Developmental aspects of morphological disparity dynamics ... · Sylvain Gerber, Gunther J. Eble, and Pascal Neige Abstract.—We have devised a simple model for assessing the role

Developmental aspects of morphological disparity dynamics:a simple analytical exploration

Sylvain Gerber, Gunther J. Eble, and Pascal Neige

Abstract.—We have devised a simple model for assessing the role of development in shaping theevolution of morphological disparity. Disparity of a clade at any given time is expressed in terms ofthe developmental dynamics that lead to the variety of adult morphotypes observed. We use assumedphenotypic manifestations of developmental processes, as they could be detected from allometriccharacterizations, to distinguish a few, nonexclusive types of evolutionary changes in ontogeny. Onthe basis of this formalization, we describe the diversification of hypothetical clades, using thestandard curve of adult morphological disparity, the curve of juvenile disparity, and the curve ofallometric disparity, the latter quantifying the diversification of clades in allometric space. Contrastsof these curves reflect the underlying developmental scheme that drives temporal changes indisparity. We then vary the parameters of the model to assess the expected signature of each metricunder specific conditions: changes in the relative frequencies of the types of evolutionarydevelopmental changes, changes in the transition magnitude attached to each of them, and effectsof temporal variation in average adult size on disparity curves and patterns of morphospaceoccupation. Results emphasize the potential contribution of these proxies for developmentaldynamics—juvenile morphological disparity, allometric disparity, and average adult size—inenriching the interpretation of standard disparity curves and the description of clade histories, withpossible process-oriented inferences.

Sylvain Gerber.* Department of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue,Chicago, Illinois 60637

Gunther J. Eble and Pascal Neige. Centre National de la Recherche Scientifique, UMR 5561 Biogeosciences,Universite de Bourgogne, 6 boulevard Gabriel, 21000 Dijon, France. E-mail: [email protected],[email protected]

*Present address: Department of Biology and Biochemistry, University of Bath, Bath BA2 7AY, UnitedKingdom. E-mail: [email protected]

Accepted: 2 September 2010

Introduction

The study of morphological disparity hasnow become a standard approach for docu-menting a clade’s history at various spatio-temporal scales and taxonomic levels (e.g.,Foote 1990, 1991, 1993; Briggs et al. 1992; Willset al. 1994; Wagner 1995, 1997; Wills 1998;Lupia 1999; Eble 2000; McGowan 2004;Navarro et al. 2005; Lefebvre et al. 2006).Disparity, when combined and contrastedwith taxonomic data, provides a finer de-scription of macroevolutionary phenomena(e.g., Gould 1989, 1991; Foote 1993, 1997).Accordingly, many empirical studies havedocumented patterns of diversity and dispar-ity, and have shown significant temporalasymmetries in clade shape in both taxonomicand morphological terms (early or late occur-rence of maxima), as well as frequent discor-dances between these biodiversity metrics(see Erwin 2007 for a recent review). These

studies assume that competing hypothesesabout evolutionary processes make differentpredictions about frequencies, modalities,and magnitudes of metric differences (Gould1991; Foote 1993, 1997; Neige 2003). To date,two main plausible causative agents havebeen primarily addressed for explainingmajor macroevolutionary events (e.g., Paleo-zoic radiations), and they have been dis-cussed largely under the ecospace versusdevelopmental hypotheses debate (Valentine1969, 1980; Erwin et al. 1987; Erwin 2007).Extrinsic factors (biotic and abiotic environ-ment) seem to have been favored in the questfor pattern explanation. This might be due tothe existence of useful proxies for their effects,making them more convenient for hypothesistesting in empirical studies. Conversely,development still often appears as a blackbox, and hypotheses about decreased devel-opmental flexibility likely lack established

Paleobiology, 37(2), 2011, pp. 237–251

’ 2011 The Paleontological Society. All rights reserved. 0094-8373/11/3702–0004/$1.00

conceptual and methodological frameworksfor allowing consistent tractability.

However, developmental dynamics includea variety of mechanisms operating at variouslevels of integration. Some of these mecha-nisms have phenotypic manifestations detect-able in paleontological archives. Heterochro-ny is such a signature of the developmental‘‘machinery’’ and it has received considerableattention (Gould 1977; Alberch et al. 1979;McKinney 1988; McKinney and McNamara1991); others include heterotopy (Zelditchand Fink 1996), allometry (Gould 1966; Shea1985a; Klingenberg 1998), fluctuating asym-metry (Smith 1998), modularity, and integra-tion (Eble 2004, 2005) (see also Webster andZelditch 2005). Here, we explore the role ofdevelopment in shaping disparity dynamicsby using a simple deterministic model basedon the exploration of juvenile and adultdisparity (Eble 2003; Zelditch et al. 2003;Gerber et al. 2007), as well as on the notionof allometric disparity (Gerber et al. 2008).From simulations, we assess (1) the expectedsignature of several large-scale disparitypatterns explicitly formulated in a develop-mental context, (2) the validity of allometricdisparity as an additional, nonredundantmetric of phenotypic disparity, and (3) theability of juvenile and allometric disparities toprovide insights into the underlying devel-opmental dynamics of disparity and oppor-tunities for mechanistic inference not tractablefrom adult variation alone.

