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Palaeontologia Electronica http://palaeo-electronica.org

PE Article Number: 8.2.31ACopyright: Paleonological Society October 2004Submission: 4 February 2003. Acceptance: 16 February 2004.

Roopnarine, Peter, D. 2004. Microevolutionary Dynamics of the Early Devonian Conodont Wurmiella from the Great Basin of Nevada. Palaeontologia Electronica Vol. 8, Issue 2; 31A:16p, 860KB; http://palaeo-electronica.org/paleo/2005_2/dynamics/issue2_05.htm

MICROEVOLUTIONARY DYNAMICS OF THE EARLY DEVONIAN CONODONT WURMIELLA FROM THE GREAT BASIN OF NEVADA

Peter D. Roopnarine, Michael A. Murphy, and Nancy Buening

ABSTRACT

The morphologically smooth basal platform margin of one conodont element (P1)in the spathognathodontid ozarkodinidids is a key diagnostic feature for taxon identifi-cation. Differences in the shape of this margin have been used as the basis for genea-logical delineation and the interpretation of evolutionary dynamics, yet very little isknown of the morphological or ontogenetic processes that generate shape variationwithin the group over geological time. Furthermore, the absence of reliably recogniz-able geometric landmarks along this margin prevents the application of standard geo-metric morphometric techniques. This paper addresses these problems by developinga new method for the quantitative description of margin shape, analyzing the ontogenyof shape change within specific stratigraphic intervals, and describing the pattern ofevolution of margin shape over geological time.

Specimens of the genus Wurmiella were obtained from the Windmill Limestone(Pragian) of central Nevada. The resulting morphometric data were used to discrimi-nate three species within the samples, Wurmiella wurmi, W. tuma, and a currentlyundescribed species, W. n. sp. The taxa are differentiated both on the basis of overallshape, as well as differences in margin allometry as described by spline shape andsize (recorded separately as centroid size). An examination of evolutionary pattern inthe W. wurmi samples, using a random walk-based technique, demonstrates that threeindependent aspects of margin shape evolved differently. The overall arch and relativeposition of the basal cavity were highly constrained and static, while the shape of themargin anterior to the basal cavity underwent an episode of significant directional evo-lution.

Peter D. Roopnarine. Department of Invertebrate Zoology & Geology, California Academy of Sciences, Golden Gate Park, San Francisco CA 94118-4599 , USA. [email protected] Michael A. Murphy. Department of Geology, University of California Davis, Davis CA 95616, USA. [email protected] Buening. Department of Geology, University of California Davis, Davis CA 95616, USA. [email protected]

KEY WORDS: conodont, Wurmiella, microevolution, morphometrics

ROOPNARINE, MURPHY, AND BUENING: MICROEVOLUTION IN WURMIELLA

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INTRODUCTION

The long-term utilization of conodonts as oneof the primary elements of Paleozoic and Triassicbiostratigraphy has resulted in a database of strati-graphic information that far exceeds that availablefor any other Paleozoic or early Mesozoic meta-zoan taxon (Sweet 1988). The geographically andsedimentologically widespread distributions ofmany conodont taxa, the group’s long stratigraphichistory, and the stratigraphic density of the con-odont fossil record make these organisms ideal tar-gets for evolutionary paleobiological questions.The present paper applies these properties of theconodont record to long-standing questions ofmicroevolutionary dynamics, an exercise notunique to this paper (for example, Murphy et al.1981), but one that has not been disseminatedbroadly into the mainstream paleobiological litera-ture. In turn, current ideas and techniques of mor-phometric analysis and the analysis of fossil time-series (Roopnarine et al. 1999; Roopnarine 2001)are applied here to the study of the Lower Devo-nian genus Wurmiella from the Great Basin ofNevada.

Microevolutionary Studies

Patterns of microevolutionary change are ofcentral importance to our understanding of organis-mal diversification over geological time. While thetime-scale of microevolution challenges the finesttemporal resolutions available from the fossilrecord, the major theory of diversification (that is,the origin of species by natural selection) claimsthat microevolution is fundamental to the produc-tion of new diversity. On the other hand, morerecent macroevolutionary hypotheses such as spe-cies selection (Stanley 1975) and the possible ran-dom nature of mass extinction events (Gould 2002)have called into question the degree to whichmicroevolutionary processes might exert any con-trol over long-term patterns of diversity. The fossilrecord remains one of the primary sources of infor-mation capable of resolving the conflict between astrict Darwinian view versus hierarchicalapproaches to selection as a structuring agent indiversification. Accessing this information, how-ever, requires work at the finest stratigraphic reso-lutions available, detailed quantitativemorphological analyses, and objective assess-ments of microevolutionary series.

