How many kinds of sclerite?

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How many kinds of sclerite? Towards a morphometric classification of gorgoniidmicroskeletal components

Sergio Vargas a,*, Odalisca Breedy b,c,d, Francisco Siles e, Hector M. Guzman b

a Museo de Zoologıa, Escuela de Biologıa, Universidad de Costa Rica, P.O. Box 1962-2100, San Jose, Costa Ricab Smithsonian Tropical Research Institute, P.O. Box 2072, Balboa, Panamac Centro de Investigacion en Ciencias del Mar y Limnologıa, Universidad de Costa Rica, P.O. Box 2060 UCR, San Jose, Costa Ricad Centro de Investigacion en Estructuras Microscopicas, Universidad de Costa Rica, P.O. Box 2060 UCR, San Jose, Costa Ricae Escuela de Ingenierıa Electrica, Facultad de Ingenierıa, Universidad de Costa Rica, P.O. Box 2-10, 2060 UCR, San Jose, Costa Rica

1. Introduction

Octocorals of the family Gorgoniidae (Alcyonacea) constitute adiverse group that inhabits tropical and subtropical shallow(<50 m) waters around the world. In the Caribbean and easternPacific waters, gorgoniid octocorals dominate the landscape ofseveral coastal marine environments where they provide structureand heterogeneity to the ecosystem and refuge to other marineorganisms (Bayer, 1961; Breedy and Guzman, 2002, 2003a,b, 2004;Sanchez et al., 2003; Williams and Breedy, 2004). The systematicsof the group has changed constantly since it was first described andthe family, which once included practically all horny octocorals,today is restricted to those forms with calcareous sclerites that areless than 0.3 mm in length and sculpted with regularly arrangedgirdles of complicated tubercles and warts (Bayer, 1951, 1953).

Gorgoniid sclerites can be grouped into four basic types—spindles, disk-spindles, capstans, and scaphoids. The presence ofthese sclerites individually or in combinations is often used toidentify gorgoniid specimens to the generic level (Lewis and VonWallis, 1991) and were the basis for Bayer’s (1953) subfamilies‘Lophogorgiinae’ (the spindle lineage that included mainly easternPacific genera) and ‘Gorgoniinae’ (the scaphoid lineage that wasrestricted to genera occurring in the West Indies), which he laterabandoned. Currently, variations in sclerite size, sculpture, andcoloration (Bayer, 1953) and the relative proportion of the differentsclerite types in the sample (Breedy, 2001) constitute the maincriteria for species delimitation.

Determining sclerite type is not a trivial procedure; it is madedifficult by the continuous variation in sclerite form within andbetween species. This continuum represents a major obstacle tothe definition and assignment of sclerite character states (Sanchez,2001, 2005; Sanchez et al., 2003; but see Breedy and Guzman,2007; Williams, 1992; Williams and Lindo, 1997) and, thus, to thededuction of phylogenetic hypotheses of many octocoral groups.Sanchez (2005) faced this obstacle in his analysis of the familyParagorgiidae, where the wide variation in sclerite form results in acontinuum between the surface and the inner medulla scleritesmaking homology assessments difficult. Similar problems occur inalmost all octocoral groups, including the Gorgoniidae. The

Micron 41 (2010) 158–164

A R T I C L E I N F O

Article history:

Received 16 May 2009

Received in revised form 1 August 2009

Accepted 2 August 2009

Keywords:

Gorgoniidae

Octocorallia

Octocoral systematics

Pacifigorgia

Sclerite morphometrics

A B S T R A C T

Gorgoniid octocorals constitute a diverse group of organisms that inhabit a wide range of marine

environments. The group is currently defined by the presence of calcareous sclerites that are less than

0.3 mm in length with regularly arranged warts. Generic and specific classification schemes are based on

the presence/absence of different sclerite classes in the sampled specimen as well as the frequency in

which each class occurs in the sample. Sclerite classification typically has been difficult because a

continuum of sclerite forms is found within and between species. Thus, the use of sclerites for

phylogenetic inference and classification is problematic. Herein, we present a methodology to obtain

quantitative measurements of large numbers of sclerites and used finite mixture modeling to assess the

number of statistically different sclerite classes present in the eastern Pacific octocoral genus Pacifigorgia.