The Model

The use of stochastic and deterministicmodels has firm methodological bases andconceptual rationale in analytical paleobiolo-gy (e.g., Raup et al. 1973; Raup and Gould1974; Gould et al. 1977; Raup 1977a,b; Foote1991; Sepkoski and Kendrick 1993; Foote 1996;Gavrilets 1999; Pie and Weitz 2005; and seeNee 2006 for a recent review of the use ofbirth-death models in macroevolution). Sim-ulations allow null hypothesis testing via thedistinction of random and nonrandom pat-terns, and nomothetic perspectives fromanalyses of average patterns based on pre-specified, assumed evolutionary mechanismsand rules (Raup and Gould 1974). In this vein,

Foote (1996) proposed a simplification ofSlatkin’s (1981) diffusion model to character-ize taxonomic and morphological temporaldiversification of clades. This study hasprovided further investigation and mathe-matical support to previous heuristic modelsof expectable patterns of diversity/disparitycontrasts (Foote 1993). The main emphasiswas on heterogeneities in clade morphologi-cal deployment and how such heterogeneitiesmight be explained by temporal changes inthe magnitude of morphological transitionsand/or in taxonomic rates.

Here we present a developmental extensionof Foote’s (1996) model. The model is intend-ed to supply some typical disparity patternsbased on the consideration of a few develop-mentally relevant, generative ‘‘rules’’ fromwhich arise adult phenotypes (the usual focusof disparity analyses). It thus allows estab-lishing and testing simple relationships be-tween the variational properties of ontogeniesand the resulting dynamics of disparity.Within this extended theoretical context, wetrace disparity at three levels explicitly incor-porating the underlying developmental char-acterization of taxa: juvenile and adult mor-phological disparity, and allometric disparity.

Evolutionary Changes in Ontogeny

Since the publication (1977) of Gould’sinfluential book Ontogeny and Phylogeny, arenewal of interest in the characterization ofevolutionary changes in ontogeny and of theirmultiple phylogenetic implications has in-spired a rich and active agenda in evolution-ary paleobiology. Allometry—the establishedframework for analyzing size, shape and theircovariation (Huxley 1932; Teissier 1934; Joli-coeur 1963; Gould 1966; Shea 1985a; Klingen-berg 1996)—presents itself as a relevant andoperational approach for the type of data athand: the focal point of development beinglargely organismal in paleobiology, size andshape data become naturally informative fordetailed ontogenetic studies. In addition, agedata are rarely available (but see Jones 1988;Jones and Gould 1999) or cannot be confi-dently inferred from proxies (e.g., McKinney1988; Godfrey and Sutherland 1995, 1996;Klingenberg 1998, for details on the confusion

238 SYLVAIN GERBER ET AL.

brought by the use of size as a proxy for agein the heterochronic literature).

Within allometric frameworks and theirlarge empirical bases, ontogenetic trajectoriesoften appear as straight lines when depictedin the space of log-transformed measure-ments (Huxley’s bivariate allometry [Huxley1932] and its multivariate generalization[Jolicoeur 1963]) or in plots of shape variablesagainst size (although deviation from linear-ity is more frequent in this latter case).Accordingly, evolutionary changes in ontog-eny, i.e., modifications of allometric trajecto-ries, can be ascribed to three differentphenomena (Shea 1985a; Klingenberg 1998):

1. Lateral transposition (LT) describes thecase where the descendant trajectoryshifts sideways (translation) relative tothe ancestral trajectory. The starting juve-nile form is different but the trajectoriesremain parallel because the ancestralpattern of trait covariation (growth dy-namics) is conserved (e.g., Shea 1983;Klingenberg and Spence 1993). It meansthat the developmental alteration hasoccurred earlier in the ontogeny, at a stagenot captured by the morphometric analy-sis.

2. Change in slope (CS) corresponds to achange in the direction of the allometrictrajectory resulting in a loss of parallelismbetween ancestor and descendant trajecto-ries (Shea 1989; Godfrey and Sutherland1995, 1996). This implies a modification ofthe growth dynamics. Relative growthrates are altered for at least a subset ofthe morphological traits.

3. Ontogenetic scaling (OS) results from anextension or a truncation of the ancestraltrajectory via heterochronic changes(Gould 1975; Shea 1985b, 1996). The de-scendant maintains the ancestral associa-tion among traits, but the rate and/orduration of growth is altered.

These three types of change do not differfrom the ontogenetic patterns that can bedetected in morphometric analyses of fossilorganisms, and thus form the set of genera-tive ‘‘rules’’ used in the model. Figure 1illustrates these possible changes. The hori-zontal trajectory expresses stochastic inde-pendence of size and shape corresponding toisometric growth (Mosimann 1970). Note thatthe representation of shape-size relationshipsusing bivariate plots is a simplification. Shapeis inherently multivariate in empirical stud-

FIGURE 1. Typology of evolutionary changes in ontogeny and parameters used in the model plotting multivariateshape space versus size. Juvenile and adult stages are represented as vertical dashed lines corresponding to small andlarge sizes. Three types of change are depicted: Lateral Transposition (LT), with a rate p(LT)t of occurrence and anassociated magnitude of morphological transition z(LT)t; Change in Slope (CS) with a rate p(CS)t and magnitude z(CS)t

(with no effect in juveniles); and Ontogenetic Scaling (OS) with a rate p(OS) and an impact on the z(CS)t value (see text).CS also entails diversification in allometric space at the rate p(CS)t and with a magnitude z(AS)t (z(CS)t being a functionof z(AS)t and of the average size difference lt between juveniles and adults).