Evolutionary change and character variationcan be expected to be largely continuous andquantitative as temporal intervals approach gener-ational timescales. Two questions of great impor-tance to understanding the role of microevolution in

macroevolutionary phenomena are 1) the extent towhich character variability within ancestral popula-tions determines variation among descendant spe-cies, and 2) whether within-species evolution is atall relevant to the differences among species. Thefirst question addresses variation at the organismallevel, such as ontogenetic change and the pro-cesses of ontogenetic change, for example allome-try, heterochrony and heterotopy. The secondreturns to one of the central arguments of punctu-ated equilibrium theory, and that is the restriction ofmajor morphological change to times of speciation(Gould 2001). Whether most of the geological spanof a species is characterized by constrained stasis(Roopnarine 2001) or oscillatory ‘no net change’evolution, the implication is that speciation, asidentified by a significant morphological discontinu-ity, is essentially independent of intraspecific evolu-tion. These issues should be addressed by highresolution, quantitative studies of intraspecific mor-phological change, coupled with methods appropri-ate for the classification of microevolutionarymodes. This paper addresses both these issues,examining within-sample variation, as well asstratophenetic change in Wurmiella.

The highly variable P1 element forms thebasic means of taxonomic differentiation in ozarko-dinide conodonts (Sweet 1988) (Figure 1). Theshape and outline of the lower profile of the ele-ment is a key feature supporting taxonomic andphylogenetic hypotheses (Murphy et al. 1981) andis the focus of analysis in this paper. The lowerprofile, however, is a curved or sinuous structurewith very few discrete landmarks and thereforedoes not lend itself to a typical geometric morpho-metric approach (Bookstein 1991). Here wepresent a new method combining a landmarkapproach and a spline-based description of the P1element’s basal platform in lateral profile. Thetechnique relies on the presence of two geometri-cally homologous landmarks on the element’s plat-form to convert spline coordinates to Bookstein-style shape coordinates for subsequent analysis ofwithin-sample dispersion and allometry, andamong-sample discrimination. Finally, the evolu-tionary mode of the stratigraphically ordinatedsamples is classified using the Hurst-estimationmethod outlined in Roopnarine (2001).

SYSTEMATIC PALEONTOLOGY

Phylum CHORDATA Bateson, 1886Class CONODONTA Pander, 1856Order OZARKODINIDA Dzik, 1976

Family SPATHOGNATHODONTIDAE Haas, 1959


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Genus WURMIELLA Murphy, Valenzuela-Ríos, and Carls, 2004

Type Species. Wurmiella tuma (Murphy andCebeçioglu 1986).The systematics of Ozarkodina (Branson and Mehl1933) was reviewed recently (Murphy et al. 2004)and the group of forms that have an apparatus sim-ilar to that of O. excavata (Branson and Mehl 1933)were classified in the genus Wurmiella. Theseauthors envisioned four long-ranging lineages asconstituting the main taxonomic units within thegenus (Murphy et al. 2004). Here we use Murphyet al.’s (2004) conclusions as our working hypothe-sis as we consider the two lineages that occur inthe middle Lochkovian, W. wurmi and W. tuma,and identify a third, W. n. sp., that was unrecog-nized by those authors (Figure 1).The genus is characterized by the simple bladewith rather even sized denticles and generallysmall expansion of the basal platform of the P1 ele-ment and the similarity of its apparatus, especiallythe Pb elements with their very high cusps, the

