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S YSTEMATIC BIOLOGY
WILLS , M. A. 1999. Congruence between phylogeny and
stratigraphy: Randomization tests and the Gap Excess
Ratio. Syst. Biol. 48:559–580.
WING , S. L., H. BAO , AND P. L. KOCH. 2000. An early
Eocene cool period? Evidence for continental cooling
during the warmest part of the Cenozoic. Pages 197–
VOL. 51
237 in Warm climates in Earth history (B. T. Huber,
K. MacCleod, and S. L. Wing, eds.). Cambridge Univ.
Press, Cambridge.
Received 18 December 2000; accepted 12 June 2001
Syst. Biol. 51(1):176–191, 2002
A Character-Based Method for Measuring the Fit of a Cladogram
to the Fossil Record
K ENNETH D. ANGIELCZYK
Department of Integrative Biology and Museum of Paleontology, 1101 VLSB, University of California,
Berkeley, California 94720, USA; E-mail: [email protected]
Although the history of life cannot be observed directly, several sources of information preserve a historical signal that allows
inferences about it. The phylogenetic relationships of organisms provide insight into
the order of appearance of clades and their
morphological evolution. The fossil record
also preserves information about the relative and absolute ages of clades and provides documentation of the existence of organisms that otherwise would be unknown.
Because only one true history exists, the signal preserved in each dataset ideally should
be the same, and so predictions based on
one can be tested with observations from the
other.
Several techniques are now available to
compare the Žt of a cladogram to the stratigraphic record (e.g., Gauthier et al., 1988;
Norell and Novacek, 1992a,b; Benton and
Storrs, 1994; Huelsenbeck, 1994; Siddall,
1998; Wills, 1999), and others use stratigraphic information directly in the construction of phylogenetic trees (e.g., Gingerich,
1979; Fisher, 1988, 1991, 1992, 1994, 1997;
Wagner, 1995; Clyde and Fisher, 1997;
Huelsenbeck and Rannala, 1997). All of these
methods use stratigraphic data associated
with taxa, proceeding from the premise that
the order of appearance of taxa on a cladogram and in the fossil record ideally should
be the same. However, cladograms also make
predictions about the order of appearance of
character states, predictions that can be compared with the order of appearance of these
states in the fossil record. Although to date,
a character-based approach has not been implemented, this type of congruence between
a cladogram and stratigraphy should be considered explicitly. Characters or complexes of
characters can evolve in a mosaic or stepwise
fashion, making it is possible for the order
of appearance of character states on a cladogram to conict with that of the fossil record,
even when the order of appearance of taxa
does not.
CHARACTERS , TAXA, AND S TRATIGRAPHY
The method proposed in this paper
is based on the principle that taxa are
hierarchically arranged lineages or clades
(or at least should be; the lineage/clade status of all taxa has not been tested). Because
lineages and clades cannot be studied directly, the distribution of synapomorphies is
the primary evidence used in reconstructing relationships among different lineages
or clades. Thus we recognize that Diictodon
and Eodicynodon (Fig. 1a) share a more recent
common ancestor than either does with Patranomodon (Fig. 1a), based on a pattern of
character-state distribution that we infer reects genealogy.
A similar process occurs when the stratigraphic range of a taxon is measured. By deŽnition, stratigraphic range implies a series of
specimens of a given taxon found to occur
in a sequence of rocks. Character states must
be used to recognize any individual specimen as a member of a particular taxon. The
earliest known occurrence of a unique, diagnostic set of character states is the Žrst appearance datum for the taxon, whereas the
latest occurrence provides a lower bound
for when the lineage became extinct. Thus,
2002
177
POINTS OF VIEW
FIGURE 1. (a) Patranomodon (redrawn from Rubidge
and Hopson, 1990), Eodicynodon (redrawn from Rubidge
and Hopson, 1990), and Diictodon (based on UCMP
V3694/42396), three genera of anomodont therapsids.
Note that each taxon is a lineage and that these specimens are recognized as members of a given lineage
based on their different suites of character states. Likewise, the distribution of character states allows inference of the cladogram showing their phylogenetic relationships. (b) Diagram of the stratigraphic ranges of
Patranomodon, Eodicynodon, and Diictodon. Each range is
made up of a series of specimens that have characters
diagnostic for each named lineage (taxon).
the fossil record actually records the appearance and disappearance of specimens having
unique combinations of character states that
are interpreted as diagnostic for different
taxa (Fig. 1b). In South Africa, the diagnostic set of features for Diictodon Žrst appears
in the lower Tapinocephalus Assemblage Zone
and can be found until its disappearance at
the end of the Dicynodon Assemblage Zone
(Rubidge, 1995).
In summary, character states are necessary
for recognizing taxa, and the fossil record
preserves the appearance and disappearance
of these diagnostic suites of characters. These
points are important to consider when measuring the Žt of a cladogram to the fossil
record. A cladogram is a branching diagram that shows the most-parsimonious
distribution of synapomorphies (Eldredge,
1979); when rooted, however, a deŽnite polarity of character transformation is established. The postulated order of appearance
can be compared with that preserved in the
fossil record, just as the appearance of taxa
on a cladogram can be compared to their
appearance in the fossil record (Angielczyk,
unpubl.). However, comparing the order of
appearance of character states rather than
taxa themselves more accurately reects how
taxa and their ranges in the fossil record
are recognized, as well as what a cladogram actually represents. Also, because character states often evolve in mosaic or stepwise fashions, the order of appearance of
character states on a cladogram may conict
with that of the fossil record, even when the
order of appearance of taxa does not. Finally,
a character-based comparison should allow
more precise measurements of incongruence
because the number of characters usually far
exceeds the number of taxa in a given dataset.