DEVELOPMENTAL MODEL OF DISPARITY DYNAMICS 239

ies, and reducing shape to a single variable ismisleading and often results in invalid evo-lutionary interpretations (Mitteroecker et al.2005; Webster and Zelditch 2005).

Morphological Disparity

Morphological disparity is a quantitativeappraisal of the variety of anatomical designsdisplayed in a clade inferred from the spreadand spacing of its taxa in a multivariatemorphospace (Gould 1991; Foote 1993, 1997).Here, morphological disparity is measured attwo developmental stages: juvenile disparityand adult disparity (Fig. 1) (Eble 2003). Inempirical studies, this requires some criteriafor recognizing homologous developmentalstages among sampled taxa (e.g., larval-juvenile transition [Zelditch et al. 2003],dental stages [Eble 2002]). In the presentallometry-based model, the juvenile stage isspecified as a given size. It is assumed thatthis size corresponds to the developmentalstage at which patterns of allometric growthare defined and at which evolutionary chang-es in these patterns (CS) are initiated (i.e.,stage at which new trait covariations aresettled).

Developmental Disparity as AllometricDisparity

Paralleling the definition of morphologicaldisparity, allometric disparity estimates thevariety of allometric designs (multivariateallometric patterns) displayed by a clade, asportrayed in allometric space (Gerber et al.2008). Allometric space is a multivariateordination of a set of taxa based on theallometric description—p allometric coeffi-cients—of their ontogenetic trajectories. Thesecoefficients can be obtained from eithertraditional or geometric morphometric ap-proaches (see Adams et al. 2004 and Mitter-oecker and Gunz 2009 for recent reviews).The whole data matrix (n taxa*p coefficients)defines the allometric space (Solignac et al.1990; Klingenberg 1996). Occupation patternof this space can then be described usingstandard metrics of disparity analyses (e.g.,total variance, total range), providing quanti-tative estimates of allometric disparity (Ger-ber et al. 2008).

Model Description

We model and describe the diversificationof a clade from taxonomic, morphological(juvenile and adult), and allometric points ofview. Because we specifically address theaverage behavior of a clade and the averageresponse of morphological and allometricdisparities to modifications of evolutionaryrules, we devise a simple analytical (deter-ministic) model and thus ignore the stochasticvariation that would be observed from mul-tiple runs of a stochastic model. As instandard allometric approaches, juvenilesand adults are described under the samemorphometric scheme (i.e., the same set ofvariables Xs is measured on them) and thuscan be portrayed in the same morphospace(shape space).

Statistical expectation of taxonomic diver-sity is based on the exponential growth model(e.g., Raup 1985; Sepkoski 1991):

Nt~Nt{l 1zpt{qtð Þ ð1Þwhere Nt, pt, and qt are the standing diversity,origination and extinction rates at time t.Origination and extinction rates have been setto pt 5 0.32 and qt 5 0.25 per lineage permillion years (Raup 1991; Foote 1996), and arekept constant in simulations throughout thispaper.

In Foote’s (1996) model, the expectedmorphological disparity Vt is obtained byfirst calculating the expected sum of squaresof the morphological variables (SX2)t. At timet, the sum of squares is expressed as the sumof squares at time t21, minus the contributionof the proportion qt of lineages that becomeextinct, plus the contribution of the propor-tion pt of lineages that branch. Half thedaughters shift positively in morphology byzt, the time-specific step size of morphologicaltransitions, while half shift negatively by zt.

SX2� �

t~ SX2� �

t{11{qtð Þz 1=2ð Þpt S X{ztð Þ2

n o

z 1=2ð Þpt S Xzztð Þ2n o

ð2Þ

which reduces to

SX2� �

t~ SX2� �

t{11{qtzptð Þ

zNt{1ptzt2 Foote 1996 : eq: 4:1ð Þ ð3Þ


Likewise, the ontogenetic characteristics of agiven lineage at time t can be expressed as theontogenetic characteristics of its direct parentlineage at t21, with specified rates andmagnitudes of transitions via lateral transpo-sition LT, change in slope CS, and ontogeneticscaling OS. Disparity is thus expressed asabove, but morphological transitions aredecomposed into transitions via LT andtransitions via CS (effects of OS are incorpo-rated later).

For juveniles (subscript J), individualchange in morphospace occupancy relativeto the previous time interval implies that thedescendant trajectory shifts sideways fromthat of its ancestor (Fig. 1). Changes injuvenile disparity are thus driven only by LT(but see ‘‘Discussion’’). Juvenile sum ofsquares expresses as follows:

SXJ2

� �t~ SXJ

2� �

t{11{qtzptð Þ

zNt{1ptp LTð Þtz LTð Þt2 ð4Þ

i.e., a proportion p(LT)t of the new lineages(Nt21pt) move away from their parent lineagetrajectories with a magnitude z(LT)t.

Contrary to juvenile disparity, changes inadult disparity (subscript A) involve both LTand CS:

SXA2

� �t~ SXA

2� �

t{11{qtzptð ÞzNt{1pt

p LTð Þtz LTð Þt2zp CSð Þtz CSð Þt

2� �

ð5Þ

where p(CS)t and z(CS)t are the proportionand magnitude of CS occurring at time t.

