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POINTS OF VIEW
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Received 23 September 1997; accepted 15 October 1998
Associate Editor: D. Cannatella
Syst. Biol. 48(2):399-406, 1999
Apomorphy Distribution Is an Important Aspect of Cladogram
Symmetry
PAUL N. PEARSON
Department of Earth Sciences, University of Bristol, Queens Road, Bristol BS8 1RJ, United Kingdom;
E-mail: [email protected]
In recent years there has been a great deal
of interest in the balance of cladograms,
which has generally come to be accepted
as meaning the extent to which the internal
nodes subtend clades of equal size (Fig. 1).
In particular, several studies have suggested
that a higher proportion of real cladograms
culled from the literature are unbalanced
(comb-shaped or pectinate) than would be
expected if they were produced by a random Markovian branching process of speciation (Colless, 1982; Guyer and Slowinski, 1991, 1993; Heard, 1992; Mooers et al.,
1995). One reason for the interest is methodological: If cladograms are statistically
unbalanced, they will contain a higher proportion of long branch lengths than would
otherwise be expected, which has implications for the accuracy with which they reect true phylogeny (Rohlf et al., 1990). A
more fundamental reason for the interest,
however, is that the Žndings may provide
important information about patterns and
processes of evolution (Heard, 1992, 1996;
Kirkpatrick and Slatkin, 1993; Mooers and
Heard, 1997; Bond and Opell, 1998).
A variety of potential methodological artifacts might produce a tendency for imbalance in cladograms, even if no such pattern
exists in the underlying phylogeny (Colless, 1982, 1995; Guyer and Slowinski, 1991;
Mooers et al., 1995; Huelsenbeck and Kirkpatrick, 1996). Nevertheless, if the methodological problems can be resolved (e.g., Farris and Källersjö, 1998), or at least if their effects can be adequately quantiŽed, it should
be possible to study patterns of evolution
through using cladogram shape. This Želd
is in its infancy (Mooers and Heard, 1997).
Perhaps the most fundamental question that
cladograms may help resolve is whether
evolution is largely stochastic and nonprogressive (e.g. Gould, 1988), or if phylogenies contain ingrained asymmetry, implying
nonrandom differences in the evolutionary
success of species.
An important aspect of cladogram symmetry has been overlooked in previous work
on the subject, namely, the distribution of
apomorphies. As discussed by Mindell et al.
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SYSTEMATIC BIOLOGY
VOL. 48
(1989, 1990) and Omland (1997), we have no
reason to presume that morphological characters are acquired in a clock-like fashion,
randomly across a particular tree. Information on apomorphy distribution may be crucial for distinguishing the evolutionary patterns that may have produced imbalance in
a cladogram. I offer suggestions about approaches for the measurement of apomorphy distribution and, in particular, I propose
an index for comparing the diversities of
clades subtended by relatively apomorphic
and plesiomorphic sister taxa. In this paper,
the symmetry of a cladogram refers not only
to the balance, but also to other factors, including the distribution of apomorphies (for
example, a balanced cladogram may have an
asymmetrical distribution of apomorphies).
STRATOPHENETIC TREES
This contribution has grown from a
paleontological study (Pearson, 1998) of
symmetry in “stratophenetic” (Gingerich,
1990) species-level phylogenies of fossil
groups, which are used routinely for biostratigraphy. Unlike cladograms, these paleontological phylogenies are constructed
from stratigraphically ordered fossil samples in which both speciations and extinctions are indicated. They tend to have an
unequal-branching or budding conŽguration, such that so-called ancestral species
persist through speciation events to coexist
with their descendants (see also the simulated phylogenies in classic paleontological
works such as Raup et al. [1973] and Stanley
[1979]). The polarity of the branching events
in such trees provided the basis for two
principal tests for phylogenetic asymmetry, called the “Ancestor–Descendant (A-D)
Speciation Test” and “A-D Extinction Test”
(Pearson, 1998). In analyzing large trees of
various fossil groups (foraminifera, nannoplankton, and graptoloids) for the various
patterns shown in Figure 2, I found that,
in general, descendant species tend to have
had both a higher probability of speciation
and, independently, a lower probability of
extinction than their coexisting ancestors
(Pearson, 1998). This result corresponds to
the so-called step-series pattern of evolution
discussed by Simpson (1953:219-221) .