We also test the ability of simple neural classifiers (perceptrons) to sort sclerites into the classes

traditionally used in octocoral taxonomy. This methodology can be used for other gorgoniids and can be

further extended to include shape quantifiers for groups other than those studied here.

� 2009 Elsevier Ltd. All rights reserved.

* Corresponding author. Present address: Molecular Geo- and Palaeobiology Lab.,

Dept. for Geo- & Environmental Sciences, , Palaeontology & Geobiology, Richard-

Wagner Str. 10, 80333 Munich, Germany. Tel.: +49 89 2180 17934;

fax: +49 89 2180 6601.

E-mail addresses: [email protected], [email protected]

(S. Vargas).

Contents lists available at ScienceDirect

Micron

journa l homepage: www.e lsev ier .com/ locate /micron

0968-4328/$ – see front matter � 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.micron.2009.08.009


Gorgoniidae also poses additional problems: the fusion of thecoenenchymal layers makes sclerite positional inferences difficultand further complicates systematic research (but see Breedy andGuzman, 2007; Williams, 1992; Williams and Lindo, 1997).

The role of the calcareous sclerites in the identification andclassification of the alcyonarians was first appreciated byValenciennes (1846, 1855) and further explored by Kolliker(1865), whose taxonomic arrangement of the group greatlyinfluences present day classification schemes (Bayer, 1961).Although sclerites are the main source of systematic informationamong the Octocorallia (Bayer, 1951, 1953, 1961, 1981; Breedy,2001; Breedy and Guzman, 2002, 2005; Fabricius and Alderslade,2000; Sanchez, 2001; Sanchez et al., 2003), little development hasbeen done concerning the morphometric study of the micro-skeletal components found in octocorals. This study represents thefirst attempt to use statistical methods to determine the number ofsclerite types within a given octocoral group.

We used the eastern Pacific genus Pacifigorgia (Bayer, 1951) tointroduce a methodology for the morphometric analysis ofoctocoral sclerites. Specifically, we used finite mixture models(sensu Strait et al., 1996) to statistically assess the number ofsclerite types within the genus. We also attempted to auto-matically classify Pacifigorgia sclerites using a simple perceptron.Pacifigorgia sclerites traditionally have been classified as spindlesand capstans, and the genus’ sclerites practically show no variationrelated to its topographical position. Pacifigorgia thereforerepresents a relatively straightforward case study the results ofwhich may also useful for other members of Bayer’s spindle lineage(‘Lophogorgiinae’ sensu Bayer, 1953).

2. Materials and methods

2.1. Specimens

We obtained Pacifigorgia specimens (Table 1) from the Museode Zoologıa, Universidad de Costa Rica, Smithsonian TropicalResearch Institute, Panama reference collections and from theCharles Darwin Research Station, Galapagos Islands, Ecuador.Fragments of the colonies were treated with sodium hypochlorite

(household bleach) for sclerite dissociation (Bayer, 1961; Breedyand Guzman, 2005); sclerites were stored in 70% ethanol until theywere analyzed.

We took series of photographs using an Olympus BX51TRFmicroscope attached to a CoolSnap-Procolor digital camera.Sclerites were mounted on regular light microscopy slides; theethanol was allowed to evaporate before the photograph wastaken, and no cover or liquid medium was used to embed thesclerites. Photographs were stored as high quality TIFF imagesusing the software ImagePro-Plus.

2.2. Image analysis

Sclerite images were processed using simple image segmenta-tion procedures. First, color images were converted to gray-scaledimages and inverted (Fig. 1A). Once inverted, gray-level thresh-olding was applied to generate a binary image (Fig. 1B) that wasused to determine the sclerite border (Fig. 1C and D). Two differentshape quantifiers were used to describe the identified sclerites:circularity and compacticity. Circularity refers to the ratio of anobject’s mean radius to its standard deviation, and compacticityrefers to the relation between the area of the object and itsperimeter squared (Siles-Canales, 2004). These two shape quanti-fiers were selected because they provide an overall estimation ofthe shape of the sclerite taking in consideration different

Table 1Pacifigorgia species used for sclerite morphometric and character analysis.

