What limits the morphological disparity of clades?

Abstract

The morphological disparity of species within major clades shows a variety of trajectory patterns through evolutionary time. However, there is a significant tendency for groups to reach their maximum disparity relatively early in their histories, even while their species richness or diversity is comparatively low. This pattern of early high-disparity suggests that there are internal constraints (e.g. developmental pleiotropy) or external restrictions (e.g. ecological competition) upon the variety of morphologies that can subsequently evolve. It has also been demonstrated that the rate of evolution of new character states decreases in most clades through time (character saturation), as does the rate of origination of novel bodyplans and higher taxa. Here, we tested whether there was a simple relationship between the level or rate of character state exhaustion and the shape of a clade's disparity profile: specifically, its centre of gravity (CG). In a sample of 93 extinct major clades, most showed some degree of exhaustion, but all continued to evolve new states up until their extinction. Projection of states/steps curves suggested that clades realized an average of 60% of their inferred maximum numbers of states. Despite a weak but significant correlation between overall levels of homoplasy and the CG of clade disparity profiles, there were no significant relationships between any of our indices of exhaustion curve shape and the clade disparity CG. Clades showing early high-disparity were no more likely to have early character saturation than those with maximum disparity late in their evolution.

1. Introduction

Much like the species and individuals that constitute them, all clades have an origin and all must ultimately suffer extinction. Their intervening histories, however, can follow a variety of complex trajectories. The study of these patterns is central to the study of macroevolution, with questions centring on whether there is a typical pattern [1–7], whether the fortunes of clades are positively or negatively correlated [8–13] and whether there are particular responses to marked environmental changes [14]. Clade evolution is commonly studied by plotting diversity (numbers of constituent species, genera or higher taxa) through time, which can highlight periods of elevated diversification, extinction and turnover, as well as potential interactions between groups [15–20]. All Phanerozoic diversity curves affirm some form of increasing trajectory, variously modified by physical and biological factors [21]. Diversity change within individual clades can be modelled using relatively simple birth/death processes with constant parameters [22], which predict symmetrical clade shapes—waxing and waning diversity through time—as a null. More complex and asymmetrical patterns result from models in which parameters are varied through time [6,23,24]. Gould et al. [25] summarized the evolutionary trajectories for extinct clades using a simple measure of their centre of gravity (CG), with a symmetrical clade trajectory having a CG of 0.5. Empirical studies revealed a tendency towards bottom-heaviness (CG < 0.5), with clades typically reaching their highest diversity relatively early in their evolution.

1.1. What is disparity?

In addition to assessments of diversity, it is increasingly common to investigate the morphological variety or disparity of clades through time (see summaries in Erwin [26] and Wagner [6]). All indices of disparity are relative and depend upon the nature of variables used to quantify form and the manner in which these variables are summarized [27]. Most use some form of morphospace; a multidimensional space-filling plot in which the distances between taxa are proportional to the measured morphological differences between them [28]. These may themselves be visualized using data reduction and ordination techniques (e.g. principal components or coordinates) to summarize variation in the original set of morphological variables within a smaller number of abstracted axes. Several indices of disparity assess the distribution of taxa in such morphospaces: for example, by adding the ranges or variances on successive axes (a boxing approach), using convex hulls or determining the mean distance between all pairs of taxa. Indices can then be used to compare the disparity of constituent subclades, or to track the morphospace occupation of one or more groups through time, thereby building up a disparity profile [6,28–32]. When multiple disparity indices are used to capture variation in the same aspects of form, these often show a high degree of congruence. However, conflicting patterns are possible, depending upon the variance structure of the data [28–32].

Counterintuitively, diversity and disparity appear to be fundamentally decoupled [6]. Some periods or clades contain modest numbers of species that are nevertheless highly distinct morphologically, whereas others contain much greater numbers of morphologically very conservative species. More broadly, some of the most speciose groups (e.g. beetles and insects more generally) have some of the most constrained bodyplans; indeed, there are suggestions that a constrained and entrenched bodyplan might even be conducive to higher diversity [33]. Because clades evolve by lineage branching, we would expect a progressive exploration of morphospace even via a random walk. Once occupied, however, random extinction processes will tend to winnow out the space, but are less likely to leave large regions entirely vacant. All other things being equal, therefore, clades might be expected to have top-heavy disparity profiles through time, although driven evolutionary trends and selective extinction patterns may easily combine to yield a diversity of profile shapes. Empirical investigations for major clades over the past 25 years also show many different patterns, but the most common counterintuitively entails comparatively high-disparity relatively early in the clade's history (see also simulations by Foote [24,34,35]). Many groups therefore appear to explore the range of available ‘design’ options quite quickly, with subsequent evolution principally serving to increase diversity, possibly by the progressively fine subdivision of niche space [7,26,36].

1.2. Why might clades show early high-disparity?

One possible explanation for early high-disparity is that there are constraints and restrictions upon the available morphospace, thereby limiting the potential for expansion [37–40]. Once filled, the space can only be subdivided or vacated unless the constraints are removed or a clade evolves so as to circumvent them [41]. Such limits can be broadly classified in four categories: geometric, ontogenetic, physical and environmental.

Geometric constraints are those that can be predicted for any form in any context (many shapes are geometrically impossible), and are not limited to biological structures. Additional limits are imposed by particular generative processes [42] such that ontogeny can sometimes also be modelled geometrically. In such cases, it may be possible to delimit a morphospace theoretically [43], subsequently plotting real specimens within this. The best-known example is the shell of molluscs [44]. All forms—from simple cones (e.g. belemnites, patelloid limpets and hyolithids) to planispiral coils (e.g. many ammonites and bivalves) and translated coils (e.g. most gastropods)—can be modelled with reference to three or fewer variables that describe growth patterns, defining the theoretical morphospace. Forms outside of this are geometrically and ontogenetically impossible; typically, because the shell cannot grow through itself. However, many regions of the theoretical space are never occupied [42]. Actualized morphologies are limited to a relatively small fraction of the space, despite the half-billion-year history of molluscs, during which time groups have repeatedly re-radiated in the wake of mass extinctions, and within which there is rampant convergence in gross form [45–47]. Additional limits must apply, therefore. There are more ontogenetic constraints upon form than those predictable geometrically. Organisms develop by the complex interplay of mutually inductive systems and feedback loops, themselves underpinned by cascades of genetic control: not all developmental trajectories and morphologies are possible [48]. Further limits to the evolution of disparity are physical, but understanding these requires additional knowledge of biological context. Form is limited by the properties of biological materials, but the performance of such materials depends upon the function of the structures that they compose, and the context and environment in which they are deployed. For example, the physical constraints upon walking [49–52] and swimming [53,54] vertebrates differ from an engineering standpoint. Environmental restrictions [6] can therefore be both physical and biological, and might be broadly defined as all those factors that determine the availability of ecospace or niche space. A lineage can only evolve to realize a particular morphology if there are selective advantages; not only to the endpoint, but also to all intermediate forms along that evolutionary trajectory. The physical and biological environments are also dynamic and coupled systems.

