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THE SHELL GAME: WHO'S UNDER WHAT?
MORPHOLOGICAL EVOLUTION AND TRA JECTORIES
THROUGH MORPHOSPACE
EXEMPLIFIED WITH SPECIES OF LAMBIS
by
J. R. Stone
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Zoology
University of Toronto
O Copyright by J. R. Stone 1997 National Library Bibliothèque nationale 1S.I of Canada du Canada Acquisitions and Acquisitions et Bibliographie Services sewices bibliographiques 395 Wellington Street 395. rue Wellington OttawaON K1AON4 OttawaON K1AON4 Canada Canada
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THE SHELL GAME: WHO'S UNDER WHAT?
MORPHOLOGICAL EVOLUTION AND TRAJECTORIES
THROUGH MORPHOSPACE
EXEMPLIFIED WITH SPECIES OF LAMBIS
Doctor of Philosophy 1997
J. R. Stone
Graduate Department of Zoology University of Toronto
Morphological space provides a means of analysing the physical forms of organisms.
Mathematical modeling allows patterns generated by biologicai processes to be analysed.
And cladistic methodology permits the formulation of phylogenetic hypotheses conceming groups of organisms. In this dissertation, a synthesis of analytical techniques is developed, in which rnorphological space, mathematical modeling, and cladistic methodology are combined to reconstruct evolutionary history. In particular, new methods for tracking changes in shape du~gontogeny and for positioning cladogram nodes in three dimensions extend the concept of morphologicai space to accommodate results of ontogenic and cladistic analyses. This approach to the study of rnorphological evolution integrares developmenral and ph ylogenetic information and permits the formulation of hypotheses of ancestral foms. Species of the genus Lombis (Mollusca: Gastropoda) are analysed to exemplify the approach. In the development of the synthesis, current generic classification of the farnily Swmbidae is unsupportable and cunent subgeneric classification within the genus Lumbir is untenable. During evolution of memben within a clade containing al1 species currently classified in -bis and some in the genus
Strombur, morphological change consisted predominantly of an increase in venical dimensions of whorls. The change was greatest early in the history of the group and dirninished thereafter. I am grateful to S. and L. Wilensky, who expired and provided shelter and numents for me (although in a different sequence) during the production of this dissertation, and T.
Stone, who accompanied me during many evenings of prolonged pondering. 1 would thank other rnembers of my family, but they probably would demand residual fees for the use of their names or some other 'barristeriological idiosyncrasy .'
This work (its author) was supponed financially by Natural Science and
Engineering Research Council of Canada Individual Grant number 4696 to M. Telford, a
University of Toronto Open Doctoral Scholarship, an Ontario Graduate Scholarship, a
Conchologists of America Research Grant. and a Centenary Research Grant from the
Malacological Society of London.
Production of this dissertation was assisted technicaily by E. Lin, R. Villadiego, P.
Khan, and B. T. Moose Ir., who ensured that radula images produced by secondary elecmn scattering were illuminating; K. Gallant and S. McKenzie, who illuminated by providing papers to 'sight;' S. Smith and A. Glinos, who assisted in the use of 'UNIX' to simuIate hermaphrodites; K. Coates, divine curator, M. Zubowski, and P. Ross for providing means of 'figuring' out specimen morphologies; J. Dix, E. Glockmann, Z. Koch, and L. Trung for their un'in-spire'ing efforts; and T. Hill, who ensured that no
specimens shipped went 'sluggish.'
Specimens were provided generously b y G. Rosenberg (curator, Academ y of
Naturai Sciences, Philadelphia), T. Kausch (curator, Agassiz Museum of Comparative
Zoology, Cambridge), 1. Loch (curator, Australian Museum of Naturai History, Sydney),
P. Mikkelson (curator, Delaware Museum of Naniral History, Wilmington), and E. Lm-
Wasem (curator, Peabody Museum of Naml History, New Haven).
Conceming material contained in the chapter titled "A MORPHOSPATIAL
ANALYSIS OF MORPHOSPACES," I extend thanks to M. A. Savageau for comments.
Conceming material contained in the chapter titled "A PHYLOGENETIC SYSTEMATIC
ANALY SIS OF MATHEMATICAL CONCHOLOGY," 1 gratefully ac knowledge D. L.
Hull and M. P. Winsor for replicating their ideas; S. C. Ackerly, G. R. McGhee Jr., and
R. D. K. Thomas for analysing my verbose descriptions of mathematical models; and M.
D. Rausher, J. G. Kingsolver, and T. Garland for suggestions, comments, and encouragement.
I thank John Machin for his ideas conceming allometric aspects of aperture scaling and for his vibrant enthusiasm toward science, which sprang fiom him and ont0 the pages of this dissertation. Jim 'Bad Moon' Rising sat beside me in JMB 170 for 5 years -- he never
completed a single problem set! However, he was an outlier on the baseball diarnond and
provided jocular camaraderie at course and cornmittee meetings -- at the Faculty Club!
Joe Repka provided many wonderfui memones, both academically and personaiiy.
He always was willing to help me find solutions to my mathematical quenes in myself.
He and his wife Debbie made me yeam for yuletide and reminded me of what terrible
cooks my mother and sisters are.
Jim, Joe, and Malcolm Telford helped to create JMB 170, and 1 was fortunate
enough to have been involveci. What a learning experience it was (for us anyway)!
Fittingly, the sinistral simdations contained in this dissertation are dedicated to them.
1 wholeheartedly thank Malcolm. In addition to participating in loquacious
lunchtirne conversations. procuring a pleasurable atmosphere in which to pontificate, providing financial and moral support, persevenng through broken noses. in tema tional espionage, and bullets through laboratory windows, Malcolm's mental alacnty prohibited my tementy and aided my perspicuity, thereby prohibiting the production of an intellectually jejune dissertation that might have resuhed from my circumlocutious verbigerations. A mie nanval philosopher, logicd thinker, kind soul, and excellent travelling cornpanion, to be mentored by Malcolm provided the oppominity of a lifetime; fortunately for me, it was my lifetime. TABLE OF CONTENTS
.. AB STRACT,...... ,..,...... -11
ACKNOWLEDGEMENTS. .... ,...... iv .- TABLE OF CONTENTS...... vu
LIST OF TABLES ...... ix
LIST OF FIGURES ...... x .. LIST OF PLATES...... XII
PREFACE...... xm m..
OVERTURE...... 1
1. A MORPHOSPATIAL ANALYSE
OF MORPHOSPACES
Morphological Spaces ...... 3
II. A PHYLOGENETIC SYSTEMATIC ANALYSIS
OF MATHEMATICAL CONCHOLOGY
Mathematical Modeling & Cladis tic Methodology...... 30
III. A CLADISTIC ANALYSIS
OF SPECIES OF LAMBIS
Cladistic Methodology Reiterated...... 78
IV. ON 'CONCHYALLOMETRY'
vii Mathematical RemodeLing ...... 1 34
V . ONTOGENIC & CLADISTIC MOWHOSPACE .. Morphological S pace Revisited...... 146
RECAPITULATION...... ,,...... 182
LITERATURE CITED ...... ,..,...... ,.,...... 185
Appe ndix 1. SPECIMEN EXAMINATION ...... 210
Appendix II . SCANNING ELECTRON MICROSCOPE TECHNIQUES USED ...... 222
Appendix III . RADIOGRAPHIC TECHNIQUES USED ...... *....*...*.....226
Appendix N . MATERIALS TESTING TECHNIQUES USED ...... 227
Appendix V . INFORMATION MATR IX ...... -228
Appendix V T. CLADISTIC CODING TECHNIQUES U SED ...... 252
Appendix Vn . MORPHOMETRIC SHELL DATA ...... 257
Appendix VI11 . CODING AND USING SHEU PARAMETERS CLADISTICALLY.... 278
Appendix IX . AS YMMETRIC COILING ...... 289 LIST OF TABLES
Table 1.1. Uses of morphospace in the past 30 years ...... 25
Table 2.1. Data for cladistic analysis of shell models ...... 57
Table 3.1. Character states of species of the family Strornbidae...... 128 LIST OF FIGURES
Figure 1.1. Use of morphospace in the past 30 years ...... 26
Figure 2.1. Parameters used in various mathematicai shell models ...... 34
Figure 2.2. Two cladograms of mathematicai shell models ...... 62
Figure 2.3. Example of the distinction between fom and growth ...... 69
Figure 3.1. Hypothetical Archetypical Lambis ('HAL') ...... ,...... -79
Figure 3.2. Effect of coding polymorphisrns as unobserved character srates for
ciadistic analysis...... 109
Figure 3.3. Separation of polymorphic terminal taxa into monomorphic subunits for
cladistic analysis...... 1 12
Figure 3.4. Denticle of a laterai tooth (character 3)...... 117
Figure 3.5. Verges of some species of Strombidae (character 8)...... 121
Figure 3.6. Mouths of some species of Stmmbidae (character 10)...... 122
Figure 3.7. Cladogram of larnbis-like species ...... 130
Figure 5.1. T, H, V Ontogenic Morphospace for lambis-like species...... 152
Figure 5.2. O, H, V Ontogenic Morphospace for lambis-like species...... 153
Figure 5.3. O, T, V Ontogenic Morphospace for lambis-like species...... 154
Figure 5.4. O, T, H Ontogenic Morphospace for lambis-like species...... 155
Figure 5.5. Functional outgroup analysis...... 158 Figure 5.6. Coded parameter values mapped ont0 the cladogram of lambis-like
species...... 162
Figure 5.7. Geomeaic algorithm for positioning cladogram nodes in threeàimensional
morphospace...... 163
Figure 5.8. T, H, V Cladistic Morphospace for lambis-like species...... 166
Figure 5.9. 0, H, V Cladistic Morphospace for lambis-like species...... 167
Figure 5.10. 0, T, V Cladistic Morphospace for lambis-like species...... 168
Figure 5.11. 0, T, H Cladistic Morphospace for lambis-like species...... 169
Figure 5.12. Ontogenic-Cladistic Morphospace used to infer ancesaal tracks ...... 172
Figure 5.13. Mapping of character states onro a cladogram consmcted hmthose
character states...... -174
Figure 5.14. Ontogenic-Cladistic Morphospace for some larnbis-like species...... 177
Figure 5.15. Ontogenic-Cladistic Morp hospace for some lm bis- like species...... -178
Figure 5.16. Ontogenic-Cladistic Morphospace for some lam bis-like species...... 179
Figure 5.17. Ontogenic-Cladis tic Morphospace for larnbis-like species...... 181
Figure AVI. 1 . Cladogram of species of Strombidae...... 256
Figure AVIII .1 . Variables and parameters used in analyses of lambis-like species...... 279
Figure AIX .1 . Coiling symmetxies...... 291 LIST OF PLATES
Plate 3.1. Scanning elecmn micrograph of a taenoglossate radula...... 81
Plate 3.2. Scanning elecmn micrographs of a taenoglossate radula ...... 82
Plates 3.3. 11. Shells of the genus Lambis ...... 98
Plate 3.13. Variable number of flanking cusps of central teeth of species of
Strombidae...... 114
Plate 3.13. Types of cusps of radular teeth of some species of Strombidae
(character 6)...... 119
Plate AI1 .1 . Scanning electron micrographs of unused and used ends of a
radula...... 224
Plate AIL2 . Manipulation of radulae for maximally informative examination ...... 225
xii PREFACE
Chapters 1 ("A MORPHOSPATIAL OF MORPHOSPACES") and 2 ("A
PHYLOGENETIC SYSTEMATIC ANALYSE OF MATHEMATICAL
CONCHOLOGY") of this dissertation are derived hmpublished manuscripts (Stone
1997a and Stone 1996a, respec tively). They were modified to provide greater unifomity among the chapters. Throughout this dissertation, measurable variables or variables in equations appear in outhed font and parameters appear in bold font. OVERTURE
A carefully constructed symphony is that collage of sounds emanating fiam percussion, wind, and string instruments that is represented as a collection of symbols on a staff- The panicular sounds emitted by any individual instrument cm be separated from the collective sounds of the other instruments and may elicit pleasure within a particular listener, but it is the hmony of sounds that conveys the composer's message. So it is with this mgnwn opus. The results contained in this composition emanate from three complementary instruments: morphological space, mathematical modeling, and cladistic methodology. Each of these instruments is used separately from the others to produce results that are interpretable individually by a particular reader, but it is the harmony of results that is the message of this work. Comparable to a symphonie score, that harmony is manifested as a collection of symbols and mathematically defined cwes contained in a
In this dissertation a methodology for analysing the morphological evoluuon of groups of organisms is developed. The combination of analytical instruments can be orchestrated to provide a novel approach to the reconsauction of ancestral forrns (shapes and sizes; defined subsequently, p 66). Species in the gastropod genus Lambis are analysed to illusrrate the approach, but this particular choice is of no significance to the Between this "OVERTURE" and the "RECAPITULATION," the three anaiytical instruments are innoduced and performed in a fugue-like manner. A morphospatial anaiysis is used to describe morphological spaces (in the chapter tided "A
MORPHOSPATIAL ANALYSIS OF MORPHOSPACES"), while cladistic methodology is used to describe mathematicai models (in the chapter titled "A PHYLOGENETIC
SYSTEMATIC ANALYSIS OF MATHEMATICAL CONCHOLOGY"). In the ensuing chapten, these instruments are applied to species of hbisin reverse order: cladistic methodology in the chapter titled "A CLADISTIC ANALYSIS OF SPECIES OF
LAMBIS," mathematical moùeling in the chapter titled "ON 'CONCHYALLOMETRY'," and morphological space in the chapter titled "ONTOGENIC & CLADISTIC
MORPHOSPACE." Harmony emerges in the "RECAPITULATION." A MORPHOSPATIAL ANALYSIS
OF MORPHOSPACES
Mor phological S pace
D'Amy Thompson has been described as "the most influential biologist ever left on the fringes of iegitimate science'' (Gleick 1987, p 199). Bookstein (1977) began the Richard
Bellman honourary issue of Mathematical Biosciences by paying homage to Thornpson.
In addition to an eloquent review of Thompson's mathematical approach to the study of the shapes of organisms, Bookstein provided a thorough recounting and elaboration of the chapter titled "On the Cornparison of Related Forms" from Thompson's opus, On Growth and Fom (1917, 1962). Bookstein claimed that Thompson's work had failed io found a discipline and that Thompson's rnethodology had failed to change the face of any field.
Nevenheless, Bookstein suggested that Thompson's approach still had potential as a morphometrical procedure because of its purely geornetx-ical nature. In this chapter, a relation between Thompson's method of comparing related forms and the investigation of rnorphological space is demonstrated. Contrary to common perception, Thornpson's ideas have infringed upon the works of several modem biologists. THE USE OF MORPHOLOGICAL SPACES
Bookstein (1977) provided an excellent review of work by several researchers who used
Thompson's (19 17) technique of coordinate grid msfomations. No recapitulation will
be attempted here. In ensuing sections of this chapter, a correspondence between
coordinate grid aansformations and sequences of points in Empincal Morphospace
(defined subsequently) is shown. This is accomplished by the presentation of applications
of morphological spaces in the past 30 years (approximately as they appeared
chronologically in the literature -- this section), the identification of features shared by
subsets of these applications to classify different types of morphological spaces (in the
section titled "WHAT IS A MORPHOSPACE?"), and the drawing of parallels between the
use of coordinate grids and Empirical Morphospaces in the analysis of fom, by reference
to a fanciful morphospatial analysis (in the section titled "A SPACE OF
MORPHOSPACES"). On the basis of the results of this exercise, it is concluded that
morphologists who study shape aansformations by investigating Empirical Morphospaces
are adherents of Thornpson. The exercise also permits a description of the types of
morphologicai spaces contained in subsequent chapters of this dissertation.
The Filling of Coiled-Shell Morphospace (Raup 1966)
One of the best known examples of a morphological space is Raup's (1966) description of coiled shells. He modeled shells as gnomonic structures (Thompson 19 l7), wherein 5 overall shape remained invariant as size increased. His mode1 consisted of a generating curve (geomeaic shape) that traced out the surface of a shell by revolving about an imaginary axis (the 'coiling axis') and following a logarithmic spiral in space. The amaction of this mode1 was that the mathematical desmption of a shell was reduced to only 4 parameters. The shape of the generating curve was defined by the parameter S. In general, the generating curve could assume various shapes (values of S), but Raup simplified it to a circle (S = l), thereby further reducing the description of shells to only three parameters. As the generathg cune revolved in space, it expanded geomeaically in its linear dimensions. The rate of this geometric increase of size was govemed by the parameter 'expansion' (W). The rate at which the generating curve travelled dong the coiling mis with respect to its radial migration away from the coiling axis was determined by the parameter 'translation' (7'). And the ratio of the distances £Yom the coiling axis to the inner and outer edges of generating curves was quantified by the parameter
'displacement' (D). Different combinations of parameter values descnbed different shell foms, and Raup simulated these, using a computer.
Raup used the parameters W, T, and D to define axes of a mathematical space.
By measuring values of shese parameters hma variety of specimens, he mapped different shell types (planispiml foms, helicoid foms, brachiopods, gastropods, and pelecypods) into the space. The different shell types occupied dismte, nonoverlapping regions and, thus. were separated into morphs. The texm 'morphospace' seems a natural term to have used to describe the space. Raup (1966, 1967) interpreted the disjunct, 6 nonfilling distribution of points in morphospace as possible consequences of geomeaical and historicai factors and suggested that morphospaces could be used to investigate the evolution of organisms.
Geometric Bivaived-Shell Morphospace (McGhee 1980; Savaui 1987)
McGhee (1980) developed a morphospace for brachiopod shells, using a constructional morphologie analysis and a 'Raupian' geomeaic model. He plotted a contour diagram for data represen~gmeasurements of shells hm324 genera of biconvex articulate brachiopods to indicate the frequencies of various realised morphologies in morphospace.
The fiequency distribution revealed that brac hiopod s hells approximate sp hem and, thereby, are designed to minimise shell surface maand maximise internai volume while remaining arciculated (McGhee 1980).
As did Raup ( l966), Savazzi ( 1987) considered geometric propenies charactenstic of coiled shells, as well as two contrasting functional constraints characteristic of bivalved shells: umbones must be positioned far enough apan frorn each other so that they cm permit adequate shell gape, and growth of the axial margin must be limited to prevent hyperextension of the ligament. Using a morphospace, Savazzi (1987) postulated morphological pathways by which these factors are achieved or circumvented by organisms possessing bivalved shells. 7
Body-Shape Meaic Space and the Differentiation of Vertebrates (Cherry et al. 1978,
1982)
Cherry et al. (1982) compared 4 metncs used to analyze differences arnong body shapes of groups of vertebrates: the M statistic (which quantifes painvise differences between mean relative trait lengths of species; Cherry et al. 1978), the Mahalanobis distance, the
Manhattan distance, and the proportionai distance. The M statistic and the Mahalanobis distance take into account inaataxon variability (and require calculation of means and variances) of traits, in their computation; the Manhattan distance is simpler in its formulation but, because it is unweighted, it emphasises changes in large traits; and the proportional distance weights smaller traits more equitably but is affected by the relatively large errors inherent in measurements of snall traits. Cherry et al. made more than 20000 simple measurernents on 184 taxa of mammals, lizards, and frogs and found that the proportional distance and the Manhattan distance were the most reliable merrics, in a statisticai sense. They also found that a strong correlation existed between these meaics and distance in taxonornic hierarchies and, therefore, concluded that simple body shape differences could be used as indicators of overall morphological differences. Furthemore, because they used only a few traits from al1 parts of the body, they found that it was unnecessary to correct for intextrait correlations in the differentiation of groups. The implications of that study are that srnaii numbers (e.g., 8) of simple, Linear quantitative traits, representing ali pans of the body, suffice to distinguish taxonomic categones in
Body-Shape Meaic Space. 8 Realised Cenon-Shell Morphospace and Geometrical Constraint (Gould 1984; Stone
1996b)
Gould (1984) examined shell shape and size diveaity within the land mail genus Cenon
and postulated that certain shell forms might be precluded by saucturai constraints. The
morphospace that he produced was an empirical map of the realised ranges of shell
heightxidth ratios @:d) for three arbitrarily defined size classes of Cerion. Gould found
that "normal"-shed (30 IB + d 1 50 mm) Cerion shells were constrained away from
occupying that pomon of morphospace representing long, narrow "smokestack" forms (h:d
2 3.0), and he atmbuted this preclusion of "smokestack" morphospace occupation to the
channelling effect of the allorneaic pwth charactenstic of Cerion shells, in particular,
and properties of spatial geometry, in general.
Stone (1996b) reexamined Gould's (1984) definitions and defined a shell h-d
Morphospace. On the basis of ranges of values realised in Cerion specimens, Stone quantified the areas of regions of h-d Morphospace that would be occupied by various
foms if variation were homogeneous and isotropie. That analysis revealed that, indeed, if
Cerion had radiated unifomly from a "normal" ances tor, "smokestack normals" should represent 10% of realised foms. Using a computer-graphical simulation mode1 of shells,
Stone mapped geomeaic variations of a "normal" Cerion shell into every region of the h-d
Morphospace. This falsified the (fomal, structural) geometric component of Gould's
(1984) hypothesis. The (his torical) phylogenetically constraining allometric growth 9 component and (hinctional) ecological considerations (Cain 1981) remain as possible
explanations of the precluded evolution of "smokestack" forms.
Stratigraphie Filling of Ammonoid-Diversity Morphospace (Saunden and Swan 1984)
Saunders and Swan (1984) performed principal components analyses on parameaic and descriptive variables, in an analysis of morphological diversity of mid-Carboniferous ammonoids. Saunders and Swan distinguished 8 morphotypes in principal component
(PC) space. Then, by examining the occupation of PC space throughout 8 successive
stratigraphic levels (chosen on the basis of biosuatigraphic correlations among three well- studied successions: the Namurian sequence of Great Britain, the Ozark Shelf sequence of
Arkansas and Oklahoma, and a sequence in the South Urals), they were able to postulate phylogenetic, functional, and ecological explanations for distribution patterns of ammonoid morphotypes in space and rime. For exarnple, the authors found that there was a marked decrease in morphological diversity of ammonoids from smtigraphic levels 2 and 3 to
Level 4, presurnably as the result of receding sea levels. Saunders and Swan also found that the overall range of forms in morphospace occupied by ammonoids in level 8 is as broad as it is in level 7, but that ammonoids from level 8 occupy morphospace more sparsely. This indicates that, although the range in morphological divenity remained the same, the rnorphological diversity within that range declined in level 8. 10 Landrnark Morphometrics Morphospace and Shape Change (Bookstein et al. 1985;
Bookstein 1991; Tabachnick and Bookstein 1990; Zelditch et al. 1993)
During the past two decades, Bookstein (Bookstein et al. 1985; Bookstein 1991 and references therein) has developed rnorphomeaic techniques based on landmark data, with the explicit intention of describing shape change in geometrical terms (Bwkstein's techniques are a subset of Kendall's use of Shape Space, though Kendall's techniques may be unsuitable, in a biological sense (Bookstein 199 1)). Books tein's (1977) contribution to the Richard Bellman honourary issue of Mathematical Biosciences (alluded to at the beginning of this chapter) reviewed works using Thompson's coordinate grid transformations. More recently, Tabachnick and Bookstein (1990) and Zelditch et al.
(1993) have combined the concept of a morphospace with the use of landmark data, in the analysis of shape.
Tabachnick and Bookstein (1990) analysed planktonic foraminifera hmthe
Miocene (Globorotalia), using landmarks obtained from spiral and apertural views. After defining a baseline, using two landmarks, and interpreting ail other landmarks as moving with respect to this, they quantified shape changes, using pairs of shape (x. y) coordinates.
Principal components analysis of shape coordinates resulted in vector diagrams in
Landmark and Chamber-Shape Morphospaces, which described shape while excluding size effects. Tabachnick and Bookstein found that, in Landmark Morphospace, individuals were distributed continuously in ellipses and showed few stratigraphie changes; whereas in 11
Chamber-Shape Morphospace, the distribution was continuous but nonelliptical and exhibited stratigraphic changes.
