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How many kinds of sclerite? Towards a morphometric classification of gorgoniid microskeletal components Sergio Vargas a,*, Odalisca Breedy b,c,d, Francisco Siles e, Hector M. Guzman b a

Museo de Zoologı´a, Escuela de Biologı´a, Universidad de Costa Rica, P.O. Box 1962-2100, San Jose´, Costa Rica Smithsonian Tropical Research Institute, P.O. Box 2072, Balboa, Panama c Centro de Investigacio´n en Ciencias del Mar y Limnologı´a, Universidad de Costa Rica, P.O. Box 2060 UCR, San Jose´, Costa Rica d Centro de Investigacio´n en Estructuras Microsco´picas, Universidad de Costa Rica, P.O. Box 2060 UCR, San Jose, Costa Rica e Escuela de Ingenierı´a Ele´ctrica, Facultad de Ingenierı´a, Universidad de Costa Rica, P.O. Box 2-10, 2060 UCR, San Jose´, Costa Rica b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 16 May 2009 Received in revised form 1 August 2009 Accepted 2 August 2009

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. ß 2009 Elsevier Ltd. All rights reserved.

Keywords: Gorgoniidae Octocorallia Octocoral systematics Pacifigorgia Sclerite morphometrics

1. Introduction Octocorals of the family Gorgoniidae (Alcyonacea) constitute a diverse group that inhabits tropical and subtropical shallow (<50 m) waters around the world. In the Caribbean and eastern Pacific waters, gorgoniid octocorals dominate the landscape of several coastal marine environments where they provide structure and heterogeneity to the ecosystem and refuge to other marine organisms (Bayer, 1961; Breedy and Guzman, 2002, 2003a,b, 2004; Sa´nchez et al., 2003; Williams and Breedy, 2004). The systematics of the group has changed constantly since it was first described and the family, which once included practically all horny octocorals, today is restricted to those forms with calcareous sclerites that are less than 0.3 mm in length and sculpted with regularly arranged girdles of complicated tubercles and warts (Bayer, 1951, 1953).

* Corresponding author. Present address: Molecular Geo- and Palaeobiology Lab., Dept. for Geo- & Environmental Sciences, , Palaeontology & Geobiology, RichardWagner Str. 10, 80333 Munich, Germany. Tel.: +49 89 2180 17934; fax: +49 89 2180 6601. E-mail addresses: s.vargas@lrz.uni-muenchen.de, sergio.vargasr@ecci.ucr.ac.cr (S. Vargas). 0968-4328/$ – see front matter ß 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2009.08.009

Gorgoniid sclerites can be grouped into four basic types— spindles, disk-spindles, capstans, and scaphoids. The presence of these sclerites individually or in combinations is often used to identify gorgoniid specimens to the generic level (Lewis and Von Wallis, 1991) and were the basis for Bayer’s (1953) subfamilies ‘Lophogorgiinae’ (the spindle lineage that included mainly eastern Pacific genera) and ‘Gorgoniinae’ (the scaphoid lineage that was restricted to genera occurring in the West Indies), which he later abandoned. Currently, variations in sclerite size, sculpture, and coloration (Bayer, 1953) and the relative proportion of the different sclerite types in the sample (Breedy, 2001) constitute the main criteria for species delimitation. Determining sclerite type is not a trivial procedure; it is made difficult by the continuous variation in sclerite form within and between species. This continuum represents a major obstacle to the definition and assignment of sclerite character states (Sa´nchez, 2001, 2005; Sa´nchez et al., 2003; but see Breedy and Guzman, 2007; Williams, 1992; Williams and Lindo, 1997) and, thus, to the deduction of phylogenetic hypotheses of many octocoral groups. Sa´nchez (2005) faced this obstacle in his analysis of the family Paragorgiidae, where the wide variation in sclerite form results in a continuum between the surface and the inner medulla sclerites making homology assessments difficult. Similar problems occur in almost all octocoral groups, including the Gorgoniidae. The