The occurrence of change in slope corre-sponds to an alteration of the growth dynam-ics and a shift in allometric space relative tothe position of the parent lineage; it thusimplies change in allometric disparity (Gerberet al. 2008):

SAS2� �

t~ SAS2� �

t{11{qtzptð Þ

zNt{1ptp CSð Þtz ASð Þt2 ð6Þ

where (SAS2)t is the sum of squares inallometric space at time t. Parameter z(AS)t

is the angular equivalent to z(CS)t. The moretaxa diffuse via CS, the more allometricdisparity increases. The relationship betweenthem is controlled by the size difference ltbetween juvenile and adult stages (Fig. 1). We

chose to set the magnitudes of morphologicaltransition via LT and CS equal at t0, with anaverage size difference l0; trigonometrically, itgives

z LTð Þ0~z CSð Þ0~tan z ASð Þ0� �

l0 ð7Þ

Change in average length of the ontogenet-ic trajectory (via OS) is expressed as follows:

lt~lt{1zp OSð Þtz OSð Þt ð8Þi.e., a proportion p(OS)t of the new lineagesincrease or decrease their adult size by z(OS)t.Note that OS does not affect the magnitude ofchange in allometric patterns z(AS)t, but onlyits impact on adult disparity z(CS)t, as afunction of lt:

z CSð Þt~ z CSð Þ0lt

� ��l0, which is

equivalent to z CSð Þt~tan z ASð Þt� �

lt ð9Þ

For algorithmic convenience, the expectedmean morphology is equal to zero and theexpected mean trajectory is isometric. Juve-nile, adult and allometric disparities, mea-sured as variance, are then computed bydividing their respective sums of squares(SXJ

2, SXA2, SAS2) by the standing diversity

Nt.

Developmental Dynamics andDisparity Patterns

Simple Diffusion in Morphospace andAllometric Space

In this first simulation (p and q kept con-stant), LT and CS are equiprobable (p(CS) 5

p(LT) 5 1/3), and of constant equal magni-tude (z(CS) 5 z(LT) 5 1 arbitrary unit), and nochange in size occurs (p(OS) 5 0; effect of OSis explored later). Figure 2 shows the resultsof this simulation by depicting curves oftaxonomic diversity, juvenile morphologicaldisparity, adult morphological disparity andallometric disparity.

In this case, taxonomic diversity displaysexponential increase (this holds for all simu-lations here), whereas adult morphologicaldisparity displays a characteristic linear in-crease (Slatkin 1981; Foote 1996: Fig. 4.6).Indeed, as specified, LT and CS have similareffects on adult disparity and could beenvisioned as a single phenomenon. Juvenile


disparity (standardized relative to adult dis-parity maximum) also shows a linear in-crease, but with a lower slope, because itsonly contributor is LT. The ratio of adult/juvenile disparity reflects this differential:

Adult/juvenile disparity ratio 5 (p(LT)t

z(LT)t2 + p(CS)tz(CS)t

2) / p(LT)tz(LT)t2, which

simplifies to (p(LT)t + p(CS)t) / p(LT)t, ifmagnitudes are the same.

For the same reason as for morphologicalmetrics, allometric disparity also shows alinear increase through time.

Temporal Change in Processes

Increasing complexity of genetic and/ordevelopmental systems has been advanced asa possible explanation for the decline in thesize of morphological transitions documentedover time (e.g., Valentine and Campbell 1975;Gould 1991). In the present context, temporalchanges in the frequencies of developmentalmechanisms could be responsible for suchpatterns, if we assume that decreased devel-opmental flexibility could be the result ofshifts between mechanisms having different

morphogenetic implications and differentmorphological effects.

Abrupt Change from LT to CS (Fig. 3A).—During the first 50 time units (50 Myr), ratesare set to make LT the only operatingprocess. In the second half of the simulation,rules are inverted. This parameterizationmay appear biologically unrealistic, but itallows a clear characterization of the respec-tive effects of LT and CS on juvenile, adult,and allometric disparities. In the first part,because only LT occurs, juvenile and adultdisparities present concomitant and similarlinear increases, while allometric disparityremains at zero value. Complete reversal at t5 50 implies the deployment of taxa withinallometric space outlined by the suddenincrease in allometric disparity. Conversely,juvenile disparity stops increasing and re-mains constant. Adult disparity keeps in-creasing, and because rates and magnitudesare similar, shift from LT to CS has no effecton its curve.

Progressive Change from LT to CS (Fig. 3B).—The global pattern is roughly the same,

FIGURE 2. Expected curves of taxonomic diversity (dashed line), adult morphological disparity (solid line), juvenilemorphological disparity (dotted line), and allometric disparity (dot-dashed line; see up left insert) in a case of simplediffusion, expressed as percentage of their maximum (except for juvenile disparity, which is standardized in terms ofadult maximum). All disparity estimates are measured as variance. Taxonomic rates, and magnitude and relativefrequencies of occurring developmental changes are kept constant (origination rate p 5 0.32, extinction rate q 5 0.25,p(LT) 5 p(CS) 5 1/3, p(OS) 5 0). Diversity increases exponentially. Disparities increase linearly.


although the progressive transition rendersthe disparity signals more complex. Juveniledisparity, whose behavior is similar to thatof adult disparity at the very beginning ofthe simulation, shows a progressive declinein its rate of increase. Allometric disparitydisplays an exponential evolution reflectingthe increase of CS occurrences through time.Again, the adult disparity pattern does notdiffer from a diffusion pattern given thevalues assigned to parameters (exact com-pensation of LT and CS effects at the adultlevel).