Several taxon-based methods to measure
the Žt of cladograms to stratigraphy have
been proposed, including the Spearman rank
correlation (Gauthier et al., 1988; Norell and
Novacek, 1992a,b), the relative completeness
index (RCI; Benton and Storrs, 1994), the
stratigraphic consistency index (Huelsenbeck, 1994), the Manhattan stratigraphic metric (Siddall, 1998), and the gap excess ratio
(GER; Wills, 1999), but there has been no
attempt to measure Žt by using a characterbased approach. Thus I propose a new stratigraphic metric, the character consistency
ratio, deŽned as follows:
CCR D 1 ¡ (i = n)
(1)
The variable i represents the number of
character-state changes required by a rooted
cladogram that are inconsistent with the fossil record. An inconsistent change is deŽned
as any character-state transformation that
178
S YSTEMATIC BIOLOGY
requires the relatively derived state to occur in the stratigraphically older member
of a pair of sister taxa (Fig. 2). Instances in
which a character-state change requires the
relatively derived state to occur in a clade
for which a sister group is of equal or older
stratigraphic age are considered consistent
with the fossil record (Fig. 2). A more detailed description and justiŽcation of these
deŽnitions is being prepared for publication
elsewhere (Angielczyk, unpubl.). The variable n is the total number of character-state
transformations required by a given cladogram (i.e., length). Possible values for the
CCR range from 0 (all changes are inconsistent with the fossil record) to 1 (all changes
are consistent with the fossil record).
Note that this method is appropriate only
for use with rooted cladograms; characterstate changes in an unrooted network have
no polarity and cannot be compared with the
polarized fossil record. Furthermore, when
calculating the CCR, one must take into account the local polarity of a particular character state. Thus, a globally basal character
state will be treated as a locally derived state
if a reversal has occurred in a clade with
a different locally basal state (Fig. 2). Also,
if a character state exhibits homoplasy in a
particular cladogram, each change to that
character state must be examined individually to determine whether it is compatible
FIGURE 2. Hypothetical cladogram highlighting
three character-state changes. Numbers represent the
stratigraphic interval in which each terminal taxon appears. A represents a character-state transformation that
is consistent with stratigraphy because both sister taxa
are of equal stratigraphic age (Type I consistent state
change). B also is consistent with the stratigraphic record
because the relatively derived state occurs in the stratigraphically younger lineage (Type II consistent state
change). Note also that although taxa 5 and 6 possess
the globally basal character state, this state represents
the derived state locally. C represents a character-state
transformation that is inconsistent with the stratigraphic
record because the relatively derived state occurs in the
stratigraphicall y older sister taxon (inconsistent state
change).
VOL. 51
with the fossil record. These considerations
are especially important with fossil data because these datasets frequently show signs of
character-state exhaustion (Wagner, 2000a).
Thus, homoplasies and reversals should become more common as younger taxa are
added to a given dataset (Wagner, 2000a).
Cases in which both taxa joined by a node
possess different relatively derived states are
considered consistent with the fossil record.
Although some taxon-based stratigraphic
metrics have been proposed as explicit measures of the completeness of the fossil record
(e.g., RCI), I do not intend the CCR to be
used in this manner. The CCR only measures
how well the order of appearance of character states on a particular cladogram matches
that observed in the known fossil record. Incongruence between the two datasets could
be the result of poor sampling in the fossil
record, an inaccurate cladogram, or both, and
the CCR cannot distinguish between these
options. However, the CCR might be useful for choosing a subset of preferred cladograms from a larger set of morphologically
parsimonious cladograms if we assume that
cladograms that Žt the known fossil record
well are better supported or likely to be more
accurate than those that Žt more poorly. Such
a procedure would be analogous to Analysis
1 of Clyde and Fisher (1997), although the
method used to calculate stratigraphic debt
is different. Fox et al. (1999) found that stratocladistics, which simultaneously seeks to
maximize morphologic parsimony and the
Žt to stratigraphy, recovered the correct phylogeny in more than twice as many cases
as cladistic analyses in which stratigraphy
was ignored. Inaccurate cladograms also are
known to imply erroneous gaps and range
extensions for taxa in the fossil record
(Wagner, 2000b; Wagner and Sidor, 2000).
Furthermore, simulation and empirical studies (e.g., Kuhner and Felsenstein, 1994;
Lamboy, 1994; Wagner, 1999) have shown
that parsimony can be misled in cases in
which character-transition patterns are biased (e.g., driven trends sensu McShea,
1994), resulting in inaccurate cladograms
that imply large and erroneous gaps in the
fossil record. Given these observations, there
may be some a priori justiŽcation for preferring cladograms with relatively high CCR
values. However, before the CCR can be regarded as a useful metric, an understanding of possible biasing factors in necessary.
2002
POINTS OF VIEW
In other words, if two cladograms have
different CCR values, is the difference caused
only by their Žt to the fossil record or is
it also inuenced by factors such as speciation rate, the probability of character-state
change, or the completeness of the fossil
record?
In the following analysis, I use simulations to examine how frequently derived
character states are sampled before basal
states are sampled in the fossil record under variable evolutionary and preservational
rates. These simulations provide insight into
how the CCR might be affected by various
aspects of the fossil record. Furthermore, to
compare the CCR with taxon-based methods, I apply it and two common taxon-based
stratigraphic metrics to two versions of a
sample dataset.
M ETHODS
Simulation Analysis
The simulation analyses were performed
by using the program CHSTER (CHaracter
STate Evolution Routine). CHSTER, was developed by David Fox, Daniel Fisher, and
Lindsey. Leighton to generate sample datasets to study stratocladistics, and is described
in some detail in Fox et al. (1999). The simulations conducted here were used to examine
how frequently derived character states are
sampled before basal character states are in
the fossil record under various levels of completeness, various rates of speciation (¸) and
extinction (¹), and various probabilities of
anagenetic and cladogenic changes in character states. Because the frequency at which
derived character states appear in the fossil
record before basal states is the raw material
for calculating the CCR, these simulations
should provide insight into how the CCR is
affected by these parameters. I did not calculate CCR values for the simulated datasets
because that would have been prohibitively
time-consuming.