Pacifigorgia adamsii (Verrill, 1868)

Pacifigorgia bayeri (Breedy, 2001)

Pacifigorgia cairnsi (Breedy and Guzman, 2003a)

Pacifigorgia curta (Breedy and Guzman, 2003a)

Pacifigorgia dampieri (Williams and Breedy, 2004)

Pacifigorgia darwinii (Hickson, 1928)

Pacifigorgia elegans (Milne Edwards and Haime, 1857)

Pacifigorgia eximia (Verrill, 1868)

Pacifigorgia firma (Breedy and Guzman, 2003a)

Pacifigorgia irene (Bayer, 1951)

Pacifigorgia rubicunda (Breedy and Guzman, 2003a)

Pacifigorgia rubinoffi (Breedy and Guzman, 2003b)

Pacifigorgia samarensis (Breedy and Guzman, 2003a)

Fig. 1. Segmentation technique used to determine the sclerite border (solid black line) in this study. (A) Gray-level inversion, (B) gray-level thresholding, (C) sclerite border

detection, and (D) zoom of the detected sclerite border superposed on the original sclerite image.

S. Vargas et al. / Micron 41 (2010) 158–164 159


measurements at a time, for instance the area/perimeter ratio andthe variation of the radius of the sclerites. Another advantage ofthese two quantifiers is that both are dimensionless variables,which makes scale calibration unnecessary for images taken underthe same optical conditions.

After all of the images were processed, a matrix was created byhand containing the data for all of the sclerites measured. Thismatrix was then refined by taking out joined elements (Fig. 2B) orelements whose form was evidently distorted (e.g. brokensclerites; Fig. 2C); the resulting refined matrix was used for allsubsequent analyses.

2.3. Sclerite type determination: how many sclerite types?

We used finite mixture modeling to assess the number ofstatistically different sclerite character states present in the dataset generated for the genus Pacifigorgia. Strait et al. (1996) firstused finite mixture modeling as a coding technique for continuousvariables; these authors discuss the method in detail so we presentonly a brief description and refer to them for further details.

A data set is considered to be mixed if it contains representa-tives from more than one population (i.e. class). Finite mixturemodels describe mixed data sets using well-known statisticalconcepts and proceed by first identifying the form of thedistribution (i.e. Gaussian, Poisson, etc.) of each componentpopulation (i.e. class) in the data set and then fitting, usuallyusing a maximum likelihood approach, a mixture density functionthat describes the distribution of the mixture observed in the data

set. For instance, one can statistically describe a data set as amixture of three normally distributed populations, each with agiven mean and variance value (Fig. 3). Once the mixture modelhas been determined, each instance in the data set can be classifiedwith a given probability as member of one of the componentdistributions (i.e. classes).

We used the statistical computing environment R (R Develop-ment Core Team, 2008) in conjunction with the package MCLUST(Fraley and Raftery, 2002, 2006) to find the number of classespresent in our data set for both circularity and compacticity. Wetested mixtures with up to nine component Gaussian distributionsand selected the best mixture model using BIC.

2.4. Capstans and spindles

MCLUST is an automatic classification program; it looks for thenatural classes present in the data set without any prior knowledgeof class membership (i.e. unsupervised classification). Therefore,the spindle or capstan sclerite categories may not appear in theMCLUST classification schemes. To explore whether the classifica-tion found by MCLUST corroborates the existence of the traditionalspindle and capstan sclerite categories, we visually classified eachsclerite in the data set as spindle or capstan. Following Breedy andGuzman (2002), spindles are sclerites with a straight or a slightlycurved axis, generally with more than two whorls of tubercles andwith acute ends. Capstans are sclerites with two whorls oftubercles or warts, with a clear median space. In most cases,tubercles and warts are present at the ends of capstan sclerites andfuse at different levels to form terminal tufts (Fig. 4).

