Syst. Biol. 64(5):838–852, 2015
Published by Oxford University Press on behalf of Society of Systematic Biologists 2015. This work is written by US Government employees and is in the public domain in the US.
DOI:10.1093/sysbio/syv040
Advance Access publication July 3, 2015
The Implications of Stratigraphic Compatibility for Character Integration
among Fossil Taxa
PETER J. WAGNER1,∗
AND
GEORGE F. ESTABROOK2,†
1 Department of Paleobiology, National Museum of Natural History, Smithsonian Institution MRC-121, PO Box 37012, Washington,
DC 20013, USA and 2 Department of Ecology and Evolutionary Biology, University of Michigan, 2039 Kraus Natural Science Building,
830 North University, Ann Arbor, MI 48109, USA
∗ Correspondence to be sent to: Department of Paleobiology, National Museum of Natural History, Smithsonian Institution MRC-121,
PO Box 37012, Washington, DC 20013, USA; E-mail: [email protected].
† Deceased.
Received 24 January 2015; reviews returned 2 April 2015; accepted 9 June 2015
Associate Editor: Ron DeBry
Abstract.—Two characters are stratigraphically compatible if some phylogenies indicate that their combinations (state-pairs)
evolved without homoplasy and in an order consistent with the fossil record. Simulations assuming independent character
change indicate that we expect approximately 95% of compatible character pairs to also be stratigraphically compatible over
a wide range of sampling regimes and general evolutionary models. However, two general models of rate heterogeneity
elevate expected stratigraphic incompatibility: “early burst” models, where rates of change are higher among early members
of a clade than among later members of that clade, and “integration” models, where the evolution of characters is correlated
in some manner. Both models have important theoretical and methodological implications. Therefore, we examine 259
metazoan clades for deviations from expected stratigraphic compatibility. We do so first assuming independent change
with equal rates of character change through time. We then repeat the analysis assuming independent change with separate
“early” and “late” rates (with “early” = the first third of taxa in a clade), with the early and late rates chosen to maximize the
probability of the observed compatibility among the early taxa and then the whole clade. We single out Cambrian trilobites
as a possible “control” group because morphometric studies suggest that integration patterns are not conserved among
closely related species. Even allowing for early bursts, we see excess stratigraphic incompatibility (i.e., negative deviations)
in significantly more clades than expected at 0.50, 0.25, and 0.05 P values. This pattern is particularly strong in chordates,
echinoderms, and arthropods. However, stratigraphic compatibility among Cambrian trilobites matches the expectations
of integration studies, as they (unlike post-Cambrian trilobites) do not deviate from the expectations of independent change
with no early bursts. Thus, these results suggest that processes such as integration strongly affect the data that paleontologists
use to study phylogeny, disparity, and rates. [Cambrian; correlated change; early bursts; evolvability; fossils; integration;
stratigraphic compatibility.]
The simplest models of morphological evolution posit
equal rates of independent change among characters
over time and across phylogeny. However, it is well
established that morphological evolution is much more
complex than that. These complexities encompass many
basic issues, including simple shifts in overall rates of
character evolution (Erwin 1992), “evolvability” making
new sets of characters available to some clade members
(Wagner and Altenberg 1996), and linkages from
common selective factors or the genetic, developmental,
and/or functional integration of characters (Olson and
Miller 1958). These seemingly distinct issues share one
factor in common: rates of change for some characters
differ in different portions of a phylogeny. On the one
hand, this means that morphological character data offer
rich fodder for testing a variety of macroevolutionary
hypotheses predicting such rate heterogeneities (i.e.,
heterotachy sensu Heath and Moore 2014). On the
other hand, variable rates and correlated character
change induce incorrect phylogeny reconstruction in
simulations (Kuhner and Felsenstein 1994; Wagner
1998; Huelsenbeck and Nielsen 1999; Wright and Hillis
2014). Even if we reconstruct general phylogenetic
relationships correctly, then rate heterogeneities will
complicate tip-dating analyses using morphological
data (e.g., Pyron 2011; Ronquist et al. 2012; Heath and
Moore 2014). Thus, the ability to recognize complex
modes of character evolution serves multiple ends.
Recognizing the effects of rate heterogeneities is
particularly important with fossil data. Fossil taxa
provide many examples of early bursts in which inferred
rates of character evolution decrease over time (Cloutier
1991; Anstey and Pachut 1995; Wagner 1997; Ruta et al.
2006; Brusatte et al. 2008; Lloyd et al. 2012). The
associated pattern of high early disparity within clades
is an even more general occurrence (Hughes et al.
2013). Fossil data also provide evidence that sets of
characters evolve in correlated suites. In some cases,
new partitions of character space become available to
derived clades, elevating evolvability for the whole
clade (Eble 2000; Wagner et al. 2006). Fossils also
can document how the conservation of integration
patterns changes over time (Webster and Zelditch
2011a, 2011b; Gerber 2013), across phylogeny (Eble 2005;
Goswami 2006b; Bell et al. 2011), and among character
types (Polly 1998; Webster 2015). Fossils also provide
cases connecting integration and evolvability when
linked changes increase the subsequent probability
of change in previously static characters (Goswami
et al. 2014). Although most integration studies rely on
morphometric analyses, the models themselves extend
to and make predictions about discrete characters
(O’Keefe and Wagner 2001; Webster 2007; Dávalos
et al. 2014). Moreover, stratigraphic distributions
provide information about temporal sequences, which
might be a powerful tool if it can be shown
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WAGNER AND ESTABROOK—IMPLICATIONS OF STRATIGRAPHIC COMPATIBILITY
FIGURE 1.
Stratigraphic compatibility and incompatibility.
Two compatible characters are stratigraphically compatible if the
intermediate combination (state-pair) appears before at least one of
the other state-pairs: a) The intermediate state-pair (00) appears before
both of the other state-pairs (01 and 10). b) The intermediate statepair (10) appears before one of the remaining pairs (11). Stratigraphic
incompatibility is the case where the intermediate state-pair (10)
appears after the other two state-pairs (00 and 11). c) State-pairs
evolve in a 00 → 10 → 11 sequence, but we fail to sample taxa bearing
10 until after we sample more-derived taxa bearing 11. d) A direct
00 → 11 transition followed by a later 00 → 10 transition. e) A direct
00 → 11 transition followed by a later 11 → 10 transition. For unordered
multistate characters, different binary breakdowns are evaluated
separately. f) The intermediate state-pair for both breakdowns (10)
appears before the one combination from each set (11 from 00+
10+11 and 12 from 00+10+12). Note that 00+12+11 does not
have an intermediate state-pair and thus cannot be evaluated. g)
The intermediate state-pair in one breakdown (00 from 02+00+10)
precedes the other two combinations, but the intermediate state-pair
in the other breakdown (10 from 00+10+11) is the last state-pair to
appear. The latter demands a scenario such as illustrated in (c–e) above.
