apparently stronger (i.e. the
bootstrap percentage is higher) when transitions are
considered to be more likely than transversions. Even
the Unweighted least-squares method provides some
support for monophyly, because the negative branchlength that contradicts
the monophyly
is actually
quite short.
It is thus reasonable to conclude from this analysis
that the ssrRNA sequence data do support monophyly of Sarcocystis, and thus also support the way in
Invited
Table
3-Results
Tree-building
method”
Neighbor-joining
ti=tv
ti=2tv
Unweighted
least-squares
ti=tv
ti=2tv
Weighted-parsimony
ti=tv
ti=hv
Maximum-likelihood
ti=tv
ti=2tv
of the cladistic
Review
analysis
Optimality
measure
Treeb
-e
-e
611
of
Surcocystis ssrRNA
Permutation
percentagec
Bootstrap
percentaged
A
A
-e
85
91.5
0.00241’
0.00335r
C
c
0
0
25
42.5
3298
473h
B
A
0
0
91
98
- 2499.7’
-2502.1’
A
A
0
0
99
99.5
e
“ti=tv,
transitions
and transversions
equal; ti=2tv.
transitions
twice as likely as transversions.
‘As shown in Fig. 5.
‘Percentage
of the permutation
replicates
that produced
trees at least as optimal as the observed
tree.
dPercentage
of the bootstrap
replicates
that support
monophyly
of Sarcocystis.
‘No optimality
criterion,
and so no calculations
possible.
‘Sum of squares.
aNumber
of character-state
changes.
‘Number
of weighted
character-state
changes.
‘Log-likelihood.
which the Sarcocystidae is currently divided into 2
subfamilies
(if the recently-described
Neospora is
included in the Toxoplasmatinae)
(note that in a
Popperian sense the data actually “fail to disprove”
the hypothesis rather than “support”
it). This conclusion is robust both to variations in the evolutionary model and to the tree-building
method used. It is
not, however, necessarily robust to the sequence
alignment used (see Ellis & Morrison,
1995).
There does, however, seem to be some uncertainty
with respect
to the placement
of Smuris and S.
neurona (which is the source of non-monophyly
detected by the previous studies of ssrRNA referred to
above). This uncertainty is only likely to be resolved
by including
in the analysis other species that are
closely-related to these 2 species (i.e. that will join the
tree on the terminal branches leading to these 2
species). This is the obvious direction to take for
future research into the question
posed for the
analysis presented here.
Some advice for phylogeny reconstruction. The following is a list of topics that need to be considered
when carrying out a cladistic analysis. The topics are
more-or-less in the order in which they will need to be
considered in practice.
Include in the analysis all of the taxa for which
there are data. Adding or deleting any taxon may
affect
the outcome
of the analysis.
This is one of
the biggest sources of problems
when analysing
molecular data.
Include samples from more than 1 individual
or
population if possible. This is the norm when assessing
morphological
characters,
because if intra-taxon
variability exists then it will be confounded with intertaxon variability in the analysis. For molecular data, a
consensus sequence can be used for each taxon.
The ingroup must be monophyletic
for the cladogram to accurately reflect phylogenetic
history. If
the analysis shows that the ingroup and outgroup
taxa are inter-mixed
in the cladogram,
then it is
not possible to root the cladogram in such a way
that the ingroup
is monophyletic.
You should
thus seriously consider your original rationale
for
assuming monophyly.
Long
branches
on a cladogram
(indicating
apparently extensive phylesis) should be avoided if
this is possible. They can often be shortened by
including taxa that join the tree on these branches
(i.e. the branches actually show speciation rather
than phylesis, but they are not doing so because the
relevant taxa are not in the data set).
The outgroup should consist of more than 1 taxon
closely-related
to the ingroup. The more distantlyrelated is the outgroup then the more arbitrary is the
apparent position of the root on the cladogram.
612
D. A. Morrison
For molecular data, use entire sequencesif they are
available. There is no reason to expect part of a gene
sequence (effectively a sample) to reflect accurately
the total gene sequence, unless all of the nucleotide
positions agree on the phylogenetic branching order.
Homology assessments should be taken very
seriously. For molecular data, this means that sequence alignment should be given careful consideration, using models of secondary structure if they are
available. If computer programs are used, then vary
the weighting parameters available in order to detect
those parts of the sequence alignment that are not
robust, and delete these regions from the analysis.
Assess the characteristics of the data before the
cladogram is constructed (e.g., GC-content for
nucleotide data), in order to choose rationally among
the available tree-construction algorithms.
Use several cladogram-construction algorithms if
this seemsto be appropriate for the data. If heuristic
tree-search methods are used then describe them
precisely, so that the likely successof having found
the optimal tree can be assessed. For nucleotide
data, correct for multiple character-state changes if
possible.
Assessthe magnitude of the phylogenetic signal in
the cladogram.
Assessthe robustness of the monophyletic groups
represented on the cladogram.
Quantitatively compare the cladograms if there is
more than one (e.g., multiple optimal trees, trees
from different cladogram-construction algorithms, or
trees from different data sets).
Remember that the cladogram represents a series
of hypotheses that are amenable to further test. It is
not a representation of reality, nor is it the final word
on the phylogeny of the taxa analysed.
Conclusion.
Many biologists treat data analysis in
a manner that is completely antithetical to their
apparent attitude to the other, more biological
aspects of their scientific pursuits (cf. Felsenstein,
1988). In particular, there is a widespread view
among non-experts that there should be only 1
correct method for phylogenetic data analysis, and
that it is about time that the experts told us what it is.
This view is clearly rather naive, because it assumes
that all phylogenetic data sets have identical characteristics. This is patently untrue, as it will be for UN
data sets(whether biological or not) that incorporate
an historical component. Furthermore, currently no
methods are simultaneously efficient, powerful, consistent and robust (Penny et al., 1990, 1992), and so
there is no single ideal method.
The future development of cladistic techniques will
presumably follow the well-documented path taken
by statistics, in which a series of mathematical tests
have been developed (and are still being actively
developed) that make different assumptions about
the nature of the data to be analysed, so that after the
data have been evaluated an informed decision can
be made about which test is the most appropriate for
the particular task at hand. Thus, out of the current
plethora of phylogenetic techniques should emerge a
subset of mathematical methods that are known to be
robust and consistent under certain circumstances,
and it will be from amongst these methods that an
objective choice (based on efficiency and power) will
be made by the cladist.
The current vogue for simply presenting the results
of analyses using several tree-building methods is
thus both creditable and naive. It is creditable
because it emphasizes our current uncertainty about
cladistic analysis; and it is naive because there
appears to be no rationale being used for the choice
from among the available methods. Clearly, what
must be done for each phylogenetic data set is for the
nature of the data to be evaluated, and then for a
reasoned choice to be made about which methods
might be appropriate for subsequent analysis, along
with an assessment of the support for the phylogenetic hypotheses generated. Two recent studies
that incorporate a carefully-reasoned evaluation of
the data, followed by a series of phylogenetic
analyses that are themselves then subjected to reevaluation, are those of Lento et al. (1995) and
Penny et al. (1995), and these could serve as useful
models.
Acknowledgements-Thanks
to
Steve
Barker,
Peter
Baverstock,
Dave
Booth,
Mike
Crisp,
John Ellis, Dan
Faith, Alan Johnson
and John Trueman
for commenting
on
an earlier version
of the manuscript;
and to John Ellis for
providing
the ssrRNA
data file.
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