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Gorgoniidae also poses additional problems: the fusion of the coenenchymal layers makes sclerite positional inferences difficult and further complicates systematic research (but see Breedy and Guzman, 2007; Williams, 1992; Williams and Lindo, 1997). The role of the calcareous sclerites in the identification and classification of the alcyonarians was first appreciated by Valenciennes (1846, 1855) and further explored by Ko¨lliker (1865), whose taxonomic arrangement of the group greatly influences present day classification schemes (Bayer, 1961). Although sclerites are the main source of systematic information among the Octocorallia (Bayer, 1951, 1953, 1961, 1981; Breedy, 2001; Breedy and Guzman, 2002, 2005; Fabricius and Alderslade, 2000; Sa´nchez, 2001; Sa´nchez et al., 2003), little development has been done concerning the morphometric study of the microskeletal components found in octocorals. This study represents the first attempt to use statistical methods to determine the number of sclerite types within a given octocoral group. We used the eastern Pacific genus Pacifigorgia (Bayer, 1951) to introduce a methodology for the morphometric analysis of octocoral sclerites. Specifically, we used finite mixture models (sensu Strait et al., 1996) to statistically assess the number of sclerite types within the genus. We also attempted to automatically classify Pacifigorgia sclerites using a simple perceptron. Pacifigorgia sclerites traditionally have been classified as spindles and capstans, and the genus’ sclerites practically show no variation related to its topographical position. Pacifigorgia therefore represents a relatively straightforward case study the results of which 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 Museo de Zoologı´a, Universidad de Costa Rica, Smithsonian Tropical Research Institute, Panama reference collections and from the Charles Darwin Research Station, Gala´pagos Islands, Ecuador. Fragments of the colonies were treated with sodium hypochlorite

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

adamsii (Verrill, 1868) bayeri (Breedy, 2001) cairnsi (Breedy and Guzman, 2003a) curta (Breedy and Guzman, 2003a) dampieri (Williams and Breedy, 2004) darwinii (Hickson, 1928) elegans (Milne Edwards and Haime, 1857) eximia (Verrill, 1868) firma (Breedy and Guzman, 2003a) irene (Bayer, 1951) rubicunda (Breedy and Guzman, 2003a) rubinoffi (Breedy and Guzman, 2003b) samarensis (Breedy and Guzman, 2003a)

(household bleach) for sclerite dissociation (Bayer, 1961; Breedy and Guzman, 2005); sclerites were stored in 70% ethanol until they were analyzed. We took series of photographs using an Olympus BX51TRF microscope attached to a CoolSnap-Procolor digital camera. Sclerites were mounted on regular light microscopy slides; the ethanol was allowed to evaporate before the photograph was taken, and no cover or liquid medium was used to embed the sclerites. Photographs were stored as high quality TIFF images using the software ImagePro-Plus. 2.2. Image analysis Sclerite images were processed using simple image segmentation procedures. First, color images were converted to gray-scaled images and inverted (Fig. 1A). Once inverted, gray-level thresholding was applied to generate a binary image (Fig. 1B) that was used to determine the sclerite border (Fig. 1C and D). Two different shape quantifiers were used to describe the identified sclerites: circularity and compacticity. Circularity refers to the ratio of an object’s mean radius to its standard deviation, and compacticity refers to the relation between the area of the object and its perimeter squared (Siles-Canales, 2004). These two shape quantifiers were selected because they provide an overall estimation of the shape of the sclerite taking in consideration different

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.


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set. For instance, one can statistically describe a data set as a mixture of three normally distributed populations, each with a given mean and variance value (Fig. 3). Once the mixture model has been determined, each instance in the data set can be classified with a given probability as member of one of the component distributions (i.e. classes). We used the statistical computing environment R (R Development Core Team, 2008) in conjunction with the package MCLUST (Fraley and Raftery, 2002, 2006) to find the number of classes present in our data set for both circularity and compacticity. We tested mixtures with up to nine component Gaussian distributions and selected the best mixture model using BIC. 2.4. Capstans and spindles

Fig. 2. Wrong or distortedly determined sclerite border (solid black line). (A) Regular Pacifigorgia sclerite, (B) joined elements, and (C) deformed or truncated sclerites.

