CLADISTIC ANALYSIS OF MEANDRINIDAE AND OCULINIDAE (ANTHOZOA: SCLERACTINIA) WITH COMMENTS ON NOT APPLICABLE CHARACTERS. by Troy Robert Fadiga

Transcription

1 CLADISTIC ANALYSIS OF MEANDRINIDAE AND OCULINIDAE (ANTHOZOA: SCLERACTINIA) WITH COMMENTS ON NOT APPLICABLE CHARACTERS by Troy Robert Fadiga A thesis submitted in partial fulfillment of the requirements for the Master of Science degree in Geoscience in the Graduate College of The University of Iowa July 2011 Thesis Supervisor: Professor Ann F. Budd

2 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL MASTER'S THESIS This is to certify that the Master's thesis of Troy Robert Fadiga has been approved by the Examining Committee for the thesis requirement for the Master of Science degree in Geoscience at the July 2011 graduation. Thesis Committee: Ann F. Budd, Thesis Supervisor Christopher A. Brochu Hallie J. Sims

3 ACKNOWLEDGMENTS I d like to thank my parents for their patience and support. I d like to thank the committee, especially Dr. Budd, for the nearly infinite patience shown towards me and without which this thesis would not have been completed. ii

4 TABLE OF CONTENTS LIST OF TABLES... iv LIST OF FIGURES...v CHAPTER I. INTRODUCTION Coral Phylogeny Coding Inapplicable Characters...3 II. METHODS AND MATERIALS Taxa Characters Tree Search and Evaluation Outgroup Selection Landmark Analysis...16 III. RESULTS Character Delineations Phylogenetic Analysis Character Independence...23 IV. DISCUSSION Character Coding and Geometric Morphometrics NACTL Conclusions...27 APPENDIX A. FIGURES AND TABLES...28 APPENDIX B. CD-ROM SUPPLEMENTARY FILES...76 REFERENCES...77 iii

5 LIST OF TABLES Table A1. Step matrix preserving the patristic distance between the character states of a composite of three characters A2. Step matrix attempting to preserve the patristic distance between the character states of a composite of four characters, but violating triangular inequality A3. List of taxa used in the phylogenetic analysis A4. Character matrix for the corals used in the cladistics analysis A5. List of landmarks and semi-landmarks used to delineate character-states of the primary septa A6. List of species and specimens used in the geometric morphometric analysis A7. Variance explained by relative warps of the costae landmark data A8. The nine models used to fit the first relative warp of the costae landmark data A9. Variance explained by relative warps of the wall landmark data A10. The top twenty models, as selected by AICc, for the first three relative warps of the wall landmark data...64 A11.Variance explained by relative warps of the septum landmark data A12. The top twenty models, as selected by AICc, for the first three relative warps of the septae landmark data A13. The top twenty models, as selected by AICc, for the first two relativewarps of the septae landmark data and the log centroid size iv

6 LIST OF FIGURES Figure A1. SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments ) image of Meandrina meandrites(sui ) A2. SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Dendrogyra cylindrus (SUI ) A3. SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Eusmilia fastigiata (SUI ) A4. SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Oculina diffusa (SUI ) A5. SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Cladocora arbuscula (SUI ) A6. SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Solenastrea bournoni (SUI ) A7. Relevant portion of the coral phylogeny in Fukami et al (2008) A8. Relevant portion of the coral phylogeny Kitahara et al. (2010) A9. Relevant portion of the coral phylogeny returned from Barbeitos et al. (2010) A10. Consensus tree of the example adapted from Madison (1993). There are two less taxa than the original example and taxa with tails have been placed into two named clades, Dangles and Solidos. The character states for tail have been demonstrated above the tips of the tree. R stands for red and B stands for blue A11. Tree 11.1 and 11.2 optimized with a reductive coded matrix A12. Tree 11.1 and tree 11.2 optimized with an absence coded matrix. Both trees have an equal tree length and show the correct character optimization. The tree length is higher than it should be due to redundancies A13. Trees and relevant characters taken from Strong and Lipscomb (1999) A14. Graph showing the characters and logical dependencies for a hypothetical tail character complex. Characters of different ranks are colored differently and higher ranks are toward the top of the graph A15. Graph showing the characters and logical dependencies for a hypothetical tail character complex with the character scale shape composited up into the tail covering character. Characters of different ranks are colored differently and higher ranks are toward the top of the graph v

7 A16. Three graphs showing the same character complex with differing levels of compositing. All three would show identical levels of support for all trees A17. Graphical representation of different coding strategies for NA characters. Purple arrows indicate transitions that should contribute to the calculation of tree length. Red arrows indicate transitons that should not contribute to the calculation of tree length, they are either accidental assumptions or redundancies A18. Visualization of the calculations for the Not Applicable Corrected Tree Length (NACTL). The NA matrix is a matrix composed of only characters with some taxa coded as NA. The NA characters are then recoded as a binary characters indicating applicable or NA A19. A flow chart indicating which method would be the most convenient and appropriate method for dealing with different character complexes A20. The practical steps involved in preparing the two matrices needed for the NACTL method A21. Character states for character one, corallum for (a) Oxysmilia rotundifolia solitary, (b) Dichocoenia stokesi mound, (c) Dichocoenia n. sp. ramose, (d) Meandrina meandrites flat-topped, (e) Goreaugyra memoralis pillar, (f) Meandrina trinitatis flat-topped flabellate form, (g) Phyllangia reptoid A22. Character states for characters four, six, and seven; series sinuosity, attachment to substrate, and basal plate reinforcement. (a) Meandrina alveolus (4:0) straight, (b) Meandrina costatus slightly sinuous (4:1), (c) Meandrina braziliensis very sinuous (4:2), (d) Rhizosmilia gerdae attached (6:0) and with exothecal dissepiments laid down over extended, raised costae (7:1), (e) Meandrina variabilis free-living (6:1) A23. Character states for characters thirteen and sixteen, columella and vertical coenosteum deposition. (a) Eusmilia fastigiata absent (16:3), (b) Dichocoenia caloosahatcheensis alternating (16:4), (c) Dichocoenia tuberosa solid, (d) Solenastrea bournoni spongy (13:0), (e) Goreaugyra memoralis lamellar (13:1), (f) Eusmilia fastigiata fasicular (13:2) A24. Characters and character states with logical dependencies. Characters of the same rank are shown in the same color and arrows point to the subordinate character A25. The chart shows the NA uncorrected tree length along the x-axis. This is the tree length found by optimizing an absence coded matrix onto a tree. ANTs are shown along the y-axis and is found by optimizing the applicability matrix onto a tree. The lines in the lower right show lines of equal NACTL value A26. Landmarks for the character-state delineation are marked in red, the yellow line shows the tracing that the semi-landmarks were extracted from A27. The mean consensus of the two character states for primary costae shape for a two component model with variable volumes. The numbers represent the character state they are coded from vi