Five main groups of simulations were run.
In the Žrst, the speciation rate was allowed
to vary from 0.15 to 0.90 in 0.1-unit increments after the Žrst increase to 0.20 (i.e., 0.15,
0.20, 0.30, and so forth). The extinction rate
remained constant (0.08), as did the probabilities of cladogenic and anagenetic characterstate changes (both 0.04; reversals were not
allowed in either case). Ten replicate simulations were run for each speciation rate, and
179
for each replicate, 10 datasets were generated, representing fossil records of 10% to
100% completeness. Thus, for the Žrst group
of simulations, a total of 900 datasets (9 speciation rates £ 10 replicates £ 10 datasets per
replicate) was generated. Each dataset was
then examined to determine how frequently
derived character states were sampled in the
fossil record before the basal characters states
were for all characters in which both “0” and
“1” evolved.
In the second group of simulations, the
speciation rate and both probabilities of
character-state changes remained constant
(0.20, 0.04, and 0.04, respectively), whereas
the extinction rate varied from 0.05 to 0.20
in 0.05-unit increments. Again, 10 replicate
simulations were run for each extinction rate,
and each replicate included 10 simulated fossil records of variable completeness.
For the third group of simulations, the speciation and extinction rates remained constant (0.20 and 0.08, respectively). The probability of cladogenic character-state change
was allowed to vary from 0.01 to 0.09 in 0.01unit increments, and the probability of anagenetic character-state change was Žxed at
0.00. Again, 10 replicate simulations were run
for each probability of character state change,
and each replicate included 10 simulated fossil records of variable completeness.
Because the probability of cladogenic
character-state change is directly related to
the speciation rate, the fourth group of
simulations considered the cumulative effects of these two parameters. For these simulations the extinction rate and the probability of anagenetic character-state change
were held constant (0.08 and 0.00, respectively). The speciation rate also was held
constant (0.20), but the probability of cladogenic character-state change was allowed to
vary so that the product of the speciation
rate multiplied by the probability of cladogenic character-state change varied from 0.01
to 0.09 in 0.01-unit increments. Ten replicate
simulations were run for each total probability of character-state change, and each replicate included 10 simulated fossil records of
variable completeness.
For the Žfth group of simulations, the
speciation and extinction rates, as well as
the probability of cladogenic character-state
change remained constant (0.20, 0.08, and
0.00, respectively). The probability of anagenetic character-state change was allowed
180
S YSTEMATIC BIOLOGY
to vary from 0.01 to 0.09 in 0.01-unit increments. Ten replicate simulations were run
for each probability of character state change,
and each replicate included 10 simulated fossil records of variable completeness.
The simulated datsets differ from real data
in several ways. For example, all of the
characters were constrained to be binary
and reversals were not allowed. None of
the datasets contained missing or misidentiŽed characters. Furthermore, the rates of
character-state change used in each simulation did not vary among lineages or clades
or between characters or character states,
although rate heterogeneity has been observed in real datasets (e.g., Smith et al., 1992;
Jackson and Cheetham, 1994; Sanderson and
Donoghue, 1994; Purvis et al., 1995; Flynn,
1996; Wagner, 1997, 2001). The evolution of
all characters was independent of all other
characters. Speciation and extinction rates
were treated as independent in the simulations in which they were allowed to vary, although in reality they probably are linked
(Raup, 1985). Also, these rates were constant for all lineages and clades in a given
simulation, which clearly has not been the
case in the real history of life. When taxa
were removed from datasets to simulate
an incomplete fossil record, the deletions
were random. Thus, differences in preservation potential between taxa—resulting from
factors such as geographic range, environmental preference, or possession of certain
character states—were ignored. Finally, I
did not examine how taxonomic philosophy
might affect the CCR, although this has been
shown to be a potential source of bias for
several other stratigraphic metrics (Wagner,
2000b; Wagner and Sidor, 2000).
Empirical Analysis
The dataset used in this analysis is from
a recent phylogenetic study of dicynodont
therapsids (Angielczyk, 2001). Dicynodonts
are a diverse group of nonmammalian
synapsids known from the Permian and Triassic of every continent. The stratigraphic
record of dicynodonts, especially that of the
Karoo Basin of South Africa, has a long history of study (e.g., Seeley, 1892; Broom, 1906;
Watson, 1914; Keyser and Smith, 1977–1978;
Kitching, 1977; Rubidge, 1995; Lucas, 1996,
1998) and has been well-collected, making
dicynodonts an appropriate choice to study
comparisons of phylogeny and stratigraphy.
VOL. 51
Two versions of this dataset were used.
The Žrst, a preliminary, unpublished version of the dataset presented in (Angielczyk,
2001), consists of 39 morphologic characters
coded for 20 ingroup taxa and 2 outgroup
taxa. The second version of the dataset is
that presented in Angielczyk (2001) and consists of 40 morphologic characters coded for
18 ingroup taxa and 2 outgroup taxa. Although based on the Žrst dataset, two taxa
were excluded, one character was added and
most other characters were highly modiŽed,
and all taxa were recoded in the construction of the second dataset. Although the two
datasets are generally similar, they produce
different results and provide an instructive
example of how changes in interpretations
of characters and taxa might affect the CCR.
Both datasets were subjected to maximum parsimony analysis by the heuristic
search algorithm of PAUP¤ 4.0b4a (Swofford,
2000). One thousand random addition sequence replicates were run to prevent the
searches from becoming trapped in a local
treelength minimum (Maddison, 1991). All
characters were treated as unordered and
equally weighted.
The analysis of the Žrst version of the
dataset recovered 13 most-parsimonious
cladograms with a length of 103 steps
(Fig. 3a). Analysis of the second dataset
resulted in a single most-parsimonious
cladogram with a length of 125 steps (Fig. 3f).
Details of the analyses and results as well as
justiŽcations for the characters and taxa used
are presented in Angielczyk (2001).