1.3. Can we detect the operation of limits on disparity from levels and patterns of homoplasy?

If a clade has evolved to explore the limits of its morphospace, then its constituent lineages (variously prevented from exploring novel morphologies) might be more constrained or restricted to revisit previously occupied regions. This could be realized as increased levels of character state reversal and convergence. Overall levels of homoplasy might therefore be expected to be higher in constrained clades than in those free to colonize new regions of their morphospace. Most indices of homoplasy are influenced by dataset dimensions [55], but the homoplasy excess ratio (HER) of Archie [56] is a relatively unbiased ensemble metric that can be compared across clades [57]. The commonly reported ensemble consistency index is simply the ratio of the minimum possible number of steps (i.e. the number of derived states; MINL) to the number of steps observed on the optimal tree(s) (L). By comparison, the HER includes a term for the mean number of steps in optimal trees inferred from randomized data (MEANNS); specifically, a large number of matrices in which the assignment of states has been randomized within characters but across taxa. The HER is then given by

Nonetheless, overall levels of homoplasy may be less informative than the trajectory with which homoplastic changes are accrued in transitioning from the root to the terminals of a phylogeny. Wagner [58] noted that the rate of novel character state evolution usually decreased over the lifetime of a clade [59,60], with some groups approaching an asymptote and therefore character state exhaustion. If the disparity profile of clades were shaped by such exhaustion patterns, then we might expect clades reaching the bounds of their morphospaces early in their evolution (early high-disparity and low CG) to approach an earlier asymptote in numbers of realized states (character state saturation). We therefore test for such relationships here.

2. Methods

2.1. Indices of disparity

A comprehensive discussion of methods, in addition to a presentation of discrete character morphospaces, disparity profiles and summary statistics is given in Hughes et al. [7]. A brief summary is provided here. Our 93 discrete character matrices for metazoan clades were all sampled uniformly with respect to higher taxonomy, or were edited (by generating composite taxa) in order to standardize coverage [7]. For each clade, intertaxon distance matrices were calculated using the generalized Euclidean distance metric of Wills [32]. These matrices were ordinated in R (v. 3.0.1) [61] using principal coordinates analysis [36] and implementing Caillez's [62] correction for negative eigenvectors. Stratigraphic ranges for each constituent taxon were assigned to stages as defined in the International Stratigraphic Chart 2009 [63,64], whereas stratigraphic range data were sourced from Sepkoski Online [65], the Fossil Record 2 [66] and the Paleobiology Database [67]. Our index of disparity was calculated as the sum of variances on all principal coordinate axes (a maximum of n – 1 coordinates, where n is the number of sampled taxa), with the trajectory of disparity through subsequent time bins yielding a profile through time. A centre of gravity metric [25,68] in absolute time (CG_m) was calculated for each profile as

where d_i is the disparity at the ith stratigraphic interval and t_i the temporal midpoint in absolute time (Myr) of the ith stratigraphic interval. This was subsequently scaled between the ages of the oldest (t_oldest) and youngest (t_youngest) intervals to yield an index of observed CG (CG_scaled) between 0 and 1.

A clade with uniform disparity through time is highly unlikely to have a CG_scaled of 0.50. Rather, the null CG_scaled is determined by the durations of the time bins constituting the profile. The observed CG_scaled was therefore scaled relative to the inherent CG (CG_i) for a clade of constant disparity spanning the same intervals. A bootstrap resampling procedure was used to generate a distribution of 1000 differences between CG_scaled and CG_i. Clades for which more than 97.5% of these replicates lay either above or below the CG inherent in the timescale (p < 0.05) were deemed to be significantly top or bottom heavy, respectively [23]. Observed CG_scaled was ultimately expressed relative to CG_i as a baseline, hereafter, simply CG.

We also implemented tests for early high and late high-disparity; specifically using a bootstrapping approach to determine if the disparity observed in the first or last two stages could be distinguished from the maximum level attained by the group. The 93 study clades were thereby classified as showing early or late high-disparity, and we tested for differences in our indices of homoplasy and character state saturation in these categories using Mann–Whitney U-tests.

A simple index of the extent to which a clade was constrained within its morphospace was derived by expressing the maximum intertaxon Euclidean distance within any time bin as a fraction of the maximum distance across all time bins. Clades closest to this maximum might also be expected to show higher levels of overall homoplasy and state saturation [7].

Finally, we also derived an index of the degree to which a clade migrated throughout its morphospace during the course of its evolution, because constant levels of disparity through time need not necessarily imply the static occupation of morphospace. We modified the D_morpho index of Huang et al. [69] to provide an index (D_centroid) of the degree to which the centroid of sampled taxa migrates throughout the morphospace throughout the history of the clade. For each time bin, the mean scores of the sampled taxa on each principal coordinate axis were calculated, defining the group centroid. The difference between the positions of the centroid in successive time bins on a given axis was standardized by dividing it by the full range of values realized by all taxa in all time bins. These standardized univariate distances were then used to calculate Euclidean distances between the centroid positions in successive time bins (univariate standardized distances were squared, summed and the total square rooted). Finally, the distances between all successive time bins were summed (n – 1 comparisons for n time bins; the first time bin being a reference). Where time-series data were missing, the centroid was assumed to have remained stationary from the preceding bin.