2.5. Automatic sclerite classification: can simple perceptrons

differentiate Pacifogorgia sclerite classes?

We attempted to classify sclerites automatically using a simpleone-cell perceptron. Perceptrons are simple artificial neurons thatcan be trained to solve separable problems. In general, perceptrons‘‘learn’’ from a number of example cases the way in which theclasses in the dataset can be differentiated. Perceptron learningproceeds by adjusting a set of weights that multiply the inputvalues describing the example cases. If the problem at hand isseparable the perceptron learning algorithm will converge to astable set of weights in a finite number of steps (Gallant, 1990).After training, the perceptron can automatically classify unseencases present in the dataset.

We trained the perceptron using circularity only, compacticityonly, and circularity and compacticity together as input values. Werandomly selected sclerites from our dataset to form twopartitions: one to train the perceptron (i.e. a training partition),and one to validate the perceptron classification ability (i.e. a

Fig. 2. Wrong or distortedly determined sclerite border (solid black line). (A)

Regular Pacifigorgia sclerite, (B) joined elements, and (C) deformed or truncated

sclerites.

Fig. 3. Finite mixture modelling. Histogram of a mixed population (left) and its mixture model (right) showing three component distributions representing the classes within

the population. Taken with permission from Strait et al. (1996).

S. Vargas et al. / Micron 41 (2010) 158–164160


validation partition). The single-cell perceptron was allowed toiterate over the example sclerites on the training partition until thenumber of misclassified sclerites in the training dataset reached10%, or the number of iterations reached 5 times the total numberof example sclerites. After training, the classification ability of theperceptron was tested on the, so far unseen, sclerites from thevalidation partition. The perceptron was allowed to iterate over thevalidation partition only one time, after which we calculated theerror rate of the perceptron as the number of misclassified scleritesdivided by the total number of sclerites in the validation set. A totalof 50 cross-validation partitioned datasets were generated forcircularity only, compaciticity only, and circularity and compac-ticity together. We report the error rates reached by the perceptronfor each combination of input values.

3. Results

3.1. Sclerite morphometrics

A total of 665 sclerites were measured using the methodoutlined above. Circularity and compacticity frequency distribu-tions fitted a log-normal distribution (data not shown), thus weused the log-transformed values for compaticity and circularity aswell as the untransformed values for both variables in the finitemixture-model analyses, as the results obtained in terms of thenumber of classes obtained for each variable we present the resultsbased on the untransformed values. Sclerite circularity valuesranged from 41 to 86 units with a median value of 56 units; scleritecompacticity values ranged from 18 to 55 units with a medianvalue of 29 units.

By visual determination, capstans appeared more compact (i.e.had lower compacticity values) and circular (i.e. had highercircularity values) than spindles. Both circularity and compacticitydistributions showed no overlap when the first and third quartileswere considered (Fig. 5). The existence of this gap between thecapstan and spindle circularity and compacticity distributions maybe used as a simple preliminary way to corroborate sclerite classmembership after visual classification has been done. Spindles canbe treated as sclerites with circularity values ranging between 47and 53 units and compacticity values between 31 and 41 units;sclerites with circularity values between 55 and 67 units andcompacticity values between 23 and 28 units can be treated ascapstans.

Table 2BIC values for circularity and compacticity mixture models tested with MCLUST.

The selected models appear in bold.

Number of component

distributions

Shape quantifier

Circularity Compacticity

1 �4860.048 �4507.548

2 �4785.096 �4413.0023 �4758.338 �4426.619

4 �4771.799 �4429.034

5 �4773.260 �4432.125

6 �4779.274 �4444.384

7 �4792.717 �4457.442

8 �4804.964 �4463.046

9 �4818.157 �4465.462

Fig. 4. Spindles and capstans of Pacifigorgia adamsii under light microscopy. Note

the acute ends of the spindles and the lack of a unique median space in contrast to

the capstan’s more rounded tips and clear median space.