Again, 02+10+11 lacks an intermediate state-pair and thus cannot be
evaluated.
that models such as early bursts and integration
make different predictions about the stratigraphic
distributions of characters and character combinations
than do null models of homogeneous rates and
independent change.
In this article, we use stratigraphic compatibility
(Estabrook and McMorris 2006; Wagner and Estabrook
2014) to evaluate how frequently patterns in the fossil
record deviate from the expectations of homogeneous
rate models. Stratigraphic compatibility represents
a particular case extension of general compatibility
(e.g., Le Quesne 1969): compatible character pairs
can be mapped onto some phylogenies with no
homoplasy; stratigraphically compatible characters can
839
be mapped onto some trees with no homoplasy and have
state-pairs evolve in an order matching the order in
which they appear in the fossil record (Fig. 1a,b).
Assume that the oldest sampled species possesses
the 00 combination (hereafter: state-pair). There are
two possible patterns of stratigraphic compatibility:
“divergent,” in which taxa with 10 and 01 combinations
appear in younger strata (Fig. 1a), and “hierarchical,” in
which taxa with the 01 (or 10) combination appear in
younger strata and species with 11 combination appear
in the youngest strata (Fig. 1b).
Stratigraphic incompatibility is the third alternative
(Fig. 1c,e): the case where the intermediate state-pairs
(e.g., 10 given 00, 10, and 11) is the last to appear in the
fossil record. There are three simple explanations for this.
One is that species with 10 evolved before species with 11
did, but we failed to sample early species with 10 (Fig. 1c).
The other two explanations invoke both homoplasy
and concentrated change early in clade history. In both
cases, species with 11 evolve directly from species with
00 (concentrated change). Species possessing 10 evolve
later, either from species with 00 (parallelism; Fig. 1d) or
from species bearing 11 (reversal; Fig. 1e).
We can extend stratigraphic compatibility to
multistate characters using binary breakdowns of
those characters. Suppose that we observe taxa with
00, 10, 11, and 12 state-pair (Fig. 1f). There are two
binary sets of three state-pairs (00, 10, 11, and 00, 10,
12) in which one state-pair is intermediate between the
other two (10 in both cases). Taxa bearing 00 appear
first and taxa bearing 11 and 12 appear last. Because
the intermediate state-pair (10) appears before the final
state-pair (11 and 12, respectively), both breakdowns are
stratigraphically compatible. Suppose a different two
sets with three combinations: 00, 02, 10, and 00, 10, 11
(Fig. 1g). Taxa with 00 again appear first and taxa with
02 and 10 appear last. The intermediate pair of the first
set (00) precedes the other two pairs and therefore is
stratigraphically compatible. However, the intermediate
pair for the second set (10) appears last and therefore is
stratigraphically incompatible.
Given the probabilistic nature of sampling, we
expect stratigraphic incompatibility because of missing
fossils (e.g., Fig. 1c) at some frequency. Moreover,
the probabilistic nature of character evolution means
that we expect joint change followed by homoplasy
(e.g., Fig. 1d or e) at some frequency under even
the simplest models of independent change. However,
alternate models explicitly predict evolutionary patterns
matching Figure 1d,e. Early bursts should encourage
00→11 transitions on early branches simply by making
the probability of two changes relatively high. This sets
the stage for subsequent 00→10 or 11→10 transitions.
Both correlated change and elevated evolvability
scenarios make similar predictions: if the probability of
linked characters changing together is much higher than
the probability of the individual characters changing
independently, then 00→11 transitions preceding 00→10
or 11→10 transitions should be common (see, e.g.,
Goswami and Polly 2010; Goswami et al. 2014).
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The purpose of the article is 2-fold. Our primary
goal is to assess whether stratigraphic compatibility
in metazoan clades indicates that integration and/or
related processes strongly affect the distribution of
anatomical character states. However, because the
properties of stratigraphic compatibility have been
little explored to date, we first must assess how
sampling and a variety of alternative evolutionary
models besides those matching integration models
affect expected stratigraphic compatibility. This is the
second aim of our article, which we do using a variety
of simulations. We then use Monte Carlo analyses
based on these simulations but tailored to individual
data sets in order to assess whether we observe too
little stratigraphic compatibility in fossil data even
after using evolutionary and sampling parameters
that minimize the expected stratigraphic compatibility
given independent change models. Finally, independent
studies indicate that integration patterns differ more
among closely related Cambrian trilobite species than
among closely related post-Cambrian trilobite species
(Webster 2007; Webster and Zelditch 2011a, 2011b). This
in turn predicts that stratigraphic compatibility should
be greater among Cambrian trilobites than among postCambrian trilobites and thus allows us to use trilobites
as a control group when assessing our results.
METHODS
Establishing General Relationships between Sampling,
Evolutionary Models, and Stratigraphic Compatibility
Analytic solutions providing exact expectations for
compatibility would require integrating over all possible
phylogenies (Felsenstein 1981). This is impossible for
any large number of taxa (e.g., Felsenstein 1978).
Therefore, we use simulations first to assess the effects
of different evolutionary and sampling parameters
on expected stratigraphic compatibility, and then to
assess whether published data sets deviate from null
expectations. Paleobiologists have a long history of
simulating morphological evolution over phylogenies
in order to examine how different evolutionary
models and sampling regimes affect patterns such as
morphological disparity (e.g., Raup and Gould 1974;
Foote 1991, 1994, 1996b). Following these examples, we
simulate morphological evolution and phylogeny first
to assess the effects of several parameters on expected
stratigraphic compatibility and second to provide Monte
Carlo tests of whether observed data sets deviate from
the expectations of simple models of morphological
change.