The distribution of named species in Chamber-Shape Morphospace was consistent with stratigraphic evidence and hypotheses of evolution: G. zealandica had been interpreted (Snnivasan and Kennet 1981) as origina~gearlier than the other species that
Tabachnick and Bookstein analysed and was iocated at high values of principal component 1 (PCI),whereas later forms progressively filled regions of lower values of
PC1. Tabachnick and Bookstein also pointed out that the distribution of individuals in morphospace was uninformative in an evolutionary sense: it showed no discrete groups, no evidence for the branching of one entity into othea, and no evidence for the gradua1 change of the central tendency of a single entity. Instead, they proposed that analyses of distributions in morphospace provide means of descnbing diversity patterns in space and time and in terms of variation, rather than in terms of taxonomie names.
Zelditch et al. (1993) used a thin-plate spline as a mode1 to describe the deformation of landmarks on rodent skulls. Conceptually, this technique analogises shape changes to the surface bending energy of a hypothetical, infinitely thin metal plate on which certain points are landmark homologues situated vertically above the system of original shape coordinates (Zelditch et al. 1992). Components of residuals of unifom
(homogeneous or affine) mnsformations -- those that describe shape change without bending -- are called 'partial warps' and can be converted into mean trajectones surrounded by ellipses, as diagrammatic means of describing shape changes. Using this
mode1 on a growth series of skulls of the Cotton Rat Sigrnodon fuiviventer, Zelditch et al.
(1993) identified three types of developmental constraints: (1) 'canalization,' or age-
detennined constraint to relatively constant form -- diagrammatically, this corresponded to
a shnnking ellipse; (2) 'chreods,' or loss of degrees-of-fieedom (pnmarily orthogonal to
the mean trajectory) by coordinated character variation -- diagrammatically, this
corresponded to an ellipse with a shrinking minor axis; and (3) 'opposition,' or reduction
of variance dong the mean tmjectory -- diagrarnmaiically, this corresponded to an ellipse
with a shnnking major axis.
Evolution in Polyplacophoran-Shape Morphospace (Watters 1991)
Watters (1991) consnucted a morphospace for chitons, based on simple, bivariate
allomenic relations between linear variables (e-g., length and width). He examined
vermiformity within the trio of families Leptochitonidae, Ischnochiionidae, and Chitonidae
and in the families Mopaliidae and Cryptoplacidae. By comparing the orientation of their corresponding regression lines in morphospace, Watters showed that Mopaliidae and
Cryptoplacidae differ from the trio of families primady in absolute size (an incmase in
the value of the allometric coefficient). He interpreted this as an exarnple of Cope's Rule
(a trend of increasing size within a lineage) following the Pemo-Triassic, during which the majority of chiton genera went extinct. The progressive increase in body size decreased surface area to volume ratios (reducing desiccation) and increased pedal surface 13 area (increasing stability and tolerance of wave-action), thereby enabling the chitons to occupy new, intertidal habitats.
Fish Ecomorphospace (Winemiller 199 1)
Winemiller (199 1) analysed 30 morp hological features of dominant fis h species from lowland strearns and backwater habitats in 5 widely separated geographical regions. using principal components analysis. Morphological features were chosen carefully to act as surrogates for ecological data, using measurements such as relative body width, body depth, fin height, area of caudal and pectoral fins, and relative head length. Each measurement analysed was related to some aspect of feeding, swimming behaviour, or habitat. As a result, Winemiller argued, the principal components analysis produced an
Ecological Morphospace ('Ecomorphospace').
Winemiller pointed out the importance of considering the overall arnount of morphospace occupied if an ecological perspective of dispersion patterns is assumed. As species numbers increase locally, the average nearest-neighbour distance can remain constant while the volume of morphospace occupied increases; the average nearest- neighbour distance cm decrease while the total volume of morphospace occupied remains the sarne, but the pattem of dispersion becomes more homogeneous; or the nearest- neighbour distance cm decrease while the volume of morphospace occupied remains constant or decreases, and the pattern of dispersion becomes more random. Therefore, 14 high levels of species packing in morphospace can be associated with increased resource sharing by species possessing generalised anatomical features, as opposed to the divergence that would result fmm resource partitioning.
Anatid-Feeding Morphospace and the Evolution of Performance (Kooloos and Zweers
1991)
Kooloos and Zweers (1991) modeled pecking, filter feeding, and drinlang mechanisms of waterfowls. For each mechanism, a simulation mode1 compnsed of 4 elements was developed: storage capacity of the rostral mouth cavity, transport capacity of the rostrd mouth tube, storage capacity of the caudal mouth cavity, and transport capacity of the caudal mouth tube. Using the simulation rnodels, the investigators considered how changes in each element, in turn, affected the amount of food obtained by each mechanism during 1 s of performance. Combining graphs of performances for various values of the elements in the models, Kooloos and Zweers constnicted a morphospace, a space representing the range of feasible modifications of mouth design.
Taking an unspecialised, pigeonlike or chickenlike pecking system, similar to but simpler than that of a mallard (Anus plaryrhynchos), as ancestral, Kooloos and Zweers showed that there was a large arnount of morphospace available within which more elaborate functioning systems that still maintained adequate performance could evolve.
Furthemore, they explained morphologies and performances of other anatid feeding 15 systems as modifications of those found in mallards. In particular, they concluded that, to increase filter feeding performance, the volume of the rostrai mouth cavity must increase; this necessitated a widening, flattening, and elongation of the beak, as well as a phase shift in rnaxillar motion with respect to mandibulx and lingual motions. Also, they concluded that, to increase pecking performance, the transport capacity must increase; this necessitated a shortening of the rostral mouth tube via a shortening of the midportion of the mouth, giving the beak a shortened, stout appearance.
Analyses of the Temporal Filling of Morphospace (Foote 1989, 1990, 1992a. 1992b,
1993a, 1993b, 1994, 1995)
In a series of interesting papers, Foote analysed temporal changes in occupation of morphospace by several groups. FoHowing Iaanusson (1981), Runnegar (1987), and
Gould (1989, 1991), Foote (1993b) used the term "disparity" to descnbe the morphological variety within a group, and, following Cherry et al. (1982), quantüied disparity as mean dissimilarity (distance in morphospace) among members of a group
(Foote 1992a, 1993a. 1993b, 1994). The advantage of using this quantification is that mean dissimilarity is insensitive to sample size, whereas other measures, such as volume of morphospace occupied, become positively biased with increased sample sizes (Foote
1992a, 1993a, 1993b, 1994).
In his initial analyses, Foote (1989, 1990) used the coefficients hmFourier 16 descriptions of North American ailobite cranidia to consauct a 12-dimensional
morphospace. He then used a nearest-neighbour analysis of points to show that
morphospace û occupied more continuously by trilobites from the Cambrian than by trilobites from the Ordovician. The increased clustering of Ordovician trilobites, however, is the result of an expansion of the realised morphospace during that time epoch - the absolute nearest-neighbour distance actually increases. Thus, trilobites hmthe Cambrian occupy a relatively smaller amount of morphospace homogene~usly~whereas their
Ordovician descendants occupy a larger arnount of morphospace but with gaps. In other
studies, Foote ( l992a) has shown that the echinoderm subphylum Blastozoa reac hed their zenith of disparis, relative to divenity early in their history, prior to their peak in taxonomic diversity, and he found that a similar trend existed for crinoids from the
Ordovician-Devonian and the entire Paieozoic (Foote 1994, 1995).
Requisite to his analyses of particular groups are methods for exarnining distributions of points in time, and Foote has formulated several ways of analyzing morphospaces temporally. Rarefaction (Sanders 1968; Raup 1975; Foore 1992b) is a technique that quantifies morp hological vanety (here, total range in a morp hological variable) while accounting for taxonornic diversity (number of species). Using rarefaction techniques, Foote (1992b)concluded that trilobites from the Middle to Late Ordovician occupy a larger range of morphospace per unit taxonornic diversity than do ailobites from the Middle to Late Cambrian and that the echinodenn class Blastoidea from the Permian had a greater ratio of disparity:taxonomic diversity than did theu predecessors in the 17
Devonian. He also reanalysed the Namurian ammonoid data previously analysed by
Saunders and Swan (1984). Using rarefaction techniques, Fmte (1W2b) comborated
quantitatively two of the findings made by Saunden and Swan (1984; discussed
previously, p 9), which they had visuaily interpreted from PC space plots, and
reinterpreted two others: morphological diversity increased, as opposed to having
remained constant (Saunders and Swan 1984), during biostratigraphic levels 4 and 5; and
diversity remained relatively constant, as opposed to having increased sharply (Saunders
and Swan 1984), in biostratigraphic level 6 as cornpared to biostratigraphic level 5. Foote
(1993b) also presented two methods for partitioning group disparity into components
attributable to subgroups: one merhoci used average squared distances of individual points
from the overall group centroid and, therefore, was analogous to standard analysis of
variance tests; the other method involved comparing the disparity of a group with its disparity after each subgroup was omitted sequentially and, therefore, was analogous to jackknifing across subgroups.
Coleopteran Morphospace and Modes of Evolution (Drugmand et al. 1993)
Drugmand et al. (1993) used principal componenrs, canonical discriminant, and cluster analyses to determine relative positions of 12 coleopteran taxa in a morphospace. Twenty measurements, representing many different parts of the body, were used. The results of the cluster analysis comborated cladistic branching patterns; the discriminant andysis correctly reclassified 97% of the specimens as members of their respective original genera; and the p~cipalcomponents analysis produced overlapping 95% confidence
ellipses in PC space. The morphological continuum evidenced by the principal
components analysis led the authors to conclude that species compnsing the 12 genera of
Cryptobiina have followed a neo-Danvinian mode of evolution -- by small, progressive
leaps.
Echinoid Functional Morphospaces (Moore and Ellers 1993; EUers 1993)
Moore and Ellers (1993) used a functional morphospace to describe the stability in wave- swept environments conferred to sand dollars by their possession of peripherai belts of calcite. The morphospace was defined by two dimensionless morphological parameters: k,, the areal density, described the ratio of the relative mass per unit area of the peripheral region to that of the central region of an idealised circular sand dollar; and f, the location number, quantified the fraction of the radius of the sand dollar at which the peripheral calcite belt began. Within the rnorphospace, values of rotational inertia per mass per radius squared (the inertia number) were plotted as a contour map for various values of k, and f, forming ridges of stability and valleys of instability. Moore and
Ellen demonstrated that, in addition to an increase in overall weight, the distribution of calcite in a peripheral belt increased a sand dollar's rotational inertia and decreased the probability of dislodgement in wave-swept environments.
Independently, Ellers (1993) used a mechanicai mode1 of sea urchin growth to 19
consmict a morphospace. The mode1 made use of the analogy between the shape of a
drop of liquid sitting on a flat surface and the shape of an urchin test (Thompson 19 17).
The morphospace was defined by two terms that describe the shape of drops of liquid:
the gradient of pressure with respect to depth divided by intemal pressure, and r, the
apical curvature. Curved lines in the two-dimensional morphospace represented different
urchin test outlines.
Skeleton Space and the Examination of Structural Constraints (Thomas and Reif 1993)
In an intriguing study, Thomas and Reif (1993) defined a 7-dimensional morphospace, based on fundamental geomeaic and physical properties of skeletal materials. Using this
"Skeleton Space," they examined strucniral constraints, engineering principles that govem development and physical limitations prescribed by function, of animal skeletons. Thomas and Reif concluded that skeletal complexity may exhibit no inverse correlation with evolutionary age, that vertebrates and molluscs are more diverse morphologically than are arthropods, and that terrestrial and aerial modes of life physically constrain the range of skeletd designs usable by organisms in those habitats. From the results, they also inferred that the evolution of skeletal design is govemed by skeletal elements, which are representable in Skeleton Space as fixed-point amactors. Walks through Plant Morphospace (Niklas 1994)
NMas (1994) consmicted a morphospace containing 200000 'phenotypes' that mimicked
the shapes of early vascular land plants. Each phenotype was simulated graphically on a
computer, using only 6 variables. Beginning with the oldest vascular land-plant
phenotype, known from Silurian fossil remains of Cooksonia, Niklas used a computer-
dnven aigorithm to guide walks through the morphospace. Each walk consisted of N
steps, and each step represented a morphological transformation to a more-fit phenotype.
Fitness was assessed by a plant's mechanical stability, ability to intercept light, and ability
to reproduce. The volume of morphospace that had to be searched before the next more-
fit phenotype was found was quantified by its diameter. When the cornputer-driven
algonthm identified two or more phenotypes with equivalent fitness, the walk was allowed
to branch. A walk was complete when al1 phenotypic maxima (within a single-function
landscape) or dl phenotypic optima (wirhin a multifunction landscape) were obtained.
Niklas found that the nurnber of phenotypes that were able to reconcile conflicting morphologicai requirements increased in proportion to the number of functional obligations an organism had to perform and that waiks in multitask fitness landscapes required fewer but larger phenotypic rransformations than those through single-task fitness landscapes. In addition, the multitask optima had lower ovemil fitness in iess steep landscapes and occupied a greater volume of theoretically available morphospace than did single-task maxima. These hdings support Sewall Wright's (Provine 1986) conception of evolution as a search for adaptive peaks.
Other Uses of Morphospace
McGhee's (1991) account of several morphospatial analyses includes discussion of colony
form in Bryozoa (McKinney 1981; McKinney and Raup 1982; Cheetham and Hayek
1983), planispird foraminiferal test growth (Berger 1969; De Renzi 1988), graptolite
growth (Foney 1983), skeleton latticework in silicoflageUates (McCartney and Loper
1989), and stromatoporoid morphology (Kershaw and Riding 1978). McGhee also
considered the similarities berween Dobzhansky's (1970) interpretation of Wright's
(Provine 1986) concept of adaptive landscapes (multidimensional spaces consisting of al1
possible combinations of genes) and morphospaces. McGhee noted, however, that the
concept of adaptation may play no part in the construction of morphospaces, in which
case the absence in nature of hypothetically possible forrns could be explained equally
well from a neutralist point of view as it could from an adaptationist view: evolution may
have yet to produce certain hypothetically possible forms, or these forms rnay be
nonadaptive.
WHAT IS A MORPHOSPACE?
That the concept of morphospace has been used to study a vast range of organisms demonstrates its versatility as a morphometrical tool; it is indicative of the ingenuity of 22 the morphomeaicians who have employed morphospaces; but it also is indicative of the lack of a formai defmition for the term morphospace. The lack of a mathernatically rigorous definition. for instance, has resulted in a plethora of procedures used to defme morphospace parameters, including simple measurement, linear regression, multivariate statistical analysis, mathematical modeling, and even determination of dimensionless ratios.
Purists might claim that the realm of a scientific discipline must be clearly demarcated; however, fuzzy boundaries might be the saength of certain scientific disciplines (Mandelbrot 1977). Some researchers find the flexibility of the terni morphospace particularly attractive; nevenheless. sorne also recognise that a certain amount of decomrn could be established by at Ieast attempting to characterise what is meant by the term morphospace.
Several general descriptions of what is meant by the concept of morphospace have been given: citing Luli and Gray (1949), Bookstein et al. (1985, p 206) descnbed it as
"the arena for cornparison of real forms 10 other imaginable forms;" Savazzi (1990, p
196) described it as "a space containing dl geometrically possible [shell] shapes;" whereas
Gould (1991, p 420) described it as "the abstract (and richly multivariate) space into which al1 organisms may fit."
McGhee (1991) discussed the concept of morphospace in great detail. He concluded that there is a fundamental difference between morphospaces produced hm mathematical and statistical analyses of actual measurement data and those based on mathematical models. Because morphospace parameters composed of combinations of morphomeaic measurements are based on analyses of those measurements, the dimensional nature of the resulting morphological spaces changes with the addition or rernoval of specimens or measurements or both (e.g., principal components analysis) or with the use of different specimens in the measurement procedure (e-g., Fourier analysis).
McGhee (1991) called such spaces "Empirical Morphospaces." Empincal Morphospaces represent distributions of realised forms and can serve as the empincal basis of hypotheses of why particular shapes and sizes are observed in nature: variation (Savazzi 1987;
Tabachnick and Bookstein 1990), adaptation (Watters 1991; Moore and Ellers 1993; Ellers
1993), or modes of evolution (Saunders and Swan 1984; Winemiller 1991; Foote 1989,
1990, 1992a, 1992b, 1993a, 1993b, 1994, 1995; Dnigmand er al. 1993; Niklas 1994). In contrast, McGhee (1991, p 87) called a morphospace based on a mathematical mode1 a
"Theoretical Morphospace," which he defined as "the possible range of morphological variability which nature could potentialiy produce by ... systematically varying the parameter values of a geometric mode1 of form." A Theoretical Morphospace, thus, represents a set of foms (shapes and sizes) attainable by a group of organisms. Some of the fmns within a Theoretical Morphospace may have no counterpms in nature. These hypothetical forms are interpreted as gaps in the realised dismbutions of forms that are representable by morphospaces and cm form the basis of hypotheses of evolutionary constraint (Raup 1966; Gould 1984; Stone 1996b; Zelditch et al. 1993; Kooloos and 24
Zweers 1991; Thomas and Reif 1993) - organisms that cannot or have yet to evolve.
Hickrnan (1993a,b) extended the domain of morphospatial analyses by describing
"Theoretical Design Space" as a means of exarnining pnnciples of structurai and
functional biodiversity. The dimensions of Theoretical Design Space include ecological, behavioral, hinc tional, or physiological, in addition to morp hological aspects of organismal design. Hichan (1993a) illustrated how Theoretical Design Space permits the generation and testing of hypotheses of organismal design and evolution, using wheel space and trochoidean gastropod suspension-feeding space as examples.
A SPACE OF MORPHOSPACES
On the basis of the definitions presented in the preceding pages, the extent to which each of the mes of morphological space in the past 30 years represents Empirical Morphospace.
Theoretical Morphospace, and Theoretical Design Space can be scored arbitrarïly (Table
1.1). A plot of these data indicates that the use of morphological spaces has accorded well with the definitions, the studies clustering into distinctive groups (Figure 1.1 --
Theoretical Design Space potentially may subsume Empirical and Theoretical
Morphospaces in theory but seems not to have done so in practice): Skeleton Space,
Coiled-S hell Morphospace, and Bivalved-Shell Morp hospace are pmly theore tical and occupy that corner of this space of morphospaces. Fish Ecornorphospace is a Theoretical
Design Space, but it also has an empincal aspect to it; whereas Anatid-Feeding Space and Table 1.1. Uses of morphospace in the past 30 years.
Scores (quartiles) quantiffing the extent to which various uses of morphospace in the past
30 years represent Empincal Morphospace, Theoretical Morphospace, and Theoretical
Design Space. Uses of morphospace in the past 30 years
Coiled Shell Bivalved Shell Body Shape Cerion Shell Ammonoid Diversity Landmark Morphometrics Polyplacophoran Shape Fish Ecomorphospace Anatid Feeding Temporal Filling Coleopteran Echinoid Functional Skeleton Plant Thompson Figure 1.1. Use of morphospace in the past 30 years.
A plot of data in Table 1.1 reveals that the use of morphological spaces in the past 30 years accords well with definitions of Empirical Morphospace, Theoretical Morphospace, and Theoretical Design Space. Empirical
Theoretical
-
Theoretical Design 27 Plant Morphospace also are Theoretical Design Spaces, but they have both empirical and
theoretical aspects to them. These three uses of morphospace form a loose cluster in the
Theoretical Design region in the space of morphospaces. Echinoid Functional
Morphospace has theoretical, theoretical design, and ernpirical aspects to it; whereas
Ammonoid-Diversity Morphospace and Cerion-Shell Morphospace predominantly are ernpirical but have theoretical aspects to them. These three spaces bridge the gaps between the cluster of spaces in the Theoreticai region, the loose cluster of spaces in the
Theoretical Design region, and a large cluster of spaces in the Empiricai region in the space of morphospaces. And, if the use of coordinate grid transformations is included in the space of morphospaces, 'Thompson Space' falls among the cluster in the Empirical region (Figure 1.1).
The results of this entertaining analysis suggest that contemporary uses of
Empirical Morphospace are similar to Thompson's classic method of coordinate grid transformations ("Thompson" in Figure 1.1); or, in words, the parameters delimiting the axes of an Empirical Morphospace and the forms of the organisms that the values of these parameters represent paraIlel Thornpson's use of coordinate grid transformations, in the description of organismal fom.
For example, Thompson (1917, Fig. 122) considered the shapes of cannon bones in various ungulates as mathematical transformations of one another in Cartesian (X, Y) coordinates. Beginning with the cannon bone of an ox, with its longitudinal axis 28 onentated parailel to the Y-axis, if the X coordinate is rescaled by a factor of 2/3, a longer, slender cannon bone, resernbling that of a sheep, is obtained (Thompson 1917).
Thus, in classic Thompsonian transformation, a Cartesian grid is consmicted with reference to an actual morphology, and deformation of this grid is analysed with reference to transformations required in fitting the grid to other, actual morphologies. There is no morphology in the Canesian coordinat€ system, only the mutually orthogonal grid lines.
Therefore, Thompson's methodology was purely empirical (Table 1.l), and the fonns that his transformations represented equally could be represented by different values dong the axes of Ernpirical Morphospace.
Despite recognizing that it was not "the only story which Life and her Children have to tell," Thompson's (1917; 1962, p 9) sole purpose in writing On Growth and Fom was "to correlate with mathematical statement and physical law certain of the simpler outward phenornena of organic growth and structure or form." Few have followed directly in his footsteps, but his spirit dwells even today in Ernpirical Morphospaces.
ADDENDUM
In the two types of nonempincal morphospaces (Theoretical Morphospace and
Theoretical Design Space) dwells a spirit of a more ethereal nature. Actual morphologies can be referenced only with respect to forms represented by combinations of parameter 29 values (i.e., by points) in morphospace. Some of the morphospaces ased in the remainder of this dissertation are theore ticai. A PHYLOGENETIC SYSTEMATIC ANALYSIS
OF' MATHEMATICAL CONCHOLOGY
Mathematical Modeling & CIadistic Methodology
Ideas evolve. Unlike the situation with groups of organisms, however, sometimes the origin of each member in a group of closely related, published ideas can be localised precisely in space and time, permanently preserved as 'holotype specimens' in jomals and dissertations such as this. In such a situation, the relationships arnong published ideas within a discipline can be reviewed analytically, and the results obtained cm be compared to 'stratigraphie evidence' provided by journal articles to assess the accuracy and menu of the analytical techniques used.
In this chapter, major developments in the mathematical modeling of shells are reviewed. This is accomplished using cladistic analysis, treating each model as a species and various attributes of each model as its character States. Cladistics has proven a powerful tool for the reconsmiction of patterns of organic evolution, hypotheses that are represented as branching-line diagrarns ('cladograms'). By using cladistics. a concise, graphical summary of the individual 'species' that comprise the history of the discipline of shell modeling is provided Although the processes underlying the development of 31 scientific ideas may be only approximately andogous to the processes underlying the evolution of organic species, by interpreting branching patterns phylogenetically (Le., by considering them as phylogenetic trees), interesting relationships among the various models are revealed. Because, in the discipline under consideration. the origins of species are documented precisely, this exercise rnay be interpreted as a test of the appropriateness of an evolutionary model as a description of the development of scientific ideas.
INGROUP SPECIES
In a cladistic analysis, the group of interest is calied the 'ingroup.' Shell model species may be grouped ahistorically as cornputer-graphical models and non-computer-graphical models. For convenience, such a division is used in the species descriptions contained in this section.
Although its ongins cm be traced back to the works of Anstotle (Thompson
1917), the mathematical modeling of shells proper began with Moseley's (1838) geometric analysis. Since then, many morphologists have developed different mathematical models of shells, and, with the invention and increasing availability of cornputers during the past half century, the field has blossomed. Researchers have combined geornetric models with cornputer graphics to classify (Raup 1966) or anaiyze shells (Raup 1967; Raup and
Chamberlain Jr. 1967; Raup and Graus 1972; Bayer 1977; McGhee 1978, 1980; Okamoto
1984, 1988), for intellectual pursuiis (Lavmip and von Sydow 1974, 1976; Levmip and 32 L@vtrup 1988; ïllen 1982, 1989; Savazzi 1985, 1990, Ackerly 1989; Cortie 1989; Stone
1995a). and for sesthetic purposes (Fowler et of. 1992).
corn puter-Gra phical Models
Raup 1961-66
Raup (1961, 1962, 1966; Raup and Michelson 1965) pioneered the computer-graphical simulation of shells. Basing his model on equiangular spirals, Raup (1966) described shells as the result of the revolution of a generating curve about a coiling axis. His model consisted of 4 parameters: shape of the generaung curve (S), rate of whorl expansion
(W), displacement (D), and rate of translation (T).
