Early bursts of disparity and the reorganization of character integration

Abstract

‘Early bursts' of morphological disparity (i.e. diversity of anatomical types) are common in the fossil record. We typically model such bursts as elevated early rates of independent character change. Developmental theory predicts that modules of linked characters can change together, which would mimic the effects of elevated independent rates on disparity. However, correlated change introducing suboptimal states should encourage breakup (parcellation) of character suites allowing new (or primitive) states to evolve until new suites arise (relinkage). Thus, correlated change–breakup–relinkage presents mechanisms for early bursts followed by constrained evolution. Here, I analyse disparity in 257 published character matrices of fossil taxa. For each clade, I use inverse-modelling to infer most probably rates of independent change given both time-homogeneous and separate ‘early versus late' rates. These rates are used to estimate expected disparity given both independent change models. The correlated change–breakup–relinkage model also predicts elevated frequencies of compatible character state-pairs appearing out of order in the fossil record (e.g. 01 appearing after 00 and 11; = low stratigraphic compatibility), as one solution to suboptimal states induced by correlated change is a return to states held before that change. As predicted by the correlated change–breakup–relinkage model, early disparity in the majority of clades both exceeds the expectations of either independent change model and excess early disparity correlates with low stratigraphic compatibility among character-pairs. Although it is possible that other mechanisms for linking characters contribute to these patterns, these results corroborate the idea that reorganization of developmental linkages is often associated with the origin of groups that biologists recognize as new higher taxa and that such reorganization offers a source of new disparity throughout the Phanerozoic.

1. Introduction

A common pattern in the fossil record is for the range of distinct anatomical forms (i.e. morphological disparity) to be high early in clade histories [1]. Early bursts of disparity are consistent with rates of anatomical change early in clade history being greater than rates of change late in clade history [2]. One general model explaining early bursts of disparity is that intrinsic (e.g. developmental or genetic) constraints on anatomical change are lower among early species in a clade than in later ones, which makes the probability of novel anatomies higher early in clade history than it is later [3,4]. The developmental model that has received the most attention for constraining anatomical change is integration [5–13]. Increased integration among characters should reduce frequencies of change in two ways: (1) reducing cases of single character changes; and, (2) introducing deleterious states when multiple characters change together [14]. Empirical and simulated integration studies at least partially corroborate this model by showing that, with some exceptions [12,13], elevated integration typically corresponds to reduced overall disparity [7–11].

Given that integration is documented in Cambrian animals [15,16], and given that bursts of disparity occur throughout the Phanerozoic [1,17], continuous increase in developmental constraints over time cannot explain all early bursts. An alternative explanation is that some bursts of disparity are driven by unusual ecologic opportunities (e.g. ‘empty ecospace') inducing elevated rates of change and bursts of disparity [18–21]. Another explanation is that early bursts are not products of rate shifts, but instead reflect clades exhausting or saturating a restricted range of distinguishable character states [22,23]. ‘Constraint' here is not from character-linkages, genetics or function, but instead from architectural limitations. Although empirical analyses indicate that character-state exhaustion is the norm for fossil data [24], exhaustion/saturation does not explain the generation of new morphospace [17]. Another explanation for early bursts comes from the developmental theory used to explain decreasing rates of change [6–8]. Modularity treats complexes of integrated characters as semiautonomous homologies, with distinct states for individual characters appearing more often through interactions with other characters in the same module than through independent processes or interactions with characters in other modules [25]. Moreover, modules and the specific patterns of integration they entail evolve over time [5,26]. The breakup of modules (i.e. parcellation [27]) and subsequent evolution of new modules and integration patterns is a means for innovations to ‘overcome' constraints [14]. If so, then we should see correlated change among linked characters, followed by independent changes among ‘parcellated' characters before they become tightly linked to other characters in new modules. Disparity should increase rapidly due to the initial correlated change altering multiple characters in a module and then due to elevated rates of independent change after parcellation. New integration patterns then would often limit additional disparity.