Our “assessment” simulations run until 32 species
are sampled, with extinction rates set to 90% of the
origination rates. Unless otherwise stated, sampling
is set to 31% of the extinction rate, which means
that we expect to sample 31% of species having the
median species duration. Unless otherwise stated, we
use 100 binary characters with 150 changes among those
characters. We use two different branching (speciation)
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models that have been documented in real clades (see,
e.g., Wagner and Erwin 1995; Huang et al. 2015): a
bifurcation model in which ancestral morphospecies
become pseudo-extinct at speciation (e.g., Slowinski and
Guyer 1989), and a budding model in which ancestral
morphospecies persist after cladogenesis and can give
rise to daughter species at any time over their duration
(e.g., Raup and Gould 1974). We describe the “test”
simulations (i.e., Monte Carlo analyses) in more detail
below. A C program used to conduct these analyses is
available in the Supplementary Material available on
Dryad at http://dx.doi.org/10.5061/dryad.h5971).
Simulations (Fig. 2a) corroborate the first principle
predictions that compatibility should be common
among characters with little or no homoplasy
(Le Quesne 1969; Estabrook 1983). However, the proportion of compatible character-pairs that are stratigraphically compatible remains very high (over 90%)
regardless of the overall frequencies of compatibility
(Fig. 2a). Thus, although homoplasy reduces expected
compatibility, it does not affect expected stratigraphic
compatibility when character-pairs are compatible.
Simulations also show sampling intensity does not
affect expected stratigraphic compatibility (Fig. 2b): over
a wide range of sampling intensities, we still expect over
90% of compatible character-pairs to be stratigraphically
compatible (see also Angielczyk 2002; Wagner and
Estabrook 2014). This might seem surprising. However,
prior simulation studies show that compatibility among
individual characters is highest for those that change
infrequently among the sampled taxa (O’Keefe and
Wagner 2001; Wagner 2012). From this, it follows that pertaxon rates of change for highly compatible characters
are much lower than per-taxon rates of sampling. The
absolute rates of sampling or character change are not
important: if 30 sampled species represent 45 or 300
total species, then our expectations concern characters
that are changing infrequently among the 30 sampled
species. Therefore, it is not just that we expect many
species retaining an original 00 state-pair to evolve before
the first species with a 10 or 01 state-pair evolves (e.g.,
Estabrook 1977); we also expect to sample multiple
species diagnosed by 00 before we sample the first
species diagnosed by a derived state-pair.
Sampling is not uniform over time and space, or
among closely related taxa (Smith 1988; Foote 2001;
Wagner and Marcot 2013). However, this has little effect
on expected stratigraphic compatibility in simulations.
For example, simulations with lognormal variation in
sampling rates over time so that 32% of intervals have
sampling either less than one half or greater than twice
the median sampling rates yield essentially identical
results (Fig. 3a). We examine the effects of one particular
type of variable sampling model, low sampling early in
clade history, below.
How finely we can resolve stratigraphic data varies
among fossil groups. For example, in some cases we
might resolve first and last appearances only to stages
(e.g., the Campanian or Maastrichtian) whereas in other
cases we might resolve first and last appearances to
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WAGNER AND ESTABROOK—IMPLICATIONS OF STRATIGRAPHIC COMPATIBILITY
841
FIGURE 2.
Expected relationships between stratigraphic compatibility and a) overall compatibility and b) overall taxon sampling based
on simulations of 32 taxa with 100 binary characters. Pale shades reflect simulations using bifurcating cladogenesis in which ancestral species
become pseudoextinct at cladogenesis; dark shades reflect simulations using budding cladogenesis in which ancestral species persist after
cladogenesis. Box plots represent 1000 simulations each. a) Effects of increasing rates of homoplasy on expected proportions of character pairs
that are compatible (green), and the expected proportion of compatible pairs that are stratigraphically compatible (blue). Simulations here
assume per-taxon sampling rates = 0.312×extinction rate. b) Effects of per-taxon sampling rates on expected proportions of taxa sampled and
stratigraphic compatibility. Per-taxon sampling rates are given as a proportion of per-taxon sampling rates: thus, 1.0 means that we expect to
sample a lineage with the median duration once. Simulations here assume 150 steps.
FIGURE 3. Effects of other aspects of variable sampling on expected stratigraphic compatibility. a) Variable sampling over time (stratigraphic
units), where per-taxon sampling rates follow a lognormal distribution in which 32% of intervals have sampling either greater than twice or less
than one half of the median sampling. b) Effect of finer versus coarser stratigraphic resolution yielding the same origination, extinction, and
sampling probabilities over the same length of time. At ×4, we can resolve first and last appearances to units one-fourth of one “time” unit (×1);
at ×¼, we can resolve first and last appearances to units four times the length of ×1. Extinction rate at ×1 is 0.45, as in Figures 2 and 4 as well as
3a and c. c) Proportion of character data scored as “missing” because of incomplete preservation. Simulations here as in Figure 2, with 150 steps
and a median per-taxon sampling rate = 0.312×extinction rate.
particular zones within stages (e.g., the Pachydiscus
neubergicus or Menuites fresvillensis ammonite zones
within the Maastrichtian). Conversely, sometimes we
are forced to use coarser stratigraphic resolution (e.g.,
lumping the Maastrichtian, Campanian, etc. as the
Late Cretaceous). Simulations using different levels
of stratigraphic resolution with the same origination,
extinction, and sampling rates over “one” stratigraphic
unit yield similar expectations until sampling is so coarse
that fewer than 10% of taxa are expected to survive
one interval (Fig. 3b). The logical extreme is using
stratigraphic bins so coarse that all first and last are in
the same interval (e.g., the “Cretaceous”); in such cases,
we cannot detect stratigraphic incompatibility.