For a shell that has its apex at the origin of a three-dimensional cylindricai coordinate system (with variables r, B. and z), Raup (1966) defined the r-value of a point on the generating curve with shape S as
where 4 is the angle of revoluîion about the coiling axis, r, is the radial distance frorn the coiling axis to the point on the generating curve when 8 is zero, and W is the rate of expansion (Figure 2.1). Raup's (1966) equation for displacement may be written as where r, and r,, are the radial distances to the axial and outer margins, respectiveiy, for any generating cwe (Figure 2.1). Displacement is determined to a large extent by expansion and, therefore, is an algebraically interdependent parameter (Schindel 1990).
Raup's (1966) equation for mslation may be written as
where z, is the value of the z coordinate after 8 / 2x revolutions of the generating curve, r-, is the radial distance to the centre of the initial generating curve, and W is the expansion (Figure 2.1 ; Okarnoto (1988) interpreted the denominator differently). From equation 2.3,
As expansion increases, translation decreases. Themfore, like displacement, translation is a function of expansion and an algebraically interdependent parameter.
Assuming a circula. generating curve (S = l), Raup (1966) ~sedthe remaining three parameters as axes to defme a mathematical morphospace, with which he exarnined Figure 2.1. Parameters used in various mathematical shell models.
Circles represent whorl cross sections. = Svertical shoriroatal w = router 1 ro D = Taxiai 1 router T = zzx (rcbnrral(W 1)) w = r2 / rl k = v, / v, n = normal vector of Frenet frame b = binormal vector of Frenet frame t = tangent vector of Frenet frame
router ---w.cIœ-œl)-I the distribution of parameter values exhibited by invertebrates that grow (or once grew) coiled shells. He also analysed shell coiling in ammonoids to examine the relationships between their shelis' geometries and functional constraints (Raup 1967); he determined equations for the calculation of volumes and centres of gravity of ammonoid shells (Raup and Chamberlain Jr. 1967); and he determined equations for the calculation of volumes and surface areas of logarithmically coiled shells (Raup and Gram 1972).
Despite its elegance, Raup's pioneenng model was limited in its scope. Inherent in his definitions, as a result of their being based on equiangular spirals, was a geometrically similar model of form: shape was invariant with changes in size. The parameters were constants and, therefore, had to be altered in an ad hoc manner throughout construction to produce anisometric forms (Raup 1966).
Stasek 1963
Though he provided no explicit mathematical description, Stasek (1963) described gnomonic growth in bivalves, using a model that, conceptually, was similar to Raup 1961-
66: a generating curve spiralling logarithmically around a fixed axis. Stasek conceded that most bivalve shells exhibit imprecise logarithrnic coiling and still less precise logarithmic changes in shape, and, hence, represent only approximate spiral growth.
Nevenheless, he identified several adaptations that may have resulted from approximate spiral growth of certain bivalve shells. Lgvmip et al. 1974-88
The parameters Raup (1966) used were ratios and referred to no particular aspect of
growth per se. His model drew shells in reverse, beginning at the body whorl and
moving up the spire (Raup and Michelson 1965). The Lavtmps and von Sydow wvtrup
and von Sydow 1974, 1976; Lgvmip and Lgvmip 1988; henceforth Lavtrup et al. 1974-
88) attempted to animate Raup's (1966) model. The parameters they used more closely
refened to the biological process of shell accretion: w, the rate of whorl expansion,
described the change in the size of the aperture; k represented the ratio of growth rates (v)
at two points on the growing mantle edge (the mathematical definition of this parameter
varied -- that contained in Lg~tnipand L~vtnip1988 is presented here),
p differentiated clockwise and counterclockwise coiling; and T' represented accretion in time (Lgvtnip and L@vtrup1988; Figure 2.1). Although it consisted of parameters that were modified with respect to Raup's (1966), their model still consisted of a generating curve revolving about a coiling mis.
Bayer 1977, McGhee 1978, and Savazzi 1985 (BMS 1977-85)
Bayer (1977) developed a shell model in which the coordinates describing the surface of a 37
shell were defined by difference equations. Because shell growth is a stepwise process,
Bayer's rnodel, containing mathematically discrete equations, produced realistic
simulations. Using his model, Bayer considered allorneaic aspects of septai growth in
am monoids .
McGhee (1978) reworked Bayer's discrete model, to describe the phenornenon of
bivalve sheii 'torsion' (a twis~gof the shell about the hinge axis normal to the antero-
posterior direction). Later, based on McGhee's interpretahon of Bayer's model, Savazzi
(1985) developed a cornputer program that used sets of equiangular helicospirals to model mollusc shells (Savazzi's definition for the variable y, differs slightly from McGhee's):
That model contained the parameters W, the whorl expansion rate. and H, the helical element, and the parametric variable 1, the incremental magnitude of each fmite growth step. Savazzi's W was the same as Raup's (1966) W, and Savaui's H, which connolled movement along the coiling axis, was similar to Raup's (1966) T. Savazzi constmcted the surface of a shell by connecting successive points along each helicospiral with line segments, forming a longitudinally striped, coiled cone. In addition, at successive growth increments, neighbouring points on adjacent helicospirals were connected by line 38 segments, forming closed polygons or rings. Each of these rings represented the aperture at that particular stage of conswction. The condition
ensured isometric shell simulations. However, following McGhee (1978), Savazzi was able to Vary the shape of the rings by varying the values of the parameters differentially dong the helicospirals. thus permimng allornetric scaling of the aperture. Hencefonh, these models are considered as a single species, BMS 1977-85.
McGhee 1980
McGhee (1980) developed a continuous mode1 that sirnulated anisornetric ontogenic variation in brachiopod shells. This mode1 still was based on equiangular spirals and
Raup's (1966) parameters, but McGhee (1980) used an exponential equation to modify the rate of expansion so that it was a function of age and defined a new parameter, the specific expansion rate, as
This allowed for anisometric scaling of the aperture. Using this rnodel, McGhee (1980) combined constructional morphology and geometry in his analysis of brachiopod shell 39 foms. He concluded that biconvex brachiopod shells are consmicted in a manner that minimises surface area and maximises volume while maintaining functional articulation
(McGhee 1980).
Illert 1982-89
An intnguing interpretation of shell fom was proposed by Illen (1982), in an attempt to answer "the fundamental question of theoretical conchology " -- w hether or not large-scale organizing pnnciples responsible for the spiral geometries of living creatures exist? His mode1 also described shell foms as the product of motion through space of a generating cume about a coiling axis, but his analytical approach, from a mechanical point-of-view, was original. He described the motion of a generating curve in a Cartesian coordinate system, using vector-valued functions pararnetnsed by the variables $, which described the revolution of the generating curve about the coiling axis, and 8', which described the angle subtended by the various points on the generating cwe about its centre of mas.
For a circular, inclined generating curve with radius b9 that has its centre of mass translaied a units along the x-axis and h units along the z-axis (Figure 24, the equation describing a shell surface was 40 From this function, nlen derived symmetry equations and energy functionals, in a manner
similar to the potential functions of electmstatic or spring mechanic theories. Considering
the centre of the spiral locus as an infinitely thin, infinitely extensible, perfectly elastic
wire, he applied Hooke's Law to it and derived a potential energy function. By applying
the conservation laws of classical physics to the mathematics of shell forms, nlen
determined that organisms optimise their shell strengths by growing their shells in the
shape of spirai cwes that resemble clocksprings! Thus, his model explained why spiral coiling was smicturally advantageous. Later, nlert (1989) incorporated Frenet bes
(Okamoto 1984-88, below) into his original model, which dilated the clockspnng wire into
tubular, spiralled surfaces, complete with onhociinal growth rings, corrugations, and flares.
Okamoto 1984-88
Okamoto's (1984) original tube model, which he formulated to analyze ammonoids, went unnoticed in a Iapanese journal of limited circulation in the West. Okamoto employed differential geometry and Frenet frames, so his mode1 made no reference to an external coordinate system. The Frenet frame, a reference system that moved dong with the growing mantle edge (represented as a circular cross section), consisted of three mutually orthogonal unit vectors, which specified the directions of growth of the shell surface in space (t. b, and n in Figure 2.1). Okamoto's (1988) growing tube model describeci growth as the motion of a circular cross section subject to three parameters: E, the radius 41 enlarging ratio; C, the standardised curvature; and Tt the standardised torsion. The
pararneter E described the rate of change of size of the tube. Exaemely large values of E
enlarged the tube greatly; such forrns characterise pelecypod valves. The pararneter C
represented the degree of bending and was between the values O and 1. When C was O
the tube grew straight; such forms characterise orthoconic cephalopods. When C was 1
the tube closed up, forming a toms. The parameter T represented the revolution of the
generating curve. The sign of T determined the direction of coiling (dextral or sinisual);
when T was 0 the tube was planispiral. Okamoto's (1988) model ~p~sentedthe motions
involved in accretion at a mantle edge, in conformity with biological reality.
Ackerly 1989
In an analysis of brachiopods, Ackerly (1989) proposed a moving reference frame,
kinematic model in which the aperture was the focus of the analysis. The growth lines on
shells indicate that shell accretion is a stepwise process. Descnbing growth as an episodic, discrete process in which an aperture migrated frorn position to position,
Ackerly's mode1 described a shell as the locus of points traced out by an apemue as it moved according to locally defined rules. The aperture nanslated, rotated, and dilated about the centre of its area, according to three parameters (y, a, and 6, respectively,
Figure 2.1). Ackerly chose the centre of the aperture as the landmark point, because it was unaffected by dilations. Because he made reference to no coiling axis, his model was more generai in terms of its coiling characteristics than were models that made reference 42 to fixed axes. The important aspect with the kinematic model, as far as parameters of coiling were concerned, was the decoupling of h-anslation, rotation, and dilation.
Come (1989) developed a comprehensive multiparameter shell model, which considered the orientation of the apertural plane, surface omamentation, and anisomen-ic variation during ontogeny:
(2-IO)
The parameter D' determined the direction of coiling; A represented the radial distance from the main ongin of a Cartesian coordinate system (x, y, z) to the origin of the aperture at 8 = 0; P' was the angle between the z-axis and a line from the aperture origin to the x, y, z origin; R was the length of the apem-generabng vector; s lepresented the angular rotation of the generating curve; 6' determined the "tilt" of the major axis of the ellipticd generating curve; R conmlled the azimutha1 rotation of the generating curve; p represented the "leaning over" of the aperture; and a' was the equiangular angle of the 43 spiral. Cortie simulated sculpturing of a shell's surface by superimposing a function
(containing the remaining parameters) that periodicaliy introduced "bumps" onto the generating curve, as it revolved around a fixed mis. He introduced ontogenetic variation by making the parameter that desmibed the equiangular angle of the spiral (a') increase with an increase in one of the polar coordinates (O). Biologically, this represented the minimisation of aperture area and maximisation of interna1 volume, as might be required by snails subject to predation through their apertures.
Savazzi 1990
Savazzi (1990) modified Okamoto's (1988) growing tube model with the inclusion a new parameter, P', the angle of post-torsion, which controlled the rotation of the circular mss section about its centre. In addition, to rnodel bivalve shells, Savazzi reinstituted the use of generating curves: he defined the initial shell aperture by choosing an arbitrary set of points dong its perimeter, then, at each growth stage, he scaled these points by a growth factor. Since an existing shell aperture was used to mould the next one, he named this model "the template method" of shell morphogenesis.
Fowler et al. 1992
Fowler et al. (1992) modifed Raup's (1966) model, using pararnemc equations (in the
Bézier form) to define the shapes of the generating curves. These complex curves were 44 revolved around a coiling axis in a three-dimensional cylindrical coordinate system
described by the variables 8, r, and z, producing veIy realistic surfaces. They also
incorporated Frenet fiames, to describe shell ornamentahon and sculpture. In addition,
they projected pigmentation patterns onto the surfaces of the shells, using a reaction-
diffusion model. In this model, the concentrations of an activator and substrate were
described by differential equations. Varying the parameters in the equations, Fowler et al.
altered the pattems on the shells. The images generated were almost indistinguishable
fiom real specimens.
Stone 1995
Stone (1995a) developed a mathematical model to explore the effects that changes in
aspects of growth have on shell fom. Conceptually, shell form was divided explicitly
into two components: the path that the aperture follows during growth, the "aperture
trajectory," and changes in the dimensions of the shell aperture throughout growth, the
"apemire scaling." Mathematically, shells were described as surfaces traced out by ellipses that followed aajectories and changed dimensions according to Huxley's (1932) allometnc equation. The parameters 'offset' (0)and 'horizontal expansion' (H) affected radial aspects of aperture tmjectones and scalings, whereas 'translation' (7') and 'vertical expansion' (V) affected abapical aspects. The cornputer-graphical program containing the model, CerioShell, was capable of sirnulating shelIs that grow allometricdly. Stone used
CerioShell to falsie a hypothesis of geomemc consaaint proposed by Gould (1984) to explain the absence of high spired, "smokestack normal" Cerion sheils.
Non-corn puter-Graphical Models
In addition to computer-graphical models, several non-computer-graphical models of sheils
have been fonnulated since the 'ongin' of Raup 196 1-66.
Kohn and Riggs 1975
Kohn and Riggs (1975) developed a geometric model to analyze Conw (cone) shells.
Their model consisted of 8 parameters: the shape of the generating curve, the rate of whorl expansion, the rate of translation. the rate of spire manstation, relative whorl heigh t, convexity, position of maximum diameter, and relative diameter. The first three were parameters of Raup's (1966) model. The latter 5 were developed specifically to analyze the geometry of Conus shells. Using their model, Kohn and Riggs were able to differentiate among three geographically distinct populations of C. miliaris from the southeastem Pacific. They also determined the region of the morphospace defined by
Raup (1966) that these Conus shells occupied.
Eckaratne and Crisp 1983
Eckaratne and Crisp (1983) developed a geomemc mode1 of gastropod shells, which 46 consisteci of parameters that were very similar to those of Uvmp et ai. 1974-88 (though
Eckarame and Crisp cited those of Raup's (1966) model): h, the ratio between diameten of successive whorls; P'. the semi-apical angle; and p. the ratio of length to breadth of the generating curve. Eckaratne and Crisp derived a relationship, called the shell conversion factor, that quantified the ratio benveen the length dong a shell's spiral (h) (with angle a') and its total height (HJ:
They analysed the turbinate shells Nucella lapiflus and Linorino iinoreo and determined that empincal values for the shell conversion factor did not differ significantly from values determined theoreticaily.
Hutchinson 1989
Hutchinson (1989) proposed a "road-holding" model, in which a snail uses the shape of a preceding whorl to determine the placement of the next one. Hutchinson provided an etyrnological description of the model but only the skeleton of its mathematical formulation. The mode1 described isometric apenural growth but allowed for anisometric coiling.
Hutchinson used this mode1 to hypothesise why doming is common in land snails 47 but rare in marine snails and why doming demases with growth. Bnefiy, an umbilicus
acts as a catalyst for doming. A juvenile sheIl with an umbilicus (common in land snails,
rare in marine snails) has a dome-shaped sheii. As growth proceeds, doming causes the
constriction of the urnbilicus, necessitating a reduction in doming, lest pomons of a whorl
one half revolution apan should interfere with each other. in this way, Hutchinson's
(1989) mode1 (at least in its coiling charactenstics) is biologically realistic.
Sc hindel 1990
Schindel (1990) reworked Raup's (1966) analysis hman architectural point-of-view. He analysed shells using three algebraically independent parameters: W', the shell expansion rate; M', the suture migration rate; and U, umbilical expansion rate. Each of these parameters referred to rneasurements made at specific points on the surface of a shell.
The shell expansion rate was the antilogarithm of the regression dope between the logarithm of the radial distance hmthe coiling axis to the outer edge of a shell and whorl number; the suture migration rate was the antilogarithm of the regression slope between the logarithm of spire height and whorl number; and the umbilical expansion rate was the antilogarithm of the regression slope between the logarithm of the radial distance from the coiling axis to the axial margin of a shell and whorl number (Schindel 1990,
Figure 10.3). Schindel showed that prosobranchs were distributed more widely in a morphospace defined by his parameters than they were in the morphospace defmed by
Raup (1966), when the shells of 53 species were analysed according to the respective models. Thus, the intercie pencience among Raup's (1966) parameters showed the magnitude of its effect.
The implication of the interdependence of parameters in Raup's (1966) mode1 is critical. Raup (1966) delimited regions within his W, T, D morphospace by assuming that each parameter was independent of the others and that al1 combinations of the three parameters were possible. Because the parameters are algebraically interdependent, their combinations do not represent the mespectmm of geometrically possible shell foms
(Schindel 1990).
Johnston et al. 1991
Johnston et al. (1991) descnbed shell morphology, using the deformation of landmarks on shell surfaces. They used a local coordinate system in which the direction of coiling was specified with respect to the present location of the rnantle edge, with the advantage that few assumptions were made as to the shapes that could be formed, The impetus for this approach was to treat form in a pmly geornetric rnanner and without the use of an extemai reference system.
Checa and Aguado 1992
Checa and Aguado (1992; Checa 1991) used sectorial expansion to analyse shell coiling 49
of Disrorsio, a knobbly ribbed whek with distorted, bulging whorls. In their approach,
Checa and Aguado tiled the surface of a shell with planar polygons (usually aiangles), or
sectors, in a manner similar to fuiite element analyses. Two sides of each aiangular
sector were delineated by vectors joining sequences of homologous points on the shell, resulting from accretion at the made edge. These represented growth vecton. On actual shells these were longitudinal omaments. In these respects, this analysis was similar to multihelicospiral models (McGhee 1978; Savazzi 1985). The intersection of an apemire
with both vectors, a chord @"), defmed a triangle. The rate of sectorial expansion was defined as the rate at which D" varied with respect to any other shell parameter. Checa and Aguado (1992) plotted sectonal expansion maps, which resembled topographical maps, having dense regions of rapid expansion and sparse regions of contraction. These maps documented the variation in growth of Distorsio shells. The writers observed that
Distorsio alternately expands and contracts its apertural mantie during shell deposition; regions of expansion facilitate retraction of the body deep into the shell, by providing extra roorn.
OUTGROUP SPECIES
Cladistics is a comparative technique. Therefore, in the construction of data matrices to be subjected to cladistic analysis, taxa (the 'outgroups,' Maddison et al. 1984) possessing features that may be cornpared with those among ingroup taxa must be selected and examined. Ideally, outgroups possess many features found among only some members of 50 the ingroup, while sets of other members of the inpup possess features shared among only members of those sets. At least two outgroups should be used in the coding of features as character States (described subsequently in the section titled "STATEMENT
OF CHARACTERS AND DEFINITION OF CHARACTER STATES," p 51).
The models of Moseley (1838) and Thompson (1917) were chosen as outgroups.
These both predate the development of elecmnic cornputers and the formulation of al1 non-computer-graphical models. One of the advantages of working with ideas is that
'stratigraphic fossils' (journal references stored on dusty library shelves) relate one-to-one with the temporal origins of the species they represent.
Moseley 1838
The mathematical mode hgof shells began with Moseley's ( 1838) paper reac 1 before the
Royal Society of London in 1838 (although Thompson 1917 reviewed works since antiquity). Moseley explicitly determined equations for the surface described by a generating curve that increased isometricaily in size, as it revolved about a fixed axis.
That the coiling of a shell could be described by a logarithmic spiral was expected, claimed Moseley, for various functional reasons. For instance, if the facility with which aquatic shelled organisms control their buoyancy is to remain constant as they grow, there must be a disproportionate increase of unoccupied space (in non-body whorls) compared to body mass, with an increase in size (Moseley 1838). Logarithmic spiral surfaces 51 exhibit such growth. Using this model, he derived equations for the volume, surface area, and centre of gravity of shells, some of which he modified later (Moseley 1842).
Thompson 19 17
D'Arcy Thompson (1917), in his magnificent monograph, On Growth and Form, recapitulated the major ideas of shell geometxy since antiquity, including those of
Moseley. Thompson used the geomerrical analyses of those before him to generalise description of shells, using only three parameters: a", the angle of the equiangular
(logarithmic or Bernoulli) spiral; P", the angle that a tangent to the whorls makes with the coiling axis; and y'', the "angle of retardation," which expressed the retardation of growth of the inner, as compared with the outer, pan of each whorl.
STATEMENT OF CHARACTERS AND DEFINITION OF CHARACTER STATES
Cladistic anaiysis is performed on states (individual observable features) of independent characters (defined subsequently in the section titled "ANALYSIS," p 56) possessed by taxa under consideration. In the constniction of a rnatrix for cladistic analysis, those states shared among members of the outgroup and ingroup are defined as 'plesiomorphic,' whereas states shared only arnong memben of the ingroup are defined as 'apomorphic'
(Wiley 1981). The use of at least two outgroups ensures that plesiomorphic states are general and apomorphic states are specific with respect to the ingroup. States of a 52 character that have ken determined as plesiomorphic and apomorphic are said to be
'polarised' Table 2.1 shows the various characters and their polarised States for each
mode1 species. Each character is described briefly here.
No Reference to an Extemal Coordinate System
As with Moseley 1838 and Thompson 1917, defmitions and measurements of shell parameters or descriptions of aperture or generating curve motions of the majority of shell models are made with reference to an extemal coordinate system (i.e., a fixed or coiiing axis). The models Okamoto 1984-88, Ackerly 1989, Hutchinson 1989, Savazzi 1990, and
Johnston et al. 1991 share the apomorphic condition of making no reference to an extemal coordinate system.
Anisomeaic CoiIing
The models Moseley 1838 and Thompson 1917 are based on equiangular spirals. A consequence of this is that the coiling charactenstics of shells remain constant throughout growth. Departures hmthis plesiomorphic idealisation are necessary for accurate simulations and analyses of irregularly coiled shells. The models BMS 1977-85, Okamoto
1984-88, Ackerly 1989, Corrie 1989, Stone 1995, Hutchinson 1989, Savaui 1990,
Schindel 1990, Johnston et al. 1991, and Checa and Aguado 1992 share this latter, apomorphic state. Anisomemc Scaling of the Aperture
The models Moseley 1838 and Thompson 1917 are based on isometric growth, wherein aperture shape remains constant as size increases (plesiomorphic state). The allomemc scaling of apenural dimensions is an important, but neglecte aspect of shell morphology
(McNair et al. 1981 is a rare example of such considerations). A shell is, ultimately, the cumulative accretion of material ont0 its aperture. The models BMS 1977-85, McGhee
1980, Okamoto 1984-88, Ackerly 1989, Come 1989. Stone 1995, Savazzi 1990, Schindel
1990, Johnston et al. 1991, and Checa and Aguado 1992 al1 are capable of sirnulating shell hswith anisometrically scaled apertures.
Generating Curve Independence
The models Moseley 1838 and Thompson 1917 epitomise the plesiomorphic smte of using a generating curve to represent an aperture moving through space. The models BMS
1977-85, Okarnoto 1984-88, Ackerly 1989, Hutchinson 1989, Schindel 1990, Johnston et al. 1991, and Checa and Aguado 1992 share the apomorphic state of describing an apemire without recourse to a generating curve.
Longitudinal Helicospirals
The models BMS 1977-85 and Checa and Aguado 1992 each employ longitudinal 54 helicospirals to describe shell fom, whereas al1 other models use some sort of aperture outlines.
Frene t Frames
First used by Okarnoto (1984) to describe the motion of a circular cross section as it naced out a tube in space, Frenet frarnes also were used by Illen (1989) and Fowler et al.
(1992) to include flues, sculptunng, and ornamentation on shell surfaces. Savazzi's
(1990) version of Okarnoto's (1988) growing tube mode1 also used Frenet frames, of course. Al1 other models make no use of Frenet frarnes.
Algebraically Independent Parameters
Algebraicaily independent parameters may be defined as a set of parameters in which a change in any one of the pararneters has no effect on any of the others (the interdependence among Raup's parameters was alluded to in the description of Schindel
1990, pp 47-48). The models Illert 1982-89, Ackerly 1989, Code 1989, Stone 1995.