To measure the Žt between the mostparsimonious cladograms and stratigraphy,
I computed the CCR and two taxonbased stratigraphic metrics, RCI (Benton and
Storrs, 1994) and GER (Wills, 1999), for
all of the most-parsimonious cladograms.
The RCI compares the minimum implied
gaps (Fisher, 1982; Paul, 1982; Smith, 1988;
Norell and Novacek, 1992a,b; Weishampel
and Heinrich, 1992; Norell, 1993; Benton and
Storrs, 1994) required by a phylogenetic hypothesis to the sum of the simple range
lengths (Storrs, 1993) of the included taxa. A
high RCI value corresponds to a good Žt to
stratigraphy. Also, because the RCI takes into
account time duration and missing time, it
may provide an estimate of the completeness
of a clade’s fossil record implied by a phylogenetic hypothesis (Hitchin and Benton,
1997a,b; but see Alroy, 2000; Wagner, 2000b).
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POINTS OF VIEW
181
FIGURE 3. (a) Strict consensus of 13 morphologically most-parsimonious cladograms from the Žrst dataset.
(b) Preferred topology of the RCI and GER (strict consensus of three morphologically most-parsimonious cladograms
from the Žrst dataset with the best RCI and GER scores). (c) Preferred topology of the CCR under the default character
optimization algorithm of MacClade 3.08 (morphologically most-parsimonious cladogram from the Žrst dataset
with the greatest CCR score under this optimization). (d) Preferred topology of the CCR under the ACCTRAN
optimization algorithm of MacClade 3.08 (strict consensus of two morphologically most-parsimonious cladograms
from the Žrst dataset with the greatest CCR score under this optimization). (e) Preferred topology of the CCR
under the DELTRAN optimization algorithm of MacClade 3.08 (strict consensus of three morphologically mostparsimonious cladograms from the Žrst dataset with the greatest CCR score under this resolving option). (f ) Single
morphologically most-parsimonious cladogram from the second dataset.
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VOL. 51
S YSTEMATIC BIOLOGY
TABLE 1. Imbalance Index (Im), relative completeness index (RCI), gap excess ratio (GER), and default,
ACCTRAN, and DELTRAN character consistency ratio (CCR) values for the most parsimonious cladograms
of this study. Note that several of the cladograms with identical RCI and GER scores have unique CCR scores.
Cladograms 1 to 13 are from the unpublished preliminary dataset, whereas cladogram 14 is from the dataset
presented in Angielczyk (in press).
CCR
Cladogram
Im
RCI
GER
Default
ACCTRAAN
DELTRAN
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0.573
0.480
0.591
0.591
0.503
0.497
0.497
0.520
0.520
0.515
0.532
0.509
0.509
0.573
0.487
0.282
0.487
0.487
0.410
0.282
0.282
0.410
0.410
0.436
0.385
0.410
0.410
0.632
0.810
0.683
0.810
0.810
0.762
0.683
0.683
0.762
0.762
0.778
0.746
0.762
0.762
0.863
0.728
0.641
0.738
0.728
0.718
0.670
0.641
0.728
0.718
0.777
0.738
0.786
0.757
0.897
0.689
0.563
0.699
0.699
0.641
0.573
0.573
0.650
0.650
0.670
0.631
0.621
0.660
0.873
0.680
0.563
0.689
0.670
0.660
0.583
0.553
0.680
0.660
0.718
0.728
0.728
0.728
0.817
The RCI is affected by the choice of taxa
and magnitude of time examined (Benton
and Storrs, 1994; Hitchin and Benton, 1997a)
as well as the number of taxa, clade asymmetry, taxonomic philosophy, diversiŽcation
method (i.e., budding vs. bifurcating cladogenesis), and sampling (Siddall, 1996, 1997;
Wagner, 2000b,c; but see Hitchin and Benton,
1997a,b; Benton et al., 1999). These biases
should not be a problem in this analysis because the amount of time represented, the
sampling of the fossil record, and the taxa
included are nearly the same for all of the
examined cladograms. Slight differences in
symmetry as measured by the Imbalance Index of Heard (1992) (Table 1) exist among
the cladograms but are unlikely to be large
enough to bias the results.
The GER measures the Žt of a cladogram
to stratigraphy by examining the amount of
ghost range required (Wills, 1999). The GER
represents the excess ghost range (Norell,
1987, 1992, 1993) beyond the minimum possible value for a set of stratigraphic data,
expressed as a fraction of the total range
of ghost values possible for those data
(Wills, 1999). Higher GER values imply fewer
gaps and thus a better Žt to stratigraphy. The GER appears not to be biased by
the number of taxa included, but it can
be affected by cladogram asymmetry, taxonomic philosophy, diversiŽcation model
(budding vs. bifurcating cladogenesis), and
sampling (Benton et al., 1999; Wills, 1999;
Wagner, 2000b,c). As noted above, these
potential sources of error should not strongly
affect this analysis.
Because it is based on character-state transformations, the method used to optimize
characters on a cladogram will affect the
CCR. In this study I used the default (unambiguous changes only), Accelerated Transformation (ACCTRAN) and Delayed Transformation (DELTRAN) algorithms of MacClade
3.08 (Maddison and Maddison, 1999) to optimize character-state changes on each of
the most-parsimonious cladograms. Also, I
used the correlation coefŽcient to determine
whether the CCR was correlated with (i.e.,
was measuring a similar signal as) the RCI
or GER.