even curvature of the M elements and the incre-mentally larger posterior denticles of the Sc ele-ment. Wurmiella wurmi (Bischoff and Sannemann 1958)Holotype by original designation = Spathognatho-dus wurmi Bischoff and Sannemann, 1958, pl. 14,fig. 5.Diagnosis. A species of Wurmiella with a combi-nation of the following characteristics in the P1 ele-ment: biconcave to convexo-concave lower profilein lateral view, moderate shoulder with or without adenticle on the shoulder on the inner side of theblade or without a shoulder; ledge at the base ofthe denticle row; 17-27 denticles depending on thesize and stratigraphic level of the specimen.Description. P1 element gently twisted, slightlymore strongly near the extremities; basal cavitysmall, asymmetrical, with inner side moreexpanded; basal grooves appressed at their distalends and with straight anterior segment in smallerspecimens; lower profile in lateral view biconvex toconvexo-concave; upper margin in lateral viewbiconvex; cross section of blade (below the denti-cles) low walled, thick at maturity; ledge normallydeveloped on inner side at base of denticles; flanksof blade inflated below ledge and with a narrowpinch zone close to the lower margin; height ofboth parts (anterior and posterior) of blade aboutequal; thicker (wider) and higher denticles concen-trated near the centers of anterior and posteriorparts of blade; at the position of basal cavity ledgebulges laterally to form shoulder on inner side ofsome specimens and in some specimens on bothinner and outer sides; denticle number varies from17-27, counting all germ denticles and dependingon the size of element; denticles straight, stout,with elliptical cross sections, and blunt to moder-ately sharp tips.Comparison. Wurmiella wurmi differs from W.excavata in the greater number of denticles andthe biconcave lower margin of the blade that isangulate in W. excavata; from W. n. sp. in having abiconcave lower margin as opposed to a uniformlyarched one, and a basal platform with a well-devel-oped inner lip and shoulder above it.Discussion. We have recognized three commonmorphs in this taxon that may be of restricted strati-graphic distribution and, thus, broad diagnosis.They are 1) the type or tau morph (τ) with a well-developed inner shoulder and strongly biconvexlower profile; 2) the alpha morph (α) with a denticledeveloped on the shoulder; and 3) the beta morph(β) without a shoulder and fewer denticles.

Figure 1. Wurmiella P1 elements. A) Wurmiella tuma;B) W. wurmi; C) W. n. sp. All specimens approximatelyx90.


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Wurmiella n. sp.Diagnosis. A Wurmiella species based on P1 ele-ments with the following combination of characters:arched lower profile; element bowed or twisted inupper view; basal cavity small, asymmetrical, onlyslightly or not at all expanded on the inner side.Description. Element gently bowed in basal view,slightly more strongly near the extremities; basalcavity very small to small, asymmetrical withexpansion at base on outer side of blade; basalgrooves appressed or open to inverted in somemorphs; lower profile moderately arched withsomewhat stronger curvature in posterior portion ofthe element; flanks moderately inflated with narrowpinched zone at base; blade height short with pos-terior shorter than anterior half; upper profile bicon-vex with broader and higher denticles concentratedaround the position of the cusp and in the anteriorone third of element; a slight ledge may be devel-oped at base of denticles; denticle number variesfrom 17-22 counting all germ denticles dependingsomewhat on size of element.Comparison. Differs from W. excavata in the morestrongly arched and bowed blade and greater num-ber of denticles; from W. wurmi in having an archedas opposed to a biconcave lower profile, and inlacking a shoulder.

METHODS

Samples and Collection

Conodont samples were collected from morethan 70 superposed beds within the Lower Devo-nian Windmill Limestone (Lochkovian) (Johnson1970) at the SP-VII section, Coal Canyon, northernSimpson Park Range, central Nevada (Berry andMurphy 1975; Murphy and Berry, 1983). The SP-VII section exposes a regressive sequence thatbegins in the upper part of the deep-water, grap-tolitic Roberts Mountains Formation and the overly-ing allodapic carbonate and interbedded shaleslope deposits of the Windmill Limestone (Johnsonand Murphy 1984). The section is very fossiliferousin both formations with a well-documentedsequence of graptolite (Berry and Murphy 1975),conodont (Murphy and Matti 1983), brachiopod(Johnson 1973), and ostracode (Evola 1983) fau-nas that have served as the basis for zonation ofthe middle Lochkovian and as a standard of refer-ence for the interval (Murphy and Valenzuela-Ríos,1999). The SP-VII section has been correlated pre-viously to the Copenhagen Canyon section of theMonitor Range (COP IV-V), the latter section serv-ing as a standard reference for the region (Murphyand Berry 1983). The section spans approximately

10 million years of the Lower Devonian (graptoliteZones uniformis, praehercynicus, and hercynicus).

Specimens of Wurmiella were recovered frommore than 50 beds, of which 15 with adequatesample sizes (> 10 specimens) were selected asthe basis of the present statistical work. The low-est stratigraphic level sampled is denoted as sam-ple 200, but thereafter stratigraphic levels(samples) are enumerated 8 to 15 in ascendingstratigraphic order, with sublettering (for example,9H) indicating successively higher samples. W.wurmi was not included in the derivation of thegraphic correlation relationship between sectionsSP-VII and COP IV-V.