Schindel 1990, Johnston et al. 1991. and Fowler et al. 1992 share the apomorphic state of algebraically independent parameters. All other models contain aigebraically coupled pararneters (the plesiomorphic state), except the models of Hutchinson 1989 (no formally defined parameten) and Checa and Aguado 1992 (only one parameter), which were coded as possessing character States of inapplicable homology (i.e., as -). Variable Parameters
The plesiomorphic state is for a mode1 to possess parameters that are constant. Of course, parameten can be made to Vary. For example, Raup (1966) was able to produce anisomeaic shells by varying his parameters throughout a simulation in an ad hoc manner.
But inherent in his mode1 are constant parameter values. In contrast, the models BMS
1977-85, McGhee 1980, Okamoto 1984-88, Ackerly 1989, Cortie 1989, Stone 1995,
Savaz~1990, Schindel 1990, Johnston et al. 1991, and Checa and Aguado 1992 have parameters that inherently cm change in value throughout shell simulation. Hutchinson
1989 (no formally defined parameters) was coded as possessing a character state of inapplicable homology (i.e., as -).
Cornputer-Graphical Simulation
Like the models Moseley 1838 and Thompson 1917, the models Kohn and Riggs 1975,
Eckaratne and Cnsp 1983, Hutchinson 1989, Schindel 1990, Johnston et al. 1991, and
Checa and Aguado 1992 are non-computer-graphical models. The models Raup 1961-66,
Stasek 1963, Lgivtrup et al. 1974-88, BMS 1977-85, McGhee 1980, Illert 1982-89,
Okamoto 1984-88, Ackerly 1989, Cortie 1989, Stone 1995, Savazzi 1990, and Fowler et al. 1992 are cornputer graphical. Parameters
Al1 models except Moseley 1838 and Hutchinson 1989 contain fomally defined
parameters.
ANALYSE
In a cladistic analysis, each shared apomorphic (synapomorphic) state provides
information that can be used to group taxa in a hierarchical manner, and the states of each character provide a basis with which the information provided by the states of each of the other characters used can be falsified. A character, therefore, rnay be considered as a hypothesis that a group of taxa possesses an observable feanire (synapomorphic character state) that distinguishes it from other groups included in a cladistic analysis. By using rnany independent characters in a cladistic analysis, an evolutionary biologist ensures that a large number of potentially mutually excluding hypothetico-deductive tests extract from a data set information that can provide the most economical hierarchical classification of the ingroup (Wiley 1981). Such a classification is represented in the form of a cladogram, the brmching pattern of which may be interpreted. a posteriori. as depicting the evolutionary history of the ingroup (Brooks and McLennan 1991). Each subset of taxa sharing a common node within such a hierarchical classification is a 'clade,' and each clade rnay be interpreted as a monophyletic group (i.e., a group sharing a common ancestor). Table 2.1. Data for cladistic analysis of shell models.
Abbreviations used: NRECS = no reference to an extemal coordinate system; AC = anisornetic coiling; AS = anisometnc scding of the aperture; GCI = generating cuve independence; LH = longitudinal helicospirals; FF = Frenet frames; AI = algebraic independence of pararneters; VP = variable pararneters; CG = cornputer-graphical simulation; P = parameters. Plesiomorphic character states are coded as 0, and apomorphic character states are coded as 1. Models are designated by sumarne of author and range of publication years (except LSL 1974-88 = L~vtrupet al. 1974-88; KR 1975 =
Kohn and Riggs 1975; BMS 1977-85 = Bayer (1977), McGhee (1978), and Savazzi
(1985); EC 1983 = Eckaratne and Crisp 1983; O = Okamoto 1984-88; H = Hutchinson
1989; JTl3 1991 = Johnston er al. 1991; CA 1992 = Checa and Aguado 1992; and FMP
1992 = Fowler et al. 1992). Data for cladistic analysis of shell models
NEECSAC AS GCI LH FF AI VP
Moseley 1838 Thompson 1917 Raup 1961-66 Stasek 1963 LSL 1974-88 KR 1975 BMS 1977-85 McGhee 1980 Illert 1982-89 EC 1983 O 1984-88 Ackerly 1989 Cortie 1989 H 1989 Savazzi 1990 Schindel 1990 JTB 1991 CA 1992 FMP 1992 Stone 1995 58
A cladogram is a hypothesis based on data. Given a matrix of data, the hypothesis most sensitive to the addition of new data, and, hence, further falsification, is the cladogram that makes the most efficient use of the information available, and, therefore, requires the fewest ad hoc interpretations. In a cladistic analysis, an ad hoc interpretation of a character state represents a mistaken character state coding, that is, a falsifiai hypothesis of synapomorphy ('homoplasy,' Wiley 1981). The most economical use of information, therefore, results in a cladogram with the fewest number of state changes
('steps,' which are interpretable as 'evolutionary transitions').
The assumption implicit in the interpretation of a cladogram as a phylogeny is that, during the course of evolution, homologous character states outnumber analogous character states (Le., correctly interpreted synapornorphic character states outnumber homoplasous character states), so hierarchicai groupings of taxa supported by synapomorphies (nested clades) can be interpreted as phylogenies. Implicit in this assumption is the tacit assumption that the rate of change of observable features of taxa
(character states) is low relative to the rate of taxonomie diversification (cladogenesis). In cases wherein many independent characters with slowly changing states are used, results obtained from other methods of cladistic analysis (e-g., maximum likelihd) accord with those obtained from panimony-based methods (Felsenstein 1984).
The data in Table 2.1 were analysed using the cornputer program Hennig86 (Farris
1988) and invoking the implicit enurneration option (ie*). This option guarantees that al1 59 most-economical cladograms are found Two cladograms, with lengths of 19 steps,
consistency indices of 528, and retention indices of 8346, resulted hmthe analysis
(Figure 2.2).
DISCUSSION
Rationale for a Phylogenetic Approach
The hindamental assumption made in taking a phylogenetic approach to review sheU
models is that their evolution is analogous to that of organic species. Of course, this
analogy may be imperfect for various reasons. Fust, a researcher may combine ideas
from previously published models, creating a new, hybrid species (cross-lineage bomwing
of Hull 1988a). The representation of such a process requires a pattern that is inherently
noncladistic. Second, the designated species may be inappropriate units with which to
perform the analysis. Perhaps groups of models fonn research programs, in which case it may be more appropriate to analyze the research prograrns themselves, rather than the
shell mode1 species. The dilemma, then, is whether the models should be treated as historical individuals or as natural kinds. If the models are historical individuals, a phylogenetic approach is appropnate, whereas if they are natural kinds, a phenetic approach may be more appropnate. 60
Much verbiage has been expended concerning the study of the development of scientific thought. Some authors favour evolutionary models (Popper 1987; Hull 1988a.
1988b, 1988c; Mishler 1990; Bmdie 1990, Bechtel 1988 and responses of other authors in the sarne volume as Hull 1988b; Carpenter (1987) performed a parodistic analysis of cladists), others find such models intriguing but wanting in certain aspects (Cain and
Darden 1988 and responses of other authors in the same volume as Hull 1988b). Others reject such models oumght (van der Steen and Sloep 1988), and still others favour less explicitly biological models (Kuhn 1970). No resolution of this dialogue is attempted here. Instead, in the remainder of this chapter, the novel aspects of assuming an evolutionary mode1 of theory development for shell modeling are discussed, and the extent to which cross-lineage borrowing and the formation of research programs affect such a mode1 is shown to be negligible.
Because this is a review of historically related, individual species, a phylogenetic approach has been taken. From a practical point-of-view, a cladograrn provides a concise, graphical summary of the discipline of shell modeling: the branching pattern logically groups the works of various researchers, according to synapomorphic character States, in a hierarchical fashion. In addition, through character state transformations, the cladogram interpreted as a phylogenetic hypothesis provides insights into different approaches taken by researchers; by delimiting groups, it permits the differentiation and classification of models into clades (interpretable as monophyletic groups, or groups of taxa sharing a common ancestor, p 56) of form and growth-like species; and, via character state 61 distributions, it allows the identification of both anagenesis and historical constraints in
the development of ideas in this field Thus, whether ideas in this field have evolved like
organic species, shell researchers still may benefit by means of the metaphor.
Interpretation of the Phylogeny of Shell Models
Character State Transformations: Different Approaches to Shell Modeling
Two mes result from the analysis of the shell mode1 data in Table 2.1 (Figure 2.2). The
cladograms are incompletely resolved because only 10 binary characten were used to
group 20 species, but this detracts little from the descriptive and predictive power of a
phylogenetic approach to review shell modeling. The introduction of discrete parameters
(P) distinguishes al1 other shell models from Moseley 1838 (the most-basal outgroup).
The models Kohn and Riggs 1975 and Eckaratne and Cnsp 1983 form a nichotomy with
Thompson 1917, the second outgroup; there are no synapomorphic character States that differentiate any two of these species from the other one. Kohn and Riggs (1975) and
Eckaratne and Crisp (1983) were interested in measuring parameter values of, and depanures fiom, theoretical formulae exhibited by actual specimens, and, so, intended their models to be similar to the geometrical analysis of Thompson (1917).
The ancestor of the rest of the models (node iii in Figure 2.2) shares a common Figure 2.2. Two cladograms of mathematical shell models.
The most economical branching patterns (cladograrns) based on the data in Table 2.1 may be interpreted phylogenetically: Moseley 1838 and the remaining species form a monophyletic group (sharing node i); after parameters (P) had evolved, a trichotomy consisting of Thompson 1917, Kohn and Riggs 1975 (KR 1975). and Eckarame and Crisp
1983 (EC 1983) onginated; thereafter, the evolution of corn puter-graphical simulation
(CG), combined with the presence of parameters, in an environment replete with powefil mathematical processors, permitted a proliferation of species, which resulted in the ongin of two groups: fonn species (sharing node iii) and growth-like species (sharing node iv).
Hierarchical relationships within groups differs between the cladograrns. Character states are mapped ont0 branches (homologous apomorphic character states are indicated with black bars; analogous character states, parailelisms and revends, with grey bars and white bars, respectively). The names of models and syrnbols for characters appear as they do in
Table 2.1.
63 ancestor (node ii in Figure 2.2) with the trichotomy of Thornpson 19 17, Kohn and Riggs
1975, and Eckarame and Crisp 1983. Node ii possesses ideas contained in the body of work that preceded the computer graphical treatment of the subject This body of work probably includes the nongraphical rnodels of Lison (1942, 1949), Owen (1953), Fukutomi
(1953), and Rudwick (1959). which, together with ideas homologous with those contained in Thompson 19 17 and Moseley 1838, provided the framework on which Raup (1961,
1962, 1966; Raup and Michelson 1965) and Stasek (1963) were to build theû graphical models. The rest of the rnodels share the apomorphic state of cornputer-graphical simulation (CG -- though this character is found in the plesiomorphic state in the models
Hutchinson 1989, Schindel 1990, Johnston et al. 1991, and Checa and Aguado 1992;
Figure 2.2).
The evolution of formally defmed parameters and cornputer-graphical simulation, together, may be thought of as a "key innovation" (sensu Lauder 198 1; Jensen 1990;
Cracraft 1990), a combination of shared derived features that affects a multicomponent network in an evoiving lineage. Such proposed evolutionary novelties may be associated with an increase in speciation rates within a lineage when the novelties are examineci in the context of a historical hypothesis relating the taxa comprising the lineage. Although the cause-effect relationship between the evolution of a key innovation and a proliferation of species rarely can be demonstrated de facto, in the present context, a strong case can be made, because simplified geomemcal descriptions using formally defined parameten and the advent of electronic cornputers facilitateci analyses employing shell models and increased their usefulness. Thus, the introduction of formally defined parameters and
cornputer-graphical simulation (P and CG in Figure 2.2) may explain the relative
proliferation of shell models duxing the past quarter century.
From node iii dong both cladograms, four identical clades unfold: thrre
monotypic clades, Raup 1961-66, Stasek 1963, and Uvmp er al. 1974-88, and a clade
consisring of 'sister-species' (species sharing a node that is unshared with other species
and, therefore, interpretable as nearest genealogical relatives) Illen 1982-89 and Fowler er al. 1992.
Illert 1982-89 and Fowler et al. 1992 share the possession of Frenet hes(FF).
Their mdels are capable of producing shells with comgations, flares, and ornamentation, which enhance the simulation of realistic images. In their use of Frenet frames, Fowler et al. (1992) cited only Illen (1989). Illen (1989) did not cite Okarnoto (1984, 1988), though Okarnoco's (1984) was the fmt mode1 to employ Frenet frames. Therefore, Frenet frames evolved two times independently (Figure 2.2). Illen 1982-89 and Fowler et ai.
1992 also share the homoplasous apornorphy of algebraically independent parameters (AI), which evolved three times (Figure 2.2).
The 11 models remaining, McGhee 1980, Cortie 1989, Stone 1995, BMS 1977-85,
Savazzi 1990, Okamoto 1984-88, Ackerly 1989, Hutchinson 1989. Johnston et al. 1991,
Schindel 1990. and Checa and Aguado 1992, share the capability of producing shells with 65
anisometricaily scaied apextures (AS), though this charmer is found in the plesiomorphic
state in Hutchinson 1989, and the possession of variable parameters (VP) (Figure 2.2).
The models Cortie 1989, Stone 1995, BMS 1977-85, Savazzi 1990, Okarnoto 1984-88,
Ackerly 1989, Hutchinson 1989, Johnston et al. 199 1, Schindel 1990, and Checa and
Aguado 1992 share the ability to produce shells with anisometric coiling (AC). The
models Cortie 1989 and Stone 1995 share algebraically independent parameters (AI). And
the models BMS 1977-85, Savaui 1990, Okarnoto 1984-88, Ackerly 1989, Hutchinson
1989, Johnston et al. 1991, Schindel 1990, and Checa and Aguado 1992 share a synapomorphic independence hmthe use of generating curves (GCI), though the use of generating curves was reestablished in Savazzi 1990.
Of the 8 models remaining, only the painng of Savazzi 1990 and Okamoto 1984-
88 is congruous on both trees. On one tree (Figure 2.2, top), Checa and Aguado 1992 is the sister-species of BMS 1977-85, while Hutchinson 1989, Schindel 1990, and Johnston et al. 199 1 form a trichotornous sister-group to Ackerly 1989; on the other tree (Figure
2.2, bottom), Checa and Aguado 1992 is the sister-species of Schindel 1990 and, together, these fom a aichotomy with Hutchinson 1989 and Johnston et al. 1991. The inapplicable
States of algebraic independence of parameters (AI) and variable parameters (VP) for
Hutchinson 1989 (no formally defined parameten) each were treated as 1 by the cornputer algonthm; algebraic independence of parameters for Checa and Aguado 1992 (only one parameter) was treated as O on one me (Figure 2.2, top) and 1 on the other (Figure 2.2, bortom). 66
A general trend in mathematical models of sheiis is apparent: species that produce more realistic images have evolveà. This is expected, given the technological advances in computing power since the mid-1960's. But the me shows that this evolution has taken two routes. Some species produce more realistic images by simulating the appearance of form using mathernatical models, while others achieve the sarne ends by simulating growth using mathematical models. These two clades of species are described in the following subsubsection.
Defining Clades: On Form and Growth
A shell is a static, inanimate object that results from the dynamic, organic process of shell growth. Here shell form is defined explicitly as the combined shape and size of a shell -- the periostracum, the larnellar layer, and the nacreous layer -- that results from accretion at a mantle edge. Models of shells may be classified into two clades, as noted in the preceding subsubsection: form models (sharing node iii in Figure 2.2) that describe shape and size, and growth-like models (sharing node iv in Figure 2.2) that describe accretion.
A dilemma exists because models that describe form refer to a coiling axis, which may have no biological reality. These models fail to describe accretionary growth at a mantle edge (sensu stricro). It would be difficult to reconsmict irregularly coiled shells using these rnodels (e.g., ammonoids, Okamoto 1988). However, models that most closely describe accretionary growth (Okamoto 1984-88, Ackerly 1989, Hutchinson 1989, Savavi
1990, and Johnston 1991) have no parameters that quantify fom. The parameters in 67 rnodels that refer to no external coordinate systems represent the accretionary motion of the aperture at each step of growth but not where it has been previously. It is difficult to reconstruct the history of apertural motion and, therefore, to quantify shell morphology using these growth-like models (Ackerly 1989).
The significance of the distinction between form and growth-like models becomes apparent when the purpose of investigation is determined. If accretionary growth is king investigated, then the model employed should represent the biological process of shell accre tion. The aperture should move fkely but incrementally through space (mimicking accretion), unrestricted by reference to any extemal coordinate system; it should rotate, expand, and cwe, and a moving reference frame model, such as Savaui's (1990) modification of Okarnoto's (1988) model, should be employed. If, however, form is being investigated, then the mode1 needs to duplicate only the shape and size of the shell. In this case, aspects of shell architecture, such as height to width ratios, or the relative motion of the aperture from one portion of accretionary growth to the next, are rneasured
(Schindel 199û), and a fixed axis model may be more appropriate (Ackerly 1989).
A shell with a given shape and size cm be described by two or more mathematically different growth-like rnodels, but only one mode of growth actuaily occm at the mande edge of the snail. On the other hand, a shell produced by accretionary growth can be reproduced graphically by two or more different form models. The theoretical differences between form and growth-like models have practical consequences. 68
For example, a fom model rhat fails to account for the rotation of a shell's aperture will fail to trace out the same surface in space, point for point, that the accretionary process presnbed. The resulting shell wiil possess improper growth lines, though it will possess the proper shape and size (Figure 2.3). Similarly, the pigmentation pattern on a shell's surface is laid down incrementally during accretionary growth but cm be produced in roto and wrapped onto a surface with a model that reproduces only the shape and size of a shell. Though they both are capable of producing similar images, the type of model that best suits the subject of an investigation -- form or growth -- should be chosen. Such distinctions should be made explicitly in any analysis of shells.
Whereas growth-like models can mimic the geometric freedom of accretionaxy growth found in irregularly coiled shells, even these models fail to capture the biological processes involved in secretion at a mantle edge. It follows that changes in the values of model parametee, which induce geometric variation in shell form, can be only inferred to represent changes in processes occumng at a mantle edge. To model shell secretion, parameters that represent accurately the cellular processes occming at a mantle edge must be used-
Cross-Lineage Borrowing
If the ideas within a scientific discipline evolve, then the character States of a lineage of ideas may be used to reconsmict its history of development. Although potentially Figure 2.3. Example of the distincuon between forrn and growth.
A shell with a portion of a whorl deleted. The missing piece cm be reconstructed mathematically by form and growth-like rnodels. Many different form models could describe a tube with a cross section that changed in dimensions to join a to A, b to B, and C to C. In reality, a unique growth process occun. In this case, the missing tube would be described by a growth-like mode1 that mimicked accretion at one end (abc).
Ultimately, point a may be homologous to any point on the other end (ABC), depending on rotation of the aperture. Form rnodels facilitate shell morphometrics, while growth-like models conform more closely to the biological pmess of shell accretion. problematic, the occurrence of cross-lineage borrowing need not render such an evolutionary analogy inappropriate. In fact, provided that it occurs infrequentiy, a basis for establishing that cross-lineage borrowing has occurred may be provided by a cladistic analysis because, when a researcher inhents an idea through cross-lineage borrowing, the representative character state cm be identified as homoplasy on the tree (i-e.,as apparent independent evolution of an idea when it really is homologous with that of another researc her ).
For exarnple, Checa and Aguado (1992) explicitly acknowledged the inheritance of longitudinal helicospirals (LH in Figure 2.2) in their mode1 by citing ideas used by
Savazzi (1985) in his model. Therefore, the apomorphic presence of longitudinal helicospirals in Checa and Aguado 1992 might be interpretable as a homology, a corroborated hypothesis that Checa and Aguado 1992 and BMS 1977-85 are sister-species
(Figure 2.2, top). However, if a cladistic analysis falsifies this hypothesis (Figure 2.2, bottom), and it is maintained that longitudinal helicospirals arose only once, either of the following two a posteriori interpretations musr be made: species that originated after the derived state (possession of LH, coded as 1) had arisen have this character in the ancesaal state (coded as O) because of a reversal; or the ancesaai state in these species represents a different denved state (e.g., 2). Either of these scenaios requires 5 steps in addition to those depicted on the tree (Figure 2.2. bottom). A more economical interpretation of the data in Table 2.1, that most amenable to future falsification, is that the presence of longitudinal helicospirals in Checa and Aguado 1992 is a case of cross-lineage borrowing. This is represented as a parallelism on the tree (Figure 2.2, bottom).
Cross-lineage bomwing has occurred infRquently in the history of shell modeling
(the other two parallelisms, algebraically independent parameters (AI) and Frenet frames
(FF), are tme independent events, as discussed in a preceding subsection, pp 61-66;
another example of cross lineage borrowing, anrigenesis of BMS 1977-85, is presented in
the penultimate subsection of this section, pp 72-75). Therefore, the extent to which an
identifiable, hierarchical. and historically interpretable pattern has been disrupted by cross-
lineage borrowing is negligible.
Research Programs
Whether cornputer-graphical shell modeling and non-cornputer-graphical shell modeling are independent research programs cm be tested by analyzing a matrix containing character States of members of both types (Table 2.1). If they uuly are independent research prograrns, a cladistic analysis will cluster them into separate, similar groups. In such a case, a phenetic andysis might be a more appropriate type of review, because the field of shell modeling could be considered as being composed of clusters of similar, natural kinds rather than evohing species.
From the results, it appears that the individual models are, indeed, appropriate units with which to perform a cladistic analysis. Non-cornputer-graphical models occupy 72 intermediate positions among the computer-graphical species in the ingroup (Figure 2.2).
This indicates that the hierarchical relationships arnong the models supersede
categonsation as research programs. In other words, sheM models may be considered true
species grouped by synapomorphies.
Character State Distribution: Anagenesis and Constraint
An interesting aspect of considering models as species, and one that supports an evolutionary analogy, is the concept of anagenesis. The models are not static, etemal entities but undergo modiFication with the passage of time. For exarnple, definitions of parameters in Raup 1961-66 changed over the course of time. Originally, Raup (1961) defined expansion as the factor by which any linear dimension of the generating curve was enlarged during one fuli revolution about the coiling axis. Similar definitions can be found in his other publications (Raup 1962, 1967, 1966; Raup and Michelson 1965).
However, the mathematical defmition of expansion (W in equation 1) differs slightly from this verbal definition, because the mathematical definition refers to the radial migration of points on the generating curve from the coiling axis (Raup 1966; Figure 24, whexeas the verbal definition refers to the expansion of the whorl itself.
Displacernent also underwent some modifications. Onginally, Raup (1962) defined displacement as the relative position of the generating curve with respect to the coiling axis. Later, he defined it as the distance between the generating curve and the coiling axis (Raup and Michelson 1965). Despite nurnerous subsequent interpretations as such
(Raup 1966; Currey 1970; Kohn and Riggs 1975; Rex and Boss 1976; McGhee 1978,
1980; and Okarnoto 1988), displacement in its present form (Raup 1966; D in equation 2)
is rarely a measure of the distance of the generating curve from the coiling axis. D
provides definite positional information only when it is zero, when the axial margin of the
generating cuve is in contact with the coiling axis. In fact, displacement is a static ratio of measurements made on a single aperture. So, although the axial margin of two shells may move away hmtheir respective coiling axes at the same rate, they may have different values of D. depending on their rates of expansion (Schindel 1990).
In developing his model, Savazzi (1985) borrowed ideas hmboth Bayer (1977) and McGhee (1980). This cenainly is a case of cross-lineage borrowing because Savazzi
(1985) explicitly culled and cited ideas contained in the works of these authors. However, precisely because Savazzi (1985) acknowledged the sources of these ideas, his model can be interpreted as a later stage of anagenesis in the species BMS 1977-85. Similarly,
Illen's (1989) incorporation of Frenet Frames into his original rnodel (nlen 1982) may be viewed as a case of anagenesis.