Fig. 5. Box plot showing circularity and compacticity values for Pacifigorgia sclerites (n = 665) measured. The sclerites were visually classified as capstans (C) or spindles (S)

prior to the analysis.



3.2. Sclerite classes: circularity

A three-class model was selected (Table 2) when circularity wasused as the shape descriptor for Pacifigorgia sclerites. The classeswere associated with sclerite categories (Fig. 6A): spindles wereincluded almost exclusively in class 1, whereas capstans weredistributed among the three classes (1, 2, and 3). The circularity

classification differentiated long capstans (included in class 1 andclass 2) and short capstans (class 3), which reflects Bayer’s (1953)sclerite categories.

Visual differentiation of spindles and capstans traditionally hasbeen difficult because of the continuum in sclerite form. Categoriessuch as blunt spindles or elongated capstans (Breedy and Guzman,2002) were developed mainly to accommodate intermediate

Fig. 6. Sclerite type (spindle or capstan) by circularity based classification. (A) All elements included. (B) Elements classified with a posterior probability �0.95.

Fig. 7. Sclerite type (spindle or capstan) by compacticity based classification. (A) All elements included. (B) Elements classified with a posterior probability �0.95.



sclerite forms that cannot be strictly classified as either capstans orspindles but share some overall visual similarity.

Mixture modeling using sclerite circularity also suffers fromthe difficulties associated with intermediate sclerite forms, andour model included within the spindle class many of the scleritesthat we had visually classified as capstans. Mixture modeling,however, provides an objective way to solve classificationproblems because sclerite class assignment is done in aprobabilistic way after the mixture model has been determined.This way sclerites assigned with low posterior probability to aclass (i.e. ambiguously classified), can be detected and the analysiscan be restricted to elements classified with a probability higherthan a specified threshold value, for instance p � 0.95. When weused this criterion, the ambiguity in sclerite classification wasreduced although capstans were still present in the spindle class(i.e. class 1; Fig. 6B).

3.3. Sclerite classes: compacticity

The compacticity classification selected was a two-classmixture model (Table 2). As in the circularity based classification,one of the classes (i.e. class 1) included mostly capstans and theother mostly spindles (class 2; Fig. 7A).

We used the proposed probabilistic threshold value (p � 0.95)to choose only unambiguously classified sclerites; after this limitwas set, almost all capstans were removed from the analysis andonly spindles were selected (Fig. 7B). Compacticity appeared to bea good morphometric measure for spindles; they were classifiedwith high posterior probability values when this shape descriptorwas used. In contrast, it was not possible to assign most capstans toany class with high posterior probabilities based on compacticity(i.e. capstan classification using compacticity values was uncer-tain).

3.4. Perceptron classification experiments

In general, our one-cell perceptron was able to classify scleriteswhen circularity only and circularity and compacticity togetherwere used as input values. When circularity only was used as theinput value, convergence of the learning algorithm was sensitive tothe learning rate used in training the perceptron. On the contrary,using both circularity and compacticity as input values for traininglead the learning algorithm to converge independently of thelearning rate used. It was impossible to classify sclerites based oncompacticity only, independently of the learning rate used to trainthe perceptron (Table 3). It is important to note that our perceptronachieve only �80% accuracy, that is it misclassified �20% of thesclerites present in the validation partitions when both circularity,or circularity and compacticity were used as input values.

4. Discussion

Sclerites are calcium carbonate (calcite) elements of complexmorphology. The importance of sclerites for octocoral systematicshas been repeatedly acknowledge by authors since the days ofValenciennes and Kolliker (Bayer, 1961), and recent cladisticstudies of several groups have shown sclerite-based characters tobe highly informative (Sanchez, 2001, 2005). Despite theirimportance, studies dealing with sclerite classification are lacking.

In this study, we attempted to use quantitative methods basedon the conjunction of image analysis and statistical classificationtechniques to avoid setting arbitrary limits to sclerite classes, andto explore the ability of simple classifiers (i.e. perceptrons) tohandle sclerite classification. Our results, in particular our mixture-model analyses, corroborated the existence of three scleriteclasses, namely spindles, long capstans, and short capstans(Fig. 8). Blunt spindles (Fig. 8B), a category used in the taxonomic

Table 3Mean error rates� standard deviation by learning rate used for perceptron classification using circularity only, compacticity only, or circularity and

compacticity together as input values.