FIGURE 1. (a) A perfectly balanced cladogram. (b) A
perfectly unbalanced cladogram. If we assume a random speciation model, most real cladograms would
be expected to have a topology between these two
extremes.
Cladograms, of course, have a bifurcating V-shape conŽguration, and so, at Žrst
sight, the approach used in the paleontological study discussed above would seem
to be inapplicable to them. However, the
bifurcating conŽguration of a cladogram
is a methodological necessity and not in
any way evidence that speciation actually
was equally divergent in a morphological
sense. Obviously, if a real speciation event
was asymmetrical, wherein one daughter
species changed its morphology with respect to the ancestor more substantially than
the other, the cladogram would still be constrained to a bifurcating conŽguration. Nev-
1999
POINTS OF VIEW
401
(Mayr, 1974); a similar pattern also can occur
under sympatric conditions (e.g., Sorhannus
et al., 1988; Lazarus et al., 1995; Pearson et al.,
1997). It is important to investigate the signiŽcance of Hennig’s deviation rule in the
context of cladogram symmetry.
FIGURE 2. Patterns of asymmetry in stratophenetic
phylogenies that have a budding topology (Pearson, 1998). In these diagrams, vertical lines represent
the stratigraphical occurrence of Linnaean typological
species. The horizontal axis represents morphological
separation, but the scale is arbitrary. In each case, an
ancestor and its descendant coexist at time t1 . (a) The
Ancestor–Descendant Speciation Test. In example 1, a
new species is derived from the ancestor of the previous
bifurcation; in example 2, it is derived from the descendant. (b) The Ancestor–Descendant Extinction Test. In
example 3, the ancestor becomes extinct Žrst; in example 4, the descendant becomes extinct Žrst. In a random
model of phylogeny, we should not be able to predict
which of two species at t1 is most likely to speciate or become extinct Žrst. In Pearson (1998), the frequencies of
these patterns were summed across the nodes of large
stratophenetic phylogenies of various fossil groups and
compared by using the chi-square statistic. It was found
that typically, ancestors were simultaneously less likely
to branch and more likely to become extinct than their
descendants, producing a “step-series” type pattern of
evolution.
ertheless, the two resulting daughter species
would be likely to possess unequal numbers of apomorphies (Fig. 3). In an extreme
case, one of the daughter species might be
a “metaspecies,” possessing no unique apomorphies at all (see Smith, 1994:132) .
Hennig (1966:207) proposed the rule that
“when a species splits, one of the two daughter species tends to deviate more strongly
than the other from the common stem
species” (see Farris, 1976). This expectation
accords with the allopatric speciation model
A MARKOVIAN BRANCHING MODEL
Let us assume an extreme case in which
all speciations are asymmetrical in a morphological sense and are expressed on the
cladogram as nodes about which there are
unequal numbers of apomorphies. Figure
4 shows the Žrst three iterations of a random Markovian branching model, akin
to that discussed by Harding (1971) and
used in many subsequent studies of cladogram balance. If we examine the cladograms
FIGURE 3. (a) A speciation that is equally bifurcating in a morphological sense (left) would be expected
to produce daughter species with equal numbers of
apomorphies (right). (b) A speciation event that is unequally branching in morphology would be expected to
produce sister species with unequal numbers of apomorphies. A pure budding event in which the ancestral species persists unchanged through the speciation
event produces a “metaspecies” that lacks autapomorphies. A, a taxon equally or more apomorphic than its
sister; P, a taxon that is plesiomorphic compared with
its sister.
402
SYSTEMATIC BIOLOGY
VOL. 48
FIGURE 4. A random Markovian branching algorithm produces six cladograms that have four terminal taxa.