2.2. Phylogenies and indices of homoplasy

A single outgroup taxon was used to infer ancestral character states at the base of each focal ingroup clade. Phylogenies were inferred in the program 'Tree analysis using New Technology' (TNT) [70] using Xmult level = 10, which performs a random sectorial search combined with ratchet, drift and tree fusing, followed by TBR branch swapping. The resulting most parsimonious trees (MPTs) sometimes differed from those in the source publications, especially where the taxon sample had been reduced. In cases where multiple MPTs were obtained, we selected the tree most congruent with that presented in the original publication. The character exhaustion analysis required fully resolved (dichotomously branching) trees, so polytomies were resolved stratigraphically (branching in a pectinate sequence matching their order of first fossil occurrences). It has been demonstrated that the precise trees used in character exhaustion analyses have relatively minor effects upon the results [58]. Moreover, using incorrect MPTs introduces a conservative bias because they minimize the number of steps required to achieve the observed number of character states; longer trees (even if more accurate) necessarily imply greater exhaustion by implying that greater ‘sampling’ of character space fails to yield additional novel states. Overall homoplasy levels were assessed using the HER of Archie [56], an index that is relatively insensitive to differences in data matrix dimensions. Five hundred randomly permuted matrices were used in each case, each subjected to TNT searches as above.

Character exhaustion analyses were performed using the method and scripts of Wagner [58] (figure 1). Character states for ancestral nodes were reconstructed using Fitch parsimony [71], and all nodes were numbered. A traversal of the tree from the root to the terminal branches was used to tally a cumulative total of character change steps and novel states. Working from the basal node, branches were added in order of their stratigraphic age (as given by the age of the oldest fossil representative of the clade that the branch leads to), then by their nodal proximity to the root, and finally according to the smallest numbers of novel states evolving along them. As fossil data are unavailable for unsampled internal nodes, many of the internal branches could not be ordered by stratigraphic age and so were ranked according to the last two criteria. This does leave ties. For example, consider six taxa that appear in the same stratigraphic interval with hypothesized relationships ((A,(B,C)),(D,(E,F)). The basal node necessarily precedes the (A,(B,C)) and (D,(E,F)) nodes, and those two nodes necessarily precede the (B,C) and (E,F) nodes, respectively. However, neither the (A,(B,C)) nor (D,(E,F)) sister nodes necessarily precede each other [72], and the ‘cousin’ nodes (B,C) and (E,F) cannot be ordered relative to each other either. Therefore, such sister-taxon and ‘Xth cousin’ ties were resolved randomly, but with second cousin nodes preceding third cousin nodes. This ordering strategy is the most exact possible without recourse to stratigraphic data of higher resolution to subdivide branches. Such data are unavailable for the vast majority of our sampled clades. In addition, it is not uncommon for multiple fossil taxa to have their first occurrences at the same locality, resulting in ties, regardless of the temporal resolution available. Another approach would be to use arbitrary evolutionary models to calibrate branch lengths [73–75], and to assign character changes between known occurrences [76]. However, such models will bias results towards favouring character exhaustion. Longer branches with more novel character states will be pulled closer to the root, causing novel states to appear earlier in evolutionary time. This will be more pronounced if rate-variation among characters is permitted, because characters with a greater number of novel states will evolve at a faster rate, thereby concentrating the novel state changes on branches with deeper divergence times. In addition, it has been shown that different branch scaling methods can markedly influence the evolutionary inferences derived from trees [77]. Our approach is therefore a conservative one, insofar as it is more likely to defer the appearance of novel character states until later in our character exhaustion curves (inferred exhaustion will be less marked) and is not contingent upon arbitrary models of character evolution.

Figure 1.

Generating character saturation curves. (a) Step 1: ancestral states are reconstructed on a phylogeny in order to determine character transitions along each branch. Horizontal bars on branches indicate character state changes. Asterisks denote homoplastic changes (steps) that are not also new states. Branches are numbered within squares, and pairs of numbers above these indicate number of steps and number of novel states respectively. (b) Step 2: branches are ordered by stratigraphic occurrence, proximity to the root and number of new states. (c) Step 3: the number of steps and new states along each branch in the resulting sequence (denoted by the values in boxes) are calculated, along with running totals. (d) Step 4: the cumulative total of new states is plotted against the cumulative total of steps to generate a saturation curve. The dotted line indicates the trajectory (gradient of 1.0) for the hypothetical situation where there is no homoplasy, and all steps are novel states. (Online version in colour.)

For each branch in the ranked sequence, the total number of character state changes (steps) and the total number of novel character states (states) was calculated and added to the cumulative total. Plotting the cumulative number of states against the cumulative number of steps yielded a states/steps curve for each of the 93 clades.

All subsequent analyses were implemented in R (v. 3.0.1) [61]. The shape of each states/steps curve was quantified in two ways (figure 2). First, we recorded the fraction of total observed steps at which an arbitrary threshold (50%) of the maximum number of observed states was reached. Second, we calculated the CG for each states/steps curve (in an analogous manner to the CG for disparity profiles) and scaled this relative to the number of steps in the clade. The most convex curves with the highest initial gradients (i.e. those more quickly approaching an asymptote) yielded the lowest values for both indices. We also estimated the overall degree of saturation at clade extinction by fitting Michaelis–Menten nonlinear regression curves [78–80] to the data based on the assumption that the number of character states would eventually reach an asymptote (i.e. that the character space was finite). We then expressed the maximum number of observed states as a fraction of the inferred maximum. Low values in this context indicated clades that were further from saturation at their extinction.

Figure 2.

Quantifying character saturation from state/steps curves. (a) The 50% threshold is defined as the number of steps taken to reach 50% of the total number of character states (a) divided by the total number of observed steps (a + b). (b) The fraction of maximum states is defined as the total number of observed character states (c) divided by the estimated maximum number of possible character states (d) from the asymptote of the Michaelis–Menten curve. (Online version in colour.)

Finally, each dataset was fitted to Wagner's idealized models of character evolution [58]. Log-likelihood values were used to assess whether a null model of a step-independent (linear) model of character evolution could be rejected in favour of step-dependent models indicating exhaustion.