Findly, researchers may identih histoncal constraints in theory development, using phylogenetic mes. For example, Okamoto's (1984, 1988) analyses of ammonoid shells required a model that described irregular coiling. No such models existed, so he had to formulate one. The inclusion of Frenet frames (FF), which move with the apeme during 74 acmtionq growth, may be viewed as the evolution of a new character state (perhaps by sudden 'mutation') that better adapted his model for the description of irregularly coilexi shells in the face of historical constraints.
Similarly, Schindel (1990) wished to determine whether or not the distribution of
Raup's (1966) parameter values representing coiled shell forms in morphospace was due to their algebraic formulation rather than morphologicai variation in the shell foms themselves. To test this required a model that was comprised of algebraically independent parameters. Only with such a model was Schindel (1990) able to compare the distribution of parameter values exhibited by shell forms in Raup's (1966) rnorphospace to that defined by a model with truly algebraically independent parameters to determine to what extent they differed. Schindel (1990) may have been unaware of those models containing algebraically independent parameters that had been published prior to 1990 (Ackerly 1989 and Cortie 1989). The cladograms provide a concise summary of the works in the field of shell modeling and, so, would have assisted, or perhaps discouraged, Schindel in formulating his model, had he been unaware of these species. Alternatively, Schindel may have ken aware of these species but prefemd form models (and, hence, disregarded
Ackerly 1989) comprised of few parameters (and, hence, disregarded Cortie 1989) and, therefore, decided to formulate his own. The formulation of a phylogenetic hypothesis forces researchers to identify character States not only to consmct a cladogram but, also, to interpret the evolutionary history of the members of the clade. The identification of the lack of form models with few, algebraically independent parameters in the history of shell 75
modeling, and the availability of a phylogenetic hypothesis with which amibutes of
models cm be analyseci, would have been beneficial to Schindel in developing his model, even if he had been aware of the models Ackerly 1989 and Code 1989. Herein lies the
usefulness of an evolutionary approach.
Assessrnent of the Evolutionary Mode1
Despite the fact that the branching pattems, in general, refiect the temporal history of shell modeling, there are some incongniities in the dates of origins of the species and their ordering on the aees (Figure 2.2). If the aivia1 explanation that these incongruities result from delays in publication is disregarded, the temporal discombobulation on the mes has its roots neither in a paucity of information nor in the inappropriateness of a cladistic analysis but, rather, in the imperfection of the analogy. Unlike those of organic
"replicators" (sensu Hull 1988a), the mechanisms of inheritance of ideas may be free from physical interactions. Therefore, the processes involved in the speciation of ideas may be less consnained than those of organic species, and temporally disjunct branching patterns may reflect accurately the evolution of scientific ideas: in general, the pattern of speciation of ideas, detected cladistically, is insensitive to publication dates.
This distinction of pattern and process mirrors the same distinction found in discussions of organic evolution (Cracraft 1985) and, likewise, persists at different scales.
For example, the classification of models into fonn and growth-like species is, itself, a distinction of pattern and process: form models reconstruct morphological patterns,
growth-like models mimic accretionary processes. Also, as exemplified in a preceding
subsection of this section (pp 79-82), knowledge of dates and citations and interpretations
of patterns may be used to identify instances of cross-lineage borrowing in the process of
scientific development, one of the problems inherent in employing an evolutionary model.
And, finally, phylogenetic msallow the identification of anagenesis and consaaints in
the evolution of a scientific discipline. Sheli researchers, therefore, rnay benefît fkom this
exercise by knowing what conceptual obstacles have been and have yet to be overcome by
their colleagues, in the ongoing dynarnics between pattern and process in this area of
research. Therefore, though it may be imperfectly analogous, an evolutionary mode1
provides a concise and, simultaneously, illuminating summary of the history of the
discipline of shell modeling.
ADDENDUM
Other systematic reviews of shell models have been published before (Savaui 1990, 1993;
McGhee 1991); these were alpha-taxonomie classifications with descriptive power. A final justification of the cladistic approach taken in reviewing shell models lies in its predictive power. G. R. McGhee (pers. corn., 22 May 1995), a shell modeler and one of the referees of an earlier cirafi of this chapter, offered the following review: "1 can attest that your technique does have predictive power. 1 was very entertained with your analysis of the "BMS clade", comprising the papers written by Bayer, McGhee, and Savazzi in the 77
years 1977-1985. You characterize these papers as a case of "magenesis" within a
"species" lineage, and your analysis is precisely correct. This came as quite a surprise to
me, as you are a total stranger to me, and 1 assume (as you indicated you are a graduate
student, and thus just beginning your career) that you have not met Bayer in Gemany nor
Savazzî in Sweden. You could not know, for example, that Ulf Bayer, Enrico Savazzi, and 1 dl have personally known one another for years, have spent many hours taiking with each other, even have overlapped in multiple research stays at the Univenitat
Tübingen. Not knowing any of this you still have been able to conclude that these models are in fact an anagenetic transition of a single model, and not three separate model
"species". That conclusion speaks highly of the power of your technique." A CLADISTIC ANALYSIS
OF SPECES OF UBIS
Cladistic Methodology Reiterated
Lambis is a genus of marine gasaopods endemic to the indo-Pacific. Species of Mis reside on sandy, coral rubble, or algal-rich substrata, at shallow depths. Colonies usually are associated with corai reefs, and distributions of individu& within colonies range hm sparse to dense.
Documentation of life-histories for species of Lambis is scant. Development is indirect; ontogeny proceeds hmegg to prototroch to veliger larva Postlarval ontogeny may be divided into three stages, defined with respect to sheIl growth: juvenile, in which shells grow continuously and isome~cally;immature, in which shells grow allomemcally; and adult, in which shells attain final size and exhibit a thickened, Eiared lip with circum- apertural projections (Savazzi 1991; Figure 3.1). As is the case with aii genera in the farnily Strombidae (a member of the superfamily Smmbacea, the tme conchs, and which is comprised of the quanet of genera LambLÎ, Strombus, Terebellwn, and Tibia) growth to Figure 3.1. Hypothetical Archetypical Lambis ('HAL').
A drawing (ventral view) of a hypothetical snail with features charactenstic of species of
Lambis. Abbreviations useci: flared lip (fl), circum-apertd projections (cap), verge (v). stmmboid notch (sn), propodium of foot (pf), metapodium of foot (mo,operculum (O), opercular serrations (os), snout (s), right ommatophore (om), left tentacie (t), left eye (e).
80 the adult stage is believed to be rapid (Savazzi 1991), but tïmes associated with particular stages of life-history are unknown (Clench and Abbott 1941, D'Asam 1965, Berg Jr.
1976, Brownell 1977, and Davis et al. 1993 provide details conceming timing of Strombur ontogeny),
Species of Misare dioecious, and genders are distinguishable by extemal observation of morphology: a male bears a verge, or penis, dorsally on the right half of the body (Figure 3.1). In addition to differences of size (fernales are larger than males), shells of these species present some of the most striking examples of sexual dimorphism among marine gaswpods. For example, circum-apertural projections emanating hm shells of female Lambis lambis are directed dorsally, while those of male L. lambis are directed posteriorly. During copulation, each participant positions its shell so that its stromboid notch (a parabolic impression at the antenor portion of the aperture of most strombid shells; Figure 3.1) is adjacent to that of its partner. The spatial arrangement of circum-apernual projections enhances coition of shells and may facilitate mating (Abboa
1961).
Al1 species of Lombis possess a taenoglossate radula consisang of rows of seven
'teeth: ' a central, median, or rachidian tooth flanked on either side by a single lateral tooth and two marginal teeth, or uncini (Plates 3.1-2). Radular teeth are cuneiform (i.e., wedge-shaped). Species of Lumbis are herbivorous and consume primarily red algae
(Abbott 1961). As is the case with many herbivorous gasrropods and most taenoglossate Plate 3.1. Scanning electmn micrograph of a taenoglossate radula.
Radula of mismillepeda (scale bar represents approximately 150 pm)-
Plate 3.2. Scanning elecmn micrographs of a taenoglossate radula.
Radula of Strornbus maculatus (scale bar represents approximately 250 pm (top) and 10 pm (bottom)). Abbreviations used: central tooth (c), lateral tooth (l), inner and outer marginal teeth (i and o. respectively).
83 Mesogasiropoda, species of Lambis have a style sac (a prolongation of the antenor end of
the stomach) and a crystalline style (a cylindrical rod that projects into the stomach and
abuts on a heavily cuticularised area therein, the gasaic shield; Hyman 1967). Food
rasped by the radula is passed to the stomach in mucous sirands by rotation of the style
(Yonge 1932, cited in Hyman 1967). Species of Lambis are remarkable in possessing the
longest styles (and style sacs) among gastropods. For example, Yonge (1932, cited in
Hyrnan 1967) recorded a specimen with a shell 180 mm long and a style 80 mm long.
Species of Lumbis are preyed upon by crabs and fish (Palmer 1979; Savazzi 1991).
Typically, the sickle-shaped operculum incompletely seals the shell aperture, and an individual relies primarily on its shell for protection (Palmer 1979; Savazzi 1991; Hyman
(1967) considered the operculum to be in the process of degeneration). Humans consume particular species of Lambir (L. lambis, L. truncata, L. chiragra), but some are narcotic or too bitter (cg., L. rnillepecla); bittemess and narcotic effects may be associateci with their diet (Abbott 1961).
The fmt of a strombid is highly regionated. A narrow constriction separates the anterior propodium from the posterior metapodium (Figure 3.1). As do most strombids,
Species of Lambis locornote by inserting theû sickle-shaped opercula (Figure 3.1) between themselves and subsûata and pushing downward, using their opercula as levers and
'vaulting' (leaping, Savazzi 1991). Occasionally, such behaviour results in oveming.
Reorientation, or righting, is accomplished by lifting the operculum over the left side of 84 the animal, lowering it into the substratum, and kicking laterally (Savazzi 1991). As a
consequence of their heavy shells, adult Lonibis often require several unsuccessful kicks
More reorientation is accomplished (Savazzi 199 1). A similar opercular motion has been
observed as a defence mechanism against fish and crab predators (Jung and Abbott 1967;
Melvin 1973; Savazzi 1991; Vermeij, pers. corn.).
Individuals of some species bwow into substrata. using rheir aaembolic
(completely invaginable) snouts (Figure 3.1; the mouth is at the anterior end) to displace
sediment, and purponedly may maintain an infaunal or semi-infaunal attitude (Savazzi
1991). The mantle edge of many Recent stmmbids has a posterior pomon consisting of a füament that extends extemdly to the apex of the shell. The function of this mande filament is thought to be tactile, infoming an animal whether its shell is buried completely (Jung and Abbott 1967; Savazzi 1991). This filament is reduced or absent in
Mis,so individuals probably maintain only semi-infaunal attitudes. Memben of other species maintain epifaunal amtudes, the circum-apenural projections serving to distribute the weight of an animal over an extended area, allowing the shell to rest on soft substrata by 'snowshoeing' (Savazzi 199 1).
Stmmbids have been observed to exhibit behaviour that is a rernarkable example of the interplay between fom and function. When a strombid snail is active, it extends one of its two ommatophores (usually the right one), or eyestalks, into the stromboid notch.
Situated at the tip of each ommatophore is a well developed eye (a tentacle arises from 85 each ommatophore as a slender branch). The physical properties of smmbid eyes (large
apertures and large rhabdom diameiers) confer photosensitivity and probably permit
Nnlight activity of the animals (Seyer 1994). The strornboid notch probably protects the
ommatophore from predators, while alIowing observation of a snail's sumoundings.
Abbott (cited in Jung and Abbott 1967) described a fascinating behaviour performed by Terebellum terebellum:
"As each animal ploughed down into the sand, one of its eyestaiks was extended upward and back over the shell. As this raised eyestak was contacred by the sand which came to cover the antenor dorsal region of the shell, the organ was moved in such a way that the terminal blue eyebail was placed just above the sand surface. The animals continued to move fonvard and down, burying themselves, but each one 'left behind itself one eye proauding above the surface. Since the exposed eye remained stationary relative to the sand around it, the eyestalk hidden below the sand was clearly elongating at at rate which matched the forward movement of the animal. When the shell was largely buried and its antenor end was judged to be approximately one inch ahead of the exposed eye, the siphon was extended upward through the sand at this point, the siphonal fol& closely appressed to form a closed cone. Once at the surface, the siphonal folds flared open terminally, and a swift current of water was drawn down into the mantle cavity.
Following this inhalation, the second eye, thus far conceaied below the surface of the sand with the rest of the animai, passed upward through the lumen of the siphon. With the 86 second eye now exposed, the siphon folds unrolled and the siphon was pulled down out of sight, leaving the blue eyebail just at the surface of the sand Simultaneousiy, the first eye, an inch to the rear, was withdrawn below the surface and disappeared. These actions were observed to be repeated with only minor variations as the animal burrowed dong, their shells covered by a layer of sand perhaps a centimeter [sic] in depth. Forward progression below the sand was nearly continuous, but the eyes were 'walked' fonvad, wirh one of them dways staaonary and exposed at the surface like a periscope during the
Other strombids 'periscope' as well (Savazzi 199 1).
In laboratory snidies, individuals of Strombus raninus were attentive to a circular object (diameter of 100 mm) moving at distances of 500 to 600 mm; rapid retraction into the shell was observed when the circular object was moved suddenly toward the animal or when doors were closed at distances of 4000 mm (Seyer 1994). Stmmbid gastropods respond to a variety of chemical and tactile stimuli. In fact, chemical stimuli alone are sufficient to elicit escape responses (Berg 1974). However, the laboratory observations of visual reaction suggest that strombids may use their eyes for more than photodeiection.
The most outstanding morphological feanires of species of LMtbis are the circum- apenural projections emanating fiom the edges of their flared apenural lips (Figure 3.1).
The number of projections (excluding the siphonal canal) varies among species, spanning 87 the range 5 (L. chiragra) to 11 (L. violacea), except for 7. With respect to species in the genera Srrombus and Terebellum, those of Lambis have reduced mande fiIarnents or want them entirely (as noted on p 84), lack denticles on laterai radular teeth. and possess moderately long tentacles.
The etymology of the word Lambis is uncertain, but it has been suggested to mean
"something that licks, like a flarne" (Melvin 1973, p 3 13). Perhaps the word refers to the tongue shaped, flared outer lip. Species of Lrunbis are referred to as scorpion or spider conchs.
Currently, nine species are recognised in the genus Lambis (Abbott 1961): L. lambis (Linné, 1758), L. crocata (link, 1807), L. truncata (Humphrey, 1786). L. rnillepeda (Linné, 1758), L. digitata (Perry, 181 1), L. robusta (S wainson. 1821). L. scorpius (Linné, 1758), L. violacea (Swainson, 1821), and L. chiragra (Linné, 1758).
Abbott (1961) grouped L. lambis, L. crocnta, and L. truncata together as the subgenus
Lambis S.S. Roding, 1798; L. rnillepeda, L. digitata, L. robusta, L. scorpius, and L. violacea as the subgenus Millepes Morch, 1852; and L. chiragra as the lone member of the subgenus Horpago Morch, 1852. Brief descriptions of each species fotlow (some radula information and much of the shell information and natural history is reiterated from
Abbott 1961; radula and sofi-body information were obtained from specimens; Appendices r-v). Descriptions of S pecies of Lambis
mislambis, the 'common spider conch,' is the type species and most cornmon and widely distributed member of the genus. Populations range from East Africa to
Mimnesia and eastern Melanesia. Colonies inhabit reef flats with sand or coral rubble substrata, at depùis ranging between the zone of low tide and several metres.
Shell length (measured fiom apex to the most abapical point on the shell surface) of a typical adult L. lambù ranges between 90 and 200 mm, consists of 10 or 11 whorls, is enveloped by a thin periostracum, and includes a well-developed smmboid notch, 6 circum-apertural projections emanating from a flared lip, and a long, twisted siphonal canal (Plate 3.3, p 99). Apical sculpture is absent; whorl sculpture includes threads and beads; the aperture is rose, tan, crearn coloured, or orange; and the smooth columella is black and brown (Plate 3.3).
Radular rows consist of a central tooth with 1 medial cusp flanked by 2 or 3 srnaller cusps; lateral teeth with 1 cusp at the edge proximal to the cenaal tooth and 3 or
4 smaller cusps extending to the edge proximal to the inner marginal teeth; inner marginal teeth with 4 to 6 cusps; and outer marginal teeth with 4 to 6 cusps (formula: 2-1-2 or 3-
1-3; 1-3 or 1-4;4, 5, or 6; 4, 5, or 6). Tips of the cusps are oblique (Plate 3.13, p 119). 89 The operculum is srnooth; the verge is simple (Figure 3.5, p 121); the mouth is stmmboid
(Figure 3.6, p 122); the ctenidial filaments are moderately thick; and the ratio
ommatophore:tentacle length is between 4 and 10.
Lambis crocata
uunbis crocata, the 'orange spider conch,' is distributed unevenly as two subspecies: L. c. crocata (Link, 1807) and L. c. pilsbryi Abbott, 1961. Lambis crocata crocata populations are widespread, ranging from East Africa to Samoa and the Ryuku Islands, to northern Australia. Colonies live on seaward reefs, at depths ranging between the low tide mark and approximately 3 meues. Lombis crocata pilsbryi populations are known only frorn the Marquesas Islands, Polynesia. Shells of adult L. c. pilsbryi are twice the size of those of L. c. crocara, have straighter 3", 4&, and 5* projections, and have a larger knob on the dorsal shoulder; cornparatively, they also lack a prominent ndge on the parietal callus (a thickening of the inner lip of the aperture, Arnold 1965), have an apex buried by the fvst digitation, and have a weak columellar ridge at the postenor end of the aperture.
Shell length of a typical adult L. crocata ranges between 100 and 150 mm, consists of 8 or 9 whorls, is enveloped by a moderately thick periostracum, and includes a weU-developed stromboid notch, 6 circum-apertural digitations emanating from a flared lip, and a long, curved siphonal canal (Plate 3.4, p 100). Whorl sculpture consists of threads, and the aperture is orange (Plate 3.4).
The radula consists of 40 rows of teeth, each containing a centrai tooth with 1 medial cusp fianked by 2 smaller cusps; lateral teeth with 1 cusp at the edge proximal to the central tmth and 2 smaller cusps extending to the edge proximal to the inner marginal teeth; inner marginal teeth with 5 cusps, and outer marginal teeth with 5 cusps (formula:
2- 1-2; 1-2; 5; 5). The operculum is smooth, and the verge is simple (Figure 3.5, p 121).
Lambis truncata, the 'truncate spider conch,' also is disaibuted as two subspecies: L. t. truncata (Humphrey, 1786) and L. t. sebae (Kiener, 1843). Lambis truncata mncata populations inhabir the Indian Ocean, ranging from central East Africa to the Bay of
Bengal and Cocos Keeling Atoll. Colonies live near reefs, at depths ranging between approximately 4 and 5 rnetres. Lombis truncata sebae populations inhabit the Red Sea and the tropical Pacific Ocean and range from the East Indes to eastem Polynesia.
Colonies live on sandy, algal, and coral mbble bottoms near coral reefs, at depths ranging between approximately 5 and 10 metres. The name truncata refers to the flat, planispird apex of Lambis tmncata truncara; the apices of sIightly smaller-shelled Lambis truncata sebae are more pointed and acutely angleci. Othenvise, the two subspecies differ insignificantly. 91 Shell length of a typical adult L. nuncara ranges benveen 225 and 380 mm, consists of 9 or 10 whorls, is enveloped by a moderately thick periostracum, and includes a well-developed smmboid notch, 6 circum-apemiral digitations emanating from a flared
lip, and a short siphonal canal (Plate 3.5, p 101). Whorl sculpture includes cords and threads; the apemire is white, purple, and rose; and the columella is smooth (Plate 3.5).
The radula consists of 55 rows of teeth, each containing a central tooth with 1 medial cusp flanked by 2 or 3 smaller cusps; lateral teeth with 1 cusp ai the edge proximal to the central tmth and 3 or 4 smaller cusps extending to the edge proximal to the inner marginal teeth; inner marginal teeth with 5 or 7 cusps; and outer marginal teeth with 6 ro 8 cusps (formula: 2- 1-2 or 3-1-3; 1-3 or 1-4; 5 or 7; 6, 7, or 8). Tips of the cusps are oblique (Plate 3.13, p 119). The operculum is smooth; the verge is broad with a process (Figure 3.5, p 121); the ctenidial filaments are fine to moderately thick; and the ratio ommatophore:tentacle length is between 4 and 10.
hmbis millepeda, the 'millepede conch,' is common but limited in its distribution to the cenaal portion of the Western Pacific Arc, from the Philippines to New Guinea.
Members of this species live in shallow water, to a depth of approximately 4 mems.
Shell length of a typical adult L. millepedu ranges between 90 and 145 mm, 92 consists of 11 whorls, is enveloped by a thin periostracum, and includes a well-developed
stmmbuid notch, 6 circum-apemiral projections emanating fiom a flared lip, and a short,
twisted siphonal canal (Plate 3.6, p 102). Whorl sculpnire consists of beads; the aperture is brown and mauve; columellar sculpture consists of lime (fine raised lines or grwves,
Arnold 1965); and the columella is brown (Plate 3.6).
Radular rows consist of a central tooth with 1 medial cusp flanked by 2 or 3 smailer cusps; lateral teeth with 1 cusp at the edge proximal to the centrai tooth and 4 cusps extending to the edge proximal to the inner marginal teeth; inner marginal teeth with 5 or 6 cusps; and outer marginal teeth with 6 cusps (formula: 2-1-2 or 3-1-3; 1-4; 5 or 6; 6). The shape of cusps is unique among species of &bis (Plate 3.13. p 119). The operculum is smooth; the verge is simple (Figure 3.5, p 121); the termination of the anus is tapered; the mouth is stromboid (Figure 3.6, p 122); the ctenidiai filaments are moderately thick; and the ratio omrnatophore:tentacle length is between 4 and 10.
Lambis digitata
Lambis digitata, the 'digitate conch,' is uncornmon but distributed widely, ranging fiom
East Afiica to Samoa Members of this species probably live associated with coral reefs, at depths between approximately 2 and 6 metres.
Shell length of a typical adult L. digitata ranges between 98 and 145 mm, consists of 10 whorls, is enveloped by a thick periostracum, and includes a well-developed
stromboid notch, 8 or 9 circum-apertural projections emanating hma flared Iip, and a
short, twisted siphonal canal (Plate 3.7, p 103). The aperture is mauve, columellar
sculpture consists of lime, and the columeila is pqle and mauve (Plate 3.7).
Lambis robusta
Lambis robusta, the 'robust conch,' is another rare species and is restricted to southeastem
Polynesia. Members of this species probably inhabit deep water off ocean-side edges of coral reefs.
Shell length of a typical adult L. robusta ranges between 110 and 150 mm, consists of 9 whorls, is enveloped by a thin periostracum, and includes a well-developed smmboid notch, 6 circum-apenural projections emanating fiom a flared lip, and a long, curved siphonal canai (Plate 3.8, p 104). The apex is sculptured; the aperture is yellow and crearn coloured, and the coIumella is cream coloured (PIate 3.8).
Radular rows consist of a central tooth with 1 medial cusp flanked by 3 smaller cusps; lateral teeth with 1 cusp at the edge proximal to the central tooth and 3 smaller cusps extending to the edge proximal to the inner marginal teeth; inner marginal teeth with 4 or 5 cusps; and outer marginal teeth with 6 or cusps (formula: 3-1-3; 1-3; 4 or 5;
6). Tips of the cusps are punctate (Plate 3.13, p 119). The operculum is smooth; the 94 verge is simple (Figure 3.5, p 120); the mouth is stromboid (Figure 3.6, p 121); and the ratio ommatophore:tentacle length is between 4 and 10.
Lambis scorpius
Lambis scorpiur, the 'scorpion conch,' is another species that is distributed widely as two subspecies: L. S. scorpiur (Linné, 1758) and L. S. indomris Abbott, 1961. The distribution of Lambis scorpius scorpius is vast, ranging from Indonesia and the Ryuku
Islands to Samoa. Colonies live on coral reef flats, at depths ranging between less than 1 and approximately 3 metres. Populations of Lambis scorpius indomaris inhabit the western and central Indian Ocean. With respect to shells of adult L. S. scorpius, shells of adult L. S. indomaris have a lobe on the Ieft side of the first digitation that either is reduced substantially or bent around the shell apex, have stunted 3d, 4&, and S" circum- apertura3 projections, and usually have slightly darker pigmentation on the dorsal side of the terminal halves of projections and the siphonal canal.