measurements at a time, for instance the area/perimeter ratio and the variation of the radius of the sclerites. Another advantage of these two quantifiers is that both are dimensionless variables, which makes scale calibration unnecessary for images taken under the same optical conditions. After all of the images were processed, a matrix was created by hand containing the data for all of the sclerites measured. This matrix was then refined by taking out joined elements (Fig. 2B) or elements whose form was evidently distorted (e.g. broken sclerites; Fig. 2C); the resulting refined matrix was used for all subsequent analyses. 2.3. Sclerite type determination: how many sclerite types? We used finite mixture modeling to assess the number of statistically different sclerite character states present in the data set generated for the genus Pacifigorgia. Strait et al. (1996) first used finite mixture modeling as a coding technique for continuous variables; these authors discuss the method in detail so we present only a brief description and refer to them for further details. A data set is considered to be mixed if it contains representatives from more than one population (i.e. class). Finite mixture models describe mixed data sets using well-known statistical concepts and proceed by first identifying the form of the distribution (i.e. Gaussian, Poisson, etc.) of each component population (i.e. class) in the data set and then fitting, usually using a maximum likelihood approach, a mixture density function that describes the distribution of the mixture observed in the data

MCLUST is an automatic classification program; it looks for the natural classes present in the data set without any prior knowledge of class membership (i.e. unsupervised classification). Therefore, the spindle or capstan sclerite categories may not appear in the MCLUST classification schemes. To explore whether the classification found by MCLUST corroborates the existence of the traditional spindle and capstan sclerite categories, we visually classified each sclerite in the data set as spindle or capstan. Following Breedy and Guzman (2002), spindles are sclerites with a straight or a slightly curved axis, generally with more than two whorls of tubercles and with acute ends. Capstans are sclerites with two whorls of tubercles or warts, with a clear median space. In most cases, tubercles and warts are present at the ends of capstan sclerites and fuse 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 simple one-cell perceptron. Perceptrons are simple artificial neurons that can be trained to solve separable problems. In general, perceptrons ‘‘learn’’ from a number of example cases the way in which the classes in the dataset can be differentiated. Perceptron learning proceeds by adjusting a set of weights that multiply the input values describing the example cases. If the problem at hand is separable the perceptron learning algorithm will converge to a stable set of weights in a finite number of steps (Gallant, 1990). After training, the perceptron can automatically classify unseen cases present in the dataset. We trained the perceptron using circularity only, compacticity only, and circularity and compacticity together as input values. We randomly selected sclerites from our dataset to form two partitions: one to train the perceptron (i.e. a training partition), and one to validate the perceptron classification ability (i.e. a

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).


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Table 2 BIC values for circularity and compacticity mixture models tested with MCLUST. The selected models appear in bold. Number of component distributions 1 2 3 4 5 6 7 8 9

Shape quantifier Circularity 4860.048 4785.096 4758.338 4771.799 4773.260 4779.274 4792.717 4804.964 4818.157

Compacticity 4507.548 4413.002 4426.619 4429.034 4432.125 4444.384 4457.442 4463.046 4465.462

3. Results 3.1. Sclerite morphometrics

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.

validation partition). The single-cell perceptron was allowed to iterate over the example sclerites on the training partition until the number of misclassified sclerites in the training dataset reached 10%, or the number of iterations reached 5 times the total number of example sclerites. After training, the classification ability of the perceptron was tested on the, so far unseen, sclerites from the validation partition. The perceptron was allowed to iterate over the validation partition only one time, after which we calculated the error rate of the perceptron as the number of misclassified sclerites divided by the total number of sclerites in the validation set. A total of 50 cross-validation partitioned datasets were generated for circularity only, compaciticity only, and circularity and compacticity together. We report the error rates reached by the perceptron for each combination of input values.

A total of 665 sclerites were measured using the method outlined above. Circularity and compacticity frequency distributions fitted a log-normal distribution (data not shown), thus we used the log-transformed values for compaticity and circularity as well as the untransformed values for both variables in the finite mixture-model analyses, as the results obtained in terms of the number of classes obtained for each variable we present the results based on the untransformed values. Sclerite circularity values ranged from 41 to 86 units with a median value of 56 units; sclerite compacticity values ranged from 18 to 55 units with a median value of 29 units. By visual determination, capstans appeared more compact (i.e. had lower compacticity values) and circular (i.e. had higher circularity values) than spindles. Both circularity and compacticity distributions showed no overlap when the first and third quartiles were considered (Fig. 5). The existence of this gap between the capstan and spindle circularity and compacticity distributions may be used as a simple preliminary way to corroborate sclerite class membership after visual classification has been done. Spindles can be treated as sclerites with circularity values ranging between 47 and 53 units and compacticity values between 31 and 41 units; sclerites with circularity values between 55 and 67 units and compacticity values between 23 and 28 units can be treated as capstans.