3. Results

All summary statistics are given in table 1. Of our 93 sampled clades, only two realized the maximum intertaxon Euclidean distance for the entire morphospace within a single time bin. Most appeared relatively free to evolve within the morphospatial bounds, with a mean maximum observed distance (as a fraction of the maximum possible) of 0.712. HERs had a mean of 0.470 with a fairly typical distribution [55,56]. States/steps curves exhibited a range of shapes although most were asymptotic and reached a slope less than 1 (figure 3), indicating that some degree of character state saturation occurred in most groups. Of the 68 clades tested for fit with Wagner's models, the null model of a linear increase in new character states was rejected in 60 cases. Although nearly all clades showed a decrease in the rate at which new states appeared after about 30% of the maximum number of steps, 12 maintained a much reduced but constant rate of addition of states over the remainder of their evolutionary history (e.g. cinctans; figure 3c). Some groups, such as Aplodontoidea (mammalia; figure 3f), had stepped patterns, indicating that the origin of novel states was concentrated in a relatively small number of branches equidistant from the root. This is similar to the pattern recently documented within post-Palaeozoic echinoids [177]. The mean fraction of steps at which 50% of states were realized was 0.307, with values ranging between 0.103 (the most convex curve with fastest saturation) and 0.625 (the most nearly linear curve with the least saturation). Michaelis–Menten curve fits all inferred asymptotes in excess of the realized maximum at extinction; observed maxima varied between 0.067 and 0.896 of the inferred, with a mean of 0.583. These two indices of state saturation were strongly negatively and highly significantly correlated (r_s = −0.873, p < 0.001; those clades taking longest to reach 50% of the realized maximum tended to be those in which the realized maximum was the smallest fraction of the inferred, because the empirical curves were truncated by extinction at the steepest gradients). CG indices for the empirical curves showed a narrow range of values as expected (0.571–0.704), but correlated highly significantly with both the empirical 50% thresholds (r_s = 0.631, p < 0.001) and the realized fraction of inferred states (r_s = −0.578, p < 0.001).

Table 1.

Summary metrics for the 93 clades in the dataset. Ext: N = does not terminate coincident with a mass extinction boundary; Y = does terminate coincident with a mass extinction boundary. HER: homoplasy excess ratio. T50%: 50% threshold for character states. SCG: Saturation CG. Fchar: fraction of total character states relative to the estimated maximum from Michaelis–Menten asymptotes. CG: Disparity profile centre of gravity. CDev: Summed centroid deviance. Euc: Maximum Euclidean distance between taxa in any given time bin as a fraction of the maximum across all time bins. W: Top, significantly top heavy; Bot, significantly bottom heavy; N, CG neither top nor bottom heavy. ESat: Y, disparity in the first two stages not significantly different from maximum; N, disparity in the first two stages significantly different from maximum. LSat: Y, disparity in the last two stages not significantly different from maximum; N, disparity in the last two stages significantly different from maximum. Clades that realize the maximum inter-taxon Euclidean distance are highlighted in italic.