In terms of balance, there are only two distinct topologies in the top row of this Žgure (see text). However, when
plesiomorphic and apomorphic sister taxa are distinguished (P = plesiomorphic, A = apomorphic), there are Žve
distinct topologies. If branching order is also considered, there are six.
in the top row of Figure 4 and consider Žrst
the balance, we can see that only two distinct
topologies are present: a balanced topology
(the middle two) and an unbalanced topology (the rest). Note that the unbalanced trees
are considered as having the same topology because one can rotate freely about the
nodes of a cladogram to produce identical
conŽgurations. Various authors have compared the topologies of real cladograms of
different sizes with their expected frequencies as predicted by this model (e.g., Simberloff et al., 1981; Savage, 1983; Guyer and
Slowinski, 1991). However, if we also consider the distinction between apomorphic
and plesiomorphic sister taxa, the various
topologies can no longer be considered identical because, effectively, one can no longer
rotate freely about the nodes. In the case of
dendrograms, in which the temporal order
of branching is recorded, all six trees are distinguishable. In the case of cladograms, the
two perfectly balanced cladograms in the
third generation are indistinguishable because the relative branching order in different parts of the phylogeny is not preserved,
but the others are distinct.
PATTERNS OF EVOLUTION
As is clear from the branching model (Fig.
4), apomorphy distribution can be consid-
ered an aspect of the symmetry of a cladogram. But what might it indicate, in an evolutionary sense? Consider two contrasting
patterns of evolution, iterative and stepseries evolution (Fig. 5). In iterative evolution, a series of taxa are repeatedly derived from a more conservative ancestral
stock. This stock is, of course, agrantly paraphyletic, but it may preserve a coherent
aspect in the eyes of traditional taxonomists
by virtue of the fact that it changes little
over time by comparison with its more apomorphic descendants (Mayr, 1974). Such a
pattern may occur if the ancestral group
occupies a more stable environment than
its descendants. An example of this is the
stickleback Žsh Gasterosteus, in which a
stable marine “species” has apparently
given rise to vast numbers of short-lived descendant species in transient freshwater environments (Schluter and McPhail, 1992). Iterative evolution also has been invoked by
paleontologists to account for the multiple
evolution of shelf-sea taxa, like particular
kinds of ammonites and trilobites, from
more conservative and long-lived deepwater ancestral groups (Raup and Stanley,
1978:365–368).
Step-series evolution is, in a sense, the
opposite of iterative evolution. In this pattern, newly evolved taxa are more likely to
1999
POINTS OF VIEW
give rise to further taxa than are their coexisting ancestral species (and they may also
be less likely to become extinct). A stepseries pattern may result from cladogenetic
evolution along an environmental gradient
(Grant, 1963) or be a consequence of the competitive superiority of newly evolved taxa
over preexisting forms (Simpson, 1953).
The key point of this contribution is that
although the iterative and step-series evolutionary processes are opposites, both tend
to produce an unbalanced cladogram. The
cladograms may be distinguished, however,
by their distribution of apomorphies (Fig. 5).
An iterative-type process would be expected
to produce a comb-shaped cladogram in
which the apomorphies are concentrated on
the external (terminal) branches. In contrast,
a step-series process would be expected to
produce a comb-shaped cladogram in which
the apomorphies are concentrated on the
internal (nonterminal) branches. Therefore,
by considering apomorphy distribution, it is
possible to differentiate these evolutionary
patterns.
MEASURING APOMORPHY D ISTRIBUTION
A variety of evolutionary processes may
affect the distribution of apomorphies on a
cladogram, and consequently, a variety of
fruitful approaches may be taken in assessing that distribution. One aspect has already
been examined in the pioneering study of
Mindell et al. (1989, 1990), who used lizard
allozyme data to test the punctuated equilibrium model of evolution by searching for
a correlation between the number of branching events a species-lineage has experienced
and the number of characters it has acquired. To do this, they assumed a clock-like
null model in which character changes occurred randomly on all branches. Because
they found a correlation, their study was
upheld as supporting the punctuated equilibrium model. However, this has recently
been contested on the grounds that an inappropriate method of data coding was used
and that in fact there are a large number
of equally parsimonious trees for the data,
many of which may not exhibit such a correlation (Murphy and Lovejoy, 1998).