A different aspect of sampling is the proportion of
characters that fossils yield (Mannion and Upchurch
2010). As the proportion of missing character data
increases, the expected stratigraphic compatibility
decreases (Fig. 3c). This reflects: (1) missing data
causing us to miss “fourth” combinations demonstrating
homoplasy and (2) additional opportunities to miss
intermediate state-pairs when we cannot observe the
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FIGURE 4. Effects of additional evolutionary parameters on expected stratigraphic compatibility. Simulations here assume 150 steps and
per-taxon sampling rates = 0.312×extinction rate. a) Diversity dependent cladogenesis, where rates of diversification start at R but decrease as
richness approaches some maximum K. As R/K increases, expected stratigraphic compatibility increases slightly. Exponential diversification is
the case where R/K = 0. b) Lognormal variation in rates of change among characters, where m gives the relative rate increase/decrease 1 standard
deviation away from the mean. c) Rate shifts contrasting rates during the first third of clade history with that of the last two-thirds. At 1.0, rates
are continuous through time; at < 1.0, there are delayed bursts; at > 1.0, there are early bursts. d) Correlated character evolution, in which the
probability of change is ×3 greater than the probability of independent change. Each character set includes five characters, and each character
in these sets has three states. e) Evolvability introducing new character space. We again use sets of five characters with three states each. Here,
all five characters shift upon introduction, with independent change afterwards.
characters on taxa truly possessing the intermediate
combinations.
The simulations summarized above show a consistent relationship between stratigraphic compatibility
and speciation models: bifurcation slightly elevates
expected stratigraphic compatibility relative to budding
(Figs. 2–4). This reflects the anagenetic component of
bifurcation making it impossible to sample ancestral
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WAGNER AND ESTABROOK—IMPLICATIONS OF STRATIGRAPHIC COMPATIBILITY
species in younger strata than we sample descendant
species. That in turn removes one possible source of
stratigraphic incompatibility.
The simulations above assume exponential
diversification, which is the simplest diversification
model (e.g., Raup 1985). However, fossil data provide
considerable support for diversity-dependent models
(e.g., logistic diversification; Sepkoski 1978; Alroy
2010). Simulations using logistic diversification, in
which net cladogenesis begins at some initial rate
of intrinsic diversification (R) and subsequently
decreases as richness (S) approaches some threshold
(K), generate slightly more stratigraphic compatibility
than do simulations using exponential diversification
(Fig. 4a; note that exponential diversification is
essentially a special case of logistic in which K = ∞
and R/K effectively equals zero). Moreover, expected
stratigraphic compatibility rises slightly as R/K
increases (and thus as S more rapidly approaches K).
This is akin to the effect of ancestral pseudo-extinction
in the bifurcation model: when S ∼
= K, most speciation
will happen only after extinction; this in turn reduces
the possibility of sampling taxa (and thus state-pairs) in
an incorrect sequence.
The simulations above assume consistent rates of
change among characters even though basic rates
of change likely vary among characters (Clarke and
Middleton 2008; Wagner 2012; Harrison and Larsson
2015). However, rate variation (here using lognormally
distributed rates yields expectations essentially identical
to uniform rates (Fig. 4b). Similarly, the simulations
above assume consistent rates of change over time
although numerous studies provide contrary examples
(e.g., Hopkins and Smith 2015). Hughes et al. (2013)
suggest that one such pattern, “early bursts” (Gavrilets
and Losos 2009), is common in fossil clades. Increasing
the relative rate of early change decreases the expected
stratigraphic compatibility considerably (Fig. 4c). Note
that “early burst” effectively doubles as a “low early
sampling model”: if we sample (say) only half the
branches among early taxa that we typically sample
among later taxa, then we expect approximately twice
as much change on those early branches even if true
rates were constant through time (e.g., Smith 1988;
Wagner 1995a). Thus, both secular decreases in rates
of change and secular increases in preservation rates
should decrease stratigraphic compatibility.
Finally, the simulations above assume that characters
change independently from each other. As discussed
in the introduction, many studies provide contrary
examples. Simulating character evolution under
two models in which sets of characters (and thus
probabilities of change) are linked to each other
also diminishes expected stratigraphic compatibility.
Correlated sets of characters, in which the probability
of independent change is much lower than that of
mutual change, make it more probable that the first
change for Character A accompanies a change for
linked Character B instead of happening alone. As the
proportion of characters in correlated sets increases,
843
expected stratigraphic compatibility decreases (Fig. 4d).
(Simulated characters in correlated suites now have
three states, so there is only a 50% chance of reversing
to 0 after an initial change to 1.) Similarly, change
among linked characters followed by alteration
of linkages patterns among those characters (akin to
increasing evolvability by altering modules of integrated
characters; e.g., Goswami et al. 2014) also increase the
probability of introduced Character C changing at
the same time as introduced Character D followed
by independent reversals. Correspondingly, as the
proportion of characters in introduced sets increases,
expected stratigraphic compatibility decreases (Fig. 4e).
Monte Carlo Tests
The simulations above set up the basis for Monte
Carlo tests for assessing whether we see too little
stratigraphic compatibility in data sets given the most
“liberal” expectations of independent change (see also
Wagner and Estabrook 2014). For any one data set,
we can estimate expected stratigraphic compatibility by
simulating morphological evolution over phylogenies as
follows:
1) Diversification is exponential with budding
cladogenesis (both of which minimize expected
stratigraphic compatibility relative to alternative
models).
2) Per-taxon origination, extinction, and sampling
rates follow either empirical estimates given
observed stratigraphic ranges (see Foote and Raup
1996) or separate Monte Carlo analyses that find
the combinations of relative rates maximizing the
probability of the same fossil record.
3) The number and distribution of missing characters
matches that of the original data.
4) The number of states per character matches that of
the original data.
Morphological evolution continues until the overall
compatibility of the simulated matrix matches that of
the original data. We repeat these 1000 times to generate
a distribution of expected stratigraphic compatibility
proportions using C programs written by the senior
author.
The analyses outlined above test a null hypothesis of
independent change with no major rate shifts. Because
rate shifts might be common (see Hughes et al. 2013), and
because there might be lingering concerns that sampling
is chronically low early in clade histories, we ran a second
set of analyses with separate rates for “early” (the firstthird of species) and “late” (the last two-thirds of species)
taxa. We obtain the relative “early” and “late” rates as
follows.
1) We identify the oldest S/3 taxa from a clade of S
species, rounding up if S is not evenly divisible
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SYSTEMATIC BIOLOGY
by three. If Species 6–9 in a clade of 20 species
all appear in the same interval, then we designate
the two species with the lowest average phenetic
distances from the initial five species as Species 6
and 7 (Wagner and Estabrook 2014).
2) We run 2500 Monte Carlo simulations to estimate
the number of steps maximizing the probability of
the observed compatibility among the “early” S/3
taxa (X) and among all S taxa (Y).
2X
3) We approximate the relative “early” rate as (Y−X)
.