Progressive Change from CS to LT (Fig. 3C).—This is the opposite phenomenon for purposeof comparison. The figure shows a decline inthe rate of allometric diversification and atemporal increase of the rate of diffusion ofjuveniles in morphospace.

In these three cases, the curves of adultdisparity display a similar pattern. Eventhough the specification of parameter valuesis arbitrary here, this similarity of patternspoints out that transition between develop-mental processes of comparable rate ofoccurrence and/or magnitude could havevery subtle effects on adult disparity signalsand thus could remain undetectable with thesole consideration of adult forms.

Change in Magnitude ofMorphological Transition

In addition to or instead of changes inoccurring processes, degree of developmentalflexibility can result from the differentialmagnitude of transition allowed by theseprocesses. Figure 4A and B shows the dispar-ity signature of decline in magnitude for LTand CS transitions, respectively. In the twocases, curves of adult morphological disparityare indistinguishable and show a decline inthe rate of diffusion in morphospace. Incontrast, juvenile and allometric disparitycurves reveal two different patterns: a declinein the magnitude of transitions allowed by LT,as outlined by the similar behavior of adultand juvenile curves (Fig. 4A), and a decline inthe magnitude of transitions allowed by CS,which has no effect on juvenile disparity, butentails a deceleration of the clade diffusion inallometric space (Fig. 4B).

FIGURE 3. Expected curves of taxonomic diversity, adultmorphological disparity, juvenile morphological dispar-ity, and allometric disparity in an exponentially diversi-fying clade with change in the dominance of develop-mental processes generating adult disparity. A, Abruptchange (at t 5 50) from pure LT change to pure CS (withz(LT)t 5 z(CS)t), all other parameters being held constant(see legend Fig. 2). For morphological evolution exclu-sively driven by LT, adult and juvenile disparity curvesare merged and allometric disparity is bounded to zero.For the extreme opposite case, juvenile curve displays nomore variation (plateau phase) and allometric disparityshows its expected linear increase. B, Same phenomenonbut with progressive change in process dominance (p(LT)t

5 1 to 0; p(CS)t 5 12p(LT)t). C, The inverse processtransition (from dominant CS to dominant LT). Note thatcompensatory effects of frequency changes (here, rate andmagnitude of morphological change do not vary throughtime) ensure a linear increase of adult morphologicaldisparity despite major changes in the ontogeneticpathway leading to adult phenotypes.


Change in Size: Impact of Ontogenetic Scaling

Ontogenetic scaling (OS) has been exten-sively discussed in allometric literature (e.g.,Huxley 1932; Gould 1966; Cock 1966; Shea1981, 1985b, 1996; McKinney 1988; Klingen-berg 1998). With the exception of taxagrowing isometrically, any change in sizeresults in net change in shape—the magni-tude of the change being a function of thedegree of deviation from isometry. OS canthus have a significant effect on morphospaceoccupation and disparity value, although itdoes not seem to have been empiricallyexplored in detail. In the model, this point istaken into account by the explicit character-ization of CS as a function of the angular

magnitude of deviation from parent lineageand the adult size. At constant angularmagnitude z(AS)t, a decrease in adult size ltwill result in smaller allowed morphologicaltransition z(CS)t, when CS occurs.

Figure 5A shows the effect of a suddendecrease in clade average adult size. Theadult disparity curve outlines a significantdecline in the rate of morphological diversi-fication. In the absence of allometric andjuvenile data, such a pattern (this holds forgradual decrease as well) is not distinguish-able from a decline in the magnitude of

FIGURE 4. Expected curves of taxonomic diversity, adultmorphological disparity, juvenile morphological dispar-ity, and allometric disparity in an exponentially diversi-fying clade with decline in the magnitude of morpholog-ical transitions allowed by the developmental processesgenerating adult disparity. LT and CS are equiprobablebut their respective effects in deployment in morpho-space (magnitude) are subject to modification (from 100to 1 unit). A, Decline in magnitude of morphologicaltransitions via LT. B, Decline in magnitude of morpho-logical transitions via CS. Although they have a similareffect on the adult pattern, declines in magnitude for LTor CS have clearly different signatures when based onallometric and juvenile curves.

FIGURE 5. Expected curves of taxonomic diversity, adultmorphological disparity, juvenile morphological dispar-ity, and allometric disparity in an exponentially diversi-fying clade experiencing significant change in the averagefinal size reached at adult stage (based on parameter lt inthe model). A, Abrupt decrease of average size (at t 5 50)to one-half of its initial value (10 to 5 units). The adultcurve shows a subsequent decrease in the rate ofmorphological diversification (weaker slope). B, Expectedadult patterns for progressive changes in size of differentmagnitude and polarity (for increase and decrease of25%, 50%, and 75% of the initial size value). The curve forunchanging size is in bold (it is a straight line as in Fig. 2).All morphological disparity curves are scaled accordingto the maximum of the adult curve with 75% increasedsize. In the absence of adult size and ontogenetic data,such patterns may be easily misinterpreted as temporalchanges in magnitude of transitions.


morphological transitions, or a decline intaxonomic rates (Fig. 4) (see Foote 1996: Fig.4.7, 4.8).