Shell length of a typical adult L. scorpius ranges between 100 and 165 mm, consists of 9 to 11 whorls, is enveloped by a thin periosûacurn, and includes a well- developed stmm boid notch, 6 circum-aperturai projections emanating from a flared lip, and a long, curved siphonal canal (Plate 3.9, p 105). The aperture is purple; columellar sculpture consists of lirae; and the columella is brown and purple (Plate 3.9). The radula consists of 46 rows of teeth, each containing a central tmth with 1 medial cusp flanked by 2 smaller cusps; lateral teeth with 1 cusp at the edge proximal to
the central tooth and 3 or 4 smaller cusps extending to the inner marginal teeth; inner marginal teeth with 4 or 6 cusps; and outer marginal teeth with 5 or 6 cusps (formula: 2-
1-2; 1-3 or 1-4; 4 or 6; 5 or 6). Tips of cusps are punctate (Plate 3.13, p 119). The operculum has 10 serrations; the verge is simple (Figure 3.5, p 121); the mouth is stromboid (Figure 3.6, p 122); the ctenidial filaments are fine to moderate; and the ratio ommatophore:tentacle length is between 4 and 10.
Lambis violacea
Lambis violacea, the 'violet conch,' is rare. Robably fewer than 100 specimens of this species have been recorded. Most of these came from Mauritius, but members of this species are distnbuted in the Indian Ocean, ranging from the Seychelle Islands, to
Mauritius, to Madagascar, to Zanzibar. The species probably lives on sand and algal-rich substrats, at depths between approximately 6 and 30 metres.
Shell length of a typical adult L. violacea ranges between 73 and 114 mm, consists of 9 whorls, includes a well-developed stromboid notch, 10 or 1 1 circurn-apemual projections emanating from a flared lip, and a long, twisted siphonal canal (Plate 3.10, p
106). Whorl sculpture consists of cords and ihreads, and the aperture is purple (Plate
3.10). Lambis chiragra
Lombis chiragra, the 'Chiragra spider conch,' is another species that is distributed
unevenly as two subspecies: L. c. chimgro (Link, 1807) and L. c. arthririca Roding,
1798. Lambis chiragra chiragra populations are widespread, ranging from the eastem
Indian Ocean to eastem Polynesia. Colonies live on seaward reefs, in sand between rocks
and coral heads, in tide pools, among masses of coral in channels between seaward reefs
(at depths between approximately 1 and 3 metres), and associated with sand, coral, or
algal covered reefs where there are surging oceanic waters. Lombis chiragra anhritica
populations extend from East Africa to the central Indian Ocean. Compared to shells of
L. c. chiragra, those of adult L. c. urrhritica lack the deep, elongate well or depression at the presumed posterior end of the aperture ("upper end" of Abbott 196 l), have white
spiral liîae on the parietal wail running parallel with spiral cords (instead of slightiy obliquely), and have a yellowish rose (rather than pinkish rose) aperture.
Both subspecies exhibit sexual dimorphism, which is much more pronounced arnong members of L. c. chiragra. Shell length of a typical adult female L. c. chirugra ranges between 150 and 250 mm, has a whitish rose aperture with purple markings, a smooth columella, and a white depression at the presumed posterior end of the apertwe; the ultimate and penultimate knobs on the shoulder are larger than others present and are welded together, the 5' circum-aperniral projection produces a very high ndge on the dorsal side of the base of the last whorl. Shell length of a typicd adult male L. c. 97 chiragra ranges between 100 and 175 mm, has a rose aperture with purple markings, a strongly lirate columella, and a white and purple depression at the presumed posterior end of the aperture; the final two knobs on the shoulders are srnail and separate; the Sb projection produces a very low ridge on the dorsal side of the base of the last whorl.
Apart from differences of adult shell lengths, there are insignificant differences between female and male specimens of Lombis chiragra arthririca.
A typical adult shell of L. c. chiragra consists of 10 or 11 whorls, is enveloped by a thin periostracum, and includes a well-developed stromboid notch and 5 circum-aperturai projections emanating from a flared lip (Plate 3.1 1, p 107). Whorl sculpture consists of cords and threads; the aperture is white; colurnellar sculpture consists of lirae; and the columella is purple and pink (Plate 3.1 1).
Radular rows consist of a centrai tooth with 1 media1 cusp flanked by 2 or 3 smaller cusps; lateral teeth with 1 cusp at the edge proximal to the centrai tooth and 3 or
4 smaller cusps extending to the inner marginal teeth; inner marginal teeth with 5 cusps; and outer marginal teeth with 6 or 7 cusps (formula: 2- 1-2 or 3- 1-3; 1-3 or 1-4; 5; 6 or
7). The operculum has 16 semtions; the verge is simple (Figure 3.5, p 12 1); the mouth is stromboid (Figure 3.6, p 122); and the ctenidial filaments are moderately thick to coarse. Plates 3.3- 1 1. Shells of the genus Lambis.
Mislambis, L. crocara, L. tmncota, L. millepeda, L. digitata, L. robusta, L. scorpiur,
L. violacea, and L. chiragra.
CLADISTIC METHODOLOGY
The foregoing information conceming species of hnzbis, and similar information coded
for 26 species in the genus Srrombus and the single species in the genus Terebellwn, is
stored as binary code in a manix in Appendix V. For cladistic analysis, this 'whole
animal' (i.e., soft body and shell) information was recoded into states (individual
observable features, p 51) of 26 characters (features that function as groups of mutually
excluding hypotheses, p 56): 13 characters concem soft bodies and radulae and 13
concern shells. A discussion of characters and character states follows a bnef discussion
concerning coding polymorphic character states for use in cladistic analyses.
Coding Polymorphic Character States
Coding polymorphic character states for use in cladistic analyses cm be problematic.
Early in the history of cladistics, practitioners coded polymorphic character states exactly as they coded unobserved, or "missing," character states (Le., using the symbol ?; Nixon and Davis 1991; Platnick et al. 1991). Cornputer programs that perform cladistic analyses mat unobserved states as equivalent to multiple codings in which each one of al1 possible states of a single character occurs or al1 possible state combinations of multiple characters occur (Nixon and Davis 1991; Figure 3.2). Thexfore, if only some of al1 possible states of a single character or state combinations of a taon are observed. the coding of polymorphisms as missing may prohibit finding some or al1 of the most Figure 3.2 Effect of coding polyrnorphisms as unobserved character States for cladistic analysis.
A data mairix consisting of 5 taxa (tl-5) and 5 characters (cl-5) is shown (centre). The state of one character (c5) in one taxon (t3) is polymorphic and is coded as unobserved
(? Computer programs designed to analyse data matrices cladistically mat the ? coding as equivalent to O or 1. Therefore, two equally parsimonious cladograms result from the analysis: one in which the ? is treated as O (top; c5 is an autapomorphy of t4), and one in which the ? is treated as 1 (bottom; c5 is a synapomorphy of t3 and t4). Graphic elements on the cladogram follow the convention used in Figure 2.2.
110 parsimonious cladograrns that accurately represent information available (Nixon and Davis
1991). Furthermore, coding polymorphisms as unobserved states neglects the possibility that states other than any one of the various states observed may occur; it also neglects the possibility that polymorphisms rnay be inherited, that is, may be acquired by an ancestor and inhented by descendants (Platnick et al. 1991).
Unobserved, inapplicable, and polymorphic states should be coded distinctly, as the epistemologicai nature of the observations these terms represent are logically (if not computationally) different (Platnick et al. 1991). For example, states that can be assigned binary numbers to represent the manifestations of characters ought to be coded in a manner that represents either O or 1, if they are unobserved; neither O nor 1, if they are inapplicable; and both O and 1, if they are polymorphic (Platnick et al. 1991). Herein, the following conventions are followed: unobserved states for characters are coded using the symbol ? (equivalent to either O or 1 for characters representable by binary states, as discussed above) and inapplicable states (Le., states that are impossible to assign to a taxon) are coded using the symbol -. The coding of polymorphisrns is discussed beiow.
One approach to coding polymorphisms is to maintain the philosophical tenet that each terminal lineage in a cladistic analysis should bear only one state for each character.
If each one of al1 possible states of a single character or dl possible state combinations of multiple characters occur in terminal taxa, polymorphisms may be coded as unobserved
(i.e., using the symbol ?) and included in a cladistic analysis. The coding of 111 polymorphisms as unobserved in such cases is an expedient and has no affect on determination of the topology of the most parsimonious cladograrn(s). The distribution of characters on the most panimonious cladogram(s), however, will include "hidden homoplasy," and the length of the cladogram can be corrected using a mathematical formula (Nixon and Davis 1991). If only some of al1 possible states of a character or state combinations of a taxon are observed, terminal taxa should be separated into unique combinations of states known to occur (i.e., polymorphic terminal taxa should be recoded as monomorphic subunits; Figure 3.3) and included in a cladistic analysis.
There are algorithms and rules (Maddison et al. 1984) to determine the simplest
(Le., most parsimonious) hypothesis of character state polarisation even when terminal lineages bear multiple states, provided that outgroup cladograrns are resolved sufficiently.
Ingroup cladograrns based on synapomorphic states according to these niles and algorithms are globally most parsimonious cladograms (Le., cladograms with the fewest hypotheses of homoplasy for al1 characters exarnined within both the ingroup and outgroup). When outgroup relationships are unknown, two procedures for using characters with multiple states have been proposeci: rhe predominant states method and selection from various "candidate ingroup cladograms" (Maddison et al. 1984).
Implementing the predominant states method is tantamount to assuming that the state most common among outgroups is plesiomorphic. This cm veld cladograms that fail to fulfd global parsimony criteria. Altematively, using each of the possible outgroup states or state combinations, candidate ingroup cladograms can be resolved, and those candidate Figure 3.3 Separation of polymorphic terminal taxa into monomorphic subunits for cladistic analysis.
The two interpretations of the unobserved state (?) of character 5 for taon 3 in the data matrix of Figure 3.2 is distributeci between two taxa: taxon t3a represents the case in which ? is interpreted as O; taxon t3b represents the case in which ? is interpreted as 1.
Two characters (6-7) are added to the matrix of Figure 3.2 to maintain the monophyly of t3a and t3b (centre). Two equally parsimonious cladograrns equivalent to those presented in Figure 3.2 result fiom analysis. Graphic elements on the cladogram follow the convention used in Figure 2.2.
113
ingroup cladograrns that accord to the global parsimony critenon cm be selected A strict
consensus cladogram of those candidate ingroup cladograms selected (Le., a cladogram
consisting of only those clades common to al1 candidate ingroup cladograms that accord
with the global parsirnony criterion) rnay be chosen as the most appropriate ingroup
cladogram.
For this particular cladistic analysis of species of Lambis, polyrnorphisms are
assumed to be inheritable and are coded as character states distinct from the individuai
states comprising the polymorphisms. While the validity of this assumption may be debated, such an assumption provides a coherent, recoverable, and reproducible coding
scheme with which a cladistic analysis cm be performed. Disgmntied readers are invited to recode the information contained in Appendix V, perfonn a cladistic analysis, and substitute the cladogram obtained for the one presented here, in the rernainder of this dissertation. (Those readers also are invited to re-read the OVERTURE -- the thesis of this composition concems a methodology for formula~ghypotheses of morphological evolution, not the construction of a cladogm for Lambis). In the next paragraph, the coding of a central tooth character is exernplified.
The number of Banking cusps on central teeth is variable both within and arnong the various members of the Strombidae examined (Plate 3.12). For example, the cenaal tooth of Terebellwn terebellwn has 1 media1 cusp flanked by 3 or 4 smaiier cusps; that of
Strombus camriwn has 1 medial cusp flanked by 3 to 5 smailer cusps; and that of mis Plate 3.12. Variable number of Banking cusps of centx-ai teeth of species of Strombidae.
A centrai tooth of a specimen of S»-ombuc variabilis with 2 or 3 flanking cusps (top; scale bar represents approximately 25 pm). Radula of Sirombus margimtus with variable number of flanking cusps (bottom; cental tooth with 2 or 3 indicated with wedge; scale bar represents approximately 75 pm).
115 i&is has 1 medial cusp flanked by 2 or 3 smaller cusps (Appendix V). In sumrnary,
specimens of strombid species examined have a single medial cusp fianked by 2, 2 or 3, 2
to 4, 3, 3 or 4, or 3 to 5 smaller cusps. Therefore, states of the character 'number of
flanking cusps of central teeth,' which establish 6 hypotheses (each coded as a state), may
be defined: 2 coded as 2, 3 coded as 3, 2 or 3 coded as 5, 2 to 4 coded as 6, 3 or 4 coded as 7, and 3 to 5 coded as 8. The numerical values of these codings are inconsequentid, provided that states are unordered during analysis (i.e., changes between any two states count as one step on the cladogram), and are chosen for convenience (Le., codings are sums of states used in definitions: 2 = 2, 3 = 3, 2 + 3 = 5, 2 + 4 = 6, 3 + 4
= 7, 3 + 5 = 8). Each hypothesis proposes that there are strombids that possess a parricular number of flanking cusps to the exclusion of other rnembers of the Strombidae.
Similar schemes were used to code states for other characters (Appendix VI).
Schemes accompany descriptions of character states in the next subsection.
Statement of Characters and Definitions of Character States
Table 3.1 shows the various characters and their states for each species. Each character is described briefi y here. 1. Number of Flanking Cusps of Cenaal Teeth
Centrai teeth consist of a single medial cusp flanked by srnaller cusps in a series that
extends to the lateral teeth. Numben of cusps in the series are coded as distinct states (2
cusps are coded as 2; 3 as 3; 2 or 3 as 5; 2 to 4 as 6; 3 or 4 as 7; or 3 to 5 as 8).
2. Number of Cusps of Lateral Teeth
Lateral teeth usually consist of a single cusp proximal to the central twth and smaller cusps in a senes that extends to the inner marginal teeth. Numbers of cusps in the series are coded as distinct states (2 cusps are coded as 2; 3 as 3; 4 as 4; 2 or 3 as 5; 2 to 4 as
6; 3 or 4 as 7; or 3 to 5 as 8). Two species have lateral teeth that consist of 4 equivalent cusps (Strombus huemastorna and S. dilaratus -- coded as 9).
3. Denticle of Latexal Teeth
Lateral teeth of some species have a denticle ("peg" of Abbott 1960 and Abbon 1961).
Absence (coded as O) or presence (coded as 1) of a denticle are defined as states (Figure
3.4). Figure 3.4. Denticle of a lateral tooth (character 3).
Abbreviation used: denticle (d).
4. Nurnber of Cusps of Inner Marginal Teeth
Numben of cusps of inner marginal teeth are coded as distinct states (4 or 5 cusps are
coded as 1; 4 to 6 as 2; 5 or 6 as 3; 5 or 7 as 4; 5 as 5; 4 as 7; 6 or 7 as 8; or 4 or 6 as
9)-
5. Number of Cusps of Outer Marginal Teeth
Numbers of cusps of outer marginal teeth are coded as distinct states (5 cusps are coded as 1; 5 or 6 as 2; 6 as 3; 7 or 8 as 4; 4 or 5 as 5; 5 to 7 as 6; 6 or 7 as 7; 4 to 6 as 8; or
6 to 8 as 9).
6. Type of Cusps
Three types of cuneiform cusps of teeth common to several species are observed: punctate-tipped (coded as O), obtuse-tipped (coded as 1)' and elongated (coded as 4; Plate
3.13). Five types of cusps are unique to single species: 'millepedoid' (coded as 2)'
'chiragroid' (coded as 3), 'mutabiloid' (coded as 5)' 'plicatoid' (coded as 6). and
'vittatoid' (coded as 7) (Plate 3.13). Plate 3.13. Types of cusps of radula teeth of some species of Strombidae (character 6).
Types of cusps (location; species shown; approximate scale bar representation): punctate-
tipped (top, lefr; Strombus haernastoma; 50 pm), obtuse-tipped (top, nght; Lambis
rruncata; 650 pm), elongated (second from top, left; S. thersites; 200 pm), 'millepedoid'
(second from top, right; L. rnillepeda; 150 pm), 'chiragmid' (second hmbottom, left; L. chiragra; 150 pm), 'mutabiloid' (second from bottom, right; S. rnurnbilis; 100 pm),
'plicatoid' (bottom, left; S. plicatus; 100 pm), and 'vittatoid' (bottom, right; S. vittanu;
150 pm).
Numbers of serrations of the operculum varies (Appendix V). Srnooth operculae (with no serrations, coded as 0) and operculae with one of 6 combinations of semtions (10 coded as 1; 6 or 7 as 2; 7 as 3; 7 or 8 as 4; 12 as 5; or 16 as 6) are defined as States.
8. Verge Forrn
The verge is "simple" (following Jung and Abbott 1967 and Abbott 1960, 1961; coded as l), broad wiîh a process (coded as 2), simple with a process (coded as 3), broad (coded as
4), 'plicatoid' (coded as S), 'epidromoid' (coded as 6)' or 'marginatoid' (coded as 7)
(Figure 3.5).
9. Posterior Anal Canal
The posterior anal canal is untapered (coded as 1) or tapered ("short V-shaped channel" of
Jung and Abbon 1967, coded as 2).
10. Mouth Type
The mouth is 'stromboid' (coded as 1)' elongate (coded as 2), 'variabiloid' (coded as 3),
'epidromoid' (coded as 4), or 'luhuanoid' (coded as 5) (Figure 3.6). Figure 3.5. Verges of some species of Suombidae (character 8).
Verge forms: simple (top, left), broad with a process (top, right), simple with a process
(second from top, left), broad (second from top, nght), 'plicatoid' (second from bottom, left), 'epidromoid' (second from bottom, right), and 'marginatoid' (bottom).
Figure 3.6. Mouths of some species of Strombidae (character 10).
Mouth types: 'stromboid' (top), elongate (second from top), 'epidromoid' (second from bottom), and 'luhuanoid' (bottom). The mouth of Srrombus variablis is stromboid or elongate.
1 1. Ctenidial Filament Form
The state of the ctenidium is defined according to the form of ctenidial filaments: fine
(coded as O), fine to moderate (coded as l), moderate (coded as 2), moderate to coarse
(coded as 3), or coarse (coded as 4).
12. 0rnmatophore:Tentacle Length
The ratio ommatophore:tentacle length is defined as three arbitrary (but absolutely distinct) States: exceeding 10 (coded as O), between 4 and 10 (coded as 1). or less than 4
(coded as 2).
13. Mantle Filament Length
The mantle filament is absent (coded as O), short (coded as 1), of moderate Iength (coded as 2), or long (coded as 3).
14. Apical Sculpture
Sculpture of the shell apex is absent (coded as O) or present (1). 15. Whorl Sculpture
Various combinations of types of whorl sculpture are observed (Appendix V). Threads
(coded as O), carinae (prominent keels, Arnold 1965) and threads (slender linear surface
elevations, Arnold 1965) (coded as l), threads and beads (coded as 2), lime and ribs
(coded as 3), carinae, Iirae, ribs, and threads (coded as 4), ribs, varices and threads (coded
as 3,lirae, varices and threads (coded as 6), varices and threads (coded as 7), carinae, ribs, or threads (coded as 8), or beads (coded as 9) are defined as states.
16. Columella Sculpture
Various combinations of types of columellar sculpture are observed (Appendix V). A smwth columel1a (coded as 1) and one of 4 combinations of sculpturing (lirae coded as 2; smwth with lirae as 3; lirae with threads as 4; or lirae with ribs as 5) are defined as states.
17. Columella Colour
Various colours of the columella are observed (Appendix V). Black and brown (coded as l), brown (coded as 2), white (coded as 3), white and brown (coded as 4), mauve (coded as 6), crearn colour (coded as 7), brown and purple (coded as 8), or purple and pink
(coded as 9) are defined as states. 1 8. Aperture Colour
Various colours of the aperture are observed (Appendix V). White (coded as l), purple
(coded as 2), orange (coded as 3), rose and orange (coded as 4), rose, tan, and orange
(coded as 3,white, purple, and tan (coded as 6), brown and mauve (coded as 7), purple and mauve (coded as 8), or yellow and mm coiour (coded as 9) are defined as States.
19. Siphonal Canal Length
The siphonal canal is absent (coded as O), short (coded as 1), of moderate length (coded as 2), or long (coded as 3).
20. Twisted Siphonal Canal
The siphonal canal is untwisted (coded as O) or twisted (coded as 1).
21. Curved Siphonal Canal
The siphonal canal is uncurved (coded as O) or curved (coded as 1). 22. FIared Outer Lip
The outer lip is unflared (coded as O) or flared (coded as 1).
23. Circum-Aperturai Projections
The number of circurn-apertural projections is either O (coded as O), 1 (coded as l), 10 or
Il (coded as S), 3 (coded as 3), 5 (coded as 3,6 (coded as 6), 8 or 9 (coded as 8), or 9
(coded as 9).
24. Periostracurn Thic kness
The penostracum is thin (coded as l), moderately thick (coded as 2), or thick (coded as
25. Stromboid Notch Developmen t
The stromboid notch is pwrlydeveloped (coded as l), moderately-developed (coded as
2), or well-developed (coded as 3). Various combinations of whorl number are observed (Appendix V). An adult sheii of 7
(coded as O), 9 (coded as 1), 9 or 10 (coded as 2), 9 to 1 1 (coded as 31, 10 (coded as 4),
10 or 11 (coded as 3,11 (coded as 6), 7 or 8 (coded as 7), 8 or 9 (coded as 8)- or 8 to
10 (coded as 9) whorls are defined as States. Table 3.1. Character States of species of the iamily Strombidae.
States (nurnbers in columns) of characters are presented in order: (1) number of flanking cusps of cenaal teeth; (2) number of cusps of lateral teeth; (3) denticle of lateral teeth; (4) number of cusps of inner marginal teeth; (5) number of cusps of outer marginal teeth; (6) type of cusps; (7) operculum serration; (8) verge form; (9) postenor anal canal; (10) mouth type; (1 1) ctenidid filament fom; (12) ornmatophore:tentacle length; (13) mande filament length; (14) apical sculpture; (15) whorl sculpture; (16) columella sculpture; (17) columella colour, (18) aperture colour; (19) siphonal canai length; (20) twisted siphonal canal; (21) curved siphonal canal; (22) flared outer lip; (23) circum-apertural projections;
(24) periosuacum thickness; (25) suomboid notch development; (26) whorl number. Character states of species of the family Strombidae
Species Character States
Terebellum terebell um 7-08- 0-111 003 Strombus canarium 8-O-- 04212 121 Strombus thersites 3-?-4 40?11 22? Strombus urceus 5512- 05111 42- Strombus labiat us 55175 O-?22 22- Strombus rnicrourceus 2215- 03111 22? Strombus mutabilis 52112 5-121 12- Strombus maculatus 22?51 01?11 22? Strombus erythrinus 53152 0-111 12? Strombus haemastoma 59?-- 0??1? O?? Strombus dentatus 2-132 05221 223 Strombus fragilis 23152 03?21 222 Strombus plicatus 5-04- 6-521 42? Strombus dilatatus 29?73 O-?12 22? Strombus marginal us 57153 0-712 221 Strombus variabilis 6611- 4-1-3 12? Strombus minimus 56116 0-411 123 Strombus epidromis 5-13- 0-624 12? Strombus vittatus 550-5 7-111 221 Strombus v, campbelli 361-- 03112 22? Strombus lentiginosus 27036 0-321 42- Strombus aurisdianae 67016 02111 22- Strombus bulla 23071 ????? ??? Strombus vomer 23052 041?2 ??? Strombus 1 uhuanus 58024 0-325 22? Strombus decorus 58112 ?23?1 ??3 Strombus gibberulus 7708- 03312 22? Lambis lanbis 57028 10111 210 Lambis truncata 57049 1021? 310 Lambis crocata 22051 ?01?? ?10 Lambis millepeda 54033 20121 210 Lambis digitata ??O?? ????? ??O Lambis robusta 33017 001?1 ?10 Lambis scorpius 27092 011-1 110 Lambis violacea ??O?? ????? ??O Lambis chiragra 57057 361-1 310 The data in Table 3.1 were analyseci (states unordered) using the cornputer program
Hennig86 (Farris 1988) and invoking the mhennig (mh*) and branch breaking (bb*) options. These options guarantee that ail most-economicd cladograms detemined from a single heuristic search of the data matrix (in which only one tree is retained) are found
A consensus cladograrn of the 1246 equaily parsimonious cladograms (Le., a cladogram containing clades common to al1 1246 cladograms) resulting from the analysis (with lengths of 225 steps, consistency indices of 52%, and retention indices of 50%) is presented in Appendix VI. A clade within that cladogram, including al1 species currently recognised and named as Lombis (the ingroup) and thne species of Strombus is presented in Figure 3.7. Members of this monophyletic clade henceforth will be called 'lambis-like species. '
INTERPRETATION OF THE CLADOGRAM OF LAMBIS-LIKE SPECIES
The classification obtained from this cladograrn diffen substantiaily from previous, alpha- taxonornic classifications of genera of Strom bidae (e-g., Abbott 1961). According to the cladogram (Appendix VI), the genus Smmbuc is polyphyletic and Lnmois is paraphyletic.