This leaves us with three models predicting elevated early bursts of disparity: exhaustion/saturation of limited character space with continuous rates of change (hereafter: Model 1); elevated early independent rates due to ecologic opportunities and/or looser developmental constraints (hereafter: Model 2); and correlated change-breakup-relinkage (hereafter: Model 3). The compatibility and stratigraphic compatibility of the characters generating the disparity offer means of teasing out these different models. Two characters are compatible if they have no necessary homoplasy (e.g. a pair of binary characters with ≤3 of the four possible combinations [28,29]; figure 1a versus figure 1b). Increasing rates of change within a character space decrease expected compatibility [30]. Therefore, we can use inverse modelling to find the frequencies of change that maximize the probability of observed compatibility within a clade [31]. This, in turn, allows us to assess the probability of early disparity under most probably version of Model 1. We can do the same for Model 2 by estimating the most probably early rates of change given compatibility among early species, and then the probability of early disparity given the most probably version of Model 2.

Figure 1.

Compatibility, incompatibility and stratigraphic compatibility with correspond disparity patterns for hypothetical taxa with two binary characters. Disparity patterns give the maximum possible pairwise dissimilarity (= differences/2), which occurs when equal numbers of species possess each state-pair [1]. (a,d) Compatible and stratigraphically compatible state pairs showing no necessary homoplasy and with the state pairs appearing in the fossil record in an expected order. (b,e) Incompatible character pair with necessary homoplasy. (c,f) Stratigraphically incompatible pair, in which the intermediate condition (01) appears after the other two pairs.

Unfortunately, the extremely large number of possible ‘modules' for even small numbers of characters leave inverse modelling unsuitable for finding best-candidate hypotheses for Model 3 [30]. Fortunately, compatibility and stratigraphic compatibility [32] provide means for rejecting Model 2 (high early independent rates) in favour of Model 3 (correlated change–breakup–relinkage). A compatible pair is stratigraphically compatible if the intermediate state-pair appears first or second in the fossil record, which is consistent with either a 00 → 01 → 11 or a 00 ← 01 → 11 character-state tree (e.g. figure 1a). If taxa with 01 appear after taxa with 00 and 11 (figure 1c), then there is no character-state tree without either homoplasy or implied stratigraphic gaps. Characters with high compatibility typically evolve slowly relative to the rate at which we sample taxa. Thus, we expect stratigraphic compatibility in over 90% of compatible character-pairs regardless of the quality of the fossil record under a wide variety of evolutionary and preservational models, including those encompassed by Model 1 (figure 1d) [31]. Models 2 and 3 are exceptions, as both elevate the probability of 00 → 11 transitions that increase disparity and create the possibility of a subsequent 11 → 10 changes reducing stratigraphic compatibility (figure 1f) [2,22,33]. Model 3 predicts bigger deviations in both excess disparity and surfeit stratigraphic compatibility at a given level of compatibility than does Model 2. This is because Model 3 allows linked change to a set of 5 characters to introduce 5 new states with no necessary homoplasy whereas Model 2 often requires 6+ changes to alter 5 characters. Model 2, therefore, should require more homoplasy to generate the same level of disparity. This also means that at any particular amount of compatibility, Model 3 predicts higher disparity than does Model 2. Although both models encourage 00 → 11 transitions that set up stratigraphic incompatibility, Model 3 eliminates the possibility of 00 → 01 among linked characters whereas Model 2 does not. Thus, Model 3 also predicts less stratigraphic compatibility than does Model 2 at any particular amount of compatibility. Model 3, therefore, predicts that we should find a negative correlation between in the deviations from expected stratigraphic compatibility and disparity given compatibility among early species in a clade. The goal of this work is to assess whether early disparity in empirical datasets is consistent with observed compatibility, and whether early disparity exceeding the expectations of compatibility is associated with excess stratigraphic incompatibility.

2. Material and methods

(a). Data

The analyses cover 257 published character matrices of 13+ ingroup taxa that were originally assembled for phylogenetic analyses (electronic supplementary material, appendix S1). The criteria for choosing these datasets as well as details about stratigraphic data are detailed elsewhere [31].

(b). Measuring disparity, compatibility and stratigraphic compatibility

I measure disparity using the average pairwise dissimilarity among discrete characters [18,22,34]. I treat multistate characters as unordered when calculating pairwise dissimilarity, compatibility and stratigraphic compatibility. For disparity, this means that any taxa are considered either different or the same for any coded character. With complete exhaustion of a morphospace averaging ν novel (derived) states per character, we expect disparity to asymptote to [35] (see also figure 1d–f). For compatibility and stratigraphic compatibility, unordered multistates mean that intermediate states (e.g. ‘medium' relative to ‘small' and ‘big') need not appear in between the extreme states for a character-pair to be compatible.