In Figure 5B, the same issue is addressedfor continuous increase and decrease inaverage size at various rates and magnitudes.According to the polarity and the magnitudeof size alteration, the curve of adult morpho-logical disparity displays a more or lesspronounced degree of concavity or convexity.Consideration of the putative effect of OS onmorphological disparity has important impli-cations when discussing causal factors ofmorphospace occupation (e.g., in the contextof extinction and morphological selectivity).

Discussion

Development is an important determinantof phenotypic variation. Standard adult dis-parity, the quantified degree of morphologicaldistinctness within a set of adult shapes (the‘‘endpoints’’ of ontogenetic trajectories), incor-porates development either as a direct gener-ative factor, or as the pathway through whichalternative causal determinants may act. De-spite its simplified characterization of thedevelopmental dynamics, the model outlinedabove raises several issues arguing for anexplicit focus on development when analyzingpatterns of morphological disparity.

An allometric approach is not a weakenedsurrogate for heterochronic studies. Allome-try has a large empirical basis and, from itsinitial formulation to recent years, this fieldhas greatly benefited from successive concep-tual refinement and mathematical sophistica-tion to become a major framework in studiesof evolutionary morphology (Strauss 1987).From a methodological point of view, allo-metric approaches can equally and success-fully accommodate ontogenetic data derivedfrom either traditional or geometric morpho-metrics. Allometric characterizations providecomprehensive descriptions of ontogenetictrajectories in terms of size-related shapechange (size being viewed as a latent variableor not [Bookstein 1989]). Information onbiological age is obviously a major aspect ofontogeny (Gould 1977; Jones 1988). Relevantanalyses of rate and timing of evolutionarydevelopmental changes, as well as a complete

description and interpretation of any hetero-chronic change, require age data. However,the absence of age data does not precludevaluable developmental inferences; size andshape data alone are developmentally infor-mative and their treatment in strict allometricterms allows insights into ontogenetic dy-namics with more confidence than via the useof inappropriate proxies (e.g., the size-ageissue) or the extension of frameworks andconcepts beyond their domain of validity.Because disparity analyses usually focus onlarge-scale temporal histories of extinctclades, allometry is a valid and promisingway for studying disparity with insights intoits developmental aspects.

A simplification in the model rests on thestatus of the juvenile stage. Disparity at thisdevelopmental stage has been defined asresulting only from the contribution of lateraltransposition (LT), because this stage corre-sponds to the size at which potential devia-tions from ancestral trajectory via change inslope (CS) are initiated. In most organismssuch a juvenile stage is not easy to identify.Moreover, this stage might not necessarilydetermine or be determined by a given size(see Hall and Miyake 1995, for discussion ontime metrics in ontogeny). Consequently, inempirical studies, it is likely that juveniledisparity may also incorporate the effect ofchange in slope, but to a lesser extent thanadult disparity does. The distinction of therelative contributions of the two processes isrendered more complicated but is not inex-tricable.

A second limitation is that, in the absenceof concrete studies of disparity accounting forits developmental dimension, calibrating therelative frequency and magnitude of morpho-logical transitions allowed by each mecha-nism remains largely hypothetical. The choicehas been made to arbitrarily assign commen-surable efficiency to LT and CS (and OS) inaltering adult disparity. Nevertheless, theparameterizations used in the successivesimulations have at least provided clearmanifestations of the respective, independenteffects of developmental alterations (LT, CSand OS) on juvenile, adult, and allometricdisparities.


Initial simulations were concerned withmodification in the relative frequencies ofdevelopmental changes (CS versus LT inFig. 3). Assuming LT and CS allow morpho-logical transitions of a similar magnitude,changes in their prevalence may be indistin-guishable from simple diffusion if the analy-sis is based on the inspection of adultdisparity alone (Fig. 1). Empirically, thismight be rendered even more complicated ifchanges in frequency are relatively balancedand/or partially obscured by sampling effectsand stochastic variations. Likewise, in theabsence of ontogenetic consideration, if signif-icant differences in magnitude exist betweenthe effects of LT and CS on morphologicalevolution, the shift from one mechanism to theother could be interpreted as a change in themagnitude of transition of a hypotheticalunique mechanism. The ability to distinguishcomplex patterns from simple diffusion, orchanges in magnitude from changes in oper-ating process, should be made easier by (1) theextension of disparity analyses to additionalontogenetic stages, and (2) the investigation oflarge-scale morphological evolution in devel-opmental terms. Allometric disparity appearsas a valuable proxy for the clade-wide charac-terization of the developmental dynamics.Concordances/discordances of juvenile andadult curves, and pattern of allometric diver-sification can be indeed directly related to theprevalence and the efficiency of the types ofevolutionary developmental changes involvedin the morphological patterns.

In the same way, changes in transitionmagnitudes through time should becomemore interpretable if juvenile and allometriccurves are considered as complements toadult patterns. For instance, the observationthat a decline in the magnitude of adultmorphological transition has a significant andcomparable repercussion on the juvenilecurve strongly argues for a decrease in theeffect of LT in the morphological evolution ofthe clade. Conversely, a linear juvenile curveaccompanied by an allometric disparity curvewith decreasing slope (deceleration of allo-metric and adult morphological diversifica-tion) suggests the diminishing role of CS asfactor of morphological diversification.