Clades within the monophyletic larnbis-like species assemblage are inconsistent with cwent alpha-taxonomic su bgenera assignments. Mem bers of the subgenus Lombis (L. lumbis, L. crocotu, and L. truncuta; Abbott 1961) are dispersed arnong different clades Figure 3.7. Cladograrn of larnbis-like species.
A cladogram depicting a monophyletic clade (resulting hma cladistic analysis of data in
Table 3.1) chat contains species cmntiy recognised and named LmbLr (top).
The polychotomy containhg hmbis millepedo, L. digitata, and L. chiragra is represented
by PZ. whereas the polychotomy containing L. chiragra, L. crocata, L. robusta, Srrombus
bulla, S. dilatatus, and S. vorner is represented by Pl (bottom). Synapomorphic character
states are mapped ont0 intemodes. Autapomorphies are omitted for clarity (L. nuncata:
5-(9), 8-(2), 18-(6), 24-(2), 26-(2); L. rnillepedu: 2-(4), 4-(3), 5-(3), 6-(2),9-(2) 11-(3),
15-(9). 17-(2), 18-(7), 23-(9), 26-(6); L. digitata: 17-(6), 18-(8), 23-(S), 24-(3); L.
chiragra: 4-(3, 5-(7), 6-(3), 7-(6), 11-(3), 17-(9), 18-(l), 23-(5), 26-(5); L. violaces: 18-
(2), 23-(S), 26-(1); L. lambis: 4-(2), 5-(8), 17-(l), 18-(5); L. scorpius: 4-(9), 7-(l), 11-
(1), 16-(2), 17-(8), 18-(2), 26-(3); L. crocata: 2-(S), 5-(l), 15-(O), 23-(6), 24-(3); L. robma: 1-(3), 4-(1), 5-(7), 14-(l), 17-(7), 18-(9), 23-(6), 26-(1); S. bulla: 4-17), 5-(l),
15-(8), 18-(4), 20-(l), 22-(O), 26-(3); S. dilatanc~: 2-(9), 5-(3), 10-(2), 12-(2), 14-(l), 15-
(3), 23-(0); S. vorner: 4-(7), 7-(4), 10-(2), 16-(4), 26-(6)). Sympiesiomorphic character states (plesiomorphic states shared among the ingroup and some of the outgroups) at the root also are omitted (W),2-(7), 3-(O), 8-(l), 9-(l), 10-(I), 11-(S), 14-(O), 16-(l), 17-(3),
19-(l), 20-(O), 2 1-(O), 24-( l), 26-(4)).
131 within the ingroup (Figure 3.7). Two of the 5 rnernbea of the subgenus Millepes, L. millepeda and L. digitara, fom a trichotomy with L. chiragra, the lone member of the subgenus Chiragra (Abbott 196 1); whereas the remaining members of Millepes (L. violacen, L. scorpiu, and L. robusta) are dispersai among other clades (Figure 3.7).
The distribution of character states is presented on the cladogram (Figure 3.7). It is notable that state 1 of character 23 is a synapomorphy of polychotomy Pl (Mis crocata, L. robusta, Strombus bulla, S. digitatu, and S. vomer). The presence of this feature represents an unfalsified hypothesis that members of Pl posses a single circum- apertural projection to the exclusion of other lambis-like species (p 56; this character is observed in autapomorphic states in the two species of Lambis contained in Pl, however).
The three species of Snombur contained in Pl are the only members of Srrombus examined that possess circum-apertural projections. This observation gives credence to
Abbott's cautioning remark concerning Lambis: " ... fiom a biological standpoint, some workers might wish to consider them a subgenus of Srrombus."
Since Abbott's (1961) remark, new species of the subgenus Millepes have been described (e.g., L. arachnoides Shikama, 1971 and L. wheelwrighti Greene, 1978; Shikama
197 1 and Greene 1978). Descriptions were based on shells only, and the taxa probably are of hybnd origin. Kronenberg (1993) concluded that L. arachnoides was an invalid species, a hybrid of L. nuncata sebae (Kiener, 1843) -- a member of the subgenus Lambis
-- and L. millepeda (Linné, 1758) -- the type species of Millepes (he aiso concluded that 132
L. wheelwrighri was a junior synonym of L. arachides). His conclusion was based on
the observation that shells of the hybrids were morphologically intemediate between the
two parent species and the observation that hybridisation between members of the two
subgenera occurs (e.g., L. millepeda x L. L. truncata sebae, L. scorpius scorpius x L.
crocara crocam, and L. millepeda x L. lambis; Kronenberg 1993).
The subgenus MilIepes is characterised by " ... elongate apertures bearing well
developed lirae, by a siphonal canal which is either straight or cwed to the nght, and by
the presence of six to ten labial digitations" (Abbott 1961, quoted by Kronenberg 1993).
Kronenberg (1993) suggested that, because species of the subgenus Lombis have elongated
apertures, variabiy-shaped siphonal canals, and 6 digitations, the presence of lime rnight remain as the only diagnostic character state of Millepes. However, L. nuncara seboe might have lime on the outer lip (Kronenberg 1993). Given this observation and the fact
that hybridisation between mem bers of Millepes and Lombis occurs, Kronen berg (1993)
suggested that these two taxa should be synonyrnised and the concept of Millepes as a
subgenus should be abandoned.
On the basis of Abbott's (1961) cautionary remark (p 13 l), Kronenberg's (1993) observations and conclusions (above), and the cladogram obtained from analysis of the data in Table 3.1, the validity of current subgeneric classification of Lambis is dubious.
The cladogram in Figure 3.7, therefore, may be considered a tentative alternative classification, subject to further testing and analysis. No formal systematic classification 133 will be given here, however. In the remainder of this dissertation, this cladograrn will be used as the basis for proposing a hypothesis conceming the morphological evolution of lambis-iike species (Le., it will be interpreted as a phylogenetic me; pp 56-59). ON 'CONCHYALLOMETRY'
Mathematical Remodeling
The fundamental tenet of mathematical modeling in biology is that biological processes leave patterns that can be analysed numencally. Redicting potential pattems and interpreting empirically corroborated predictions in terms of processes underlying those patterns allows the plausibility and ments of models to be evaluated.
Numerical analyses can be applied to patterns at various scales, depending on the processes being investigated For example, cladistic methodology reconstmcts patterns that result from macroevoluîionary processes (e.g., speciation), whereas genetic models cm be used to decipher paaems that result hmmicroevolutionary processes (e-g.. population dynamics); physiological techniques permit inferences concerning details of processes occumng within tissues and organs (e.g., material transport by body fluids), whereas rnolecular models allow inferences of details about processes occumng within cells and their component parts (e.g., DNA replication). ON FORM AND GROWTH OF GASTROPOD SHELLS
At the level of individual organisms, the relationship between process and pattern manifests itself in the cause-effect interplay between growth and form. In his book, On
Growth and Form, D'Arcy Thompson (1917) epitomised the analytical and geomeaical approach that can be used to reaace individual growth processes hmpatterns.
Thompson devoted a substantial pomon of the chapter titied "The Equiangular Spiral" to the analysis of mollusc shells, and, to this &y, perhaps no other biological form has been analysed more completely in the spirit that Thompson intended (Stone 1996a; cf pp 24-28, wherein it is shown that some conchologists have analysed shells in a different spirit).
Recently, Stone (1995a) formulated a mathematical model, called 'CerioShefl,' that enables analysis and computer-graphical simulation of gastropod shells and that explicitly exploits the interplay between pattem and process both inscribed in shells (pp 66-68) and epitomised by Thompson's approach. The model reconsuucts shell fom as the sum of two aspects of accretionary growth. The "aperture trajec tory" represen ts the path through space (in a mathematical reference frame) followed by the cenm of a shell aperture during growth, and the "aperture scaling" represents the change in relative dimensions of the shell aperture throughout growùi. This model provides a convenient example with which the relationship between the mathematical modeling of form and the biological process of growth cm be examined. 136 The following is a rnathematically forma1 elaboration of the mode1 Srone 1995 (pp
44-45) and includes constants representing aspects of surface comgations. The fom of a
shell may be described rnathematically by a simple extension, into three spiralling dimensions, of Huxley's (1932) allomeaic equation:
where a is the allometric coefficient, b is the allometric exponent, and Y is a measurable variable that is related to another measurable variable, X. Such an equation can be used to describe aperture trajectory (radially (r) and abapically (2)) and scaling (radially (h) and abapically (v)) 'amplitudes,' whereas sine and cosine functions can be used to describe
'frequencies. '
To obrain shell foxm data, ir is convenient to measure specimens with reference to
Cartesian coordinates (Stone 1995). To facilitate analysis for sheli modeling, however, it is convenient to parametrise the data in terms of cylindrical coordinates. Then, an aperture mjectory (first terms of the following pararnetrisations) rnay be considered a function of growth increment (i),while an aperture scaling (second terms) may be considered a function of growth increment and accretion (s) at a mantle edge: 137 x[s,i]=O[i] ajbrSin[i]+H[i]a,ih(l +a,Cos[f,s])Cos [s]Sin[il
y [s,i]=O[i]a$""os[i]+H[i]abib'( 1+acCos[f,s])~os [s]~os[i] (4.2)
~[sj]=T[i]~~+V[i]aj~(l+acCos[fs])Sin[s]
The parametric variable i ranges hmO to 2m, where w is the number of whorls of a
shell, and the parameaic variable s ranges from O to 2x. The parametrisation using i is
based on the observation that, although shell accretion is a discontinuous process, a
trajectory is an indicator of life history, because the number of whorls comprising the
shell of an adult gastropod is charactenstic of species. The pararneaisation using s
represenu the accretion of sheli material around the entire outer edge of an aperture lip
(approximated as an ellipse). The allomeaic constants (a, br, a,, b,, a, b, a., b,)
describing aperrure tmjectory and scaling amplitudes cm be determined by regression
analyses (Stone 1995a), whereas those describing surface comgation amplitude and
fkequency (a, and f,) can be determined by numerical (e.g., Fourier) analyses. These 10 constants describe aspects of an aperture aajectory and scaling in terms of biological processes (growth increment, i, and accretion, s) and have particular values for a given taxon. The parameters offset (0)and horizontal expansion (H) affect horizontal components of the aperture trajectory and scaling, whereas translation (T) and vertical expansion (V) affect vertical components (p 44). In the rnodel, these parameters initially are set to unity, and the equations reconstnict measured shell forms (Stone 1995a).
However, any of these parameters may be set to other values, or varied continuously as a function of growth increment (i), to alter corresponding aspects of the shape and size of a 138 shell image. Changes in these parameters represent variation in aspects of an aperture aajectory and scaling that are orthogonal to each other.
Although this mathematical reformulation of Stone's (1995a) model explicitly identifies components of biological growth that cm be inferred hmshell form, it captures the process of shell growth only s~pe~cially.For example, the coiling axis around which the aperture 'revolves' is a product of the Sin[i] and Cosri] tems. which describe volutions of the shell. If the formation of this axis has any counterpart in the real process of shell growth, it is encoded in the genes of the snail, camied out in the cellular interactions within its soft body, and realised by secretion and subsequent acc~etionat its mantle edge.
Models that simulate an aperture meandering through space, unresuicted by reference to a coiling axis. have been formulated (growth-like models, pp 66-68). And while they can mimic the geometric freedom of accretionary growth found in irregularly coiled shells, even growth-like models fail to capture the biological processes involved in secretion at a mande edge. It follows that changes in the values of model parameten (O,
T, H, and V in equation 4.2), which induce geometric variation of shell images, can be only inferred to represent changes in processes occumng at the made edge.
Experimentation and funher analyses are required for the transformation of these inferences into well-founded hypotheses relating form and growth. 139 The formulation of the model presented here, therefore, nicely illustrates the distinction between form and growth reflected in the mathematicai modeling and anaiysis of pattems produced by biological processes. Many details about processes can be discovered from analyses of patterns; however, unless the mode1 employed explicitly describes aspects of biological processes, these details are only unidirectional inferences from form to growth.
REACTION-DIFFUSION MODELS OF SHELL PIGMENTATION PATTERNS
Another inmguing aspect of shell modeling (that also nicely illustrates the distinction between form and growth that is reflected in the mathematical modeling and analysis of pattems produced by biologicai processes) is simulation of colour pattems, or pigmentation (Turing 1952; Wngley 1948; Waddington and Cowe 1969; Lindsay 1982;
Wolfram 1984; Hayes 1995; Meinhardt 1982, 1984, 1995; Meinhardt and Klinger 1987; also Hamison's (1987) review and Bard's (1981) model for the generation of marnmalian coat pattems). Mathematical models of molluscan pigmentation pattems belong to the
"class"of developmental theones known as Reaction Diffusion Models (Harrison 1987).
These models posit that forms and pattems are explicable in terms of rates of chernical reactions and transport processes, which are describable mathernatically by parcial differential equations. The equations contain variables representing concentrations and spatial distributions of 'morphogens,' which may be defined as (actual or hypotheticai) substances that are considered to produce a rnorphological change between their source and theû surroundings (Turing 1952; Harrison 1987). In spite of their uncannily successful predictions, these models are based on processes that have yet to be verified empirically.
Morphogens interact. in terms of chernical kine tics, every morphogen interacts with at least one other morphogen, and at least one member involved in an interaction exhibits 'autocatalysis, ' 'self-enhancement, ' 'positive feedback,' 'self-reproduc tion, ' or
'assimilation' (i.e., its production funher increases its rate of production; Harrison 1987).
These nonlinear aspects of rnorphogenic interaction allow the spontaneous emergence of pattern amidst seemingly haphazard processes (Meinhardt 1995).
The production of shell omarnentation is a discontinuous process, as is the growth of shells (here only chromatic omamentation is considered, but reaction-diffusion theory also accurately describes textural omarnentation) . Pigment is released during shell secretion, and incorporation occurs during shell accretion. Thus, elaborations on a shell surface result hmevents occurring dong the row of cells lining a made edge, that is, shell pigmentation patterns are two-dimensional records of one-dimensional processes
(Meinhardt 1995; Hayes 1995)! So, just as a shell is a temporal record of ontogeny produced by the snail inside, the spatial dimension parallel to the âkection of accretionary growth of a shell contains the temporal component of the history of events occurring at the mande edge. 141
Meinhardt (1982, 1984, 1995; Meinhardt and Klinger 1987) considered the mathematics of several different cases of morphogen interactions that reproduce observed
sheii pigmentation patterns, of which the following equation is a generalisation:
where (W6t) is the denvative with respect to time operator, M represents the concentration of morphogen M, AC is a function describing the autocatalytic properties of morphogen
M, R is a function describing the rate of removal of rnorphogen M, & is the diffusion constant of morphogen M, (62/S~Z)is the second denvative with respect to spatial dimension x (arbitrady chosen) operator, and B, is a constant representing basal production of morphogen M. Equation 4.3 equates the rate of change of concentration of morphogen M to four terms: the function AC often is a nonlinear function of M (Le., is proportional to W, where n 2 2), that is, at least two morphogen molecules form a complex in the autocatalytic process; the function R often is a linear function of hW (e.g., r,, Rd, where r- is a constant), that is, the rate of removal of morphogen is proportional to its concentration; exchange by diffusion is proportional to the second spatial denvative to ensure that the net exchange of molecules is zero if either al1 cells have the same concentration of morphogen or there exists a constant concentration difference between neighbouring celts (i.e., there exists a linear concentration gradient); the constant term B, represents a smail, basal morphogen-independent morphogen production rate that can initiate the system at low morphogen concentrations and that is required for pattern 142 regeneration, for the insertion of new maxima during growth, or for sustained oscillations.
For example, to model stripes parallel to the direction of growth of shells,
Meinhardt (1995) proposed an activator-inhibitor reaction-diffusion model. In this scheme, autocatalytic activator morphogen molecule A promotes its own production but also catalyses production of its antagonist morphogen, the inhibitor 1. The interactions are described by the differential equations
where A represents the concenrration of activator A; s represents the source density, the ability of a cell to perfonn autocatalysis; r, is the decay rate constant for morphogen M; 1 represents the concentration of inhibitor 1; 1, and 1, are basal inhibitor production rates; and DM is the diffusion constant of morphogen M.
Activator A acts over a short range, whereas inhibitor 1 diffuses rapidly.
Generally, the concentrations of both substances cm be in a steady state, wherein an increase of A is compensated by an increase of 9. However, locally. the equilibrium is unstable. Any local increase of A is enhanced further, despite the fact that 1also increases, as a result of the following interactions. Inhibitor I diffuses rapidly, so inhibitor molecules move into the surrounduig areas, retarding autocatalysis there. The local inc~easeof A, therefore, elevates funher, and activator A accumulates locally.
Mathematically, the condition necessary for these interactions is
If the antagonising inhibitor 1 reacts very quickly to a change fiom steady state, the interaction cm becorne stabIe in time. In the model, this means that inhibitor 1 has a higher turnover rate than activator A. Mathematically this condition is
Under conditions described by equation 4.6, the mantle edge will consist of regions in which there is an accumulation of activator A and regions in which the production of activator A is suppressed. Under conditions of equation 4.7, this configuration at the mantle edge will be stable in time. If the mantie edge is considered to be a ring of cells containing morphogens, some cells will produce pigment, others will not. The result will be saipes parallel to the direction of shell growth.
Interpreang variations of equation 4.3, Meinhardt (1995; Meinhardt and Klinger
1987) was able to describe morphogenic interactions responsible for other shell patterns. 144 Oblique lines result hmtravelling waves of pigment production. Branchings and
crossings result hma temporary shift between an oscillatory and a steady state mode of
pigment production. Checkered or meshwork-like patterns result when an autocaialytic
substance is inhibited by two substances, a diffusible inhibitor that generates a pattem in
space and a nondiffusible inhibitor that is responsible for a pattern in time. Wavy lines
and rows of patches result from the superposition of two patterns, one that is stable in
time and controls the oscillation frequency of the other, which detemines the pigment-
producing process. The mathematical models reproduce fine details of natural patterns
and, in addition, account for pattern regulation. the regeneration of patterns observed on
specirnens after injury.
The pigmentation patterns of shells of Lambis consist of rows of patches parallel to
the direction of accretionary growth. Such pattems can be produced as a result of the
interaction between two activator-inhibitor systerns: a stable system and an oscillating
system. The stable system (which ultimately forms the 'background' colour) is similar to
the one described by equations 4.6-7 and acts as an additional inhibitor on the oscillating
system (which forms the patches). Oscillating pigmentation (the patches) occurs in time
only dong interstices ailowed by the stable system (the spaces between the stripes).
As alluded to previously (p 68), such pigmentation patterns could be produced in
roto and wrapped ont0 the surface of a computer-graphically simulated shell. The actual events responsible for patterns of real shells, however, occur at the mantle edge during 145 sheil secretion and accretion. Embenon (1963) observed a correlation between sheil banding and subepithelial melanocytes of the mantle in Cepaea. Cain et al. (1968) demonstrated that sorne pigmentation patterns may be controlled genetically. The actual processes responsible for pigmentation patterns remain a mystery. however. despite the accurate representation of patterns by morphogenic processes. This is a fascinating area of research that demonstrates the ongoing dynarnics between pattern (fom) and process
(growth) in shell modeling (pp 75-76). ONTOGENIC & CLADISTIC MORPHOSPACE
Morphological Space Revisited
In the analyses presented here, stmmbid shells are defincd by the parameters O, TTH, and
V (pp 135- 139; Stone 1995a). Four different combinations of these parameters can be used to delimit axes of Me-dimensional morp hospaces. that is, 4 different morphospaces can be constructed by omitting each of the 4 parameters sequentially and using the other three to delimit axes (6 different two-dimensional morphospaces cm be constructed, but each of these contains only approximately 2/3 of the information that is representable in a three-dimensional diagram). In this chapter, tiuee types of morphospaces will be introduced: 'Ontogenic. ' 'Cladistic, ' and 'Ontogenic-Cladistic. '
ONTOGENIC MORPHOSPACE
General Considerations
One constraining feature of morphospatial analyses performed in the past has been the constancy of parameter values. Particular organismal forms have been represented only as static combinations of values dong axes delimiting morphospaces (i.e., as points in 147 morphospaces). The significance of such representation depends on the types of parameters delineating the axes. which, synonyrnous with types of morphospaces (pp 21-
24). may be classifed as empirical, theoretical, or theoretical design.
For example, a point in Raup's Coiled-Shell Morphospace represents a form that has constant values d expansion (W), translation (T), and displacement (D). These parameters are theoretical (pp 24-28). Each describes a rate of change of a particular geometric aspect of form from one whorl to the next, so a point in morphospace represents a shell growing at a constant rate. According to definitions of Raup's parameters, such a shell grows isometrically (Le., in a manner that maintains geometnc similarity. or constant shape with changing size) -- the number of whorls determines its size. Static combinations of theoretical parameter values in other models may represent shells that grow allometncally (Le.. in a manner which maintains no geometric similarity).
In both cases, however, every single point in morphospace has been used to represent complete ontogenic history.
In contrast, each point in Gould's (1984) and Stone's (1996b)Cerion SheIl morphospaces represents an adult fonn that has particular values of height (h) and width
(d). These parameters are 80% empincal and 20% theoretical (p 25B). Each describes a measurable Iinear dimension of form, so a point in morphospace represents a shell that is fixed and unchanging. In this case, complete ontogenic history is representable by sets of points or curves in morphospace, though this never has ken practised. 148
Ontogenic information accounts for and describes shape and size throughout the
history of growth. When only adult forms are of interest to an investigator, representation
by 'pinpoints' (single points) in morphospace may be appropriate. However, investigators
interested in growth and morphogenesis (Le., the development of organismal fom, in
addition to its ultimate adult state) need to chart changes in shape explicitly.
Mathematical models of organic form are consmicts, and parameten that represent aspects
of form in these models often change during ontogeny. To accurately analyse ontogeny,
therefore, development should be reconsmicted as series of points in morphospace (Stone
1995b).
After sufficient numbers of specimens have been examined and analysed, a locus
of points in morphospace may be defined as that particular series that most precisely
typifies development. Each point in the series represents the form of an organism at a
padcular stage of development. a pinpoint of life history; and the locus of points may be considered as a track through morphospace, a trail of forms rravened by an organism during its ontogeny. A morphospace in which such tracks are included is defined here as
an 'Ontogenic Morphospace.' On the basis of this definition, parameters that accurately represent forms as single pinpoints in morphospaces (e-g., isomemc forms in Raup's W.
T, D morphospace) may be considered special cases wherein ontogenic tracks collapse to single points. Ontogenic Morphospace for Species of Lombis
Values of parameters for lambis-like shells (species of Strombidae included in the clade containing species of Lambb; Figure 3.7, p 130) were determined using shells of
S~ombucvarinbilis as an outgroup (Stone 1997b), in the following manner (S. varinbilis was chosen because it is the nearest outgroup to larnbis-like species for which morphomemc data was available; Appendices VI, VII). Equations of fom (containing the parameters O, T, H, and V) were fit to morphometric shell data obtained from radiographs (Stone 1995a; Appendices III, VID. Values of parameters contained in equations of form for S. variabilis were set to unity. A set of parameters that mathematically equated the form of S. variabilis to that of each lambis-iike species at several stages of ontogeny was determined. This set of parameter values mathematically represents the transformation of a computer-graphical image of a S. variabilir shell into that of each of the various larnbis-like species. The parameten O, T, H, and V are theoretical, and Ontogenic Morphospaces delimited by hem, iikewise, are theoretical.