8 A28. The mean consensus of the three character states for primary wall shape for a VEV3 model. The numbers represent the character state as they are coded in the matrix A29. Plot of the first relative warp against the log centroid size of the septa. The dashed lines show the 50% envelope of the data for the lowess line A30. The mean consensus of the three character states for primary septum shape and size for a VEV3 model. The numbers represent the character state as they are coded in the matrix A31. Strict consensus for the 24 MPTs retrieved using a reductive coded matrix (TL=74). Occulinidae is shown in blue, Meandrinidae is shown in green A32. Strict consensus for the 27 MPTs retrieved using NACTL approach (TL=61). Oculinidae is shown in blue, Meandrinidae is shown in green A33. Strict consensus for the 3 MPTs retrieved using NACTL approach (TL=61) that also have a monophyletic Meandrinidae. Oculinidae is shown in blue, Meandrinidae is shown in green A34. Strict consensus for the 14 MPTs retrieved using NACTL approach (TL=61) that also have a monophyletic Meandrina. Oculinidae is shown in blue, Meandrinidae is shown in green A35. A re-rooting of the strict consensus for the 3 MPTs retrieved using NACTL approach (TL=61) that also have a monophyletic Meandrinidae. With the rerooting a monophyletic Oculinidae is possible. Oculinidae is shown in blue, Meandrinidae is shown in green vii

9 1 CHAPTER 1. INTRODUCTION 1.1 Coral Phylogeny Stony corals (scleractinians) are the framework builders of the modern reef community and play a critical ecological role in one of the most biologically diverse communities on earth. Despite scleractinians superb fossil record, their evolutionary history is poorly understood. Traditional morphological hypotheses of scleractinian evolutionary relationships have been strongly contradicted by genetic analyses (Cuif et al. 2003; Fukami et al. 2004; Fukami et al. 2008; Kitahara et al. 2010). Morphology-based interpretations of evolutionary relationships among scleractinians are problematic because: 1) traditional morphological hypotheses of evolutionary history have been based on subjective interpretation rather than modern semiquantitative cladistic practices; 2) systematists tend to focus on either scleractinians that host symbiotic algae (zooxanthellate corals) or on those that lack symbionts (azooxanthellate corals), neither of which comprises a monophyletic grouping; and 3) the seemingly simple morphology of corals, highly plastic characters, and limited number of feasible morphological forms have led many to question whether morphology can be used to infer the evolutionary history of corals (Webb 1993 and 1996, rugose corals in these cases). This chapter presents a phylogenetic analysis of two sister families, Oculinidae Gray, 1847 and Meandrinidae Gray, 1847 based on morphological characters, with permutation tests to assess the presence of phylogenetic structure in subsets of the morphological data and regressions and pairwise comparisons to assess the independence of the quantitatively delineated characters-states for three of the characters. Molecular studies have changed the understanding of Oculinidae and Meandrinidae, so membership in the former will be interpreted as anything more closely related to Oculina diffusa than Meandrina meandrites and membership in the latter clade will be interpreted as anything more closely related to Meandrina meandrites than Oculina diffusa. Figures A1, A2, and A3 all detail three species of Meandrinidae. Figures A4, A5, and A6 all detail species from Oculinidae.

10 2 Romano and Palumbi (1996) was the first phylogenetic analysis to suggest the taxonomy of corals was incongruent with their evolutionary history. The performed a parsimony analysis using 16S mitochondrial ribosomal RNA sequences. Acrhelia and Galaxea, considered part of Oculinidae by Wells (1956), were placed with more complex corals (e.g. Acropora), instead of the robust corals (e.g. Pocillopora). Romano and Cairns (2000) subsequently suggested that Cladocora, Oculina, Paracyathus, Polycyathus, Rhizosmilia maculata, Phyllangia, and Dichocoenia are closely related. This novel classification was based on 16S and 28S data set, but relied on neighbor joining methods which have been shown to be problematic. Cuif et al. (2003) applied a maximum parsimony approach and identified two clades of particular interest; (1) Cladocora + Oculina; and (2) Eusmilia, Meandrina, Phyllangia, Dichocoenia, + Dendrogyra. Fukami et al. (2004) suggested that Solenastrea was part of Oculinidae and that Oculinidae and Meandrinidae were sister taxa. Le Goff-Vitry et al. (2004) performed a Bayesian analysis and supported a sister relationship between Oculinidae and Meandrinidae. Their taxon sampling included the larger Oculinidae seen in Romano and Cairns (2000). Fukami et al. (2008) s results were consistent with Fukami et al. (2004) with greater taxon sampling (Figure A7). Kitahara et al. (2010) analyzed CO1 sequences with a greatly improved Pacific deep water taxon sampling using Maximum Likelihood and Bayesian methods. Their results place Rhizosmilia robusta very distantly from the expected place of Rhizosmilia maculata. Phyllangia papuensis was also placed very distantly from the Meandrinidae, indicating that Phyllangia is not monophyletic. They also place an Astrangia specimen sister to the Oculinidae, see Figure A8. In an analysis of coloniality and symbiosis in scleractinia, Barbeitos et al. (2010) performed a bayesian phylogenetic analysis of 80 species using 12S and 28S ribosomal RNA, eleven of which are in the ingroup of this study (Figure A9). Barbeitos et al (2010) use the analysis to discuss the possibility that the cool waters that reflooded the Mediterranean following Messinian dessication were a selective force in the loss of coloniality and zooxanthellae in lineages leading to Atlantic Phyllangia and Rhizosmilia.

11 3 1.2 Coding Inapplicable Characters Current methods of parsimony analysis are aligned with cladistics theory when there are no logical dependencies between characters. Logical dependencies between characters are common and necessitate the use of not applicable (NA) character states in character matrices. Character state information is used in cladistics to reconstruct events, which take the form of evolutionary transformations. Independent characters are required for a character matrix, which means that different character-state changes are indicating different evolutionary events. The logical dependency between many characters is different from the need for characters indicating different sets of evolutionary events. Logical dependencies place constraints on the order of evolutionary events, but they indicate separate sets of transformations. The difficulty of incorporating characters with logical dependencies into a cladistics analysis stems from the need to remove the algorithms attempts to treat the initial state of newly applicable characters the same way it treats inferred evolutionary transformations from one character-state to another character-state. The NA coding indicates places of logical incongruence between a linear matrix and the underlying network structure of some character complexes. A large proportion of the informative characters used in this analysis (37.5%) are NA for some taxa, making the treatment of NA characters influential to the results. Standard treatment of NA characters was to consider them the same as missing data until Maddison (1993) pointed out that this approach leads to the erroneous rejection of some most parsimonious trees (MPTs). Here, I use his iconic tail example to demonstrate different approaches and explain the need for the new NA corrected tree length (NACTL) method proposed in this paper. This example is illustrated in Figure A10; there are 12 taxa on the tree, two taxa that were immaterial in the Maddison (1993) example were excluded and two major clades will be referred to as Dangles and Solidos. Reductive coding is the traditional treatment of NA characters as the same as missing data. In Figure A11 there are two trees (11.1 and 11.2) with reductive coding demonstrating the original situation examined by Maddison (1993). Tree 11.1 is optimized with four changes among characters tail and tail color. Tree 11.2 is optimized with five changes. The