403
FIGURE 5. (a) An iterative pattern of evolution translates into an unbalanced cladogram in which apomorphies are concentrated on external (terminal) branches.
(b) A step-series pattern of evolution translates into an
unbalanced cladogram in which apomorphies are concentrated on internal branches.
Another simple method of assessing apomorphy distribution allied to the approach
of Mindell et al. (1989) is to compare the
number of apomorphies on internal and
external branches and see if this proportion
deviates signiŽcantly from randomness.
Alternatively, one could ignore the actual
number of apomorphies and instead determine simply whether internal branches tend
to be more or less apomorphic than their sisters. Both these approaches assume a null
model equivalent to random branching and
stasis, rather than clock-like acquisition of
characters as used by Mindell et al. (1989).
Such methods may provide a Žrst indication
of whether imbalance on a cladogram is due
to the iterative or to the step-series processes
discussed above.
Perhaps the most interesting hypothesis
to test is whether the fact a taxon is relatively apomorphic or plesiomorphic (compared with its sister) inuences its subsequent evolutionary success (as measured
by the diversity of the clade it subtends).
The simple measures discussed above do
not take account of the depth on the clado-
404
SYSTEMATIC BIOLOGY
gram at which the internal branches are situated (i.e., how close they are to the root).
If we choose instead to give more weight to
the deeper branches because they subtend
larger clades, the best approach has to be
framed more directly in terms of cladogram
symmetry. I suggest using an index similar to Colless’s (1982) well-known index of
cladogram balance (I c ) as modiŽed by Heard
(1992). Colless’s index sums, over all (n – 1)
nodes in a cladogram with n tips, the numbers of tips subtended by the right-hand (TR )
and left-hand (TL ) branches at each node and
normalizes them as follows:
P
| TR – TL |
Ic =
(all interior nodes)
(n–1)(n–2)
2
(all interior nodes)
(n–1)(n–2)
2
number of possible values for trees of particular lengths is Žxed. If, for a given tree,
Ic < 1, I a may vary between –Ic and +Ic .
The index Ia does not take account of the
actual number of apomorphies that occur
on particular branches (i.e., the extent to
which branches are more or less apomorphic
than their sisters and whether or not the plesiomorphic sister taxon contains some number of apomorphies), but further modiŽcations could easily be suggested that take
those factors into account. In addition, if a
clock-like null model were preferred to a stasis null model, the number of apomorphies
on each branch could be normalized to an
estimate of elapsed time since branching.
(1)
The index may range from 0 (completely balanced) to 1 (completely unbalanced), but for
cladograms of Žxed n, only a restricted number of values are possible because of geometrical constraints; in particular, perfect balance can be obtained only in cladograms of
certain sizes. Note that, for any given node,
the portion of the cladogram considered as
being on the right-hand or left-hand side is
arbitrary, because in a cladogram one can rotate freely about the nodes. For both cladograms in Figure 5, Ic = 1.