Because I am using cladograms that all
examine nearly the same amount of time
and include very similar numbers of taxa,
I did not explicitly examine how the CCR
is affected by these parameters. However,
both may have the potential to introduce
bias. Sampling issues related to changes
in preservation potential associated with
some character states also may be important. The cladograms examined here have
different degrees of asymmetry. Both the
RCI and GER are biased by cladogram
asymmetry (e.g., Siddall, 1996, 1997; Wills,
1999) because pectinate cladograms tend
to require more range extensions than do
symmetric cladograms. Because the CCR
may be affected similarly, I used the correlation coefŽcient to determine whether a
statistically signiŽcant relationship existed
2002
POINTS OF VIEW
between the CCR and the Imbalance Index. In all analyses, stratigraphic data
in the form of Žrst appearances were
used, taken from Rubidge (1995) for South
African taxa and from King (1988) for taxa
found outside South Africa (Appendix 2).
R ESULTS
Simulation Analysis
The results of the Žrst group of simulations
(with speciation rate as the variable) show
that derived character states are sampled before basal states with increasing frequency as
the fossil record becomes more incomplete
(Fig. 4a). However, this frequency does not
vary strongly with speciation rate. At a given
completeness level the frequencies are generally similar from low to high speciation rates,
FIGURE 4. Effects of speciation rate (¸) and extinction
rate (¹) on the frequency at which derived states are sampled before basal states in the fossil record. (a) Speciation
rate does not strongly affect this frequency. However,
the frequency increases as the fossil record becomes less
complete. (b) The frequency at which derived character states are sampled before basal ones increases as extinction rate decreases and as the fossil record becomes
less complete. Each box represents the average value of
10 replicate simulations at a given set of parameters.
183
suggesting that speciation rate alone will not
strongly affect the CCR.
The results of the second group of simulations (with extinction rate as the variable) show a similar pattern of increasing
frequency of derived states being sampled
before basal states as incompleteness increases (Fig. 4b). The frequency at which derived states are sampled before basal ones
also weakly increases as the extinction rate
decreases and suggests that the CCR may be
inuenced by extinction rates, the higher extinction rates tending to yield datasets with
higher CCR values. Such an observation is
not surprising, given that the longer a lineage or clade survives, the more opportunity
it has to evolve derived character states that
can be sampled in the incorrect order as taxa
are removed from the fossil record.
The results of the third group of simulations (with the probability of cladogenic character-state change as the variable)
show a very weak pattern of increasing frequency of derived states being sampled before basal ones as incompleteness increases
(Fig. 5a). However, the weakness of the
pattern is at least partially artifactual because of the link between the probability
of cladogenic character-state change and the
speciation rate. Thus, although the probability of character-state change at each cladogenic event varied from 0.01 to 0.09, the
total probability of character-state change
varied from 0.002 to 0.018 (i.e., the probability of character-state change £ ¸). Very few
derived states evolve at such low probabilities of change, which thus results in fewer
opportunities for them to be sampled in the
incorrect order. The peak at the lower right
corner of Figure 5a also represents a probable artifact. At low levels of completeness
and probabilities of character-state change,
very few characters in the datasets were variable. Thus, if even one or two characters that
had evolved derived states were sampled out
of order, they would represent a considerable fraction of the total number of variable
characters.
A somewhat stronger pattern of increasing frequency of derived states being sampled before basal states with increasing
incompleteness is present in the results of the
fourth group of simulations (with the probability of cladogenic character-state change ¸
as the variable; Fig. 5b). A second pattern of increased sampling of derived states
184
VOL. 51
S YSTEMATIC BIOLOGY
FIGURE 6. Effect of the probability of anagenetic
character-state change on the frequency at which derived character states are sampled before basal states in
the fossil record. This frequency increases as the probability of anagenetic character-state change increases and
the fossil record becomes less complete. Each box represents the average value of 10 replicate simulations at a
given set of parameters.
the CCR provides a measure of Žt, it also
is affected by the completeness of the fossil record, the probability of character-state
change, and the extinction rate.
FIGURE 5. Effects of the probability of cladogenic
character-state change on the frequency at which derived states are sampled before basal states in the fossil
record. (a) The frequency increases slightly as the probability of cladogenic character-state change increases.
The peak at the lower right corner is probably an artifact (see text for details). (b) The frequency at which
derived character-states are sampled before basal ones
increases as the total probability of cladogenic characterstate change (i.e., probability of cladogenic characterstate change ¸) increases. This frequency also increases
as the fossil record becomes less complete. Each box represents the average value of 10 replicate simulations at
a given set of parameters.
before basal states as the total probability of
character-state change increases also is apparent. This observation suggests that the
CCR may be affected by the probability
of character-state change, the greater probabilities of change leading to lower CCR
values.
The results of the Žfth group of simulations (with the probability of anagenetic
character-state change as the variable) mirror
the conclusions of the fourth group (Fig. 6).
Here again, the frequency at which derived
states are sampled before basal ones increases as incompleteness and the probability of character-state change increase. In general, the simulations suggest that although
Empirical Analysis
The RCI values calculated for the 13 mostparsimonious cladograms from the Žrst
dataset range from 0.282 to 0.487 (mean 0.400;
Table 1), and three RCI values are shared
by groups of three to Žve cladograms. A
strict consensus of the three cladograms with
the greatest RCI values (Fig. 3b) represents
a summarized topology of the subset of
most-parsimonious cladograms that are
most consistent with stratigraphy as measured by the RCI. The RCI value calculated
for the single most-parsimonious cladogram
of the second dataset (Fig. 3f) is 0.632.
The GER values calculated for the mostparsimonious cladograms of the Žrst dataset
range from 0.683 to 0.810 (mean 0.756;
Table 1), and three GER values are shared by
groups of three to Žve cladograms. A strict
consensus of the three cladograms with the
greatest GER values is the same as that of
the RCI (Fig. 3b). The GER value calculated
for the single most-parsimonious cladogram
of the second dataset (Fig. 3f) is 0.863. The
RCI and GER are highly correlated (® < 0.01;
Table 2), indicating that despite their different approaches, both metrics measure a similar signal.
2002
The CCR values calculated for the mostparsimonious cladograms of the Žrst dataset
using the default optimization of MacClade
range from 0.641 to 0.786 (mean 0.721;
Table 1), and three CCR values are shared
by groups of two to three cladograms. The
cladogram with the greatest CCR value has
a notably different topology from the consensus cladogram for the RCI and GER (Fig. 3b).