12 4 optimization of a blue to red transition at the base of the Dangles clade exists because of an a priori assumption that a newly evolved tail is the color blue, introduced because the base of the Solidos clade is resolved with a large number of other characters and the swathe of taxa between the named clades have had the tail color treated as unobserved rather than unobservable. This results in treating newly applicable characters inconsistently and causing equally parsimonious trees to have different tree lengths. When this accidental assumption is removed, tree 11.1 and tree 11.2 are shown to be equally parsimonious. Real data sets are not always amenable to manual inspection for the accidental assumptions introduced by reductive coding, making a reductive coding strategy for NA characters an unacceptable option. The topological implication is the rejection of equally parsimonious trees. The character optimization implications are the impossible assignment of character states to taxa where the character is unobservable. Absence coding treats the unobservable condition as a character state (Maddison 1993). This is problematic in two ways: (1) it makes the absent tail state redundant with the unobservable tail color state and (2) it asserts a homology based not on an observed attribute but the tautology that no observable difference can be observed amongst unobservable phenomena. The topological implication of absence coding is the preference for trees with monophyletic groups with NA coding. Figure A12 illustrates the optimization of the absence coded tail character on tree 11.1 and tree Absence coding s character optimization places transitions at the correct place on a tree and shows an equal number of transitions on both trees, but its logical deficiencies result in a calculated tree length that is greater than the true tree length. The miscalculation of tree length and logical deficiencies of absence coding makes it an unacceptable strategy for handling NA characters, but the correct optimization of transitions makes it useful in the new NACTL method. Composite coding takes every logical combination of character states from a set of characters and yields a single character with each logical combination as a character state (Maddison 1993). Composite coding can have the topological implication of preferring large transitions because composite coding can collapse the patristic distance between taxa. With only

13 5 two characters in the character complex, the optimization for the composite character looks the same as the absence coded character in Figure A12. Composite coding, in this case, retrieves the correct optimization of character state transitions and results in the correct tree length. Strong and Lipscomb (1999) mistakenly criticized the use of composite coding when there are secondary losses of the feature described by other characters, as shown in Figure A13. Tree 13.1 is a consensus of the trees expected by Strong and Lipscomb (1999) and tree 13.2 shows the optimization of the composite character on the consensus of the unexpected trees. The optimization shown on tree 13.3 shows the optimization of the original characters onto tree In this scenario the main feature has evolved twice making it congruent with the Maddison (1993) example. If we allow the 5:0->1 transition along the branch leading to taxon D to contribute to the tree length, then this introduces the same type of accidental assumption that plagued the reductive coding of the original example. In this case, not allowing the accidental assumption to contribute to the tree length yields the same result as composite coding the two characters. To understand why using a composite character works in some circumstances, but not in others, we must consider the acknowledged hierarchical structure of characters (Wilkinson 1995; Hawkins et al 1997; Strong and Lipscomb 1999). Characters and their logical dependence can easily be graphed and aid greatly in understanding when and how treatments of NA characters violate the logical basis of parsimony. Figure A14 shows the hierarchical structure of 5 characters. When there are logical dependencies between characters, these characters form a character complex. When a character is logically dependent on the character state of another character, this relationship is subordination and we will phrase it as a character that is subordinate to that character state, conversely the character state is superordinate to the character. In the character complex hierarchy, compositing is an operation on character states that results in a clade of subordinate characters collapsing up to an indicated rank. In Figure A15 the results of compositing the character tail coating 1 rank. The information in all the character states in characters subordinate by 1 rank to character states of tail coating are

14 6 combined and collapsed up to character states of tail coating. Compositing, as an operation, does not have to propagate down to the tips of the character complex hierarchy. Figure A16 illustrates two examples that have had a character composited, whereas the character states of character 4 have remained uncombined. If part of a character complex has only one character state to which one other character is subordinate, that part of the complex can be composited without affecting the final results. If all character complexes have this property, composite coding works without the need for additional steps. The deficiencies of these three coding methods (reductive coding, absence coding, and composite coding) can be visualized by graphing the characters with their logical dependencies, ranks, and transitions. Figure A17 shows the structure of the data and the way all three of these methods treat the hierarchical nature of characters. Graphically there are three rules that transitions need to follow to contribute to tree length. A transition cannot occur between states from different characters (absence coding violates this rule). All transitions must start at a character state and end at another (reductive coding sometimes violates this rule). The hierarchical nature of the data needs to be congruent with the structure in the coding method, composite coding sometimes violates this although incongruence is difficult to see at first and best explored algebraically. The last major approach to dealing with NA characters is to use a step-matrix. In fact, two different step-matrix approaches were suggested by Maddison (1993). In the first approach, character-state transitions for a composite coded character are weighted arbitrarily to increase the influence of characters of higher rank. Lee and Bryant (1999) discouraged the use of such stepmatrices because it violates the logical basis of parsimony by introducing requirements that can yield results with more a priori assumptions of homoplasy than is necessary, or fail to consider equally parsimonious trees. The second suggestion was to code the character as a composite and then create a step-matrix that preserves the original patristic distances. This too can work, but there are limits to the use of a step-matrix due to the algorithms used in the analysis.

15 7 If we consider the character complex from figures A14 and A15 and ignore the tail coating and scale shape characters, the necessary steps between all combinations of character states can be represented by the step-matrix in Table A1. Maddison (1993) expressed concern that it would become too cumbersome with many character state combinations. The difficulty of using a step matrix is not a compelling reason to ignore the logical dependencies that exist within a character complex. The real problem with using a single step-matrix arises with violations of triangular inequality within the matrix. Table A2 shows the step matrix for the composite character of tail coating, tail color, and tail shape. If a tree search is run with the stepmatrix from Table A2, a change requiring a cost of three steps will instead be optimized and scored as two transitions from the first state to absent and then from absent to the second state. Violations of triangular inequality result in sneaky optimizations where transition costs are less than the patristic distance (Farris 1984). The not applicable uncorrected treelength (NAUTL) is the treelength calculated from an absence coded matrix. The NAUTL includes costs congruent with the principle that initial states of newly applicable characters should not contribute to the tree length, but it also includes a cost of one for every transition from absent to the particular state of a newly applicable character. Optimizing the applicability matrix on the trees from the tree search with the composite coded matrix gives the number of applicable-not applicable transitions (ANTs). The number of ANTs for a tree is equal to the number of redundancies that the absence coded matrix optimizes on the tree. The NACTL is the difference between the NAUTL and the number of ANTs, see Figure A18. While NACTL is just the tree length, for the purposes of comparing different results using different NA character coding approaches, NACTL will be used throughout the results section. Figure A19 illustrates the steps needed to evaluate the easiest way to treat characters with NA coding. Figure A20 illustrates each step needed to perform a straight forward NACTL tree search. The R script NACTL.R (Appendix B) is not intended for large data sets, but will perform a NACTL tree search.

16 8 CHAPTER 2. METHODS AND MATERIALS 2.1 Taxa Taxa were selected to compare morphological results with the suggested clade composition given by the molecular studies up through Fukami et al. (2008). Table 3 has a list of all the taxa examined. Oxysmilia rotundifolia was included because of Cairns (1978) suggesting a close possible relationship with Phyllangia and Rhizosmilia. Sampling was much denser within Meandrinidae, especially with the numerous fossil Dichocoenia and Meandrina species. 2.2 Characters Two groups of characters were used in this study: skeletal characters with qualitatively described character-states (21 characters, 60 states) and characters with quantitatively delineated character-states using a combination of geometric morphometrics and finite mixture analyses (3 characters, 7 states). The character state codings can be seen in Table Qualitatively Delineated Characters Corallum Form The most prominent aspect of scleractinians as a whole is the variation in spatial distribution of corallites. This character is defined by the distribution, and shape of the distribution of all corallites if they were connected to their nearest neighbors by planes. Figure A21 illustrates each of the corallum form character states. Within the ingroup there are seven character states: mound (0) where the numerous corallites trace out a roughly hemispherical colony; solitary (1), where only one corallite is found unattached to any other corallite; ramose (2) which has distinct clusters of corallites diverting from one another; flat-topped (3), where the colony has all corallites at a roughly equal elevation and facing upwards; pillar (4), where the sides of the colony are roughly perpendicular to the ground with only a small top facing upwards; and reptoid (5), where corallites are both very