Standard Spline Analysis

The smooth morphology of the element basalplatform margins, and the absence of all but twogeometrically homologous Type I landmarks(Bookstein 1991) (Figure 2) means that much ofthe information of morphological variation isencompassed in the outline of the margin. A cubicspline was used to describe the platform marginoutline and hence capture the variation (Roop-narine et al. 2001).

Individual elements were imaged in lateralview with a Pulnix electronic CCD camera mountedon a Wild dissecting microscope. Elements wereimaged in a consistent lateral orientation with theelement blade coplanar to the camera. This wasaccomplished by mounting micropaleontologicalslides on a stage capable of movement in threedimensions. The lateral margin of the platform wasdigitized using TnImage for Linux; the number ofpoints used to describe a particular margindepended solely on the complexity of the marginand therefore varied among individual specimens.The digitized points were then converted to Book-stein-style shape coordinates by the sequence oftranslation, rotation and rescaling (Bookstein1991), the anterior and posterior ends of the basalcavity (the two Type I landmarks), which spans thelength of the element; these points serve as theanchors of the baseline (Figure 3). The shape ofeach margin was then reconstructed by fitting acubic spline to the shape coordinates, and thespline standardized by computing new coordinatesat fixed x-axis intervals. Intervals of 0.02, rangingfrom 0 to 1, were used for this study, resulting ineach margin being described by 51 standard splinecoordinates, of which two are redundant amongspecimens (the baseline anchors). The result isthat all specimens vary in the y-dimension only.Use of a cubic spline to reconstruct the margin out-line ensures a smooth reconstruction while mini-mizing the curvature between points; the result is


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that no extraneous information is added to thedescription of the outline. The standard splineapproach also eliminates the necessity of a fixednumber of digitized points per outline, as generallyrequired if digitization follows a fixed angle sam-pling approach or the outline is divided into a fixednumber of equally spaced points.

Singular Value Decomposition andCross-Validation Analysis

Sample homogeneity/heterogeneity wasassessed using singular value decomposition(SVD) of mean centered standard spline matrices(Sampson et al. 1996). Each sample was centeredby representing specimens as deviations from thesample mean spline. The structure of this matrix ofdeviations was then examined with SVD analysis,the resulting eigenvectors of which characterizethe major regions of dispersion of the splines withinthe sample. Each specimen was also given ascore or location on each eigenvector (a function ofthe variable loadings on the eigenvector), the valueof which reflects the shape of the spline (Figure 4).The resulting distribution of specimen scores istherefore a measure of sample homogeneity, andthis is tested further with a cross-validation analy-sis of the SVD.

The cross-validation analysis proceeds byremoving specimens from the sample one at a time(with subsequent replacement) and reconductingthe SVD with each removal. Any specimen that isa statistical outlier is expected to exert significant

influence on the results of the full-sample SVD(Reyment and Jöreskog 1996). Its removal willresult in significant alteration of the SVD eigenvec-tors, and this is detected as a reduction in the cor-relation between reduced-sample SVDeigenvectors and full-sample eigenvectors.

Ontogenetic Allometry

The exact manner in which the P1 elementincreases in size remains unknown, but the lamel-lar cross-sectional patterns of many conodont ele-ments suggest that they grow by expansion aroundthe basal cavity. Growth is not by simple accretion,since element shape changes, and structures suchas denticles are added as size increases. Quanti-fying element shape and shape variation within asample presents an opportunity to describe onto-genetic shape change in a precise manner for thefirst time.

The relationship between size and shape ofthe platform margin was examined as the relation-ship between centroid size, SVD scores, andspline shape coordinates. The correlationsbetween significant SVD eigenvectors (deter-mined as proportion of sample variance explainedby each eigenvector) and centroid size were mea-sured, a significant correlation indicating significantshape change with changing size, that is, allome-try. Following the detection of allometry, the actualassociated changes in shape are measured with amultivariate regression of the shape coordinates on

Figure 2. Lateral (upper) and basal (lower) views of a P1 element of Wurmiella wurmi. Double-headed arrows indicatethe landmarks (anterior and posterior) at which the left and right lateral margins meet, representing the anterior andposterior tips of the basal cavity.