The 2 in the numerator reflects that X steps happen
on approximately one half the branches that the
subsequent Y −X steps happen.
4) We then re-conduct the first set of Monte Carlo
analyses among all S taxa, but with the probability
2X
times
of change on “early” branches being (Y−X)
greater than that on “later” branches.
These analyses also are conducted in C programs written
by the senior author (see Supplementary Material,
available on Dryad at http://dx.doi.org/10.5061/dryad.
h5971).
DATA
We analyze 259 published character matrices
originally assembled for phylogenetic reconstruction
(Supplementary Material, available on Dryad at http://
dx.doi.org/10.5061/dryad.h5971; see also http://www.
paleobiodb.org/cgi-bin/bridge.pl?a=nexusFileSearch:
Reference number = “53238”). We use stratigraphic
data compiled from a variety of sources, particularly
from the original publications, and the Paleobiology
Database (http://www.paleobiodb.org).
We focus on species-level and genus-level analyses.
Analyses of suprageneric taxa frequently code taxa based
on the type genus of the taxon rather than the earliest
species in that taxon. As such, first appearance of the
taxon might be much earlier than the first appearances of
derived states. We make exceptions in cases where (say)
families represent the latest members of a species-level
or genus-level analysis of early members of a clade. For
example, a study of early horse species might include the
Equinae as a late-appearing taxon. Even if such studies
do not use the oldest members of the “crown” group
as exemplars, then concentrating apomorphies on late
branches will tend to elevate stratigraphic compatibility
because as there is no subsequent interval for taxa with
intermediate (e.g., 10 after 00 and 11) state-pairs to
appear.
We eliminate outgroup taxa for the same reason that
we do not use suprageneric analyses: outgroups often
are token representations of clades and thus might badly
misrepresent the appearances of character states. We
cull extant species or genera unless they have fossil
representatives. In such cases, we use stratigraphic
ranges matching their known fossil records rather than
assuming that they range through to the present. In order
to have a sample size of at least four taxa for the early rate
estimates, we analyze only studies with 12+ ingroup taxa
after these culls.
We treat multistate characters as unordered (Fig. 1f,g),
which maximizes the compatibility of multistate
characters (e.g., Meacham 1984; Salisbury 1999). This
also allows us to treat each binary breakdown with three
state-pairs as a compatible pair, which means that there
are theoretically more compatible pairs than there are
character pairs. (Note that stratigraphic incompatibility
requires three state-pairs regardless of whether binary
or multistate characters are involved.) However, we
get essentially identical results if we treat these as
fractions (e.g., one stratigraphically compatible and
one stratigraphically incompatible breakdown = half a
stratigraphically compatible pair). In all cases, character
pairs are considered stratigraphically incompatible
only if the intermediate state-pair appears last: if
the intermediate state-pair appears at the same time
as another state-pair, then we consider this to be
stratigraphically compatible.
Because of the effects of missing data, we cull
characters scored for fewer than 10 taxa. For the
remaining characters with missing data, we retain
missing entries in the same distributions. Thus, if
observed taxon 16 is scored as unknown for characters
22–25, then simulated taxon 16 is always scored
as unknown for characters 22–25. This maintains
not just the proportion of missing data, but also
the fact that which types of characters are missing
often is very non-random: for example, we typically
lose post-cranial elements more often than we lose
skull features (Kearney 2002; Sansom et al. 2010;
Smith et al. 2014). We retain autapomorphies in the
original data sets; however, if no autapomorphies were
present in a data set, then the Monte Carlo analyses
excluded simulated autapomorphies. Finally, we fixed
polymorphic characters to the state that maximized the
character’s overall compatibility. Because the probability
of character compatibility usually increases as greater
proportions of taxa are coded with the same state
(Estabrook et al. 1976), this usually meant choosing the
state seen in the most taxa. If two or more states left
the same overall compatibility for a character, then we
chose the oldest appearing state, which maximizes the
stratigraphic compatibility of the character.
RESULTS
General Patterns among Major Groups
For ease of comparison among major taxonomic
groups, we divide the data sets into four groups:
brachiopods + molluscs, arthropods, echinoderms,
and chordates. Although brachiopods and molluscs
do not share shells from a common ancestor, both
represent “simple” fossils of one or two basic homologies
(one or two shells) with many semi-autonomous
2015
845
WAGNER AND ESTABROOK—IMPLICATIONS OF STRATIGRAPHIC COMPATIBILITY
FIGURE 5.
Deviations from expected stratigraphic compatibility for different groups of metazoans assuming independent change and
consistent rates. Color shades correspond to the significance levels shown in the distributions of the P values provided on insets. The dashed
lines on the insets show the expected number of data sets with deviations that significant (see Table 1).
TABLE 1.
Numbers of data sets showing too little stratigraphic compatibility (Strat. Compat.)
P[Strat. Compat. | constant rate]
Taxa
Brachiopods and Molluscs
Arthropods
Echinoderms
Chordates
Metazoans
P[Strat. Compat. | early burst]
N
P < 0.5
P 0.25
P 0.05
P < 0.5
P 0.25
P 0.05
50
51
38
120
259
33 (0.02)
34 (0.01)
29 (8×10−4 )
75 (4×10−3 )
171 (1×10−7 )
21 (7 ×10−3 )
22 (4×10−3 )
24 (8×10−7 )
52 (9×10−6 )
119 (2×10−13 )
7 (0.01)
11 (4×10−5 )
12 (2×10−7 )
27 (4×10−11 )
57 (< 10−16 )
26(0.44)
27 (0.39)
27 (7 ×10−3 )
71 (0.03)
151 (4×10−3 )
15 (0.25)
17 (0.12)
16 (0.02)
41 (0.02)
89 (5×10−4 )
3 (0.46)
7 (0.01)
5 (0.04)
15 (1×10−3 )
31 (2×10−5 )
Notes: “Constant rates” have equal probabilities of character change throughout clade history. Early allows a separate fate for the earliest S/3
taxa in each clade of S taxa. Numbers in parentheses give the probability of observing that many data sets with such significant deviations given
that we expect 50% of clades to have too little stratigraphic compatibility, 25% to deviate at P 0.25 and 5% to deviate at P = 0.05.
regions on those shells. Arthropods, echinoderms,
and chordates all possess multi-element skeletons,
although serial repetition of hard-parts is common
in all groups. We might, therefore, expect different
levels of integration among fossilizable parts in these
groups. Finally, we also separate Cambrian from postCambrian trilobites in order to assess whether the
previously documented conservation of integration
patterns among post-Cambrian trilobites relative to
Cambrian trilobites correctly predict lower stratigraphic
compatibility among post-Cambrian trilobites than
among Cambrian trilobites.