17 9 widely spaced and encrusting of the substrate. Flabelloid coralla are coded as 4, traditionally they have been coded as a separate form, but that form can be described as one where the corallites form a single, unforking series of varying sinuosity. This would make a flabelloid coding non-independent from characters describing series and sinuosity. The presence or absence of coenosteum has no bearing on this coding of character states. Traditionally corals like Eusmilia, Cladocora, or Rhizosmilia would have been classified as phaceloid, but phaceloid is branching without coenosteum, essentially overweighting the influence of the absence of coenosteum. Furthermore, the particular distribution of corallites in Eusmilia fastigiata and Cladocora arbuscula is actually a mound, with the corallites approximately all the same distance from the center of the colony while Rhizosmilia is solitary with some of new corallites starting growth on the skeleton of other corallites. Cairns (1978) described Rhizosmilia as clumped phaceloid taxon, but the fact that each corallite forms a basal attachment structure has led to coding the taxa as solitary Maximum Corallite Series (Johnson 1998) The corallites within the coral can grow as individuals with septa completely surrounding a single stomodaeum or in series with stomodaea incompletely surrounded by septa. This character is divided into three character states and coded according to the largest series observed: monocentric corallites (0) have individual corallites with complete septal rings; short series (1), which are corals with series of about 2 to 5 corallites; and long series (2) which runs from 7 corallites on up. Traditionally the short series character state was divided into dicentric and tricentric (Wells, 1956), but distinguishing between the two proved difficult because different parts of the same colony would be dominated by either dicentric or tricentric states. This character is not applicable to solitary corals Number of Series (Budd and Smith 2005) Colonies with multi-corallite series could have the corallites in multiple series (0) or a single series (1). This character is not applicable for monocentric corals.

18 Series Sinuosity (Johnson 1998) Corallite series are coded into three character states: nearly straight (0), slightly sinuous (1), or very sinuous (2). This character is not applicable for monocentric corals. The character states for this character are illustrated in figure A Distinctiveness of Calices (Budd and Smith 2005) Individual corallites in series can be distinct (0) or indistinct (1). Distinct corallites have a small narrowing of the series between corallites. This character is not applicable for monocentric corals Attachment to Substrate (Johnson 1998) The adult coral or colony can be attached to a substrate (0) or be free-living (1) without cementing itself to substrate. The character-states for this character are illustrated in figure A Basal Plate Reinforcement When a planula lands the aboral end will attach to the substrate and then broaden to form the basal disc for both solitary corals and colonial corals. There are three character-states about skeletal reinforcement of the basal plate: no early reinforcement (0), exothecal dissepiments are laid down over extended and raised costae (1), or exothecal dissepiments laid down with gaps between dissepiments (2). State (0), no early reinforcement, does not preclude the latter augmentation of cementation of the colony with growth of the colony, indeed this later solid attachment is seen in the colonies coded as state zero. This character is not applicable to freeliving corals. Character state 1 is illustrated by figure A22d Stereoplasm Corals either lack stereoplasm (0) or have stereoplasm (1). Stereoplasm is an additional skeletal tissue deposited on the septa and inside of the wall that fills up the void space as the coral grows. It lacks centers of calcification.

19 Wall Construction (Johnson 1998) The wall of a corallite surrounds the gastrovascular cavity and within the taxa of interest can be formed in two main ways. Septothecal walls (0) are constructed from thickened septa. Parathecal (1) walls have new skeletal dissepimental tissues inserted between septa Septal Centers of Calcification (Budd and Smith,2005) The centers of calcification, viewable in thin-section and acid etchings, are areas of initial deposition of skeletal crystals. The skeletal crystals then extend outward from the center of calcification. The centers of calcification are laid down in lines. This character is divided into four states: straight lines (0) of centers of calcification; relatively straight lines of centers of calcification with sporadic jags (1); very jagged (2) centers of calcification lines; and crosshatched (3) with one main straight line of centers of calcification with small perpendicular sets of centers of calcification Parathecal Dissepiment Centers of Calcification The centers of calcification in the parathecal dissepiments show two character states: not apparent (0) and apparent (1). This character is observed in thin-section and not applicable for strictly septothecal corals Septal Outline (Longitudinal View) Outlines of septa in profile view have been placed into three different character states with gently arched septa (0) that gently slope down into the axial part of the corallite, rounded lathe-like septa (1), and acutely arched septa (2) Columella (Budd and Smith 2005) Columella, the axial skeletal structure, occurs in 5 states: spongy (0) columella is vesicular with strands of skeletal material splitting and merging ; lamellar (1) columella made of a solid, elongate structure; fasicular (2) which is composed of upright twisted ribbons; fused (3)

20 12 columella where a trabecular mass is fused into a large central mass; and, absent (4) or extremely reduced. Character-states 0-2 are illustrated by figure A23d-f Pali (Johnson 1998) Pali are coded as either absent (0) or present only in the second to last cycle (1). Pali are distinguishable from additional septal lobes by their shifting location during ontogeny. Oculina was traditionally listed as having pali, but that feature is interpreted as a very upward projecting paliform lobe. Paracyathus has also been considered a taxon with pali by West (1956), but those too have been reinterpreted as paliform lobes in agreement with Hertlein and Grant (1960). Because of the similarity in form of the pali of Paracyathus and Polycyathus, Polycyathus has also been coded as having paliform lobes and not pali Paliform lobes (Johnson 1998) Paliform lobes are skeletal lobes connected to the septal lobe far down along the innermost edge. Paliform lobes have been coded as absent (0), upward pointing rods (1), or small arches (2) Vertical Coenosteum Deposition This is how non-costate coenosteum is vertically structured. The four states are: vesicular (0), where the coenosteum is spongy; solid (1) where non-costate coenosteum is continually deposited and keeps pace, more or less, with the growth of the calices; discontinued (2) where initial solid layers of coenosteum are deposited between corallites, but is discontinued after a certain thickness; absent (3); and alternating (4) where layers of solid coenosteum are separated by small vertical pillars. This character is not applicable for solitary and flabellate corals. Character-states 1, 3, and 4 are illustrated in figure A23a-c.

21 Coenosteum Surficial Texture The texture, at the corallum surface, for non-costate coenosteum is coded into two states: smooth (0) and granular (1) with bumps and pores. This character is not applicable for corals lacking non-costate coenosteum Corallite/Series Spacing (Johnson 1998) This character roughly codes how much space is between neighboring corallites relative to corallite diameter. The character is divided into two states: distance is less (0) than the corallite valley width or the distance is equal to or greater (1) than the corallite valley width. This character is not applicable to solitary corals Single Corallite Profile A single corallite can start relatively large or grow very rapidly and have a nearly cylindrical form (0) or slowly enlarge diameter with increases in height resulting in a flared profile (1). Corals with series were coded with the elongate direction along series ignored Budding Type (Johnson 1998) New buds occur either outside (0) of the walls (extramural), inside (1) the walls (intramural), or no budding occurs (2). Paracyathus specimens occasionally will show patricidal budding where a new corallite grows out of, and in the process kills the parental coral Adult Radial Cycles (Johnson 1998) Septa occur in cycles, where new cycles are inserted in between the septa of previous cycles. Two character states are coded: three cycles (0) or at least four cycles (1). It is only coded as two states because if there were more than three cycles the total number of cycles appeared to increase with corallite diameter.