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centroid size and calculation of predicted splineshapes throughout the size range of the sample.

Mode of Evolution

Describing the mode of evolution of W. wurmiduring the time represented by the SP-VII sectionis a three-step procedure. First, all the samplesmust be aligned stratigraphically and placed on acommon temporal scale. In this case, the sampleswere placed on a composite stratigraphic scalederived from the graphic correlation of SP-VII withanother section of the Windmill Limestone, COPIV-V (Copenhagen Canyon area). COP IV-V hasserved as the standard reference section for muchof the biostratigraphic work that has been con-ducted on the Windmill Limestone sections in thisarea (Murphy and Berry 1983). Second, the sam-ples are ordinated within a common multivariatespace to facilitate standard inter-sample compari-sons. This was accomplished with a canonicalvariates analysis (CVA) of the sample SVD scores,which tests both inter-sample discrimination (with aprior multivariate analysis of variance [MANOVA])and ordinates specimens according to their canoni-cal or Mahalanobis distances.

Evolutionary pattern, and consequently mode,cannot be determined from visual inspection ofstratophenetic series, nor from straightforward sta-tistical comparisons of net differences over a strati-graphic interval. The likelihood of random walksmeeting criteria of directionality under such condi-tions, yet with no underlying deterministic mecha-nisms, precludes such approaches (Bookstein1988). A random walk and randomization tech-nique (Roopnarine 2001) was therefore used tosearch for non-randomness in the SVD I-IIIstratophenetic series. Evolutionary mode of W.wurmi in the SP-VII section was determined byanalyzing the temporal passage of the samplesthrough the conodont lower profile morphospaceas described by SVD analysis of the samples. Theanalysis used here measures the deviation of thestratophenetic series sample means from theexpectation of a random walk through the mor-phospace. It proceeds by measuring the pattern orthe information content of the series with an esti-mation of the Hurst component, which is in fact ameasure of the fractal dimension of the passage.The relationship of the calculated Hurst estimate tothat expected of a random walk is tested with com-

Figure 3. Conversion of digitized coordinates to outline shape coordinates. A) raw digitized coordinates; B) translatedraw coordinates; C) rotated coordinates; D) rescaled shape coordinates. Axes are coordinate axes only and have nobiological meaning until the baseline is established for the x-axis.


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parison of the estimate to a distribution of esti-mates derived from repeated randomization andre-analysis of the stratophenetic series. Anystratophenetic series so analyzed may then beclassified as significantly directional, random, orconstrained (static). The entire procedure isdescribed in greater detail in Roopnarine (2001).

The standard spline analysis, SVD and cross-validation SVD analyses were performed by pro-grams written in C++ and Octave for Linux, whileother statistical analyses were performed with

Stata-SE 7.0 for Linux and SYSTAT 10 for Win-dows. The Hurst estimation analysis was per-formed with Enigma-1.0 for Linux (Roopnarine2001).

RESULTS

Sample Composition and Discrimination

Singular value decomposition analysis andcross-validation SVD were performed on each stra-tigraphic sample to examine sample homogeneity

Figure 4. Standardized margin splines (upper) from a single sample illustrating an overwhelmingly common morphol-ogy, and the presence of two possible outliers. Y-axis represents variation in profile shape. Lower figure plots thespecimen scores on the first two SVD axes, with an example of the common morphology, and the less commonarched profile of the two outlying specimens.


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and detect possible outliers. Most samples werehomogeneous and without outliers, and the major-ity of specimens per sample can be assigned to asingle variable species. Throughout the section,however, there are three distinct morphotypes.The most common morphotype has a lateral profilethat is concave posterior to the basal or centralcavity and horizontal anterior to the cavity (Figure5A). These specimens are assignable to Wurmiellawurmi. The second morphotype is distinguishablefrom W. wurmi by having a convex profile posteriorto the basal cavity and is assignable to W. tuma(Figure 5B), first described by Murphy and Matti(1983) as a subspecies of Ozarkodina excavataand was later elevated to species status (Murphyand Cebeçioglu 1986) on the basis of differencesin denticulation frequency. W. tuma is stratigraphi-cally restricted, and Murphy and Cebeçioglu (1986)hypothesized that it is a cladogenetic descendantof what was considered by these authors to be O.excavata (=W. wurmi). There is no stratigraphicoverlap between the two morphotypes, with W.

tuma occurring in only a short interval in the upperportion of the section. The third morphotype com-prises individuals with significantly concavearches, and while it is dominant in only one sample(8), additional individuals do occur infrequentlythroughout the section. This morphotype is clearlyand statistically distinct from the common W. wurmimorphotype in the section, though it has beenrepeatedly referred to that species in the past (forexample, Murphy and Cebeçioglu 1986). It is des-ignated here as a potentially new species, W. n. sp.(Figure 5C). Finally, there is a single aberrant indi-vidual in sample 15 that is not yet assignable to adescribed taxon; similar specimens do not occuranywhere else in the section. This specimen is notincluded in further analyses.