I measure disparity and character compatibility separately for the earliest S/2 taxa and for all S taxa in a clade of S taxa [36] (see electronic supplementary material, table S1 and figure S1). I calculate stratigraphic compatibility for all S taxa only. Note that most palaeobiological disparity studies measure disparity only among contemporaneous taxa [1,34,37,38]: by using cumulative disparity, this study is closer to studies contrasting disparity among whole subclades [39,40] and to studies examining disparity encompassed by whole clades of extant taxa [41,42]. Analyses using the earliest S/3 taxa are presented in the electronic supplementary material. When S is odd (or not a factor of 3), I round up (e.g. (S + 1)/2). If stratigraphic binning creates ‘ties' for taxon S/2, then the taxa creating the least disparity among the first S/2 are chosen for the ‘early' analyses of both disparity and compatibility. Thus, if there are 21 taxa, and species 9, 10, 11 and 12 all appear in the same interval, whichever three of those species add least to total disparity are used along with taxa 1–8.

(c). Monte Carlo tests for expected early disparity

For each dataset, I use Monte Carlo tests simulating phylogenies and independent character change to estimate the probability of the observed compatibility and numbers of derived states given X changes among S taxa and N characters [30,31,43]. The probability of any individual character changing is uniform and simulated character state evolution is unordered. Both protocol minimize the expected number of changes needed to realize all N states in an N-state character space [22–24,44], and thus maximize the disparity expected given some level of disparity. Because real data show strong evidence of rate heterogeneity among characters [43–45], these protocols introduce a conservative bias against rejecting Models 1 and 2. Simulations are done 1000 times for each dataset for all S taxa and again using only the earliest S/2 (or S/3) taxa. The steps maximizing the probability of observed data are used for the overall and early rates, respectively.

I determine expected disparity among the first S/2 (or S/3) taxa using a second set of Monte Carlo analyses that use the best candidates from Model 1 and 2. Expected disparity is the median from 1000 simulations under Model 1 or 2.

I use two tests to assess whether early bursts of disparity exceeding the expectations of Models 1 and 2 are typical. I use binomial probability to assess whether significantly more than 50% of clades show this pattern. I use Wilcoxon signed-rank tests to assess whether the largest absolute deviations from expectations are positive (early bursts). The rank test uses log ratios so that positive deviation X and negative deviation 1/X have identical ranks based on abs(log[X]). I then use Kendall's rank correlation tests to assess correlations between the ratios of observed and expected early disparity with time, early rates and stratigraphic compatibility.

3. Results

Early bursts of disparity exceeding expectations given Model 1 (consistent independent change) occur in 203 of the 257 clades examined (figure 2a). In 91 cases, the deviations are significant at p ≤ 0.05 (electronic supplementary material, figure S2). Within each of taxonomic partition, significantly more than half of studies show excess early disparity and the summed ranks of absolute deviations is significantly biased towards excess early disparity (table 1). The pattern also is common throughout the Phanerozoic: significantly more than half of datasets show excess early disparity in 8 of 11 periods, and the summed ranks are biased significantly in favour of excess early disparity in 9 of 11 periods (electronic supplementary material, table S2). Differences between observed and expected disparity given the Model 1 correlate with the relative difference between early rates and late rates from 2-rate models for each clade (figure 2b; τ = 0.470; p < 10⁻²⁰). This association is significant within all four general taxonomic partitions (figure 2). The associations between early bursts and best-fit early rates are positive in all 11 periods, and significant at p ≤ 0.06 in 9 of 11 periods. Thus, both disparity and compatibility patterns deviate from the expectations of the consistent independent change model (Model 1; table 1).

Figure 2.

Deviations from expected disparity (D) among the first S/2 of S taxa given the uniform rates of independent change that maximize the probability of observed compatibility (Model 1). Deviations are on a log scale so that one-half and twice of expected D represent the same absolute deviation. (a) Deviations over time: τ = 0.039, p = 0.379. (b) Deviations against the ratio between early and late rates maximizing the probability of compatibility among the first S/2 taxa. Molluscs + brachiopods (purple shells): τ = 0.383, p = 1.0 × 10⁻⁴; arthropods (orange trilobites): τ = 0.443, p = 4.6 × 10⁻⁶; echinoderms (blue stars): τ = 0.411, p = 2.0 × 10⁻⁴; chordates (green fishes): τ = 0.488, p = 3.6 × 10⁻¹⁵.

Table 1.