It is very common for metazoan clades to have
less stratigraphic compatibility than predicted by
independent change and constant rates (Fig. 5; Table 1).
Moreover, it is very common for clades to show major
deviations: 119 of 259 clades show deviations that only
65 clades should show (binomial P = 2×10−13 ), and 57
of 259 clades show deviations that only 13 clades should
show (binomial P < 10−16 ; Table 1; also, insets of Fig. 7).
There is a strong correlation between the magnitude
of best-fit early bursts and excess stratigraphic
incompatibility (i.e., negative deviations from expected
stratigraphic compatibility) assuming constant rates of
846
SYSTEMATIC BIOLOGY
FIGURE 6. Association between best-fit relative rate of early change
(based on the first S/3 taxa for a clade of S taxa) and deviations
from expected stratigraphic compatibility. Numbers greater than 1
correspond to “early burst” scenarios. Shells denote brachiopods
and molluscs; trilobites denote arthropods; stars denote echinoderms;
fish denote chordates. Correlations given Kendall’s test: all taxa =
−0.226 (P = 5.9×10−8 ); brachiopods + molluscs = −0.065 (P = 0.503);
arthropods = −0.238 (P = 0.013); echinoderms = −0.342 (P = 2.5×
10−3 ); chordates = −0.237 (P = 1.3×10−4 ).
change over time (Fig. 6). This correlation is significant
within each taxonomic partition save brachiopods +
molluscs. However, Monte Carlo tests assuming these
early rates still find too little stratigraphic compatibility
among the preponderance of clades, particularly among
arthropods, echinoderms, and chordates (Fig. 7). Still,
89 of 259 data sets show deviations that we expect to
see from 65 clades (binomial P = 5×10−4 ), and 31 of 259
show deviations expected from 13 clades (Table 1; insets
of Fig. 7). Among our partitions, brachiopods + molluscs
now provide an exception: the distributions of deviations
now fit expectations assuming elevated early rates and
independent change.
Cambrian versus Post-Cambrian Trilobites
Within
arthropods,
Ordovician–Carboniferous
trilobites show significantly more deviations at the
P = 0.50, P = 0.25, and P = 0.05 levels than expected even
given possible early bursts (Table 2; Fig. 8). Conversely,
the distribution of deviations for Cambrian trilobites
is completely within expectations not just given early
bursts, but also under time-homogeneous rates.
DISCUSSION
Alternative Explanations for Excess Stratigraphic
Incompatibility
As we note above, low sampling intensities early in
clade histories can mimic “early burst” patterns (Smith
1988; Wagner 1995a, 1997; Ruta et al. 2006). Empirical
studies suggest that sampling rates within species are
VOL. 64
low early in species histories in some clades (Liow and
Stenseth 2007), although there are exceptions to this
(Wagner 2000b). However, this only changes the question
to whether peak sampling intensities of early species are
lower than that of later species. If not, then this will not
create trends in per-taxon sampling over time and thus
not mimic early bursts. It is important to distinguish
between “per-taxon sampling” and “clade sampling”
here. If per-taxon sampling remains constant, then the
probability of missing all members of a diversifying
clade decreases exponentially as richness increases.
A corollary of this is that expected stratigraphic
compatibility given our tests assumes lower sampling
of clades early in their histories by assuming continuous
exponential diversification even while assuming no
trends in per-taxon sampling (see, e.g., Foote 1996a).
Finally, even if we do attribute apparent early bursts to
relatively poor per-taxon sampling, then we still need
to explain excess stratigraphic incompatibility given the
assumptions of independent change and separate early
rates.
It is difficult to attribute our results to assumptions
about other general evolutionary processes. We get
essentially the same results if we model our “early
burst” on the first half or first quarter of taxa
as we do using the first third of taxa. Our final
tests use parameters (budding speciation, exponential
diversification, and separate early vs. late rates of
character change) that minimize expected stratigraphic
compatibility relative to alternative models (e.g.,
bifurcating speciation, logistic diversification, and
continuous rates of character change). Indeed, this
makes our results more conservative. For example,
bifurcation and other speciation modes involving
anagenetic change likely do occur in some clades
examined here (e.g., Pardo et al. 2008). Logistic or
other richness-dependent diversification patterns are
common for the groups studied here (Miller and
Sepkoski 1988; Maurer 1989; Wagner 1995b; Alroy 1996;
Eble 1998; Brayard et al. 2009). Thus, the data probably
demand an explanation beyond early bursts (or poor
early sampling) even more than our results suggest.
Because our tests retain the number and distribution
of missing characters as found in the original data sets,
we also cannot attribute the results to missing data.
It also is difficult to ascribe these results to
the way that paleosystematists collect comparative
data. Traditionally, systematists are trained to exclude
characters that are obviously correlated with one another
(e.g., Forey et al. 1992; Smith 1994). Although prior
studies suggest that workers do not completely succeed
in doing this (see, e.g., Wilkinson 1995; Rieppel and
Kearney 2002; Harris et al. 2003), these protocols still
should bias data sets against the results that we obtain.
Integration as a Likely Culprit
Our
results
suggest
that
non-independent
(=correlated) character change has a strong effect
on observed patterns of anatomical characters
2015
847
WAGNER AND ESTABROOK—IMPLICATIONS OF STRATIGRAPHIC COMPATIBILITY
FIGURE 7. Deviations from expected stratigraphic compatibility for different groups of metazoans assuming independent change and separate
early versus late rates (Fig. 6). Shades correspond to the levels of significance shown in the distributions of the P values provided on insets. The
dashed lines on the insets show the expected number of data sets with deviations that significant (see Table 1).
TABLE 2.