A multivariate analysis of variance and canon-ical variates analysis were performed on thepooled SVD scores of each morphotype in order tocompare the morphotypes. Results indicate that allmorphotypes differ significantly (Wilks’ λ=0.441,p<0.0001) (Figure 6) and the morphological dis-

Figure 5. Four morphotypes discovered in the section by the standard spline analysis, corresponding to A) Wurmiellawurmi; B) W. tuma; C) W. n. sp.; and D) a single aberrant individual. Labels in upper left corners of graphs denotestratigraphic samples. Bold aqua and blue lines represent the mean spline of the sample, while the orange spline ofthe lower right graph illustrates the single aberrant specimen.


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continuities suggest that they should be treated asindividual taxa. SVD analysis of the multiple W.wurmi samples (first morphotype), however, yieldsno obvious discrimination within this taxon, thoughthere is noticeable variation within individual sam-ples.

Allometry

The quantitative description of shape variationand separate recording of size present the oppor-tunity to examine static allometry in each sample.Most samples had broad size ranges and signifi-cant relationships between profile variability andsize, and it was therefore possible to calculate allo-metric relationships for these samples and to pre-dict shape throughout a sample’s size range. Inseveral cases there was no significant allometrywithin a sample, and in these instances the shapeof a sample was summarized simply as the meanmorphotype profile for that sample.

Figure 7 illustrates the allometries of the dom-inant morphotype in each sample. The first seriesoutlines sample allometries of W. wurmi (morpho-type 1). The general pattern throughout the sam-ples is a change of margin shape, posterior to thecentral cavity, from very straight, to slightly basal-concave at the mean size. Further growth is rela-tively isometric (for example sample 10Li), or

involves either continued increase of concavity ofthe posterior margin (for example samples 14L and15), and/or a posterior shift in the relative positionof the central cavity (for example samples 8A-9E).These stratigraphically successive allometric pat-terns are interesting both from the standpoint ofstability or stasis over brief stratigraphic intervals,as well as their fluctuation within the lineage overlonger periods of time.

The highly arched W. n. sp. is present in sig-nificant numbers only in sample 8 and exhibits noallometric change. This may be a function of smallsample size but is more likely caused by a narrowsize range preserved within the sample. Finally, W.tuma (sample 13J) does exhibit allometry, with theconcavity of the central cavity becoming more pro-nounced with increasing element size and alsoshifting to a more anterior relative position.

Microevolutionary Mode of Wurmiella wurmi

Samples of Wurmiella wurmi were discrimi-nated from the other taxa on the basis of thecanonical variates analysis (above). The pooledsamples were subjected to a single SVD analysisin order to examine intraspecific variation andmicroevolutionary dynamics. The first three eigen-vectors accounted for the majority of the variancein the pooled sample (58.23%) (Figure 8) and are

Figure 6. Canonical variates analysis of three dominant morphotypes (Figure 4). The three taxa are morphologicallydistinct from each other. Symbols, circles - Wurmiella wurmi, triangles - W. tuma, squares - W. n. sp.


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Figure 7. Allometric development in individual, single-taxon samples. Black dots represent individual specimens,whereas solid lines are least squares predictions derived from spline regressions on centroid size: violet-estimate ofshape at lowest end of size range, blue-sample mean spline, orange-estimate from upper end of size range. Samplenumbers are in the upper left corner. Samples 8 and 13J represent Wurmiella. n. sp. and W. tuma respectively, whileall other samples are assignable to W. wurmi. Axes as in earlier spline figures.


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the only eigenvectors considered for further analy-sis. The nature of the SVD analysis ensures thatthe eigenvectors are orthogonal, so they may betreated as independent characters in the analysisof microevolutionary pattern.