author	clade	extinct	HER	T50%	SCG	Fchar	CG	Cdev	Euc	W	ESat	LSat
Anderson et al. [81]	Acanthodii	N	0.796	0.292	0.635	0.509	0.446	1.492	0.837	Top	N	Y
Sigurdsen & Bolt [82]	Amphibamidae	N	0.240	0.607	0.658	0.274	0.316	1.755	0.601	N	Y	Y
Hill et al. [83]	Ankylosauria	Y	0.377	0.209	0.585	0.712	0.687	6.010	0.750	N	Y	Y
Fröbisch [84]	Anomodontia	N	0.602	0.254	0.602	0.672	0.511	2.618	0.765	Top	N	Y
Hopkins [85]	Aplodontoidea	N	0.626	0.136	0.593	0.820	0.185	3.307	0.764	N	N	Y
Dupret et al. [86]	Arthrodira	N	0.565	0.147	0.571	0.774	0.566	3.425	0.715	Bot	N	N
Fortey & Chatteron [87]	Asaphina	Y	0.502	0.438	0.693	0.255	0.611	1.753	0.803	N	N	Y
Lieberman & Kloc [88]	Asteropyginae	Y	0.194	0.233	0.605	0.718	0.641	2.434	0.713	Top	N	Y
Alvarez et al. [89]	Athyridida	N	0.236	0.302	0.627	0.723	0.526	2.910	0.690	Top	N	Y
Milner et al. [90]	Baphetoidea	N	0.095	0.266	0.599	0.639	0.451	0.685	0.909	N	N	Y
Benedetto [91]	Billingsellidina	N	0.393	0.308	0.620	0.575	0.734	2.968	0.700	N	Y	N
Bodenbender & Fisher [92]	Blastoidea	N	0.311	0.153	0.588	0.834	0.609	4.058	0.662	Top	N	Y
Foote [93]	Blastozoans	Y	0.623	0.115	0.585	0.896	0.477	3.149	0.685	Top	N	Y
Wang et al. [94]	Borophaginae	N	0.710	0.447	0.645	0.344	0.502	1.690	0.698	Bot	Y	N
Gaffney et al. [95]	Bothremydidae	N	0.587	0.335	0.633	0.544	0.471	2.027	0.512	N	N	N
Schoch & Milner [96]	Branchiosauridae	N	0.532	0.301	0.601	0.593	0.269	1.752	0.792	N	Y	Y
Mihlbachler & Deméré [97]	Brontotheriidae	N	0.549	0.103	0.614	0.860	0.415	2.658	0.516	N	Y	N
Jimenez-Sanchez et al. [98]	Bryozoa (unnamed clade)	N	0.234	0.286	0.595	0.645	0.427	3.247	0.669	N	Y	N
Sampson et al. [99]	Chasmosaurinae	Y	0.665	0.283	0.612	0.604	0.458	0.644	0.533	Bot	N	Y
Smith & Zamora [100]	Cinctans	N	0.470	0.353	0.607	0.440	0.477	1.201	0.637	N	Y	Y
Carlson & Fitzgerald [101]	Cryptonelloidea	N	0.277	0.331	0.620	0.568	0.399	3.154	0.587	Bot	N	N
Novas et al. [102]	Deinonychosauria	Y	0.607	0.334	0.603	0.541	0.635	5.566	0.720	Top	N	N
Wenwei et al. [103]	Dimeropygidae	Y	0.539	0.371	0.610	0.551	0.528	0.722	0.697	N	Y	Y
Clement & Long [104]	Dipterimorpha	N	0.417	0.268	0.584	0.681	0.225	3.881	0.753	Bot	Y	N
Foote [105]	Disparida	N	0.276	0.146	0.575	0.803	0.490	2.820	0.506	Bot	Y	N
Cotton & Fortey [106]	Eodiscina	N	0.291	0.129	0.576	0.865	0.375	2.118	0.594	Bot	Y	N
Maletz et al. [107]	Eugraptoloida	N	0.861	0.260	0.631	0.567	0.563	2.093	0.646	N	N	Y
Bloch et al. [108]	Euprimateforms	N	0.416	0.358	0.594	0.613	0.348	2.897	0.623	Bot	Y	N
Tetlie & Cuggy [109]	Eurypterina	N	0.553	0.323	0.639	0.525	0.509	3.677	0.787	N	Y	Y
Foote [105]	Flexibilia	Y	0.339	0.213	0.612	0.755	0.506	2.855	0.493	N	N	Y
Zhu & Gai [110]	Galeaspida	N	0.659	0.279	0.582	0.601	0.549	4.357	0.729	N	Y	Y
Korn [111]	Goniatitaceae	N	0.737	0.500	0.628	0.270	0.569	3.519	0.866	N	N	N
Gebauer [112]	Gorgonopsia	Y	0.697	0.422	0.635	0.424	0.514	0.694	0.991	N	Y	Y
Prieto-Marquez [113]	Hadrosauroidea	Y	0.639	0.268	0.604	0.656	0.700	0.407	0.708	Top	N	N
Wang [114]	Hesperocyoninae	N	0.636	0.481	0.704	0.404	0.520	3.467	0.668	N	N	Y
Polly [115]	Hyaenodontidae	N	0.454	0.370	0.622	0.501	0.540	1.627	0.797	N	N	Y
Motani [116]	Ichthyopterygia	N	0.699	0.372	0.614	0.415	0.359	5.625	0.770	Bot	Y	N
Trinajstic & Dennis-Bryan [117]	Incisoscutoidea	N	0.448	0.261	0.602	0.703	0.498	1.438	0.689	N	Y	Y
Sundberg [118]	Kochaspid Trilobites	N	0.122	0.313	0.650	0.561	0.485	1.225	0.660	N	Y	N
Adrain et al. [119]	Koneprusiinae	N	0.399	0.240	0.634	0.687	0.755	4.519	1.000	N	Y	Y
Klembara et al. [120]	Labyrinthodontia	N	0.301	0.214	0.576	0.706	0.368	2.492	0.658	N	N	N
Anderson et al. [121]	Lepospondyli	N	0.341	0.196	0.611	0.816	0.484	10.245	0.620	N	N	N
Pollitt et al. [122]	Lichoidea	Y	0.334	0.195	0.592	0.749	0.555	6.289	0.752	Bot	Y	N
Yates & Warren [123]	Limnarchia	N	0.344	0.224	0.599	0.741	0.437	4.957	0.640	N	Y	N
Hoffmann [124]	Lytoceratoidea	Y	0.835	0.500	0.655	0.428	0.468	2.287	1.000	Bot	Y	N
Damiani [125]	Mastodonsauroidea	N	0.342	0.302	0.575	0.533	0.394	2.592	0.726	Bot	Y	N
Young & De Andrade [126]	Metriorhynchoidea	N	0.869	0.332	0.639	0.489	0.451	5.418	0.780	N	N	N
Polly et al. [127]	Miacoidea	N	0.352	0.397	0.648	0.398	0.638	2.452	0.606	N	Y	Y
Ruta & Coates [128]	Microsauria	N	0.608	0.304	0.609	0.580	0.571	6.851	0.482	Bot	Y	Y
Lee et al. [129]	Missisquoiidae	N	0.096	0.214	0.598	0.742	0.379	2.828	0.761	N	N	Y
Bell Jr. & Polcyn [130]	Mosasauridae	Y	0.480	0.252	0.605	0.714	0.509	1.369	0.712	N	N	N
Kielan-Jaworowska & Hurum [131]	Multituberculata	N	0.465	0.310	0.628	0.540	0.520	3.535	0.774	Bot	Y	N
Pol et al. [132]	Notosuchia	N	0.435	0.353	0.621	0.482	0.355	3.968	0.500	N	N	Y
Lieberman [133]	Olenellina	N	0.147	0.276	0.625	0.666	0.507	0.698	0.732	N	Y	N
Lieberman [134]	Olenelloidea	N	0.083	0.265	0.604	0.728	0.481	1.411	0.658	N	N	N
Bajpai et al. [135]	Omomyoidea	N	0.222	0.190	0.592	0.790	0.497	8.393	0.446	Top	N	N
McDonald et al. [136]	Ornithopoda	Y	0.691	0.176	0.598	0.764	0.620	1.076	0.992	Top	N	Y
Mitchell [137]	Orthograptidae	Y	1.000	0.529	0.645	0.067	0.628	1.338	0.626	N	Y	Y
Sansom [138]	Osteostraci	N	0.552	0.266	0.599	0.682	0.499	2.894	0.520	Top	N	N
Longrich et al. [139]	Pachycephalosauria	Y	0.480	0.442	0.625	0.469	0.631	1.791	0.655	Bot	N	N
Prokop & Ren [140]	Palaeodictyoptera	N	0.077	0.314	0.625	0.521	0.351	2.316	0.861	Bot	Y	N
Jin & Popov [141]	Parastrophinidae	N	0.414	0.321	0.612	0.652	0.118	4.577	0.565	N	Y	Y
Stocker [142]	Parasuchia	Y	0.374	0.329	0.618	0.489	0.496	0.369	0.761	N	Y	N
Lopez-Arbarello & Zavattieri [143]	Perleidiformes	Y	0.346	0.213	0.604	0.730	0.471	1.422	0.791	Top	Y	N
Smith & Pol [144]	Plateosauria	N	0.426	0.450	0.628	0.761	0.672	2.313	0.771	N	N	Y
Anderson et al. [81]	Placodermi	Y	0.638	0.271	0.584	0.528	0.560	2.515	0.650	N	N	N
Ketchum & Benson [145]	Plesiosauria	Y	0.375	0.264	0.606	0.709	0.509	3.684	0.762	N	Y	Y
Smith & Dyke [146]	Pliosauroidea	Y	0.616	0.274	0.596	0.693	0.506	3.001	0.743	N	Y	Y
Cisneros & Ruta [147]	Procolophonidae	Y	0.581	0.355	0.648	0.517	0.486	2.387	0.650	N	Y	Y
Huguet et al. [148]	Protomyrmeleontidae	Y	0.046	0.305	0.629	0.585	0.435	2.051	0.851	Bot	Y	N
Nel et al. [149]	Protanisoptera	N	0.478	0.313	0.576	0.563	0.451	1.732	0.949	N	Y	N
Egi et al. [150]	Proviverrinae	N	0.214	0.297	0.634	0.557	0.184	4.303	0.773	Top	Y	Y
Parker & Irmis [151]	Pseudopalatinae	Y	0.572	0.333	0.619	0.471	0.641	1.104	0.811	N	Y	Y
Pernègre & Elliott [152]	Pteraspidiformes	N	0.336	0.248	0.586	0.644	0.471	1.492	0.709	N	N	Y
Lü et al. [153]	Pterosauria	Y	0.545	0.315	0.616	0.515	0.529	2.626	0.679	N	Y	N
Poyato-Ariza & Wenz [154]	Pycnodontiformes	N	0.279	0.308	0.627	0.568	0.487	1.878	0.590	N	Y	Y
Brusatte et al. [155]	Rauisuchia	N	0.517	0.388	0.619	0.501	0.508	3.310	0.753	N	N	N
Bates et al. [156]	Retiolitidae	N	0.578	0.333	0.623	0.517	0.557	2.765	0.704	N	N	N
Cerdeno [157]	Rhinocerotidae	N	0.327	0.131	0.586	0.831	0.517	2.379	0.772	N	Y	N
Hone & Benton [158]	Rhyncosauria	Y	0.764	0.411	0.587	0.365	0.568	2.877	0.880	N	Y	Y
Allain & Aquesbi [159]	Sauropoda	Y	0.538	0.380	0.606	0.478	0.539	3.850	0.774	Bot	Y	Y
Maidment [160]	Stegosauria	N	0.652	0.625	0.673	0.102	0.338	1.422	0.602	Bot	N	N
Carlson & Fitzgerald [101]	Stringocephaloidea	N	0.352	0.279	0.617	0.436	0.473	2.562	0.739	Bot	N	N
Schoch [161]	Stereospondyli	N	0.474	0.409	0.641	0.659	0.354	4.755	0.650	Bot	N	N
Lamsdell et al. [162]	Stylonurina	N	0.541	0.259	0.612	0.673	0.470	5.966	0.629	N	N	Y
Klug [163]	Synechodontiformes	N	0.641	0.288	0.627	0.645	0.617	1.561	0.200	Top	N	N
Gaudin [164]	Tardigrada	N	0.466	0.201	0.589	0.691	0.641	6.917	0.669	N	N	Y
Wu et al. [165]	Thalattosauria	Y	0.560	0.414	0.622	0.376	0.533	0.967	0.951	Top	N	N
Wilson & Märss [166]	Thelodonti	N	0.387	0.249	0.611	0.607	0.587	3.898	0.729	Top	Y	N
Hu et al. [167]	Theropoda	Y	0.422	0.300	0.611	0.567	0.579	2.125	0.971	N	N	N
Chatterton et al. [168]	Toernquistiidae	Y	0.141	0.308	0.593	0.593	0.462	0.793	0.653	Top	N	Y
Brusatte et al. [169]	Tyrannosauroidea	Y	0.778	0.372	0.645	0.405	0.633	3.267	0.950	Bot	N	N
Anderson & Seldon [170]	Xiphosura	N	0.896	0.575	0.590	0.076	0.266	4.934	0.803	Bot	N	N