To measure the relationship between the
apomorphic/plesiomorphic designation of
taxa relative to their sisters and the subsequent diversity of the clades they subtend (Ia ), we may simply adopt the convention that, for each node, the number of taxa
subtended by the more apomorphic branch
(TA ) must be subtracted from the number of
taxa subtended by the more plesiomorphic
branch (TP ). Hence,
P
(TA – TP )
Ia =
VOL. 48
(2)
This index may vary from –1 (in which internal branches are all relatively plesiomorphic
compared with their sisters, as in the top
cladogram of Fig. 5) to +1 (internal branches
are all relatively apomorphic, as in the bottom cladogram of Fig. 5). As with Ic , the
PROBLEMS WITH PROCEDURES AND DATA SETS
There are many potential difŽculties in applying such measures to real data. Ideally,
indices of apomorphy symmetry could be
considered alongside and integrated with
the existing indices of balance, the probability distributions of which are already
well understood (e.g., Shao and Sokal, 1990;
Heard, 1992; Guyer and Slowinski, 1993;
Rogers, 1993, 1994, 1996; Brown, 1994; Colless, 1995; Fusco and Cronk, 1995; Huelsenbeck and Kirkpatrick, 1996). Unfortunately,
apomorphy distribution is likely to be affected by the same biases in phylogenetic
analysis that plague studies of cladogram
balance (e.g., Huelsenbeck and Kirkpatrick,
1996). A particular problem is that many
cladograms are constructed by using very
few characters, leading to multiple equally
parsimonious trees with different distributions of characters. We can expect this to
make inferences based on apomorphy distribution unreliable. Another difŽculty is that
a high incidence of homoplasy would be
expected to obscure the historical pattern
of character acquisition on which the approach depends (cf. Sanderson, 1990). Also,
polytomies must somehow be taken into account, because they may indicate multiple
iterative evolution from an unchanging ancestral stock. Furthermore, there is the speciŽc problem identiŽed by Fitch and Bruschi
(1987), namely, that clades with relatively
few taxa are likely to provide less evidence
1999
405
POINTS OF VIEW
of character-state changes than are larger
clades. Also, one should determine whether
the “characters” analyzed are truly independent of one another before drawing any Žrm
conclusions (Emerson and Hastings, 1998).
In addition to the above, there are obvious
difŽculties in analyzing trees in which characters, taxa, or both have been consciously
or unconsciously selected for inclusion in
a study because they are considered to be
of particular use in elucidating an expected
phylogenetic pattern. For example, workers
may have selected multiple stem-group taxa
that lead in a step-wise manner to a more
completely sampled crown group of interest, giving an unbalanced topology. Similarly, there may be a bias towards choosing
characters that are expected to lie among the
internal nodes of a tree and so can distinguish clades, rather than characters that are
expected to lie on external branches and so
merely add further support in the form of
autapomorphies to taxa that are already well
differentiated through the use of other characters. Clearly, great care needs to be taken
in selecting suitable cladograms for analysis
and in assessing the potential biases induced
by the method of cladogram construction if
a meaningful measurement of apomorphy
distribution is to be expected.
PREDICTION
In conclusion, it is inappropriate to analyze real data sets before the problems outlined above have been properly investigated
and their effects estimated. Nevertheless,
the fact that several stratophenetic phylogenies from the better parts of the fossil record
have all been found to exhibit a strongly signiŽcant step-series pattern, as opposed to an
iterative pattern (Pearson, 1998), leads to the
following prediction: The preponderance of
pectinate cladograms in the literature is the
result of the relative success of apomorphic
taxa over their more plesiomorphic sisters,
where success is measured in terms of resistance to extinction or propensity for speciation. Thus, apomorphies will tend to be concentrated on the internal branches of cladograms, and if we apply the index I a to real
trees, the values are predicted to be positive
for most groups. Exceptions will be found
mainly in clades that have evolved repeatedly across a persistent environmental barrier between relatively stable and unstable
environments.
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Received 27 February 1998; accepted 1 August 1998
Associate Editor: R. Olmstead
Syst. Biol. 48(2):406–412, 1999
Reconciling Kingdoms with Codes of Nomenclature: Is It Necessary?
WILL H. BLACKWELL AND MARTHA J. POWELL1
Department of Biological Sciences, The University of Alabama, Tuscaloosa, Alabama 35487, USA
An inconsistency in taxonomy has been
the imperfect alignment between the kingdoms of organisms recognized and the three
a
Address correspondence to Dr. Martha J. Powell,
Department of Biological Sciences, Box 870344, The
University of Alabama, Tuscaloosa, Alabama 35487,
USA; E-mail: [email protected].
major codes of biological nomenclature:
zoological (ICZN, 1985), botanical (ICBN,
1994), and bacteriological (ICNB, 1992).
Hawksworth (1995) and Spamer and Bogan (1997) cited additional codes for cultivated plants and for viruses; however, it is
the three kingdom-speciŽc codes that concern us here. The question of kingdom and