Sample distributions for each eigenvector areillustrated in Figure 9. Sampling is not distributedevenly along the stratigraphic section, due prima-rily to the relative scarcity of W. wurmi betweenstratigraphic composite units (SCU) 75 and 150;

Figure 7 (continued).


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samples in that interval are generally specimen-poor, though current sampling efforts may remedythat situation in the near future. Each SVD axisrepresents a different aspect of margin shape, andit is obvious that the axes are not reflecting similarpatterns of evolutionary change. For example, thefirst axis is a measure of the overall arch or con-cavity of the platform, the second axis contrastsconcavity of the margin anterior and posterior tothe basal cavity, and the third axis reflects the rela-tive position of the cavity as well as the shape andconcavity of the margin posterior to the cavity (Fig-ure 9).

Visual inspection of the stratophenetic seriesin Figure 9 suggests several microevolutionary fea-tures. None of the characters seem to undergo netevolutionary change, though there are some sug-gestions of directionality. Analyses of the seriesusing the Hurst estimation procedure (Roopnarine2001) result in SVD I and III being categorized asstatic series. The SVD I trajectory moves very littleas the series is analyzed (Figure 10A), and its verylow Hurst estimate values are strongly suggestiveof a morphology that is not varying randomly but isperhaps constrained. SVD III varies more thanSVD I, and could be described as a classic stasis,

or ‘no net change’ type of pattern (Figure 10C).SVD II, however, exhibits significant directionalityin the stratigraphic interval 25-50 SCU (Figure10B), and this is documented by its trajectory’shigh values and relatively low probabilities of beinggenerated by a random process (95% c.i. of mini-mum P value of the trajectory, 0.548≤P≤0.042).Beyond that interval, however, the series becomessignificantly constrained.

DISCUSSION

Species Discrimination

A quantitative description of the Wurmiella P1element’s basal platform in lateral profile, using thestandardized cubic spline approach outlined in thispaper, is useful for understanding the nature andlevels of variation both within and among speciesof Wurmiella. Examination of the homogeneity ofindividual stratigraphic samples resulted in thedetection of three distinct morphotypes within theSP-VII section, two assignable to the describedspecies W. wurmi and W. tuma, and anotherbelonging to an as yet undescribed species, W. n.sp. The standardized spline also leads to qualita-tive descriptions of the morphological differences

Figure 8. SVD eigenvalue magnitude versus eigenvector number showing rapid decline after the first eigenvector,and then after the second and third eigenvectors.


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among the taxa. W. wurmi differs from W. tuma pri-marily in the shape of the basal cavity in lateralview; the cavity is represented by a noticeably“pinched” region of the profile in W. tuma, while inW. wurmi it marks a change in the curvature of theprofile between anterior and posterior regions. Thenew species is distinctly different, with a significantoverall crownward arching of the entire element.

Ontogenetic Variation

The use of a geometric morphometricapproach to description of the profile, including thecalculation of Bookstein-type shape coordinates,allows a clean separation of geometric shape andscale. Rescaling according to baseline lengthremoves scale information from the configurationof landmarks for each specimen thus placing allspecimens on a fixed scale for the purposes ofshape comparison. Scale information is recordedseparately as the centroid size (Bookstein 1991) ofthe standardized but unscaled spline coordinates.Information regarding size may nevertheless bepresent in scaled geometric analyses because ofthe allometric covariation of shape coordinates and

centroid size. Allometric information was recov-ered in this study by examining the covariation ofshape and centroid size, and reconstructing (viaregression) “average” splines at three points in thesize range for any single stratigraphic sample of anindividual species. The points used were the mini-mum and maximum sizes, as well as mean size.Comparison of the resulting splines lead to a set ofvery interpretable graphics of shape change, dur-ing development, of any of the species at a particu-lar stratigraphic level.

Using this analysis, one developmental fea-ture common to both W. wurmi and W. tumabecomes obvious immediately; increasing size isassociated with an increase in the degree ofcrownward arching of the element (Figure 7). Thelack of detectable allometry in the single sample inwhich W. n. sp. is dominant (8) prohibits a similarcomparison, but it is interesting to note that qualita-tive extrapolation of the growth trend of W. wurmileads to both an increase in the degree of arching,as well as a shallowing of the basal cavity, a condi-tion seen in all specimens of W. n. sp. We cannotyet determine the roles that these developmental

Figure 9. Stratophenetic illustrations of shape variability in Wurmiella wurmi described by the first three SVD eigen-vectors. Splines inset at the top of each column illustrate the range of variation described by the eigenvector andhence the aspect of margin shape being described.