22 Composite Coding Three character complexes exist in this data set and are illustrated in figure A24. Two of the character complexes involve only two characters and can be compounded very easily into a single wall construction character with the states: septothecal, parathecal with apparent centers of calcification, and parathecal without apparent centers of calcification. The attachment complex can be reduced to a single character with the states free, attached with no early reinforcement, attached with dissepiments laid down over extended and raised costae, or attached with exothecal dissepiments laid down with gaps between dissepiments. The coralla form character complex will require the NACTL method because the eight characters involved in the complex are arranged so that a step-matrix would violate triangular inequality Quantitatively Delineated Three characters, the shape of the costae in cross-section, the shape of the walls, and the shape of the primary septum within the columella, were inconsistently qualitatively coded by the author, so quantitative delineations were used. The cost for this increased objectivity is a loss in coverage since thin-sections were not available for all taxa. A geometric morphometric approach was used to quantify the shape of the primary septum and split it into three a priori groups, each coding for one of the different characters. Table A5 describes the landmark scheme used. The shape of the costae used landmarks 2, 3, and 4 along with semi-landmarks 15 through 20. The shape of the walls used landmarks 1, 2, 4, and 5 along with semi-landmarks 7 through 14 and 21 through 28. The shape of the primary septum with the corallite utilized landmarks 1, 5, and 6 along with semi-landmarks 29 through 64. The landmarks and semi-landmarks were superimposed and then reflected across the midline of the primary septum. These symmetrized configurations were fit to the finite mixture models that both delineated the character-states and assessed the strength of different classifications (See the Landmark Analysis, Finite Mixture Analyses, and Model Selection sections below).

23 15 Not all species were coded quantitatively due to either a lack of thin section or problems with the thin-section. Table A6 lists the taxa used in this analysis. The sampling for the Placocyathus subgenus was taken from a data set assembled for analyzing Meandrina costatus and Meandrina variabilis. The specimens used for these species were small because severe over-representation by only a couple of species can introduce artifacts into the finite mixture analyses. Meandrina meandrites was coded based on the results of the analysis, but it was not included in the analysis itself. 2.3 Tree Search and Evaluation TNT (Goloboff et al. 2008) was used to perform the tree search. For the three traditional approaches to treating NA characters, the process is straight forward and performed 1000 TBR replicates, saving up to 1000 MPTs for each replication. Searching for the NACTL trees requires several additional steps. Figure A25 shows a graph with NAUTL vs. ANTS with NACTL isoclines shown. The final search is performed with the absence coded matrix while retaining suboptimal trees. In order to figure out how suboptimal the search needs to be, there are several initial steps. The first is to place a maximum on the number of ANTs in the analysis. Before any search is performed the maximum number of ANTs can be calculated the same way the number of maximum steps are calculated for a retention index. After a tree search has been performed with a composite matrix, the applicability matrix can be optimized onto the trees and the maximum retrieved value will set the new upper limit on the ANTS. A traditional search using the absence coded matrix will return trees that will show the lower limit for both ANTS and NAUTL. Of these trees the NACTL was calculated with Mesquite 2.72 (Maddison and Maddison 2009). Since there is an upper limit to the number of ANTS and we have constrained the final NACTL value to some extent, the maximum number of suboptimal steps on a tree that needs to be retained are calculated. The final search uses the absence coded matrix, retains suboptimal trees, and is subsequently filtered with Mesquite to find the trees with minimal NACTL values.

24 Outgroup Selection The Montastraea annularis species complex was used as an outgroup. Previous work by Fukami et al. (2004) showed the traditional genus Montastraea to be a polyphyletic group. The a priori belief that these taxa were largely pleisiomorphic in appearance guided the selection. This notion was supported by the historic classification of Solenastrea, part of the ingroup, as closely related to Montastraea (Wells 1956). 2.5 Landmark Analysis A Generalized Procrustes Analysis (GPA) is used to quantify aspects of the primary costoseptum shape. GPA is the most widely used superposition method, and the one used in this analysis. Superimposition methods involve constructing a template and then using translation, rotation, and dilation functions to minimize the total distance between the points of a configuration and the homologous points of the template. GPA uses the mean of the configurations as the template and the least squares distance is minimized (Slice 2005). Since the influence of location, orientation, and size are removed from the numbers representing the configuration there is a loss of degrees of freedom. Dilation will remove one degree of freedom; translation removes one degree of freedom for each dimension of the data; and rotation removes one degree of freedom for each plane of rotation. Two dimensional configurations will have four fewer degrees of freedom (one for size, two for translation, and one for rotation). Three dimensional configurations will have seven fewer degrees of freedom (one for size, three for translation, and three for rotation) (Slice 2005). The geometric results of the removal of location, orientation, and size are that the configurations are distributed in non-euclidean space. In order to use more common statistical techniques the configurations must be projected from non-euclidean space to a tangent Euclidean space. This procedure is perfectly reasonable if the configurations occupy a relatively small amount of shape space. To assess the impact of the projection, the Riemannian distances (non-euclidean) are regressed against the Euclidean distances in the tangent space. Because

25 17 coincident points in one space should be coincident in the other, the regression is forced through the origin (Rohlf 2003). For interpreting the shape of superimposed configurations the common morphometric mathematical analogy of bending an ideal, infinite metal sheet is employed. The difference between a configuration and the reference configuration is seen as the bending of the ideal metal sheet. The eigenvectors of the bending energies, principal warps, describe the differences between the reference configuration and a given configuration as orthogonal displacements. The principal warps with the largest eigenvalue act on a very local scale, with smaller eigenvalues acting over larger areas. The uniform warps describe affine transformations (not localized) that describe the shearing and dilation along the configuration axes. The relative warps are principal components of the principal warps and uniform warps (Slice 2005). In computing relative warps, the partial warps (pairs or triplets of principal warps) can be rescaled by the exponent α, α=1 in all the relative warps used in this analysis. Semi-landmarks are constrained between two points, but allowed to slide parallel to the line connecting the two points. The amount of sliding imposed on the semi-landmark is the amount that minimizes the total amount of bending energy for the entire superimposition. For this study, six landmarks and 58 semi-landmarks were recorded with tpsdig2 (Rohlf 2010a). Table 5 lists and describes the landmark data, and the landmarks and curves that the semi-landmarks are extracted from are shown in Figure A26. Superimposition of the landmarks and semi-landmarks, calculation of partial and relative warps, and visualizations of changes between configurations were performed with tpsrelw (Rohlf 2010b). The regression of Riemennian and Euclidean distances was performed with tpssmall (Rohlf 2003). Regressions against the logarithm of centroid size were done with tpsregr (Rohlf 2009). The finite mixture analyses used the relative warps of a symmetrized set, where landmarks were averaged across the midline of the septum using the program SAGE v1.05 (Marquez 2004).