Another major concern highlighted by themodel is the role of ontogenetic scaling inmorphospace occupation. The effect of onto-genetic scaling (i.e., change in final, adult sizevia extension or truncation of the ancestraltrajectory) on disparity is conditioned byallometric growth. By definition, for a cladewhose taxa all display isometric growth,ontogenetic scaling, if operating, has noinfluence on morphospace occupation anddisparity patterns. The effect of ontogeneticscaling relies upon trajectories that signifi-cantly deviate from isometry. For a givenchange in size, the greater the deviation, thelarger the effect on shape. To have a signif-icant effect on disparity patterns, allometrictrajectories have to deviate from each other inaddition to deviating from isometry (i.e.,allometric disparity should not be zero).Indeed, for a set of parallel trajectories havingsimilar allometric patterns, overall change insize of a given magnitude entails positionalshift in morphospace, but no modification ofneighborhood relationships and thus nochange in disparity.

Again, in the case of an adult disparitycurve, patterns implied by increase or de-crease in average size can be easily confusedwith changes in magnitude of morphologicaltransitions (Fig. 4); juvenile and allometriccurves should help avoid such misinterpreta-tions. That said, construction of curves ofaverage size is also highly useful. Size hasmany biological implications (e.g., physiolog-ical, metabolic, behavioral and ecological) andthus appears as an important factor inevolution (Gould 1966; Bonner 1968; Smith-Nielsen 1984; McKinney 1988; Shea 1992;Dommergues et al. 2002; Trammer 2005). Forclades in which allometric growth prevails,temporal variation in size can play a majorrole in the evolution of clade disparity. Large-scale variations in size can control to a largeextent the distribution and the structuring oftaxa in morphospace. Variation in size canthus drive the disparity dynamics, even ifpervasive constraints limit the evolvability ofontogenetic trajectories of shape changethemselves. In a study of Jurassic ammonites(Gerber et al. 2008), morphological andallometric disparity analyses of the family


Hammatoceratidae revealed that, in spite ofan important allometric diversification, asubstantial decrease in adult morphologicaldisparity occurred. This decrease was causedby a significant reduction in adult averagesize buffering the effects of allometric diver-sification. Hence, size variations should alsobe examined, via contrasts of size anddisparity curves, when documenting mor-phological diversification of clades and look-ing for explanations for patterns of morpho-space occupation.

With the allometric formalization of evolu-tionary developmental changes used in themodel, morphological disparity displayed byjuveniles can never exceed that of adults. Thisresults from the fact that adults incorporatethe same contribution of lateral transpositionas juveniles, but a greater contribution ofchange in slope. However, recent studiescontrasting disparity at juvenile and adultstages have shown that juveniles can some-times be more disparate than adults (Neige etal. 1997; Zelditch et al. 2003; Gerber et al. 2007;all used a common morphometric scheme todescribe juvenile and adult forms). Thedifference between the results of the modeland some results stemming from these em-pirical studies cannot be related to a bias inthe description of allometric changes withinthe model, because allometric departure fromancestral trajectory (with or without addition-al lateral transposition) necessarily takesplace early in ontogeny. The expected patternof an unconstrained diversification in a cladeshould thus be an increase of morphologicaldisparity throughout ontogeny (i.e., top-heavy clade shape in ontogenetic time).Nevertheless, it is worth noting that themodel is meant only to explore the expectedbehavior of an ‘‘average’’ clade. In otherwords, all the stochastic variation that couldbe observed among clades evolving accordingto similar evolutionary rules is averaged(Foote 1996). Patterns of greater juveniledisparity imply two steps: an increase injuvenile disparity, mostly by lateral transpo-sition, followed by a relative decrease in adultdisparity via changes in slope preferentiallyinvolving the convergence of allometric tra-jectories and the erosion of the adult distri-

bution in morphospace. This second stepcould conceivably result (1) from extinctionof taxa with peripheral adult morphologies(by chance or not); (2) from changes in thevariance of the distribution of adult sizes (notimplemented in the model, which onlyconsiders an average adult size); or (3) frompassive trends conditioning the directionalityof change in slope (or the values of allometricgrowth parameters in the case of complexallometries with size-dependent allometriccoefficients) when juveniles reach some ex-treme morphologies (effect of location in statespace; McShea 1998, 2000). Further empiricalanalyses would be needed to assess thefrequency of this pattern (i.e., bottom-heavyclade shape in ontogenetic time) in compar-ison with other expectable patterns (Eble2003). These analyses should also allowtesting the putative control of this pattern bydevelopmental constraints and/or counter-balancing effects (non-additive interactions ofnovelties in developmental labile systems, asdiscussed by Zelditch et al. 2003).