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.


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

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

classification differentiated long capstans (included in class 1 and class 2) and short capstans (class 3), which reflects Bayer’s (1953) sclerite categories. Visual differentiation of spindles and capstans traditionally has been difficult because of the continuum in sclerite form. Categories such as blunt spindles or elongated capstans (Breedy and Guzman, 2002) were developed mainly to accommodate intermediate

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


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Table 3 Mean 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

0.1 0.001 0.000001

Shape quantifier Circularity

Compacticity

Circularity and compacticity

0.5690 (0.0645) 0.5313 (0.1231) 0.1852 (0.0133)

0.5905 (0.0201) 0.5976 (0.0245) 0.7967 (0.0195)

0.2014 (0.0437) 0.2065 (0.0483) 0.2077 (0.0241)

sclerite forms that cannot be strictly classified as either capstans or spindles but share some overall visual similarity. Mixture modeling using sclerite circularity also suffers from the difficulties associated with intermediate sclerite forms, and our model included within the spindle class many of the sclerites that we had visually classified as capstans. Mixture modeling, however, provides an objective way to solve classification problems because sclerite class assignment is done in a probabilistic way after the mixture model has been determined. This way sclerites assigned with low posterior probability to a class (i.e. ambiguously classified), can be detected and the analysis can be restricted to elements classified with a probability higher than a specified threshold value, for instance p  0.95. When we used this criterion, the ambiguity in sclerite classification was reduced although capstans were still present in the spindle class (i.e. class 1; Fig. 6B).

3.4. Perceptron classification experiments In general, our one-cell perceptron was able to classify sclerites when circularity only and circularity and compacticity together were used as input values. When circularity only was used as the input value, convergence of the learning algorithm was sensitive to the learning rate used in training the perceptron. On the contrary, using both circularity and compacticity as input values for training lead the learning algorithm to converge independently of the learning rate used. It was impossible to classify sclerites based on compacticity only, independently of the learning rate used to train the perceptron (Table 3). It is important to note that our perceptron achieve only 80% accuracy, that is it misclassified 20% of the sclerites present in the validation partitions when both circularity, or circularity and compacticity were used as input values. 4. Discussion

3.3. Sclerite classes: compacticity The compacticity classification selected was a two-class mixture model (Table 2). As in the circularity based classification, one of the classes (i.e. class 1) included mostly capstans and the other mostly spindles (class 2; Fig. 7A). We used the proposed probabilistic threshold value (p  0.95) to choose only unambiguously classified sclerites; after this limit was set, almost all capstans were removed from the analysis and only spindles were selected (Fig. 7B). Compacticity appeared to be a good morphometric measure for spindles; they were classified with high posterior probability values when this shape descriptor was used. In contrast, it was not possible to assign most capstans to any class with high posterior probabilities based on compacticity (i.e. capstan classification using compacticity values was uncertain).

Sclerites are calcium carbonate (calcite) elements of complex morphology. The importance of sclerites for octocoral systematics has been repeatedly acknowledge by authors since the days of Valenciennes and Ko¨lliker (Bayer, 1961), and recent cladistic studies of several groups have shown sclerite-based characters to be highly informative (Sa´nchez, 2001, 2005). Despite their importance, studies dealing with sclerite classification are lacking. In this study, we attempted to use quantitative methods based on the conjunction of image analysis and statistical classification techniques to avoid setting arbitrary limits to sclerite classes, and to explore the ability of simple classifiers (i.e. perceptrons) to handle sclerite classification. Our results, in particular our mixturemodel analyses, corroborated the existence of three sclerite classes, namely spindles, long capstans, and short capstans (Fig. 8). Blunt spindles (Fig. 8B), a category used in the taxonomic