The default CCR value calculated for the
most-parsimonious cladogram of the second
dataset (Fig. 3f) is 0.897.
The CCR values calculated for the mostparsimonious cladograms from the Žrst
dataset with the ACCTRAN optimization of
MacClade range from 0.563 to 0.699 (mean
0.640; Table 1), and three CCR values are
shared by groups of two cladograms each. A
strict consensus of the two cladograms with
the greatest CCR value has the same topology
as the consensus cladogram for the RCI and
GER (Fig. 3d). The ACCTRAN CCR value
calculated for the single most-parsimonious
cladogram of the second dataset (Fig. 3f) is
0.873.
The CCR values calculated for the mostparsimonious cladograms of the Žrst dataset with the DELTRAN optimization of
MacClade range from 0.553 to 0.728 (mean
0.665; Table 1), and three CCR values are
shared by groups of two to three cladograms.
A strict consensus of the three cladograms
with the greatest CCR values has a topology
similar to that of the default resolving option,
although it is somewhat less resolved (Fig.
3e). The DELTRAN CCR value calculated for
the single most-parsimonious cladogram of
the second dataset (Fig. 3f) is 0.817.
A signiŽcant correlation (® < 0.05; Table 2)
exists between all CCR values and the RCI
and GER. The CCR values obtained for the
TABLE 2. Correlation coefŽcients (r) between various metrics used in this study based on data in Table 1.
Comparison
RCI/GER
Default CCR/RCI
ACCTRAN CCR/RCI
DELTRAN CCR/RCI
Default CCR/GER
ACCTRAN CCR/GER
DELTRAN CCR/GER
Default CCR/Im
ACCTRAN CCR/Im
DELTRAN CCR/Im
¤
185
POINTS OF VIEW
SigniŽcant correlation (® < 0.05) for 14 data points.
r
0.990 ¤
0.865 ¤
0.964 ¤
0.836 ¤
0.825 ¤
0.923 ¤
0.823 ¤
0.481
0.731 ¤
0.499
default and DELTRAN resolving methods
are not signiŽcantly correlated with the Imbalance Indices, but the CCR values for
the ACCTRAN resolving method are significantly correlated with the Imbalance Index
(Table 2).
D ISCUSS ION
The CCR represents a new approach in
measuring the Žt of a cladogram to the fossil
record. However, as suggested in the simulation and empirical studies presented here,
other factors may affect the CCR as well.
Thus, although two cladograms may have
the same CCR score, they may not Žt the fossil record equally well. The recognition and
understanding of these potential biases allow
the CCR to be used conservatively in phylogenetic studies.
The simulation analyses highlight three
potential biases of the CCR. The Žrst is extinction rate; as the extinction rate decreases,
the frequency at which derived character
states are sampled before basal states increases. As noted above, this relationship is
logical, given that the longer a lineage or
clade survives, the more opportunity it has
to evolve derived character states that can
be sampled in the incorrect order in the fossil
record. Similarly, the probability of characterstate change also inuences the CCR. As
the probability of change increases, the frequency at which derived character states are
sampled before basal ones also increases.
This relationship also is expected because
derived character states are the foundation
of the CCR. The greater the probability of
change, the more likely to evolve are derived
states, which subsequently can be sampled
in the incorrect order in the fossil record. Finally, the simulations indicate that the CCR
is affected by the completeness of the fossil
record. As completeness decreases, the frequency at which derived states are sampled
before basal states increases. These observations show that the CCR does not provide
a completely unbiased measure of the Žt of
a cladogram to the fossil record. Instead, it
measures an amalgam of Žt, completeness
of record, extinction rate, and probability of
character-state change. Furthermore, these
results emphasize that the CCR cannot be
used as an unbiased indicator of the quality of the fossil record, the probability of
character-state change, or the extinction rate
186
S YSTEMATIC BIOLOGY
because multiple explanations are possible
for any single observation.
Speciation rate did not strongly affect the
frequency at which derived character states
were sampled before basal ones in the simulated datasets. The program used to generate the simulated datasets does not require character-state changes to occur when
speciation takes place. This is not unrealistic because lineages can become distinct
through such factors as geographic isolation before the evolution of the molecular
or morphological characters that distinguish
them. However, because systematists cannot recognize lineages without diagnostic
character states or combinations of character states (molecular or morphological),
perhaps the CCR will be related to empirical estimates of speciation rates when
applied to real datasets. Further simulation and empirical studies will be necessary to test this prediction. In addition, speciation rate can also indirectly affect the
CCR: As speciation rate increases, the total probability of cladogenic character-state
change (probability of cladogenic characterstate change £ ¸) also increases; moreover,
the more that lineages evolve, the greater the
opportunity for anagenetic character-state
changes.
The empirical analysis demonstrates two
other possible biases of the CCR. Because the CCR is character-based, the
method used to reconstruct character-state
changes on a cladogram obviously is an
important consideration. The default algorithm produced the greatest CCR results,
but because it only resolves unambiguous
character-state changes. The ACCTRAN and
DELTRAN algorithms include unambiguous
and some ambiguous character transformations (Maddison and Maddison, 1992), which
results in a relative increase of inconsistent
changes (the total number of changes remains the same regardless of how they are resolved). In addition to these “standard” optimizations, other optimizations also affect the
CCR. For example, characters could be optimized on a cladogram to maximize or minimize congruence with stratigraphy, which
would inate or decrease the CCR, respectively. Because such “custom” optimizations
are likely to include most or all ambiguous
character-state changes, the resulting CCR
values may tend to be lower than those for
optimizations that include only unambigu-
VOL. 51
ous changes or unambiguous and some ambiguous changes.