Deviations from expected early disparity within major taxonomic groups. ‘Studies’ refers to the number of published matrices represent clades used. ‘Excess' gives the number of studies with excess disparity in the first half of clade evolution given a single rate (‘1-rate'; Model 1) and given separate early and late rates (‘2-rate'; Model 2), with the early rate maximizing the probability of character compatibility given the earliest S/2 of S total taxa. The significance is the binomial probability of that many excess cases given the total studies and an expectation of 50%. ‘∑R' gives the signed rank statistic, which ranks deviations by absolute values but then gives each rank a +/− based on the original statistic. Deviations are ranked after log-transformation, so half the expected disparity has the same rank as twice the expected disparity. Significance is assessed on the expectation that ∑R = 0.

		Model 1				Model 2
		1-rate		1-rate		2-rate		2-rate
taxa	studies	excess	p-value	∑R	p-value	excess	p-value	∑R	p-value
brachiopods + molluscs	49	43	7.6 × 10−9	989	4.4 × 10−7	35	1.4 × 10−3	749	9.8 × 10−5
arthropods	51	40	1.5 × 10−5	872	2.2 × 10−5	33	0.024	570	3.8 × 10−3
echinoderms	38	35	5.4 × 10−9	653	1.1 × 10−6	28	1.7 × 10−3	525	7.0 × 10−5
chordates	119	85	1.3 × 10−6	3441	1.9 × 10−6	78	2.9 × 10−4	2222	1.6 × 10−3

Early disparity exceeds the expectations of Model 2 (elevated early independent change) in 174 of 257 clades (figure 3a; table 1). In 40 cases, the deviations are significant at p ≤ 0.05 (electronic supplementary material, figure S3). Excess early disparity deviates significantly from the expectations of best-fit single-rate models within the basic taxonomic partitions (table 1). In every period but the Jurassic, over half of the clades show greater disparity than predicted by elevated early rates, with five periods showing deviations significant at p ≤ 0.05 (electronic supplementary material, table S2). All 11 periods have ranked absolute deviations favouring positive (excess) disparity, with 8 of 11 periods deviating from a symmetrical distribution around zero at p ≤ 0.06. Thus, early bursts of disparity typically exceed the expectations of plausible elevated early rates of independent change (table 1).

Figure 3.

Deviations from expected disparity (D) among the first S/2 of S taxa given the early rates of independent change that maximize the probability of observed compatibility among the first S/2 taxa (Model 2). See figure 2 for further details. (a) Deviations over time: τ = 0.035, p = 0.421. (b) Disparity deviations against deviations from expected stratigraphic compatibility given the same 2-rate model. Molluscs + brachiopods (purple shells): τ = 0.191, p = 0.053; arthropods (orange trilobites): τ = 0.343, p = 3.9 × 10⁻⁴; echinoderms (blue stars): τ = 0.165, p = 0.145; chordates (green fishes): τ = 0.301, p = 1.3×10⁻⁶.

Early disparity exceeding Model 2 expectations correlates negatively with stratigraphic compatibility within clades (figure 3b; τ = −0.277; p = 1.7 × 10⁻¹⁰). This association exists in all 11 periods, although it is rarely significant (electronic supplementary material, table S3). The associations also are negative in all four higher taxonomic partitions (table 1) and significant at p ≤ 0.05 for all groups save echinoderms. Thus, as predicted by Model 3 (correlated change–breakup–relinkage), greater deviations in early disparity from Model 2 expectations correspond to a greater tendency for compatible sets of character-pairs to appear out of order in the fossil record.

4. Discussion and conclusion

As noted above, the tests used here have conservative biases favouring Models 1 and 2. What stands out here is that I get these results after attributing as much early disparity as possible to Model 2 (high early independent change) without being able to consider whether Model 3 (correlated change–breakup–relinkage) is solely responsible for early bursts. Moreover, the data themselves probably are biased against these results because systematists are counselled to exclude characters that might be correlated with other characters [46]. Although systematists are not completely successful at doing so [30,47,48], the practice still biases these data against corroborating hypotheses invoking correlated change. The results also are robust to assumptions about the timing of shifts: Monte Carlo tests looking at disparity and rate shifts among the earliest S/3 taxa generate nearly identical results (electronic supplementary material, tables S4–S5 and figures S3–S6).

Low sampling of early taxa might elevate early disparity [2]. However, Model 2 essentially doubles as a low early sampling model as decreasing the frequency of sampled species results in more time for phylogenetic branches to accumulate change [31]. Thus, rejection of Model 2 doubles as a rejection of sampling as the underlying cause of apparent early bursts.