26 Finite Mixture Analyses Finite mixture distributions are synthetic distributions that are composed by combining more than one other distribution. Finite mixtures take the form in Equation 1 where y is the dependent variable with a conditional density of h, x are the independent variables, K is the number of components, π k is the mixing proportion of component k, and θ k is the vector of parameters for component k of density function f. ( ) ( ) Equation 1 Finite mixtures of normal and multivariate normal functions were fit to the relative warps of different septum parts, where x is equal to one. The logarithm of centroid size was used as the independent variable for a mixture of linear regressions against the first two relative warps for the septum. Classification was determined by assigning each case to the component with the highest probability of membership. The finite mixture analyses of normal and multivariate normal functions were performed with the R package Mclust (Fraley and Raftery 2006) in R (R Development Core Team 2010). The mixture of linear regressions was carried out with the R package flexmix (Leisch 2004). Mclust was used to create different models of covariance for the components. The naming convention described in Fraley and Raftery (2007) for these models is used in this

27 19 analysis, followed by a number representing the number of components (i.e. VEV 3 represents a model where the variance matrix of diagonal elements that are not all equal is estimated and a scalar is estimated for each of the three components) Model Selection The Aikake Information Criterion is an unbiased estimator of the relative distances between a fitted model and the true model (Burnham and Anderson 2002). This distance is the Kullback-Liebler distance, or Kullback-Liebler information. The true K-L information is unknown because the true model is unknown; however, the relative distance for models for a given data set is knowable. Heuristically we can think of the AIC as a way of penalizing likelihood for the number of parameters used in a model. This is the statistical approach to parsimony. The second order AIC (AICc) is a minor alteration that corrects for the estimates of variation for small sample sizes (Burnham and Anderson, 2002), since the correction approaches zero with increasing sample size, it is safe to use the AICc for all models. The smaller the AICc, the smaller the K-L distance, and the more preferred the model. The models have been ranked according to ΔAICc, which is simply the difference between that model and the best model under consideration. AICc is on a natural logarithm scale, so models with ΔAICc less than two are considered strong models, models with ΔAICc between two and four are reasonable, and models with ΔAICc greater than 7 are considered very unlikely. The model fitting was performed with the R package Mclust (Fraley and Raftery 2006), the likelihood was extracted from its results and the AIC, AICc, and ΔAICc were calculated in a simple spreadsheet. Each of the three divisions analyzed as characters has an overlapping edge with one of the other two characters. To check that this isn t having a significant effect on the results the characters will be compared, after the tree search, on a set of phylogenies of particular focus to see if the state changes are significantly correlated. The pairwise comparison is calculated with

28 20 Mesquite 2.72 (Maddison and Maddison 2009) using the Pairwise comparison package 1.1 (Maddison 2006). Catalano et al. (2010) has a different approach to incorporating geometric morphometric data into phylogenetics that involves the optimization of landmark location. This approach ignores the difference between the number of values for the set of superimposed landmarks and the actual degrees of freedom available. Geometric morphometrics deals with configurations that are single entities described in a multivariate manner. The approach used in this study a priori divided the coral features into three different schemes and each scheme underwent a separate superimposition. Data reduction was performed by using only the first few relative warps for each scheme. Each scheme then describes one character. The character state codings are then chosen based on model selection criteria and finite mixture analyses

29 21 CHAPTER 3. RESULTS 3.1 Character Delineations Coding for the quantitatively delineated characters was determined by the finite mixture model with the lowest AICc. Table A7 shows the variance explained by the relative warps for the costae alignment. Table A8 shows the models and rankings for the finite mixture analysis using only the first relative warp of the costae data. The best returned model suggests two components with different variances. Less fit models suggesting 1 to 4 components with equal variance are all reasonably close to the best model. Figure A27 shows the means configurations of the two components used to code this character. Table A9 shows the variance explained by the relative warps for the wall superimposition. Table 10 shows the top 20 models and indicates that the next best model is quite a bit less fit than the top model, which has 3 components. Figure A28 shows these three character states. Table A11 shows the variance explained by the relative warps of the superimposition of the septum data. The finite mixture analysis with the first three relative warps returned a best model with three components (Table A12), but a regression of the warps against the log centroid size revealed a very strong relationship between size and septum shape (Figure A29). A permutation test with 1000 replicates gave the multivariate regression a p-value of.001, indicating a very strong significance and the fact that size could not be treated as a separate character from septum shape. Centroid size and the first two relative warps for the septa data were then treated as one character and entered into a finite mixture model to create a character that is a combination of size and septum shape. Table A13 shows the top twenty models, with the best model having three components and the second best model quite a bit worse (ΔAICc=8.8) than the best model. Figure A30 shows the three character states for this model.

30 Phylogenetic Analysis A tree search with a reductive coded matrix retrieved 24 MPTs with a tree length of 74, constraining the search to trees with a monophyletic Meandrinidae and monophyletic Oculinidae resulted in a tree length of 77. A tree search with an absence coded matrix retrieved three MPTs with tree lengths of 81. A tree search with a composite coded matrix retrieved 672,840 MPTs. The only structure retained in the strict consensus from the composite coded MPTs was a monophyletic Placocyathus + Meandrina braziliensis. In the strict consensus of both the reductive and absence coded trees (Figures A31) Meandrina is monophyletic but neither Oculinidae, Meandrinidae as modified by using molecular data, nor the genus Dichocoenia was retrieved as a monophyletic grouping. No absence coded or reductive coded tree retrieved a monophyletic Meandrinidae or convex Oculinidae. The first step in determining the number of suboptimal trees that need to be retained from a tree search with an absence coded matrix is to calculate the maximum number of ANTs with the applicability matrix, in this analysis the maximum is 66 steps. The next step was to map the applicability matrix onto the MPTs for the tree search with the composite coded matrix. A new maximum ANTs value of 33 was obtained. Next the NAUTL value was constrained to have a value no lower than 81, the length of the MPTs retrieved during the initial tree search with the absence coded matrix. The NACTL was then calculated for the trees retrieved so far, with an initial minimum NACTL value of 61. A NACTL of 61 combined with a maximum ANTs value of 33 means that the NAUTL value could vary from 81 to 94, a difference of 13 steps. A tree search was then initiated and all trees suboptimal by 13 steps or less were retained. Three separate searches were conducted; each retrieved more than 45 thousand trees. All three sets were then filtered and the same 27 NACTL MPTs were retrieved. The strict consensus of the NACTL trees, Figure A32, retains little structure. Three NACTL trees retrieve a monophyletic Meandrinidae and a convex Oculinidae, Figure A33, while 14 NACTL trees retain a monophyletic Meandrina, Figure A34. One tree retrieved a monophyletic Dichocoenia. No tree

31 23 retrieves all signals, although all three trees with a monophyletic Meandrinidae have a paraphyletic Dichocoenia. 3.3 Character Independence Pairwise comparison using the maximum number of pairs, pairs contrasting in one character, and pairs contrasting in two characters all give the same results for the three MPTs that retain a monophyletic Meandrinidae, the smallest best tail value is 0.5 between the septum coding and the wall coding. The other comparisons all had a smallest best tail value of 1.0. These values strongly indicate that the shared landmarks did not cause a large correlation between the characters.