The CCR values associated with the default and DELTRAN optimizations were not
directly correlated with cladogram shape in
the empirical analysis. However, the CCR
values based on the ACCTRAN optimization were correlated with the Imbalance Index, the greatest CCR values being associated with the most imbalanced cladograms.
This correlation may be related to the fact that
the ACCTRAN CCR is more highly correlated with the taxon-based methods than are
the default or DELTRAN CCRs. Many taxonbased methods (including the RCI) are biased
towards giving better scores for imbalanced
cladograms (e.g., Siddall, 1996, 1997; Wills,
1999), and the ACCTRAN CCR may measure
a similar signal as these metrics. However,
this observation also may be an idiosyncrasy
of the datasets used in this study, and additional empirical and simulation studies will
be necessary to determine whether a consistent bias for the CCR is involved.
Besides the biases highlighted by the empirical and simulation analyses, several other
potential biases of the CCR not explicitly
examined here are worth noting. Perhaps
the most fundamental of these biases is the
choice of characters used in the construction
of a particular cladogram. Because the CCR
is character-based, two identical topologies
could have very different CCR values if they
are based on different sets of characters. This
bias is unique to the CCR because taxonbased methods consider only the order of
appearance of taxa on a cladogram or the
gaps between taxa implied by a given topology. Thus, identical topologies will have the
same RCI or GER scores, for example, regardless of which characters the cladograms are
based on. This bias is partly a result of the
fact that systematists cannot include all possible characters in their analyses, and different workers will choose different subsets of
characters to examine. However, it also reects the fact that different characters or sets
of characters can differ in their probabilities
of change, and the evolution of certain character states might decrease the preservation
potential of taxa that possess them or might
increase the chance that derived character
states can be mistaken as basal.
Another potential bias introduced by the
activity of systematists deals with taxonomic
philosophy. Recently, Wagner (2000b) and
2002
POINTS OF VIEW
Wagner and Sidor (2000) showed that most
taxon-based stratigraphic metrics are decreased by the deliberate exclusion of paraphyletic taxa in an analysis. Those authors argue that because most fossil taxa
are morphologically diagnosed instead of
phylogenetically deŽned, and because most
character-state changes among fossil taxa result in homoplasy (Wagner, 2000a), paraphyletic fossil taxa will be very difŽcult to
distinguish from monophyletic fossil taxa
a priori. Furthermore, the probability of
sampling paraphyletic taxa in the fossil
record is not trivial (Foote, 1996). Given these
considerations, they conclude that attempting to exclude paraphyletic taxa will result in
the creation of false gaps in the sampling of
taxa. A similar concern is valid for the CCR.
Because paraphyletic taxa often include basal
character states, their exclusion may increase
the frequency at which derived states appear
to be sampled before basal states in the fossil
record. Given that the monophyletic status
of all taxa has not been explicitly examined,
this issue should be considered in analyses
that use the CCR.
The method used to construct a cladogram also may inuence the CCR. As noted
above, parsimony can produce inaccurate
results when character transition patterns
are biased (e.g., Kuhner and Felsenstein,
1994; Lamboy, 1994; Wagner, 1999). In such
cases, the resulting cladograms can imply
large gaps between taxa in the fossil record
(Wagner, 1999). Because most fossil taxa possess unique apomorphies or combinations
of character states, these gaps will probably correspond to gaps between the Žrst
appearances of different character states as
well. Furthermore, parsimony also can reverse the hypothesized polarity of character
states when trends exist, with character states
that become increasingly common later in
the fossil record being reconstructed as basal
(Wagner, 1999). Thus, CCRs may be lower
for cladograms constructed with parsimony
when trends exist in the evolutionary history
of the group in question. However, the CCR
may ultimately be useful in identifying these
situations. If some characters have unusually
low CCR values when optimized on a given
cladogram, that might indicate the presence
of a trend and the possible inaccuracy of the
cladogram in question.
The absolute amount of time examined
may have a biasing effect because the longer
187
the time considered in an analysis, the greater
the opportunity for derived character states
to evolve that can be sampled in the incorrect order. The resolution of the stratigraphic
divisions used also requires consideration. If
the intervals are too coarse (e.g., Paleozoic
and Mesozoic for animals that occur in the
Permian and Triassic), the CCR will be spuriously high. Finer intervals will produce
a lower CCR but will allow greater sensitivity to conicts between stratigraphy and
phylogeny.
In general, several factors will inuence
the CCR value obtained in an analysis. Because many of these factors (e.g., probability of character-state change, preservation probability) will vary among individual
taxa, characters, or character states, it completely controlling for them will be difŽcult, especially when comparing CCR values
based on different cladograms and datasets.
The evolutionary and preservational histories underlying each dataset may be very
different in such cases, introducing different sets of biasing factors. Thus, using the
CCR to compare cladograms based on a
single dataset with the fossil record seems
to be the most conservative approach. Although that will not completely eliminate biasing factors, it will help ensure that at least
the same evolutionary and preservational
history is underlying all of the cladograms in
question.
Whether or not the CCR will aid the selection of the most accurate topology from a set
of cladograms is another, more difŽcult, issue. Character-based and taxon-based methods measure different important aspects of
the Žt of cladograms to the fossil record. Not
surprisingly, the methods differ to some degree in their results. Characters often evolve
in mosaic fashion, and even closely related
taxa will have different combinations of relatively basal and derived character states. As
a result, the topology that requires the fewest
gaps between the ranges of the taxa included
may not be the same as that which posits the
least number of incidences in which a relatively derived character state appears in the
record before a more basal one. Because the
datasets used in the empirical analysis are
real, the absolute accuracy of the preferred
cladograms cannot be measured directly. The
simulated datasets used in this analysis may
provide some insight into this question because the true phylogeny is known in each
188
S YSTEMATIC BIOLOGY
case. However, because the CCR must be calculated by hand, carrying out such a study
is currently prohibitively time-consuming.