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


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literature (Breedy and Guzman, 2002) to group visually similar intermediate spindle-capstan forms are classified with low probabilities and cannot be assigned to any class. These sclerites would not be considered if a probabilistic approach, like the one here proposed, is used for sclerite classification. Other classes traditionally used in the taxonomic literature of the ‘Lophogorgiinae’, such as bent-spindles (Bayer, 1953), which refer to spindlelike sclerites with a curved axis cannot be corroborated or rejected by our analyses as they require a measurement of axis curvature not used here. It is interesting to note that simple classifiers such as one-cell perceptrons were able to classify with a relatively high accuracy (80%) Pacifigorgia sclerites, and that the classification ability was independent of the learning rate when circularity and compacticity were used together as sclerite descriptors. In accordance with the mixed-model experiment, compacticity alone was not suitable for spindle-capstan differentiation and the perceptron was unable to classify sclerites using compacticity alone. The fact that a simple one-cell perceptron can differentiate spindles from capstans using either 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) that additional shape quantifiers, such as axis curvature, symmetry, etc., in conjunction with more advance classifiers (e.g. retropropagation neural networks) could differentiate more complex sclerites present in other genera or families. These findings open the new and exciting possibility of a quantitative and automated sclerite classification for octocorals. 5. Conclusions Until now, morphometric analyses of octocoral sclerites have been limited by the lack of techniques capable of analyzing large amounts of data. Herein, we quantitatively analyzed a large sample of octocoral sclerites and statistically assessed the number of sclerite classes present within the measured elements. We argue that a quantitative approach to sclerite classification may help octocoral researchers overcome the difficulties inherent in sclerite character analysis and allow them to standardize sclerite classification and coding methods. Our quantitative approach corroborated the traditional sclerite classification of the genus Pacifigorgia (Breedy and Guzman, 2002) and shows that automatic sclerite classification may be possible in the future with the development and implementation of appropriate software tools. Finally, it important to highlight that the methods herein proposed for sclerite classification within Pacifigorgia can also be applied to other genera within the Gorgoniidae and extended, with the inclusion of appropriate shape quantifiers, to other families within the Octocorallia. Acknowledgements For the experiments herein exposed a C++ application for sclerite sampling and measurement was written by FS and is available as a x86 binary for UNIX/LINUX systems on request. SV wrote a simple perceptron in Python which also is available on request. We thank the Instituto Clodomiro Picado Laboratory ˜ ez, for extensive support and valuable comments, Manager, J. Nun and J.M. Gutierrez and Y. Angulo for providing access to the Instituto 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. Guevara and J. Corte´s for their cooperation and support in collecting samples. References Bayer, F.M., 1951. A revision of the nomenclature of the Gorgoniidae (Coelenterata: Octocorallia) with an illustrated key to the genera. J. Wash. Acad. Sci. 41, 91– 102. Bayer, F.M., 1953. Zoogeography and evolution in the octocorallian family Gorgoniidae. Bull. Mar. Sci. Gulf Carib. 