32 24 CHAPTER 4. DISCUSSION The new NACTL method used in this paper is important because it consistently treats new applicable characters in a consistent and logical manner that doesn t incorporate redundancies. Without this method the trees returned by reductive coded matrices and absence coded matrices would have suggested that a monophyletic Meandrinidae signal was not present in the data. With a composite coded matrix there were too many trees retrieved to see any meaningful pattern in the trees because most of the information contained in the subordinate characters obscured homologies present in superordinate characters. The NACTL approach retrieves trees showing the full range of signals but preserves the information from all characters regardless of rank to provide an appropriate level of resolution in the results. The strict consensus of the NACTL trees retains little structure due mostly to rerootings of subclades, but the number of trees is small enough that the results are easily filtered. The three NACTL trees showing a monophyletic Meandrinidae also show a paraphyletic Dichocoenia. With the appropriate re-rootings of the clade containing the paraphyletic Dichocoenia a tree with a monophyletic Meandrinidae, Meandrina, and Dichocoenia is possible. Additional taxonomic sampling would be needed to explore the chances that all three of these groupings are monophyletic. The outgroup Montastraea annularis appears rather distant in more comprehensive phylogenies, perhaps indicating it is not the ideal outgroup. With re-rooting of the ingroup, the trees that show the family Meandrinidae as monophyletic could also show Oculinidae as monophyletic, see Figure A35. This analysis provides little phylogenetic resolution, but does fit within larger trends seen in scleractinian systematics. Budd et al. (2010) discuss the growing need to include both zooxanthellate and azooxanthellate corals in phylogenetic analyses. The NACTL approach outlined in this paper will be important for including both of these ecological groups in a single morphological analysis to cope with the high number of not applicable characters that would arise. The importance of azooxanthellate taxa in resolving the basal relationships of

33 25 zooxanthellate clades is apparent in the literature and seen in this study. While the lack of resolution might be frustrating, it should be noted that the morphological results are completely congruent with the molecular results, a conclusion that wouldn t have been reached without the NACTL approach. 4.1 Character Coding and Geometric Morphometrics The approach to using geometric morphometrics in a cladistics analysis used in this paper has two advantages over previous approaches: (1) the division of the geometric morphometric data into separate characters occurs before superimposition, thus avoiding the problem of using arbitrary projections and (2) it doesn t use more degrees of freedom in the models than is a result of the actual superimposition. With the wider availability of software that can easily perform finite mixture analyses, I suspect that more researchers will use this approach when the ability to code a character consistently is suspect. Earlier work by Swiderski et al. (1998) used principal warps as characters, but as noted by Bookstein (2002) and Adams and Rosenberg (1998) these values are the result of a projection that is arbitrary from a biological perspective. González-José et al. (2008) also divided their data before the superimposition process and were able to avoid the problem of using arbitrary projections by treating the principal components for each module as additive for the parsimony part of their analysis, thus treating their data as continuous. The latest work on integrating geometric morphometrics and cladistics has been by Catalano et al (2010) using the actual coordinates of superimposed points. This results in twice as many characters as points, and four more characters than degrees of freedom for two dimensional data. What their study has neglected is that for a single point the only reasonable cladistic character is present/absent. The superimposed coordinates are the result of removing the aspects of geometry that are not shape, but that shape information does not exist in the atomized superimposed coordinates, it exists as a relationship(s) between the points.

34 26 The approach in this paper can mostly be seen as a multivariate version of the approach by Strait et al. (1996), who first advocated coding univariate continuous characters with discrete states based on a finite mixture analysis. Subsequent advances in model selection and the use of multivariate data are the only major differences between that approach and the approach used in this paper. The choice to use a finite mixture analysis is entirely based on whether or not the researcher thinks that there are discrete character states described quantitatively or whether the data is truly continuous and not just described on a continuous scale. Future work utilizing geometric morphometrics for cladistics characters will probably follow, and should follow, the pattern of dividing the landmark data into separate characters prior to the superimpositions used in the analysis. As González-José et al. (2008) rightly express, the ideal division into characters would follow observable patterns of phenotypic integration. Integration and modularity in human crania has been extensively studied so future analyses of other taxa will probably utilized the techniques discussed by Marquez (2008) and Klingenberg (2009) for analyzing models of integration to determine the division of landmark data into characters. These approaches also have the added advantage of taking into consideration landmarks shared at the boundary of character divisions during the analysis and not assess after the fact as was done in this analysis for a subset of trees. 4.2 NACTL The main limitation of the NACTL approach is the need for saving suboptimal trees in a tree search with an absence coded matrix. The tree search with TNT is very thorough in searching for optimal trees and in this analysis suboptimal trees were retained, not actively sought. This decreases confidence in the idea that all NACTL trees were retrieved. An ideal situation would active search for the tree with a minimal NACTL. Appendix B has R code that actively searches for the NACTL trees, but the speed of the search is very slow and shouldn t be used for analyses with large numbers of taxa. It mainly utilizes the functions provided by the phangorn R package (Schliep 2010).

35 27 The inability of previous approaches to cope with logical dependencies has limited the scope of morphological phylogenetic analyses and generally divided phylogenomic techniques into either sequence based analyses or genome feature based analyses (Delsuc et al. 2005). The NACTL approach holds out the possibility of uniting the two phylogenomic approaches by having sequences subordinate to characters describing gene presence or absence. More generally, gaps in sequence alignments are areas of incongruence because there has been an insertion, deletion, or combinations of the two; these indels are characters of a higher rank and have subordinate site characters with the particular nucleotide or amino acid. Parsimony is no longer widely used in sequence focused approaches, but the NACTL approach could serve as a model for a new likelihood approach. The ability to cope with NA characters also widens the amount of phylogenetic history that a morphological analysis can reasonable cover while also still allowing detailed characters pertaining to only subsets of taxa. The interaction of hierarchical character complexes and taxon sampling needs to be studied to see if sampling procedures need to focus on sampling more variation for characters higher in character complexes. 4.3 Conclusions The failure to treat not applicable characters as such, instead of the same as missing data, had been identified as a problem in phylogeny reconstruction since the early 1990s. The NACTL approach logically and consistently treats not applicable and new applicable characters, solving this problem. The NACTL approach, when applied to the character matrix of the coral families Meandrinidae and Oculinidae, retrieves a signal of monophyletic families in some of the MPTs. A result strongly supported by other molecular studies, but not retrieved using past approaches to cope with NA characters.

36 28 APPENDIX A FIGURES AND TABLES Figure A1SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments ) image of Meandrina meandrites(sui ).

37 Figure A2 SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Dendrogyra cylindrus (SUI ). 29

38 Figure A3 SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Eusmilia fastigiata (SUI ). 30

39 Figure A4 SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Oculina diffusa (SUI ). 31

40 Figure A5 SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Cladocora arbuscula (SUI ). 32

41 Figure A6 SEM images (A,B, D, and E) and thin-section (C, scale bar in 1mm increments) image of Solenastrea bournoni (SUI ). 33

42 Figure A7 Relevant portion of the coral phylogeny in Fukami et al (2008). 34

43 Figure A8 Relevant portion of the coral phylogeny Kitahara et al. (2010). 35

44 Figure A9 Relevant portion of the coral phylogeny returned from Barbeitos et al. (2010). 36

45 Absent Red + Round Blue + Round Red + Flat Blue + Flat 37 Absent Red + Round Blue + Round Red + Flat Blue + Flat Table A1 Step matrix preserving the patristic distance between the character states of a composite of three characters.

46 Absent Red Red Blue Blue Red Red Blue Blue Round Round Round Round Flat Flat Flat Flat Feathery Scaley Feathery Scaley Feathery Scaley Feathery Scaley 38 Absent Red Round Feathery Red Round Scaley Blue Round Feathery Blue Round Scaley Red Flat Feathery Red Flat Scaley Blue Flat Feathery Blue Flat Scaley Table A2 Step matrix attempting to preserve the patristic distance between the character states of a composite of four characters, but violating triangular inequality.