Figure 3.

Example Michaelis–Menten functions fitted to state/steps data for different extinct animal clades. See text for explanation of how the fraction of estimated maximum number of states was calculated. Points indicate cumulative totals as each branch is added. (a) Orthograptidae [171]. (b) Asaphina [172]. (c) Cinctans [173]. (d) Bothremydidae [174]. (e) Plesiosauria [175]. (f) Aplodontoidea [176]. (Online version in colour.)

There was a weak but significant negative correlation between overall homoplasy levels and the disparity CG (r_s = 0.227, p < 0.029): clades with a lower CG (earlier higher disparity) had greater homoplasy (lower HER) on average (figure 4). However, we found no significant relationships between disparity CG and any of our indices of saturation curve shape (r_s = 0.008, p = 0.941 for the 50% threshold; r_s = 0.091, p = 0.388 for the saturation curve CG; r_s = −0.039, p = 0.708 for the Michaelis–Menten estimate of the realized fraction of inferred states). Limiting the analysis to wholly extinct clades that did not terminate coincident with a mass extinction boundary resulted in weaker correlations for all indices of character saturation except the 50% threshold point (table 2). Finally, analysis of the CG of clades terminating at mass extinction boundaries yielded similar results for indices of character exhaustion but showed no correlation with HER values. Maximum Euclidean distance within a time bin correlated negatively with the Michaelis–Menten estimates of the realized fraction of inferred states (r_s = −0.229; p = 0.027), indicating that character saturation may be greater in clades that reach their morphospatial bounds. However, no correlation was found between character saturation metrics and the amount of centroid deviation (50% threshold: r_s = −0.173, p = 0.097; saturation CG: r_s = −0.183, p = 0.079 fraction of inferred states r_s = 0.198, p = 0.057) implying that clades that migrate through the morphospace are as likely to show saturation as those that statically occupy a defined region. The morphospace of clades that show early disparity and similar saturation values (figure 5) reveals that some clades continue to evolve new character states as they migrate through the morphospace (e.g. disparid crinoids), whereas others remain fixed and occupied space within existing bounds (e.g. lichoid trilobites). Whether a clade showed early or late high-disparity also had no effect on the degree of character exhaustion within that clade (table 3).

Figure 4.

Disparity profile centre of gravity (CG) plotted against homoplasy excess ratio (HER) and estimates of character saturation. (a) Disparity CG versus HER. (b) Disparity CG versus 50% threshold. (c) Disparity CG versus saturation curve CG. (d) Disparity CG versus fraction of the Michaelis-Menten estimate of the maximum number of character states realized at extinction. r_s and p-values are from Spearman's rank correlation coefficient tests.

Table 2.

p-values from Spearman rank tests for homoplasy excess ratio (HER) and three proxies of character exhaustion (fraction of the total number of steps at which 50% of states are realized, CG of the saturation curve, and the fraction of the estimated number of states (inferred from Michaelis–Menten curve) that are observed) correlated with disparity profile CG. Values are calculated for the entire dataset of 93 clades, the subset of 55 clades not becoming extinct coincident with a mass extinction boundary and that have no extant survivors, and the subset of 31 clades that terminate at a mass extinction boundary.