Numbers of trilobite data sets showing too little stratigraphic compatibility
P[Strat. Compat. | constant rate]
P[Strat. Compat. | early burst]
Trilobites
N
P < 0.5
P 0.25
P 0.05
P < 0.5
P 0.25
P 0.05
Cambrian
Ordovician–Permian
17
24
9 (0.50)
18 (0.011)
21 (0.43)
13 (2×10−3 )
1 (0.58)
7 (1×10−4 )
5 (0.98)
16 (0.08)
2 (0.95)
11 (0.02)
0 (1.00)
6 (1×10−3 )
Note: See Table 1 for further explanation.
and character states. Mechanisms that could create
correlated change include common selective pressures,
functional linkages, and integration. Common selective
pressures would drive sets of characters to similar
derived conditions. Numerous plausible examples of
this phenomenon come from the repeated evolution
of ecomorphologically important character complexes
among fossil (e.g., Cheetham 1987; Alroy 1998; Vermeij
and Carlson 2000; Wagner and Erwin 2006; Slater
2015) and living (Losos 1992; Gillespie 2004) taxa.
However, pervasive selection favoring particular states
also should generate driven trends (i.e., biased change
toward particular conditions; McShea 1994). Driven
trends in turn should generate copious homoplasy.
Alternatively, if multiple characters can combine in
different ways to achieve similar performance, then
we expect numerous different combinations of these
characters (Cheetham 1987; Wagner and Erwin 2006).
Both abundant homoplasy and an expectation of
many combinations of states for sets of characters
greatly decrease expected compatibility (Fig. 2).
Because character pairs first must be compatible to
stratigraphically incompatible, correlated selection is an
unlikely explanation for stratigraphic incompatibility.
A conceptually related alternative explanation is
functional linkage of characters (e.g., Wainwright
1988). Complex structures combine multiple homologies
into a functional unit (e.g., an appendage), allowing
an organism to properly well only with particular
combinations of characters. An advantage of this
848
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SYSTEMATIC BIOLOGY
FIGURE 8.
Deviations from expected stratigraphic compatibility for a) Cambrian and b) Ordovician–Carboniferous trilobites assuming
independent change and separate early versus late rates (Fig. 6). Shades correspond to the levels of significance shown in the distributions of the
P values provided on insets. The dashed lines on the insets show the expected number of data sets with deviations that significant (see Table 2).
explanation over common selective pressures is that
it predicts (or at least allows for) infrequent changes
among linked characters, which would preserve
high compatibility. We also might expect it to be
more common among echinoderms, arthropods, and
chordates than among molluscs and brachiopods
because the former group of organisms have many
more skeletal parts. However, there are two key
failings to this model. One, although functional linkage
predicts elevated 00 →11 shifts, it does not predict
the subsequent evolution of 10 forms; if such forms
evolve at all, then we expect them to be intermediate
and thus to create stratigraphic compatibility. Two, this
model does not offer a ready explanation for why
Cambrian trilobites differ from post-Cambrian trilobites
as Cambrian trilobites, as both groups should have had
similar functional demands on sets of characters. Thus,
this explanation also seems inadequate.
Integration models, particularly the developmental or
genetic linkage of characters (Olson and Miller 1958;
Cheverud 1982, 1984, 1996; Zelditch 1987; Klingenberg
2008), offer another means of non-independent character
change. Unlike the common selective forces model,
we expect integrated characters to change infrequently:
if a favorable modification to Character A coincides
with unfavorable modifications to Characters B, C,
and D, then selection often will act against the
overall change (Lande and Arnold 1983). Unlike
functional linkage, integration also allows for reversals
in some characters that would generate stratigraphic
incompatibility. If change in Character A accompanies
change in Characters B, C, and D but there is no
functional need to combine the derived states for the
four characters, then infrequent independent change for
Characters B, C, and D would have high probabilities of
persisting if they return to the original states: after all,
taxa with those states had been successful in the past.
The probability of this happening increases if integration
is subsequently reduced among the altered sets (e.g.,
facial characters in sabre-tooth felids; Goswami 2006b).
In such cases, shifts in integration will simply increase
the overall evolvability within a clade (Vermeij 1973;
Goswami and Polly 2010; Goswami et al. 2015; see also
Fig. 4e). Thus, integration models predict stratigraphic
incompatibility much better than do either correlated
selection or functional linkage.
Even without first principle arguments, the distinct
pattern among Cambrian trilobites suggests an
association between how frequently integration
patterns change and stratigraphic compatibility. We
have no reason to think that correlated selection and/or
functional linkages among Cambrian trilobites differed
from those among post-Cambrian trilobites. On the
contrary, morphometric studies of trilobite populations
do suggest that integration patterns changed more
often among Cambrian trilobites than among postCambrian species (Hughes 1991; Webster 2007; Webster
and Zelditch 2008, 2011a, 2011b). Examples of strong
phylogenetic conservation of integration patterns also
exist for chordates (e.g., Goswami 2006a, 2006b; Sears
et al. 2007, 2011; Finarelli and Goswami 2009) and
echinoderms (e.g., McKinney 1986; Kjaer and Thomsen
1999). Thus, attributing stratigraphic incompatibility to
infrequent shifts among integrated characters offers a
simple explanation for the inverse association between
phylogenetically conserved integration patterns and
stratigraphic compatibility.
Macroevolutionary Implications
Workers have paid much attention to how integration
and related concepts such as modularity might limit
or encourage the range of character states that a clade
can produce (i.e., evolvability; e.g., Riedl 1978; Plotnick
and Baumiller 2000; Wagner and Müller 2002; Eble
2015
WAGNER AND ESTABROOK—IMPLICATIONS OF STRATIGRAPHIC COMPATIBILITY
849
FIGURE 9. Depictions of relative rates under different models of character change. a) Independent change, in which individual characters
have rates of independent change only. b) Loosely integrated characters. The net probability of a character changing is the same as in a), but
with some probability of change for all four characters (dark bar) being part of that probability. c) Tightly integrated characters, in which the
most probable mode of change for some characters is joint change.
2005; Goswami and Polly 2010; Goswami et al. 2011,
2014, 2015; Wagner 2014). We can explain stratigraphic
incompatibility in these terms. If the benefits of a
derivation in one character outweigh the costs of
accompanying changes in linked characters, then the
lineage with these derivations might diversify at the
expense of related species. However, we would also
expect elevated selection favoring change in the lessoptimal characters, either by increasing the probability
that less-common independent changes are fixed, or
by favoring reduced integration among the characters
(Monteiro and Nogueira 2010). This would lead to
elevated disparity from characters moving on to still new
states and stratigraphic incompatibility from characters
reverting to the original state. If this model is correct,
then future work should show a negative correlation
between stratigraphic compatibility and how quickly
clades fill character space (see, e.g., Wagner 2000a;
Hughes et al. 2013).