47 Tail Tail color Present Present Present Present Absent Absent Absent Absent Present Present Present Present R R B B B B R R Many synapomorphies support these clades Many synapomorphies support these clades Figure A10 Consensus tree of the example adapted from Madison (1993). There are two less taxa than the original example and taxa with tails have been placed into two named clades, Dangles and Solidos. The character states for tail have been demonstrated above the tips of the tree. R stands for red and B stands for blue. 39

48 Figure A11 Tree 11.1 and 11.2 optimized with a reductive coded matrix. 40

49 Figure A12 Tree 11.1 and tree 11.2 optimized with an absence coded matrix. Both trees have an equal tree length and show the correct character optimization. The tree length is higher than it should be due to redundancies. 41

50 Figure A13 Trees and relevant characters taken from Strong and Lipscomb (1999). 42

51 Figure A14 Graph showing the characters and logical dependencies for a hypothetical tail character complex. Characters of different ranks are colored differently and higher ranks are toward the top of the graph. 43

52 Figure A15 Graph showing the characters and logical dependencies for a hypothetical tail character complex with the character scale shape composited up into the tail covering character. Characters of different ranks are colored differently and higher ranks are toward the top of the graph. 44

53 Figure A16 Three graphs showing the same character complex with differing levels of compositing. All three would show identical levels of support for all trees. 45

54 46 Reductive Absence Composite NACT Figure A17 Graphical representation of different coding strategies for NA characters. Purple arrows indicate transitions that should contribute to the calculation of tree length. Red arrows indicate transitons that should not contribute to the calculation of tree length, they are either accidental assumptions or redundancies.

55 47 Ingroup Outgroup List of Taxa Family Specimens* Solenastrea bournoni Oculinidae SUI Cladocora Oculinidae SUI Oculina Oculinidae USNM 78575; SUI Paracyathus stearnsii Oculinidae USNM Polycyathus Oculinidae USNM 48355, Rhizosmilia gerdae Meandrinidae USNM Rhizosmilia maculata Meandrinidae USNM Oxysmillia rotundifolia Meandrinidae USNM Eusmilia fastigiata Meandrinidae SUI Phyllangia Meandrinidae USNM 48543, 83525, Dendrogyra cylindrus Meandrinidae USNM 7436; SUI Goreaugyra memoralis Meandrinidae USNM Meandrina meandrites Meandrinidae SUI , Meandrina braziliensis Meandrinidae SUI ; Meandrina barretti Meandrinidae SUI Meandrina costatus Meandrinidae SUI Meandrina trinitatis Meandrinidae SUI , Meandrina variabilis Meandrinidae NMB D6250; SUI Meandrina alveolus Meandrinidae SUI ; Dichocoenia tuberosa Dichocoenia stokesi Meandrinidae Meandrinidae Dichocoenis stellaris Meandrinidae SUI Dichocoenis n. sp. Meandrinidae Dichocoenia eminens Meandrinidae SUI SUI ; SUI ;SUI SUI ; SUI ; B SUI ; SUI ; SUI Dichocoenia caloosahatcheensis Meandrinidae SUI ; SUI Montastraea 'annularis' complex Faviidae * SUI = University of Iowa Fossil Repository, USNM = United States Natural History Museum, NMB = Naturhistorisches Museum Basel Table A3 List of taxa used in the phylogenetic analysis.

56 Table A4 Character matrix for the corals used in the cladistics analysis. 48

57 Figure A18. Visualization of the calculations for the Not Applicable Corrected Tree Length (NACTL). The NA matrix is a matrix composed of only characters with some taxa coded as NA. The NA characters are then recoded as a binary characters indicating applicable or NA. 49

58 Character Complex Attributes Method Figure A19 A flow chart indicating which method would be the most convenient and appropriate method for dealing with different character complexes. 50

59 Figure A20 The practical steps involved in preparing the two matrices needed for the NACTL method. 51

60 a b c d e f g Figure A21 Character states for character one, corallum for (a) Oxysmilia rotundifolia solitary, (b) Dichocoenia stokesi mound, (c) Dichocoenia n. sp. ramose, (d) Meandrina meandrites flat-topped, (e) Goreaugyra memoralis pillar, (f) Meandrina trinitatis flat-topped flabellate form, (g) Phyllangia reptoid. 52

61 a b c e d Figure A22 Character states for characters four, six, and seven; series sinuosity, attachment to substrate, and basal plate reinforcement. (a) Meandrina alveolus (4:0) straight, (b) Meandrina costatus slightly sinuous (4:1), (c) Meandrina braziliensis very sinuous (4:2), (d) Rhizosmilia gerdae attached (6:0) and with exothecal dissepiments laid down over extended, raised costae (7:1), (e) Meandrina variabilis free-living (6:1). 53

62 a b c d e f Figure A23 Character states for characters thirteen and sixteen, columella and vertical coenosteum deposition. (a) Eusmilia fastigiata absent (16:3), (b) Dichocoenia caloosahatcheensis alternating (16:4), (c) Dichocoenia tuberosa solid, (d) Solenastrea bournoni spongy (13:0), (e) Goreaugyra memoralis lamellar (13:1), (f) Eusmilia fastigiata fasicular (13:2). 54

63 Figure A24 Characters and character states with logical dependencies. Characters of the same rank are shown in the same color and arrows point to the subordinate character. 55

64 Point(s) Type Description 1 Landmark Intersection of the interior edge of the wall and the primary septum 2 Landmark Intersection of the exterior edge of the wall and the primary septum 3 Landmark Distal-most point along the mid-line of the primary septum/ tip of the costae 4 Landmark Intersection of the exterior edge of the wall and the primary septum 5 Landmark Intersection of the interior edge of the wall and the primary septum 6 Landmark Proximal point along the mid-line of the primary septum/ tip of the septum 7 14 Semi-landmark Points along the wall between landmarks 1 and Semi-landmark Points along the costae between landmarks 2 and Semi-landmark Points along the costae between landmarks 3 and Semi-landmark Points along the wall between landmarks 4 and Semi-landmark Points along the septum between landmarks 5 and Semi-landmark Points along the septum between landmarks 6 and 1 Table A5 List of landmarks and semi-landmarks used to delineate character-states of the primary septa. 56

65 57 Species Specimen* Oculina diffusa SUI Oculina valensiensis SUI Cladocora arbuscula SUI Dichocoenia callaloosahatchensis SUI Dendrogyra cylindricus SUI Dichocoenia n. sp. SUI Dichocoenia stokesi SUI Dichocoenia tuberosa SUI Eusmilia fastigiata SUI Solenastrea bournoni SUI Meandrina costatus SUI Meandrina variabilis SUI Meandrina braziliensis SUI Meandrina braziliensis SUI Meandrina costatus SUI Meandrina costatus SUI Montastraea annularis SUI Meandrina variabilis SUI Meandrina costatus SUI Meandrina variabilis SUI Meandrina costatus SUI Montastraea faveolata SUI Montastraea franksi SUI * SUI = University of Iowa Fossil Repository Table A6 List of species and specimens used in the geometric morphometric analysis.

66 ANTs Impossible NAUTL Figure A25 The chart shows the NA uncorrected tree length along the x-axis. This is the tree length found by optimizing an absence coded matrix onto a tree. ANTs are shown along the y-axis and is found by optimizing the applicability matrix onto a tree. The lines in the lower right show lines of equal NACTL value. 58

67 Figure A26 Landmarks for the character-state delineation are marked in red, the yellow line shows the tracing that the semi-landmarks were extracted from.