The correlation between the results of the
character-based and taxon-based methods
indicates that both approaches appear to
measure a similar underlying signal. Such
a correlation is not surprising because the
Žrst appearances of fossil taxa often correspond to the Žrst appearance of a new character state or combination of character states.
Given these observations and the fact that inaccurate cladograms cause lower scores for
most stratigraphic metrics (Wagner, 2000b;
Wagner and Sidor, 2000), the greater precision of the CCR may make it more reliable
than either of the taxon-based methods considered. However, further empirical and simulation studies will be necessary to test this
prediction.
Finally, the CCR raises an interesting issue
regarding the adequacy of the fossil record.
Numerous studies have dealt with the adequacy of the fossil record (e.g., papers in
Donovan and Paul, 1998; Benton et al., 2000),
but these have focused on whether sampling
is adequate to estimate past diversity, on conŽdence intervals on stratigraphic ranges of
taxa, and on whether the fossil record preserves patterns of evolution that are not observable on short time scales. The question of
how well the fossil record estimates the range
of a given character state remains virtually
unexamined. This issue will be important to
consider not only because of its implications
for the CCR—if the fossil record faithfully
records the Žrst appearances of between the
time when a derived state evolves and when
it Žrst appears in the fossil record, the CCR
will be misled and will underestimate the
true amount of conict between a cladogram
and stratigraphy—but also because characters states form the foundation of our understanding of stratigraphy and phylogeny.
ACKNOWLEDGMENTS
I thank B. Mishler for the initial suggestion to approach stratigraphy from the standpoint of character
states. D. Fox D. Fisher, and L. Leighton generously allowed access to their unpublished program CHSTER
for the simulation analyses conducted in this study.
M. Benton and P. Wagner reviewed the manuscript
and provided numerous comments and suggestions
that greatly improved the quality of the paper.
A. Aronowsky, P. Holroyd, J. Hutchinson, L. Leighton,
D. Lindberg, B. Mishler, R. Olmstead, K. Padian, and
J. Parham provided helpful discussions and comments
VOL.
51
throughout the course of this study. All remaining mistakes and oversights are purely my own. This is UCMP
contribution 1746.
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Received XXX; accepted XXX
Associate Editor: XXX
APPENDIX 1
Data matrix showing codings for characters and taxa used in the Žrst dataset of the empirical analysis.
Patranomodon and Otsheria are outgroups. A complete character–taxon matrix for the second dataset is presented
in Angielczyk (in press).
Taxon
Patranomodon
Eodicynodon
Diictodon
Robertia
Tropidostoma
Oudenodon
Pelanomodon
Rhachiocephalus
Dicynodon
Aulacephalodon
Lystrosaurus
Kannemeyeria
Pristerodon
Chelydontops
Endothiodon
Emydops
Cistecephalus
Kingoria
Placerias
Myosaurus
Geikia
Otsheria
Character codings
0000?0000 0
010100100 0
0112111110
0111111010
011101101 0
0112011110
0112001?1 0
0112011?1 0
0112011110
0112011?1 0
1112011110
0112011110
011101101 0
0111001011
0011?0101 0
0111001011
0112001111
0112001110
0112011110
0112001111
1112011110
0000?00?1 0
000000100 1
0?1010001 0
0100100111
011010001 ?
111010001 0
111010001 0
??????001 0
??1??00110
111010011 0
1?10?0001 0
111010001 0
111010011 0
101000001 0
011000001 ?
000100011 0
1?100000 11
?11000001 ?
0010011011
110010?01 ?
00100000 11
1?1010001 0
??????10? 1
0000000?0 ?
000000110 0
000000000 0
0100?0?00 0
001110000?
0011000001
0111?0?00 ?
101110000?
011000000 1
101010?00 1
010000000 1
010001000 2
001000000 0
1010?0010 ?
100?00?10 1
001000000 ?
001?00101 2
0000000?0 ?
???0010002
001100000?
??11?0?10 ?
100010??0 ?
0??00?1000
0000010?0 0
00011110 11
0000?11?01
??0?10?1? 3
??00?1112 4
??00110?? 5
1?0?10002 3
110011102 4
1?0110002 4
120?11103 6
130?11003 7
00001000? 1
??0??01?? 1
010?00111 2
??0?11?0? 3
130?10100 3
120100001 4
?31?11?0? 8
??010010?6
??0??0?1? 5
??000000?0
2002
191
POINTS OF VIEW
APPENDIX 2
Stratigraphic ranges of the taxa used in the empirical analysis. Assemblage zones are based on those of Rubidge
(1995) and range data are taken from King (1988) and Rubidge (1995). From oldest to youngest, the assemblage
zones are Eodicynodon, Tapinocephalus, Pristerognathus, Tropidostoma, Cistecephalus, Dicynodon, Lystrosaurus,
Cynognathus, and “Post-Cynognathus.”
Taxon
Patranomodon
Eodicynodon
Diictodon
Robertia
Tropidostoma
Oudenodon
Pelanomodon
Rhachiocephalus
Dicynodon
Aulacephalodon
Lystrosaurus
Kannemeyeria
Pristerodon
Chelydontops
Endothiodon
Emydops
Cistecephalus
Kingoria
Placerias
Myosaurus
Geikia
Otsheria
Assemblage Zone
Eodicynodon
Eodicynodon
Tapinocephalus, Pristerognathus, Tropidostoma, Cistecephalus, Dicynodon
Tapinocephalus
Tropidostoma
Cistecephalus
Dicynodon
Tropidostoma, Cistecephalus
Dicynodon
Cistecephalus, Dicynodon
Lystrosaurus
Cynognathus
Tapinocephalus, Pristerognathus, Tropidostoma, Cistecephalus, Dicynodon
Tapinocephalus
Pristerognathus, Tropidostoma, Cistecephalus
Tropidostoma, Cistecephalus, Dicynodon
Tropidostoma, Cistecephalus
Cistecephalus
“Post-Cynognathus”
Lystrosaurus
Dicynodon
Eodicynodon