Unfortunately, our Cambrian examples include
only three non-trilobite clades. Thus, we cannot
assess the next obvious question: is low phylogenetic
conservation of integration patterns is a Cambrian
phenomenon or a Cambrian trilobite phenomenon?
Even among Cambrian trilobites, Webster (2015)
suggests integration patterns were more tightly
conserved in some anatomical systems than in others.
Thus, we do not necessarily expect to see “relaxed”
integration in the preserved systems of other Cambrian
taxa even if the phenomenon was relatively common in
the Cambrian. The one major benefit of stratigraphic
compatibility analyses is that our analyses do not require
the dense sampling that Cambrian trilobites commonly
offer. Thus, it can be applied to groups such as other
arthropods, echinoderms, and early chordates. Our
study simply adds another reason for paleontologists
to make advanced systematic studies of non-trilobite
Cambrian genera and species a priority.
Methodological Implications
The macroevolutionary implications of stratigraphic
compatibility patterns have corollary methodological
implications. Pervasive stratigraphic incompatibility
explains a common mismatch between stratigraphy and
inferred phylogeny. The Stratigraphic Consistency Index
(SCI; Huelsenbeck 1994) measures how frequently lower
nodes on a tree include taxa with older fossil records
than taxa within higher nodes. As random error in trees
increases, expected SCI goes to 0.5 (Wagner and Sidor
2000). However, Benton et al. (2000; see also Wills 2001)
document that over 50% of estimated phylogenies for
10+ species have SCI < 0.5. This suggests that portions
of inferred phylogenies are “upside-down”: i.e., they
reconstruct old species as derived and young species as
primitive. This in turn is consistent with our suggestion
that processes such as integration and subsequent
evolvability generating numerous 00 → 11 transitions
followed by 11 → 10 transitions as lineages “stagger” into
more optimal character state combinations. If so, then
future studies should find correlations between SCI and
stratigraphic compatibility.
Pervasive stratigraphic incompatibility re-raises the
issue about how we should model morphological
evolution. The differences between how we model
morphological change in our different simulations
point us in a general direction. Consider a model in
which all character change reflects independent rates
coming from a lognormal distribution (Fig. 9a; see
Fig. 4b). If the median rates do not decrease over
time, such models generate the very high stratigraphic
compatibility we find in most of our simulations
(Figs. 2–4). Distributed models often are better than
single-rate models for predicting many aspects of
character distributions (e.g., Clarke and Middleton 2008;
Wagner 2012; Harrison and Larsson 2015). However,
independent change models of any sort fail to predict
stratigraphic compatibility patterns in fossil taxa other
than Cambrian trilobites.
Simulations that reduce expected stratigraphic
compatibility require fundamentally different models
from Figure 9a. In addition to parameters for
independent change (the solid curves in Fig. 9b,c),
these models require an additional parameter for joint
change (the solid bar in Fig. 9b,c). In our correlated
change models (Fig. 4d), this solid bar represents the
probability of joint change; in our “evolvability” models,
850
VOL. 64
SYSTEMATIC BIOLOGY
this solid bar represents the probability of previously
static characters changing and becoming free to change
independently (Fig. 4e). (Models of joint change can
[and usually will be] more complicated than we show,
with some subsets of characters being more tightly
linked to each other than to other characters in the same
set; however, our intent is to illustrate models similar to
those used in our simulations.)
Figure 9 lays out the challenge for morphological
systematists: we not only need to identify distributions
of independent change among characters, but: (1) sets
of characters with some degree of linked change; and
(2) how to model rates of joint change among (and
even within) different sets of characters. Of course, our
study is hardly the first to make this clear: copious
“evo-devo” studies over the last decade have made this
obvious. Instead, our point is that these models can make
distinct predictions about stratigraphic compatibility as
well as general compatibility (e.g., Wilkinson 1997, 1998;
O’Keefe and Wagner 2001; Dávalos et al. 2014). Thus,
stratigraphic distributions of character combinations
can and should play an important role in identifying
and testing appropriate models even when the fossil
record consists of few or even single specimens per
taxon.
CONCLUSIONS
Under simple models of morphological evolution,
the different state-pair combinations of compatible
characters should appear in the fossil record in the
order in which they evolve in nearly 95% of cases. Thus,
compatible character pairs should be stratigraphically
compatible. Models of character change predicting
that state-pair combinations will appear in orders not
matching simple character state trees include elevated
rates, correlated change, and increased evolvability.
Monte Carlo analyses indicate that stratigraphic
compatibility is much lower in brachiopod, mollusc,
arthropod, echinoderm, and chordate data sets than
expected given independent change and constant rates.
Additional analyses allowing for early bursts still
indicate that stratigraphic compatibility is too low
in arthropod, echinoderm, and chordate data sets.
This suggests that mechanisms such as integration
that encourage correlated change and (under some
circumstances) evolvability affect the distributions of
morphological states in the fossil record. This conclusion
is further corroborated by Cambrian trilobites being
the one major exception to our general results: as
predicted by morphometric-based integration studies,
Cambrian trilobites show much more stratigraphic
compatibility than do taxa for which integration patterns
are shared among many species. These results suggest
that the stratigraphic data can join developmental
and morphometric analyses as a powerful tool for
developing and justifying complex character evolution
models, which in turn will improve phylogenetic and
macroevolutionary hypothesis testing.
SUPPLEMENTARY MATERIAL
Data available from the Dryad Digital Repository:
http://dx.doi.org/10.5061/dryad.h5971.
ACKNOWLEDGMENTS
Although this project was completed after George
Estabrook’s death, George helped design the basic tests
and concurred with the general conclusions from the
initial results. P.D. Polly, M. Wilkinson, and M. Hughes
provided invaluable constructive reviews; we also thank
an anonymous reviewer who suggested that we test the
possible effects of early burst models in more detail. For
general discussion and/or comments on earlier drafts
of the manuscript, we thank J. Alroy, D.H. Erwin, F.R.
McMorris, and J. Marcot. For discussion on how to best
illustrate linked-change models, we thank S. Darroch, R.
Racicot, C. Simpson, S. Tweedt, and R. Warnock. This is
Paleobiology Database Publication 228.
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