	HER	50% threshold	saturation curve CG	observed maximum states/estimated maximum states
disparity CG (entire dataset, n = 93)	rs = 0.227 p = 0.029	rs = 0.008 p = 0.941	rs = 0.091 p = 0.388	rs = 0.039 p = 0.708
disparity CG (clade extinction not coincident with mass extinction, n = 55)	rs = 0.285 p = 0.035	rs = −0.107 p = 0.436	rs = 0.010 p = 0.940	rs = 0.037 p = 0.786
disparity CG (clade extinction coincident with mass extinction n = 31)	rs = 0.085 p = 0.649	rs = 0.145 p = 0.438	rs = 0.099 p = 0.597	rs = 0.094 p = 0.614

Figure 5.

Differing patterns of morphospace occupation along the first two principal coordinate axes in clades showing early high-disparity. CG: disparity profile centre of gravity. Fchar: fraction of total realized character states relative to the maximum estimated from Michaelis–Menten asymptotes. Euc: maximum Euclidean distance between taxa in any given time bin as a fraction of the maximum across all time bins. (a) Disparid crinoids from Foote [178] (CG = 0.490, FChar = 0.803, Euc = 0.506) showing migration through the morphospace. PCo 1 = 23.6% total variance, PCo 2 = 12.0% total variance. (b) Lichoid trilobites from Pollitt et al. [179] (CG = 0.555, FChar = 0.749, Euc = 0.752) showing more static occupation of the morphospace. PCo 1 = 26.2% total variance, PCo 2 = 13.4% total variance. (Online version in colour.)

Table 3.

Summary statistics from Mann–Whitney U tests of differences between median homoplasy excess ratio (HER) and three character saturation metrics (fraction of the total number of steps at which 50% of states are realized, CG of the saturation curve, and the fraction of the estimated number of states (inferred from Michaelis–Menten curve) that are observed) when bi-partitioned by disparity profile shape. Bottom heavy versus top heavy: clades grouped based on a CG value significantly higher or lower than mean randomized values (with other clades omitted). Early maximum disparity: clades partitioned according to whether or not they show disparity in the first two stages that is significantly different from the maximum. Late maximum disparity: clades partitioned according to whether or not they show disparity in the last two stages that is significantly different from the maximum.

	HER	50% threshold	saturation curve CG	observed maximum states/estimated maximum states
significantly bottom heavy versus significantly top heavy	W = 216 p = 0.588	W = 288 p = 0.012	W = 219.5 p = 0.520	W = 110 p = 0.019
early maximum disparity	W = 1277.5 p = 0.131	W = 989 p = 0.482	W = 1077 p = 0.979	W = 1189.5 p = 0.407
late maximum disparity	W = 997.5 p = 0.535	W = 1095 p = 0.899	W = 1005.5 p = 0.580	W = 1051 p = 0.838

4. Discussion

The significant but weak correlation between disparity CG and overall levels of homoplasy demonstrates that clades with higher disparity earlier in their histories are more likely to show higher levels of character state reversal and convergence. While this implies the operation of some constraint or restriction (sensu Wagner [6]), the small size of the effect (R² = 0.030 if modelled linearly) suggests that some other factor or factors are much more important. The absence of significant correlation between disparity CG and any of our proxies for states/steps curve shape indicates that disparity is not shaped in any straightforward way by progressive exhaustion of the character space. Patterns of disparity through time cannot therefore be deduced straightforwardly from patterns of homoplasy increase throughout the lifetime of clades, and are only weakly influenced by overall homoplasy levels. Many clades continue to evolve new character states with no associated increase in their disparity, whereas others achieve their highest levels of disparity through homoplastic character change. Several clades (including crustaceans and priapulid worms [180,181]) occupy a similarly sized morphospace envelope throughout much of their evolution (similar disparity), but nevertheless migrate through the overall morphospace. Other clades (e.g. angiosperms, Jurassic ammonoids [182]) quickly colonize many of the morphospatial extremes (reaching maximum disparity) but subdivide the envelope progressively through time and continue to evolve new states. The major axes of our empirical morphospaces are likely to be defined by the principal patterns of covariation between character states, and it is these patterns that largely determine Euclidean eccentricity from the global centroids. Similarly, the most eccentric (extreme) morphologies may embody sets of character states that have individually evolved earlier in the history of the clade, but never before in combination. Upon its first evolution, a new state need not necessarily move a lineage to a particularly eccentric position in the morphospace, neither will it necessarily result in the expansion of the morphospace occupied by contemporaneous taxa, particularly where the space is contracting on other fronts.

In most of our sampled clades, new character states continued to evolve long after maximum disparity had been reached. Major groups often share a conserved morphological template or bodyplan (Bauplan), usually defined by character changes at the clade's base. This implies that some characters are relatively invariant or become ‘fixed’, whereas other characters continue to evolve new states. Neither conventional morphospace analyses nor our states/steps curves distinguished between characters on the basis of their evolutionary or developmental depth. State changes might therefore range from fundamental shifts in body symmetry and organization (more typical of those delimiting phyla), down to subtle changes in bristle patterns at the other (perhaps more typical of species), yet all contribute equally. Furthermore, as cladistic matrices are created with the express purpose of inferring relationships, the characters within such matrices will primarily be synapomorphies of subclades. Deep synapomorphies (which may be shared by all members of the focal clade) will usually be absent, because they contain no useful phylogenetic information. For example, characters such as the presence and absence of limbs or a notochord will not be included in a dataset of vertebrates that all share these derived features. As a result, cladistic datasets are likely to under-represent characters subjected to strong intrinsic constraints, which have already become ‘fixed’ within the clade of interest. For this and other reasons, conventional discrete character morphospaces—and the estimates of disparity derived from them—may not be best suited for recognizing the changes of deepest developmental and evolutionary significance. Morphospaces that take account of the developmental depth of characters have long been called for [3], and some moves have been made towards realizing these for particular clades [48,183–186].

Several authors have distinguished between intrinsic and extrinsic limits to disparity [7], with intrinsic factors being those that operate within the individuals and lineages that constitute a clade (broadly equating to geometric and developmental constraints) and extrinsic or ecological factors being those imposed from the outside (biological and physical restrictions) [6,26]. The precise limits on the evolution of disparity are probably unique to each clade, and comprise some combination of factors. Determining the relative importance of these is not straightforward, and direct tests are impossible with the present data. There are some strongly suggestive patterns, however.