3, 100–119. Bayer, F.M., 1961. The shallow-water Octocorallia of the West Indian region. A manual for marine biologists. Stud. Fauna Curacao Carib. I 12, 1–373. Bayer, F.M., 1981. Key to the genera of Octocorallia exclusive of Pennatulacea (Coelenterata: Anthozoa), with diagnoses of new taxa. Proc. Biol. Soc. Wash. 94, 901–947. Breedy, O., 2001. A new species of Pacifigorgia from the eastern Pacific (Coelenterata: Octocorallia: Gorgoniidae). Bull. Biol. Soc. Wash. 10, 181–187. Breedy, O., Guzman, H.M., 2002. A revision of the genus Pacifigorgia (Coelenterata: Octocorallia: Gorgoniidae). Proc. Biol. Soc. Wash. 115, 782–839. Breedy, O., Guzman, H.M., 2003a. Octocorals from Costa Rica: the genus Pacifigorgia (Coelenterata: Octocorallia: Gorgoniidae). Zootaxa 281, 1–60. Breedy, O., Guzman, H.M., 2003b. A new species of Pacifigorgia (Coelenterata: Octocorallia: Gorgoniidae) from Panama. Zootaxa 128, 1–10. Breedy, O., Guzman, H.M., 2004. New species of the gorgoniian genus Pacifigorgia (Coelenterata: Octocorallia: Gorgoniidae) from Pacific Panama. Zootaxa 541, 1– 15. Breedy, O., Guzman, H.M., 2005. A new species of alcyonacean octocoral from the Gala´pagos Archipelago. J. Mar. Biol. Assoc. U.K. 85, 801–807. Breedy, O., Guzman, H.M., 2007. A revision of the genus Leptogorgia Milne Edwards and Haime, 1857 (Coelenterata: Octocorallia: Gorgoniidae) in the eastern Pacific. Zootaxa 1419, 1–90. Fabricius, K., Alderslade, P., 2000. Soft corals and sea fans: a comprehensive guide to the tropical shallow water genera of the central-west Pacific, the Indian Ocean and the Red Sea. Science Communication, Australian Institute of Marine Sciences, Australia, 264 pp. Fraley, C., Raftery, A.E., 2002. Model-based clustering, discriminant analysis and density estimation. J. Am. Stat. Assoc. 97, 611–631. Fraley, C., Raftery, A.E., 2006. MCLUST Version 3 for R: Normal Mixture Modeling and Model-based Clustering. University of Washington, Technical Report 504. Gallant, S.I., 1990. Perceptron-based learning algorithms. IEEE Trans. Neural Networks 1, 179–191. Ko¨lliker, R.A., 1865. Die Bindesubstanz der Coelenteraten. Icones histologicae oder Atlas der vergleichenden Gewebelehre. Leipzig, Germany, pp. 87–181. Lewis, J.C., Von Wallis, E., 1991. The function of surface sclerites in gorgonians (Coelenterata Octocorallia). Biol. Bull. 181, 275–288. R Development Core Team, 2008. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Sa´nchez, J.A., 2001. Systematics of the southwestern Caribbean Muriceopsis Aurivillius (Cnidaria: Octocorallia), with the description of a new species. Bull. Biol. Soc. Wash. 10, 160–180. Sa´nchez, J.A., 2005. Systematics of the bubblegum corals (Cnidaria: Octocorallia: Paragorgiidae) with description of new species from New Zealand and the Eastern Pacific. Zootaxa 1014, 1–72. Sa´nchez, J.A., Mcfadden, C.S., France, S.C., Lasker, H.R., 2003. Molecular phylogenetic analyses of shallow-water octocorals. Mar. Biol. 142, 975–987. Siles-Canales, F., 2004. Estimacio´n de la forma y textura celular para microscopia in situ. Universidad de Costa Rica, San Pedro, Costa Rica, 150 pp. Strait, D.S., Monitz, M.A., Strait, P.T., 1996. Finite mixture coding: a new approach to coding continuous characters. Syst. Biol. 45, 67–78. Valenciennes, A., 1846. Zoophytes. In: Abel Dupetit-Thouars. Voyage autour du monde sur la fre´gate la Ve´nus, pendant les anne´s 1836–1839. Atlas de Zoologie, pp. 1–15. Valenciennes, A., 1855. Extrait d’une monographie de la familie des Gorgonide´es de la classe des polypes. C.R. Acad. Sci. Paris 41, 7–15. Williams, G.C., 1992. The Alcyonacea of southern Africa. Stoloniferous octocorals and soft corals (Coelenterata, Anthozoa). Ann. S. Afr. Mus. 100, 249–358. Williams, G.C., Lindo, K.G., 1997. A review of the octocorallian genus Leptogorgia (Anthozoa: Gorgoniidae) in the Indian Ocean and subantarctic, with description of a new species and comparisons with related taxa. Proc. Calif. Acad. Sci. 49, 499–521. Williams, G.C., Breedy, O., 2004. The panamic gorgonian genus Pacifigorgia (Octocorallia: Gorgoniidae) in the Gala´pagos Archipelago, with descriptions of three new species. Proc. Calif. Acad. Sci. 55, 55–88.

How many kinds of sclerite?  

How many kinds of sclerite? Towards a morphometric classification of gorgoniid microskeletal components

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