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characters may have played in the evolution of theWurmiella clade, because we do not currently havea phylogenetic hypothesis of sister-species rela-tionships for the genus. Nevertheless, this is thetype of morphological information, which isrequired for the addition of hypotheses of evolu-tionary process to hypotheses of phylogenetic pat-tern.

Microevolutionary Mode

The distribution of W. wurmi samples through-out the section allows an examination of the pat-tern(s) of microevolution exhibited by the species.The description of this mode uses a random walkas a null model of evolutionary change (Bookstein1988; Roopnarine 2001). Of the three most signifi-cant factors of the SVD analysis, two conformed tothe expectation of stasis (SVD I and SVD III), andone exhibited an interval of significant directionalchange (SVD II). SVD I, a description of the overallcrownward arch of the element, varied very little,undergoing no net change through the section.This type of pattern conforms to constrained stasis(Roopnarine 2001), where the degree of variationis less than what would be expected of an unbi-

ased random walk. Such patterns suggest theaction of one or more mechanisms that limit varia-tion, such as stabilizing selection or functional con-straints (Roopnarine 2001). SVD III, the relativeposition of the basal cavity, varied broadly and ran-domly in the lower part of the section, but then alsoseems to follow a constrained pattern. SVD II, onthe other hand, a description of the crownwardconcavity of the profile posterior to the basal cavity,underwent a period of directional change fromsamples 9D-10Li. The trend is a subtle, but signifi-cant decrease in concavity. Examination of theallometric curves (Figure 7) shows that the trend isrooted in the changing development of the profile,where the posterior section of the profile fails toincrease in concavity with increasing size as onemoves up the SP VII section. This is a significantconclusion since it links within-sample changes inallometry/development to a longer term microevo-lutionary trend.

The long geological history, generally highabundance, and morphological richness of con-odonts and their fossil record combine to makethem ideal subjects for long-term microevolutionarystudies. In this study we have been able to use a

Figure 10. Hurst estimate analysis of the evolutionary pattern described by each stratophenetic series in Figure 9.Hurst estimates measure deviations from randomness (random walk), with values >> 0.5 indicating increasing direc-tionality, while values << indicating increased constraint. Probability on the y-axis is the probability that that portion ofthe series is non-directional. Bold lines are mean Hurst estimates, while fainter lines are 5% and 95% confidenceintervals. A and C (SVD I and SVD III) range between random oscillation and significant constraint, while B (SVD II)exhibits a significant episode of directionality early in the series.


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single element of the Wurmiella apparatus, pre-served in a single stratigraphic section, to discrimi-nate three species, describe ontogenetic changesin individual samples of each species, describepatterns of character evolution in one of the spe-cies (W. wurmi), and link long-term directional evo-lution in one of those characters to evolution at theontogenetic level. The obvious extensions of thepresent study include 1) broader geographic sam-pling in order to understand spatial variation of thepatterns observed, 2) longer stratigraphic samplingto capture temporal variation throughout the entiregeological span of the species, including times ofcladogenesis, and 3) a phylogenetic framework ofsister-group relationships in which to test hypothe-ses of the relationship between the microevolution-ary observations and a macroevolutionary pattern.These are the basic steps toward understandingsome of the questions raised by macroevolutionarytheory, namely the role of microevolutionary pro-cesses in macroevolutionary patterns, the patternof microevolution during the non-cladogenetic spanof a species, and the distribution of microevolution-ary rates during the geological span of a species.

The combination of a good fossil record, care-ful stratigraphic sampling and analysis, and appro-priate methods for quantitative morphological andstratophenetic data analysis, will allow paleobiolo-gists to address evolutionary questions with grow-ing confidence. As paleontology continues tomove increasingly from descriptive to analyticalphases, the understanding of the quantitativenature of the discipline’s unique data will becomeincreasingly fundamental (Roopnarine 2002).

ACKNOWLEDGMENTS

We wish to thank P. Fitzgerald for valuableassistance in the laboratory, and P. Carls and I.Valenzuela-Ríos for useful discussions. C. Tangand L. Leighton kindly reviewed several versions ofthe manuscript, as did two anonymous reviewers.This work was supported by National ScienceFoundation grant EAR-9814354 to PDR and MAM.

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