Learning rate Shape quantifier

Circularity Compacticity Circularity and compacticity

0.1 0.5690 (�0.0645) 0.5905 (�0.0201) 0.2014 (�0.0437)

0.001 0.5313 (�0.1231) 0.5976 (�0.0245) 0.2065 (�0.0483)

0.000001 0.1852 (�0.0133) 0.7967 (�0.0195) 0.2077 (�0.0241)

Fig. 8. Sclerite types found in the genus Pacifigorgia. (A) Pointed spindle, Pacifigorgia adamsii; (B) blunt spindle, Pacifigorgia curta; (C) capstan, Pacifigorgia curta; (D) micro-

capstan, Pacifigorgia cairnsi.



literature (Breedy and Guzman, 2002) to group visually similarintermediate spindle-capstan forms are classified with lowprobabilities and cannot be assigned to any class. These scleriteswould not be considered if a probabilistic approach, like the onehere proposed, is used for sclerite classification. Other classestraditionally used in the taxonomic literature of the ‘Lophogorgii-nae’, such as bent-spindles (Bayer, 1953), which refer to spindle-like sclerites with a curved axis cannot be corroborated or rejectedby our analyses as they require a measurement of axis curvaturenot used here.

It is interesting to note that simple classifiers such as one-cellperceptrons were able to classify with a relatively high accuracy(�80%) Pacifigorgia sclerites, and that the classification ability wasindependent of the learning rate when circularity and compacticitywere used together as sclerite descriptors. In accordance with themixed-model experiment, compacticity alone was not suitable forspindle-capstan differentiation and the perceptron was unable toclassify sclerites using compacticity alone. The fact that a simpleone-cell perceptron can differentiate spindles from capstans usingeither one (i.e. circularity) or two (i.e. circularity and compacticity)sclerite shape descriptors is by no means trivial as it implies: (1)that spindles and captans are linearly separable, and (2) thatadditional shape quantifiers, such as axis curvature, symmetry,etc., in conjunction with more advance classifiers (e.g. retro-propagation neural networks) could differentiate more complexsclerites present in other genera or families. These findings openthe new and exciting possibility of a quantitative and automatedsclerite classification for octocorals.

5. Conclusions

Until now, morphometric analyses of octocoral sclerites havebeen limited by the lack of techniques capable of analyzing largeamountsof data. Herein,wequantitativelyanalyzed a largesample ofoctocoral sclerites and statistically assessed the number of scleriteclasses present within the measured elements. We argue that aquantitative approach to sclerite classification may help octocoralresearchers overcome the difficulties inherent in sclerite characteranalysis and allow them to standardize sclerite classification andcoding methods. Our quantitative approach corroborated thetraditional sclerite classification of the genus Pacifigorgia (Breedyand Guzman, 2002) and shows that automatic sclerite classificationmay be possible in the future with the development andimplementation of appropriate software tools. Finally, it importantto highlight that the methods herein proposed for sclerite classifica-tion within Pacifigorgia can also be applied to other genera within theGorgoniidae and extended, with the inclusion of appropriate shapequantifiers, to other families within the Octocorallia.

Acknowledgements

For the experiments herein exposed a C++ application forsclerite sampling and measurement was written by FS and isavailable as a x86 binary for UNIX/LINUX systems on request. SVwrote a simple perceptron in Python which also is available onrequest. We thank the Instituto Clodomiro Picado LaboratoryManager, J. Nunez, for extensive support and valuable comments,and J.M. Gutierrez and Y. Angulo for providing access to theInstituto Clodomiro Picado microscopy facility for SV. R. Vargas

provided valuable comments during the development of the study.P. Denyer produced the SEM plate. We are grateful to C.A. Guevaraand J. Cortes for their cooperation and support in collectingsamples.

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How many kinds of sclerite?

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