These results corroborate other meta-analyses showing that early bursts are common in palaeontological data [1]. (Note that 51 of the 257 matrices examined here were used in [1]). By using character compatibility to establish expected disparity under Model 1, these results also show that early bursts are not driven by exhaustion of character states. Moreover, the results indicate elevated rates of independent character change inadequate for explaining early bursts: compatibility indicates that there is less homoplasy than independent change models would induce while generating observed disparity. By contrast, correlated change early in clade history can maximize disparity while retaining high character compatibility by concentrating changes among linked characters [30].

Bursts of disparity associated with the correlated change–breakup–relinkage model are consistent with the expected effects of Gene Regulatory Networks [49] and Character Identity Networks [50]. The impetus would be the rare circumstance in which one or more novelties generated by change to a character complex is an innovation [51] that outweighs any maladaptive effects of changing other characters in the same complex [14,52]. In principle, this would introduce strong selection for parcellation of characters in the same module as the innovation(s) [53]. This, in turn, would allow other characters to either return to functionally superior primitive conditions (reducing stratigraphic compatibility) or develop still different states (creating further disparity). If the innovation opens up new ecologic opportunities and/or alters functional interactions with characters in other modules, then the stage is set for selection favouring reorganization of integration among other character modules [14,26,27,49–52]. Subsequent evolution of integration networks within the new modules would later diminish evolvability and discourage additional disparity. We then expect to see later bursts of disparity if taxon sampling spans enough time to include another round of correlated change–breakup–relinkage (e.g. [54]).

Although most modern discussions of integration focus on developmental and genetic linkage of characters, early definitions include functional linkage. Whereas we have developmental theory predicting the patterns summarized here, we lack formal theory involving function alone does the same. Moreover, functional linkage versus modularity could be a needless dichotomy: there is no reason why selection for new modules cannot reflect functional demands [55–57]. That axes of variation within modules can parallel selective gradients [13] might corroborate this notion. Thus, I will treat these results as corroborating the notion that shifts in integration patterns induce early bursts of disparity, but with the caveat that other forms of character linkage other developmental ones might be important in some cases. Regardless of the underlying mechanisms, the most important implication of the results presented here is that we do not observe the combinations of early disparity, character compatibility and stratigraphic compatibility predicted by independent character change models.

A corollary of the preceding paragraph is that the correlated change–breakup–relinkage model further erodes the false dichotomy between ‘developmental constraints' and ‘ecological restrictions' [4]. The ‘empty ecospace' model usually is framed in terms of elevated independent character evolution, and thus matches Model 2 here. However, if unusually empty ecospace helps create circumstances where the benefits of one novelty or a few novelties outweigh the drawbacks of associated changes [53], then parcellation of modules due ecological pressures and any variation in developmental parameters should alter the ease in which taxa can achieve different combinations of character states and different adaptive peaks [58]. If so, then examination of individual clades might suggest ecological ‘cues' associated with increases in disparity and low stratigraphic compatibility [20,59].

A question that might arise is: given that all early bursts are actually ‘delayed bursts' within a larger clade [17,54], why does elevated disparity frequently occur early given our prior definitions of taxa? A simple explanation is that (1) systematists choose groups of species for phylogenetic and/or disparity analyses based on prior higher taxonomic definitions, and (2) prior higher taxonomic definitions are based on amounts of difference and apparent ‘gaps’ in character space separating that cluster of species from other clusters of species. Gaps in character space subsequently recognized by taxonomists as distinguishing higher taxa would be side effect of correlated changes followed by reorganization of sets of integrated or otherwise linked characters. It is even possible that our prior definitions of higher taxa reflect different ‘axes' of variation in the same character states due to different modules (e.g. fig. 5 in [10]). In other words, the evolvability and disparity accompanying integration/modularity reorganization produce the anatomical differences that systematists use to decide which taxa to include in phylogenetic analyses, and thus establishes the ‘early' portions of higher taxon histories [49,52].

Data accessibility

C programs and data used to conduct the analyses are available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.h5971 [60]. Data also can be accessed at https://www.palaeobiodb.org/classic/nexusFileSearch (enter ‘53238' into Reference Number).

Competing interests

I have no competing interests.

Funding

This research was initiated under National Science Foundation grant no. EAR-0207874.