4.1. Intrinsic developmental constraints

As ontogeny becomes more complex, and genetic and other mechanisms become progressively more interdependent, increasing pleiotropy and functional linkage may result in developmental programmes that are more difficult to modify and subsequently evolve [187,188]. While some aspects of bodyplan organization may be strongly adaptive and maintained by stabilizing selection, other aspects may be largely contingent but locked down by the difficulty of effecting change in developmental programmes. The seven cervical vertebrae of mammals furnish the best-known example. Nearly all mammals—including the long-necked giraffes, gerenuks and alpacas—have just seven neck vertebrae. Other vertebrate groups retain the ability to modify this number, and invariably evolve longer necks with greater numbers of vertebrae; up to 25 in birds, 19 in sauropods [189] and 75 in the extinct plesiosaurs [190]. Two extant groups of mammals depart from the mammalian ground plan of seven; sloths have six (Choloepus) or eight or nine (Bradypus), whereas manatees (Trichechus) have six. All achieve this by homeotic frameshifts of the thoracic expression pattern (the development of ribs, etc.) relative to the underlying somites [191]. Such shifts in other mammals may be linked to highly deleterious, pleiotropic side effects, not least problems with the innervation, musculature and blood supply of the forelimbs and elevated rates of juvenile cancer [192]. Sloths and manatees appear to avoid these effects by low rates of metabolism and overall activity [178,192,193]. The pentadactyl limb of tetrapods is another example of a design that was apparently much more labile early in its evolution. Early labrynthodont tetrapods had higher numbers of digits: eight in the forelimbs of Acanthostega, seven in the hindlimbs of Ichthyostega, six in Tulerpeton. Modern lissamphibians—despite their ground plan of five digits—often develop greater numbers with no ill effects: ostensibly because limb patterning in aquatic larvae occurs prior to the phylotypic stage of development, during which time inductive interactions and interdependencies are concentrated. Many amniote groups, by contrast, have reduced digit numbers as adults (e.g. horses, non-avian dinosaurs, birds [179]), but few lineages have attained higher numbers, often evolving a variety of digit-like structures rather than extra digits per se [194,195]. Ichthyosaurs furnish the best-known exception: opthalmosaurians added digits anterior to digit one and posterior to digit five [196], whereas non-opthalmosaurians may have achieved polydactyly by interdigital or postaxial phalangeal bifurcation [197]. In most amniote groups, however, polydactyly is associated with a range of deleterious pleiotroipic effects [198–200], because limb development coincides with the phylotypic stage. Variation in this particular set of characters appears to be effectively locked down, therefore.

4.2. Extrinsic physical and biological (ecological) restrictions

In general, levels of clade disparity are often much less depleted by mass extinction events than levels of diversity. This is because numerous lineages can be lost from a morphospace while still maintaining a broad distribution of survivors [201]. Indeed, even where extinction selectively removes large subclades, disparity levels may remain high provided that the surviving clades occupy peripheral regions of the morphospace [202]. Where increases in levels of disparity coincide with marked and episodic changes in the physical or biological environment, it may be reasonable to infer that extrinsic, ecological constraints have been removed. Such shifts may occur in the immediate wake of mass extinctions, although in such cases, it may be difficult to distinguish the removal of biological constraints—for example, the extinction of competing or incumbent clades—from the physical environmental shifts that precipitate these biological changes. However, several of the largest and most conspicuous adaptive radiations have classically been understood in ecological terms. Crown group mammals evolved numerous new body forms (broadly equating to modern orders, and with many striking parallels between Eutheria and Metatheria in different settings) after the K/Pg mass extinction. This occurred not only in the aftermath of the extinction of the non-avian dinosaurs, but also coincident with the final demise of eutriconodont, spalacotheroid and multituberculate mammals [203]. Similarly, articulate brachiopods rapidly increased their disparity in the wake of the end Permian mass extinction; a pattern consistent with rebound after the removal of highly structured guilds and the freeing up of ecospace [204]. Comparable post-extinction rebounds have been observed for crinoid and blastozoan echinoderms [27], as well as ammonoids [205] through multiple events. Similarly, rapid increases in disparity may occur when a clade is first able to colonize a fundamentally new region of ecospace. Even bodyplans that are assembled piecemeal over many tens of millions of years may reach a critical threshold, thereby suddenly circumventing previous restrictions [41].

5. Conclusion

In addition to studying the phylogeny and diversity of clades throughout their evolution [21,25,30], it is increasingly common to examine the manner in which groups explore theoretical or empirical morphospaces through time [43,184], as well as their resulting temporal patterns of morphological disparity change. Disparity and diversity are fundamentally decoupled [29], and a variety of trajectories have been observed empirically. The most common pattern, however, is for disparity to peak relatively early in the history of a clade, and certainly before its peak in diversity [7]. Putative limits on disparity may either be intrinsic (e.g. developmental [48,193]) or extrinsic (e.g. ecological [27,204,205]), but both imply constraints on available morphospace that might be reflected in the rate of evolution of novel morphology throughout the lifetime of a clade. The majority of clades studied do indeed show a significant decrease in the rate of appearance of novel character states over time. However, despite a weak correlation between overall levels of homoplasy (as measured by the HER) and the CG of clade disparity profiles (greater homoplasy implies earlier high-disparity) we found no more detailed relationships between the shapes of character saturation curves and disparity profiles. Many clades continue to evolve new character states while disparity levels remain constant, which can variously be achieved by wholesale migration through the morphospace or by subdividing it. Similarly, disparity may be increased or maximized by predominantly homoplastic state changes. The anecdotally large number of clades showing the expansion of hitherto restricted morphospaces in the aftermath of mass extinctions (or upon transitioning into fundamentally new habitats) suggests that many of the limitations may be ecological. However, given the variation shown in both character saturation and morphospace occupation, limits on disparity almost certainly result from a complex interplay of clade-specific intrinsic and extrinsic factors, suggesting that a simple universal explanation for early high-disparity is unlikely.

Authors' contributions

J.W.O. co-wrote the paper, collected data, implemented analyses of homoplasy and character exhaustion and drafted figures. M.H. analysed disparity trajectories, collected data, wrote scripts and drafted figures. P.J.W. scripted the states/steps analyses and contributed to writing. S.G. analysed disparity trajectories. M.A.W. conceived the study, co-wrote the paper and drafted figures.

Competing interests

We have no competing interests.

Funding

This research was supported by grants from the John Templeton Foundation (43915), and from The Leverhulme Trust (F/00351/Z) awarded to M.A.W.