To conclude, inspecting morphological dis-parity and its developmental origin appearsas an important step for extracting quantita-tive, process-oriented descriptions of dispar-ity dynamics, and for testing hypothesesabout the putative internal factors that mayhave driven the patterns observed. Allometryseems to be an appropriate framework toaccommodate the complexity of ontogeneticprocesses. It allows the description of evolu-tionary developmental changes in terms of afew relevant types tractable from morpho-metric analyses of the most current availabledata. Once taxa have been provided with adevelopmental characterization, additionaldisparity curves explicitly carrying ontoge-netic information can be constructed (devel-opmental disparity [Eble 2003]). As definedhere, juvenile disparity corresponds to stan-dard morphological disparity, but measuredat a size corresponding to an earlier develop-mental stage. In the allometric context, juve-niles must be described by the same morpho-metric variables, so that they can be depictedwith related adult forms in a commonmorphospace (shape space). Allometric dis-parity assesses the degree of dispersion in


allometric space, in which each taxon isrepresented as a point summarizing informa-tion about the range of shape change dis-played during its ontogeny. Juvenile andallometric disparities are additional develop-mental characterizations of phenotypic varia-tion. Discordances between juvenile andadult morphological disparities, and betweenmorphological and allometric disparities,may provide finer descriptions of macroevo-lutionary phenomena as well as opportunitiesfor development-based explanations. For in-stance, what is the role of development inevolutionary radiations and extinction events(e.g., Eble 1998)? How can distinct develop-mental factors explain the differential successof clades? Are extinction patterns judged asnonselective with respect to (adult) morphol-ogy truly random, or can ontogenetic prop-erties of taxa contradict such statements tosome extent (e.g., selectivity vis-a-vis sometypes of ontogenetic trajectories detectable inallometric space, but with no detectableimpact on distribution in adult morpho-space)? The joint construction of juvenilemorphospace, adult morphospace, and allo-metric space, and the comparison of theirdifferential filling through time via the quan-tification of juvenile, adult, and allometricdisparities, is one possible way to addresssuch questions, because it articulates thedynamics of morphospace with the variation-al properties of ontogenies (e.g., Gerber et al.2008).

A material constraint is that all these testsand approaches are highly demanding inempirical data at the ontogenetic level, firstas necessary inputs for curve construction,and ultimately for clade-wide documentationand appraisal of the modalities of evolution-ary morphological changes (e.g., estimation offrequencies and magnitudes of changes viaLT, CS, and OS). This should be an enrichingeffort, however, for furthering our under-standing of the role of development inmacroevolution.

Summary

1. Morphometric analyses of size and shapedata using the concepts and tools of

allometric frameworks have come toallow a clear and informative character-ization of development in paleontology.Juvenile morphological disparity and al-lometric disparity take advantage of suchmorphological information to provide adevelopmental perspective in studies ofdisparity.

2. Juvenile morphological disparity quan-tifies the degree of morphological dis-tinctness within a set of taxa consideredat an early developmental stage. Allo-metric disparity describes the variety ofallometric growth patterns displayedwithin a clade by analyzing the ontoge-netic trajectories themselves, rather thandiscrete developmental stages sampledfrom them. Quantitative estimates ofallometric disparity are drawn from theexamination of allometric space wherethe location of any given taxon isspecified by the properties of its growthdynamics.

3. A simple model is proposed to assess theability of these developmental metrics toadequately characterize the potential ef-fect of development on large-scale dispar-ity patterns. In the simplest (but empiri-cally widespread) cases, the allometriccharacterization of evolutionary develop-mental changes allows the distinction ofthree possible evolutionary alterations ofontogenetic trajectories: the descendantallometric trajectory can change in direc-tion (Change in Slope, CS), shift sideways(Lateral Transposition, LT), and/or beextended or truncated (Ontogenetic Scal-ing, OS). These evolutionary changeshave different underlying developmentalcauses and various effects on the resultingadult morphologies.

4. Results of simulations show that contrast-ing standard curves of (adult) morpho-logical disparity with curves of juveniledisparity and allometric disparity enablesthe distinction of CS, LT and OS changes.Pure LT changes do not affect allometricdisparity, whereas pure CS changes haveno (or little) effect on juvenile disparity.Importantly, results also show that thesetypical evolutionary developmental


changes can easily generate some patternscommonly found in the fossil record (e.g.,decline in the rates of morphologicaldiversification). However, these develop-mental alterations might be indistinguish-able or even undetectable if the disparityanalysis is limited to the quantification ofadult phenotypes and adult disparity.Juvenile and allometric disparities, aloneor in combination, thus appear as relevantand useful proxies for developmentaldisparity, and should more often beincorporated into standard disparity ap-proaches when disentangling the multipledrivers of morphological evolution.

Acknowledgments

This paper is a contribution to the teamFED (Forme, Evolution, Diversite) of theUMR CNRS 5561 Biogeosciences, the GDRMEF (Morphome trie et Evolution desFormes) and the ECLIPSE II (CNRS) researchprogram. We thank M. J. Foote, M. J. Hopkins,A. Haber, E. King, Z. Krug and D. Bapst fortheir helpful comments on an earlier versionof the manuscript. P. J. Wagner, C. N.Ciampaglio, N. Hughes, and an anonymousreviewer are gratefully acknowledged fortheir constructive reviews. Research benefitedfrom a French Ministry of Education, Re-search and Technology dissertation grant(15073-2004), funding from the University ofChicago, and a Leverhulme Trust grant (F/00351/Z).

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Developmental aspects of morphological disparity dynamics ... · Sylvain Gerber, Gunther J. Eble, and Pascal Neige Abstract.—We have devised a simple model for assessing the role