Because numbers of adult shell whorls differ among the various Iambis-like species and S. variobilis and because images of early whorls on radiographs were difficult to measure precisely, values of parameters were determined only for whorls common to al1 species for which data were obtainable (whorls 5.5 to 8.5; B = 1 Ix to 172). The ontogeny of each species, therefore, is representable by 4 pinpoints in Ontogenic Morphospaces (8 = llir, 132, 151~.and 17~).Pinpoints were joined by suaight lines to form tracks in 150 morphospace (p 148). Information concerning subspecies designations of specimens used is included in Appendix 1 (insufficient information was available to conml for gender).
The htof the 4 possible Ontogenic Morphospaces (p 146) for species of Lambis is delirnited by the parameters T, H, and V (Figure 5.1). Most shells exhibit greatest variation in the parameter V, that is, vertical expansion of apertures is the predominant difference benueen S. variabilis and lambis-like species (tracks in Ontogenic Morphospace are 'vertical,' as depicted in Figure 5.1). Dunng ontogeny, shells of Lambis violacea undergo the greatest change in vertical expansion of al1 larnbis-like species; shells of L. trwicata change comparably, as do those of L. robusta; shells of L. digitara change moderately, relative to those of other lambis-Iike species; shells of L. chiragra, Strombus bulla, and S. vomer change only slightly; whereas those of L. lamois, L. crocara, L. scorpius, L. millepeda, and S. dilatatus change linle at dl.
Only shells of L. violacea, L. truncara, and L. digiiata undergo changes of any significance in H or T, relative to other larnbis-like species. Their ontogenic mcks curve accordingly. Shells of L. millepeda and L. crocata increase slightly in H and T; whereas shells of L. scorpiur decrease slightly in H and increase slightly in T. The short tracks of these larnbis-like species are onentated accordingly.
Tracks of lambis-like species in two of the other possible morphospaces (those delimited by O, H, V and 0,T, V) are similar to those in H, T, V morphospace, in a 15 1 qualitative sense (Figures 5.2-3). Track orientations differ, according to quantitative differences in parameter values, but relative positions are nearly identical (values of
pinpoint positions of tracks are tabulated in Appendix Vm). Tracks of L. mcam and L. violacea are in closer proximity to one another in O, H, V and 0, T, V morphospaces, however.
Tracks of most species in O, T, H morphospace are similar to their counterparts in the other possible Ontogenic Morphospaces (Figure 5.4; Appendix VIII). The aack of L. truncata is the only remarkable exception. Whereas in the other Ontogenic Morphospaces
L. truncata tracks were directed predominantly toward decreasing values of V, in O, T, H morphospace, this species increases in al1 parameters. During ontogeny, L. truncata shells increase in O, T, H and decrease in V.
CLADISTIC MORPHOSPACE
General Considerations
Positions of taxa in morphospace have no evolutionary significance: proximity of points in morphospace is indicative only of similaxity of form. In contrast, the task of cladistic analysis is to classify groups of organisms hierarchically by recovering patterns of shared apomorphic character states that are disànguishable from homoplasous character states (pp
56-59). The branching patterns that result from cladistic analyses can be interpreted as Figure 5.1. T, H,V Ontogenic Morphospace for lambis-like species.
Figure 5.2. 0, H, V Ontogenic Morphospace for Iarnbis-like species.
Figure 5.3. 0,T, V Ontogenic Morphospace for larnbis-like species.
Figure 5.4. 0, T. H Ontogenic Morphospace for lambis-like species.
156 reconsiructions of phylogenetic processes (pp 56-59). Therefore, in reconsmcting the
morphological evolution of groups of organisms, results of phenetic analyses in
morphospace could be interpreted in tems of results of cladistic analyses, by joining
positions of taxa in a morphospace with branching pattems of appropnate cladograms.
Because cladograrn nodes (which are interpretable as representing ancestors in phylogenetic scenarios) will occupy positions that represent particular foms in morphospace, morphologies of ancestors can be reconstructed!
Cladograms conventionally are depicted as two-dimensional line drawings. Two dimensions are sufficient to summarise analyses of information contained in data matrices, in an efficient, graphical manner. But there is no reason why cladograms cannot be extended into three or more dimensions (at least in a theoretical sense)!
Bookstein et al. (1985) discussed superimposition of branching patterns ont0 two- dimensional morphospaces (as opposed to the mapping of two-dimensional cladograms into three-dimensional morphospaces) but provided no theoretical basis for the determination of evolutionarily relevant positions of nodes. In die approach presented here, methods for determining positions of nodes in morphospace are prescribed, and mditional, two-dimensional cladograms are re-forrned (and refonned) into three- dimensional branching patterns contained in three-dimensional morphospace.
Mapping cladograms i~tothree-dimensional morphospaces can be accompiished if 157 appropriate positions for nodes common to sister-groups cm be located The IWO components that are essentiai to such a procedure are: outgroups for sister-group cornpansons and algorithms for positioning nodes.
Outgroups for Sister Group Comparisons: Gmmetric Functional Ingroups and
Outgroups
Watrous and Wheeler (1981) developed a method for polarking states of characters when multiple apomorphic states are observed in an ingroup. The methai, known as "functional outgroup analysis," makes use of the relative nature of apomorphies and the fact that information provided by states of each character is tested against information provided by states of each of the other characters, in a cladistic andysis. For example, if a character is coded as (polarised) binary states, these may be used to polarise a different character that has multipIe states (Figure 5.5). In fact, computer programs designed to perform cladistic analyses often make use of functional outgroup anaiysis.
In a similar rnanner, functional outgroups can be used for geomeaic comparisons of sister-groups in morphospace. Once the position in morphospace of each member of a sister-group (e.g., t 1 and t2, Figure 5.7, p 163) has been detemined, their common node can be detemined by using the next sister-group (e.g., tû, Figure 5.7, p 163) as a
'geomenic functional outgroup.' In this manner, procedures for locating positions of nodes (described in the next subsection) cm be applied to dl sister-groups successively, Figure 5 -5. Functional outgroup analysis.
States of a binary character (c 1) cm be used to polarise the three States of another c haracter (c2).
159 beginning at the root of the cladogram and proceeding toward the least basal pairing of taxa or vice versa (as described in the geomeaic algorithm example contained in the nexr subsection).
Algorithm for Positionhg Nodes
Three rnethods for positioning nodes will be considered: algebraic algorithms, optimisation procedures, and geometric algorithms. Because algebraic algorithms and optimisation procedures are established practices of cladistics (Felsenstein 1985; Huey and
Bennet 1987; Harvey and Pagel 199 1; Garland et al. 1992; and Wiley et al. 199 l), each is reviewed only briefly here, and use of the results is delayed until the discussion of
'Ontogenic-Cladistic Morphospace' (p 170).
Algebraic Algorithms and Optimisation Procedures
Algebraic algorithms and optimisation procedures cm be used to determine values of continuous variables at nodes of a cladogram. Therefore, values of parameten at various nodes of a cladogram cm be detemined and used to position cladogram nodes in the- dimensionai morphospace.
Algebraic algorithms (Felsenstein 1985; Huey and Bennet 1987; Harvey and Pagel
1991; Garland et al. 1992) prescribe topology-dependant algebraic fonnulae for 160 determinhg values of continuous variables at various nodes of a cladogram. The choice of algebraic algorithm used depends on the plausibility of the assumptions underlying that particular algorithm (e.g., Brownian motion mode1 of character state transformation in
Felsenstein 1985 or independent conaasts of Harvey and Pagel 1991).
ûptimisation procedures consist of mapping character states ont0 terminal branches of (two-dimensional) cladograms and infemng states at the nodes by minimising
'evolutionary steps ' (character state changes dong intemodes and terminal branches, p 58) according to various parsimony criteria. Wagner parsimony (Kluge and Famis 1969;
Farris 1970) stipulates that c haracters change states with respect to ordered sequences
(e.g., a change in state from O to 2 contributes 2 steps to cladogram length); Fitch parsimony (Fitch 197 1) places no restriction on character state changes (e-g., a change in state from O to 2 contributes only 1 step to cladogram Iength); Dollo parsimony (Farris
1977) optimises synapomorphies as unique entities on cladograms (i-e.,synapomorphies appear only once); and Carnin-Sokal parsimony (Carnin and Sokal 1965) disallows revenion of character states (i.e., once an apornorphic state has arisen on a cladogram, relatively plesiomorphic states cannot exist in subsequent clades further hmthe root).
Parameter values for 4 pinpoints of ontogeny (0 = I ln, 13r, 15n, and 17n) of each lambis-like species were coded for use in cladistic analysis (Stone 1997b; Appendix VIII') and optimised ont0 the c1adogra.m according to the Fitch parsimony criterion. States of 22 characters clustered ont0 two intemodes on the cladograrn and grouped two uichotomies 161 (Figure 5.6). Of the 22 States of characters mapped ont0 the cladogram, only two were features of translation 0;the parameter T explains the srnallest amount of morphological evolutionary change of shells of lambis-like species. These results will be used in the construction of an 'Ontogenic-Cladis tic Morp hospace for Lam bis-like Species ' (p 175).
Georneaic Algorithms
A geometric algorithm can be used to position nodes directly. For example, points representing sister-taxa in morphospace (e-g., tl and t2 in Figurr 5.7) may be joined by the quivalent sides of a nght angle isosceles triangle in three dimensions (the third side, joining the sister-taxa directly, is ornitted; Figure 5.7) . initially the vertex of the triangle,
(which represents their common node) is 'free to rotate' about a circle situated between tl and t2, perpendicular to a Line joining them (Figure 5.7). Because three points can define a plane, each isosceles aiangle, and hence each node, can be defined to lie in a plane containing the two sister-taxon endpoints (e-g., tl and t2 in Figure 5.7) and the point representing their sister-group (e.g., tû in Figure 5.7), which serves geometrically as a functional outgroup. This determines a unique point on the circle for placement of the node.
The use of isosceles triangles guarantees that the distance from the node shared by sister-taxa (the distinct, right-angled vertex of the isosceles niangle) to each of their representative points is identical. Geomeûicdly, this represents an assurnption of Figure 5.6. Coded parameter values mapped onto the cladogram of lambis-like species.
Parameter values at four stages of ontogeny for lambis-like species were coded and mapped ont0 the cladograrn of larnbis-like species, according to the Fitch parsimony criterion.
Figure 5.7. Geomeaic aigorithm for positioning cladogram nodes in three-dimensional morphospace.
Points representing sister-taxa in morphospace (tl and t2) are joined by equivaient sides of a right angle isosceles niangle in three dimensions. Taxon tO senes geometricaiiy as a functional outgroup: the plane it defines dong with tl and t2 intersects the circle at two points; that point closest to tO is the point by which their ancestor is represented.
164 equivalent amounts of morphological evolution between diverging lineages. The use of a nght angle is arbiaary and represents 'orthogonal evolution,' that is, the speciation of an ancestral taxon (the node) results in two perpendicular directions of evolution (the two orthogonal sides of the right angle isosceles aiangle).
Joining sister taxa by straight lines (the equivalent sides of right angle isosceles rriangles) guarantees that terminal branches traverse a minimal distance in morphospace.
It is a version of the Pythagorean theorem applied to morphological evolution: the shortest path of morphological change is hypothesised to have ken followed by each member of the sister-group pair. This hypothesis of morphologicid change is maximally sensitive to falsification by additional information (Popper 1987), because any datum consistent with the definition of a line will lie on that Line, whereas any datum that discords with the definition of a line will lie on any one of the infinitude of possible cuves joining the endpoints.
Cladistic Morphospace for Species of Lumbis
The geometric algorithm describeci in the preceding subsection was used to map the two- dimensional cladogram of lam bis-like species (Figure 5.6) in to the-dimensions, thus foming 'Cladistic Morphospaces,' in the following manner. Endpoints of tracks in
Ontogenic Morphospace were considered as representing (near-adult forrns of) Iambis-like species; polychotomies of the cladogram were represented by arithmecic means of points 165 representing species contained therein; and geomenic algorithms were used to detemine positions of nodes common to sister taxa, beginning with the sister-groups Lambis scorpius and the polychotomy consisting of L. crocara, L. robusta, Strombus bulla, S. dilatatus, and S. vomer, hencefonh known as 'P 1' (Figure 5.6; Figure 3.7, p 130).
For each of the 4 Ontogenic Morphospaces (Figures 5.1-4), a Cladistic
Morphospace was constructed (Figures 5.8-11). In each, Lambis truncata and a node of the cladograrn ('n4') are connected to their common node ('n5'). interpreted phylogenetically, this node (n5) represents the ancestor to al1 larnbis-like species. Because it occupies a position in morphospace, n5 might represent the form of the proto-larnbis- like ancestor! Similarly, node n4 might represent the ancestor common to 'P2' (the polychotomy consisting of L. millepeda, L. digitata, and L. chiragra; Figure 3.7, p 130) and node 'n3;' n3 might represent the form of the ancestor common to L. violacea and node 'n2;' n2 might represent the ancestor common to L. lambis and node hl;' and nl might represent the ancestor common to L. seorpius and Pl. On the basis of this phylogenetic interpretation of the Cladistic Morphospace analysis, shells of fanbis lambis,
L. scorpius, and members of Pl are similar and have changed insubstantially with respect to the forms of their ancestors, whereas those of L. truncata, members of P2, and L. violacea are dissimilar and have changed substantially with respect to the forrns of their ancestors. Figure 5.8 T, H, V Cladistic Morphospace for larnbis-like species.
Figure 5.9. 0,H, V Cladistic Morphospace for lambis-like species.
Figure 5.10. 0,T, V Cladistic Morphospace for lambis-like species.
Figure 5.1 1. 0,T, H Cladistic Morphospace for lambis-like species.
ONTOGENIC-CLADISTIC MORPHOSPACE
The branching patrems contained in the Cladistic Morphospaces described in the previous section were derived on a purely geometric basis. Positions of nodes are determined by two simplifying assumptions conceming phylogeneac processes (equivaient arnounts of morphological evolution in orthogonal directions) that cm be accommodated geometrically. The validity of these assumptions is untested but probably dubious.
Results of algebraic algorithms or optimisation procedures (described previously, pp 159-
161; Appendix VIII) use ontogenic data incomplerely. Using such techniques to determine parameter values at nodes to position those nodes neglects the temporal nature of ontogenic data (i.e., tracks in Ontogenic Morphospace collapse to synapomorphies on a cladogram). The morphological evolution of a group of organisms, which contains aspects of ontogeny and phylogeny, ought to be described by a methodology that makes efficient use of Ontogenic and Cladistic Morphospaces. Such a methodology is prescribed in the next subsection,
Coding Morphometric Parameters to Construct Ontogenic-Cladistic Morphospaces
Values of parameters used to construct a rnorphospace can be coded as character states for cladistic analysis (Appendix VIII; Stone 1997b). Using such character states, cladogram information cm be integrated into Ontogenic Morphospaces (this subsection) to construct
'evolutionary vestiges' in 'Ontogenic-Cladistic Morphospace' (in the Crescendo, p 176). 171
For example, the cladogram depicted in Figure 5.12 has the pairing of sister-taxa
'tl ' (with autapomorphy 'cl ') and 't2' (with autapomorphy 'c2') determined by
synapomorphy 'c.' Autapomorphies cl and cl are sets of parameter values and can be
used to describe the tracks of tl and t2, respectively, in morphospace. Their common
ancestor ('n'), according to a phylogenetic interpretation of the cladogram. is inferred to
be a taon that possessed synapomorphy 'c.' Synapomorphy c is a set of parameter
values that can be used to describe the track of n. In morphospace, n is representable by the track conesponding to that of 'tO' (sister-taxon to tl and t2) but with synapomorphy c as the character state, instead of the plesiornorphic state found in tO.
In practice, such an algorithm should be applied initially to the first outgroup, the sister-group to the ingroup (e.g., tO in Figure 5.12), and then to other branches of a cladograrn funher away hmthe root Tracks of ancestrai taxa (interpreted nodes of cladograms) will be determined automatically by sets of apomorphic character states dong intemodes.
Philosophical Considerations
The use or inclusion of characters in the construction of a cladogram emwded in a morphospace defined by similar characters is consistent both logically and scientifically.
Cladogram structure is determined by synapomorphies (shared apomorphic character states, pp 56-59). Synapomorphies are realised counterparts of independent testable Figure 5.12. Ontogenic-Cladistic Morphospace used to infer ancestrai mcks.
A cladograrn depicting a hierarchical classification of taxa tO, tl, and t2. Tracks in morphospace can be determined from sets of synapornorphic coded parameter values (c, cl, and c2). The track of node n may be interpreted to be the ontogeny of the ancestor to tl and t2.
173 hypotheses (characters, p 56). Because the outgroup aiterion for character state coding
(polarisation) is independent of evolutionary processes, the coding of each apomorphy is independent of the structure of the entire data matrix, the cladogram ~sultingfrom analysis of that data matrix, and the phylogenetic interpretation of that cladogram (i.e., apomorphies are "primary statements," and phylogenetic hypotheses are "secondary statements" sensu Deleporte 1993).
Therefore, concems of ckular reasoning in the testing of stare distributions of characters of particular interest ("ataibutes" sensu Deleporte 1993) on cladograms should surround character coding, not the exclusion of characters from analysis. For example, given a group of taxa for which states of 10 characters are coded, a cladogram using the fmt 7 characters might be obtained and used to test hypotheses conceming the other 3 attributes, or a cladogram using the final 7 characters might be obtained and used to test hypotheses conceming the frst 3 ataibutes. The two cladograms may differ, so the danger arises that different cladograrns wiU be used to test hypotheses conceming the same group of taxa, using the same characters (Deleporte 1993; a simpler case, involving
4 characten is presented in Figure 5.13).
A potentiai problem inherent in coding and mapping coded shell parameters ont0 cladograrns is that states of morphomeaic parameters may fail to provide synapomorphies for every intemode on the cladograrn. The result would be a loss of resolution, as clades would collapse into polychotomies. Figure 5.13. Mapping of character states ont0 a cladogram consmcted €mm those character states.
A data matrix consisting of 5 taxa (tl-5) and 4 characters (cl-4) is shown (centre). The states of one character (c2) are used to consmict a cladogram (upper) and as attributes on a cladogram constructed fiom those of other characters (lower). The two cladograrns differ.
Ontogenic-Cladistic Morphospace for Lambis-like S pecies
An Ontogenic-Cladistic Morphospace was determined for species of Lombis, in the
following manner. Values of parameters used to construct Ontogenic Morphospaces were coded as character states for cladistic analysis (Appendix Vm;Stone 1997b) and mapped ont0 the cladograrn of lambis-like species (Figure 5.6, p 162). Al1 apomorphic states on the cladograrn were detemined with respect to Snombirs varidilis (Le., parameter values of 1.00). Thus, apomorphic states were used to define pinpoints of development at which ontogenic tracks of larnbis-like species digress from that of S. variubilis.
An ontogenic ûack of S. variabilis was defined and drawn. This ontogenic aack differs frorn those contained in Ontogenic Morphospaces presented thus far (Figures 5.1-
4); it consists of pinpoints of 'actual' rnorphological ontogeny. The theoretical parameters
O, T, H, and V have been replaced with the variables r, z, h, and v, which represent empiricdly measurable aspects of form (pp 44-45; Figure AVIII. 1). Because translation
(T) accounted for the srnailest amount of rnorphological change (p Ml), the abapical distance travelled by the aperture centre (2) was the least informative variable, and the track was drawn in t, II, v rnorphospace. Similar tracks were drawn for other lambis-like species. Crescendo
In Figure 5.14, the ontogenic track for S. variabilis is presented. Also included in Figure
5.14 is the ontogenic track of the ancestor (anc2) common to members of P2 (the polychotomy consisting of L. millepeda, L. digitata, and L. chiragra) and L. violacea.
According to apomorphic parameter values, the ontogeny of this mon divergeci from that of S. variabilis by increasing the vertical dimension and radial offset of its aperture. A shell form reconstmcted from the ontogenic mck is presented at the last pinpoint.
In Figure 5.15, the ontogenic tracks of members of P2 are drawn. Tracks are orientated predominantly towards increasing vertical dimensions of apertures (v), though the various tracks differ in length. In Figure 5.16, the ontogenic mck and a reconsmicted shell form (presented at the last pinpoint of ontogeny) of the ancestor to the rest of lambis-like species (L. lambis, L. scorpiur, and members of Pl -- the polychotomy consisting of Strombus buila, S. dilatatus, S. vomer, L. crocata, and L. robusta) -- is drawn dong with tracks of those taxa. Again, the predominant trend is towards increasing v. Figure 5.14. Ontogenic-Cladistic Morphospace for some lambis-like species.
Ontogenic tracks of Strombus variabilis (Svar) and the ancestor (anc2) common to hbis rnillepeda, L. digitata, L. chiragra, and L. vioiacea depicted in morphospace. The sheil form of the ancestor is reconstmcted hmits ontogenic track (two different viewpoints are presen ted).
Figure 5.15. Ontogenic-Cladisric Morphospace for some larnbis-like species.
Ontogenic aacks of Lambis Zambis (Llam), L. scorph (Lsco), Srrombus bulh (Sbul),S. dilutam (Sdil), S. vomer (Svom), L. crocatu (Lcro),and L. robusta (Lrob) depicted in
morphospace (two different viewpoints are presented).
Figure 5.16. Ontogenic-Cladistic Morphospace for some lambis-like species.
Ontogenic tracks of Lombis lambis (Llam), L. scorpius (Lsco), Srrumbus bulla (Sbul), S. dilatatus (Sdil), S. vomer (Svom), L. crocata (Lcro), L. robutta (Lrob), and the ancestor
(ancl) to ail of these taxa depicted in morphospace (two different viewpoints are presented).
180
Elements of Figures 5.14-16 are combined in Figure 5.17. This graphic provides a visual interpretation of a hypothesis of evolution for larnbis-like species. Tracks in this
Ontogenic-Cladistic Morphospace are 'vestiges, ' mces of ontogeny recoverable through phylogeny. The ancesaal mcks represent 4 stages of ontogeny of foms that may have speciated to give rise to extant lambis-iike species (fossil specimens to test this hypothesis were unavailable for this dissertation -- they are scarce (Abbott 1961); however, extensive study of fossil Strombidae currently is ongoing (Voskuil, Ponder, and Loch pers. corn.)).
In this sense, Figure 5.16 recapitulates the ideas of Haeckel (1879, quoted in Cuemer et al. 1996), albeit in reverse order
"The ontogeny or individual developmental history of every organism (em bryology and metarnorphology) produces a simple, unbranched or ladder-like chain of forms, and likewise that part of phylogeny which contains the paleontological evolutionary history of the direcr ancesrors of each individual organism. On the other hand, the whole phylogeny, which we encounter in the naturai system of each organic trunk or phylum. and which repeats the paleontological evolution of al1 ramifications of this trunk, forms a branched or tree-like evolutionary series, a genuine evolutionary me." Figure 5.17. Ontogenic-Cladistic Morphospace for lambis-like species.
Ontogenic tracks of lambis-like species, evolutionary vestiges depicting diverging developmental stages, according to phylogenetic history.
RECAPITULATION
1. A morphospatial anaiysis of uses of morphological space demonstrated that this instrument can be exploited to examine organic form mathematically in three different ways: empirically (Empincal Morphospace), theo~tically(Theoretical Morphospace), and functionally (Theoretical Design Space). New methods for tracking changes in shape during ontogeny and for positioning cladograrn nodes in three dimensions extended the concept of morphological space to accommodate developmental and phylogenetic information.
2. A phylogenetic systematic anaiysis of mathematical conchology showed that this instrument has evolved as two subgroups of models: one primarily considenng patterns of form, the other primarily processes of growth.
3. A cladistic analysis of species of Strornbidae pemined the formulation of a phylogenetic hypothesis for larnbis-like species.
These three cornplementary instruments (morphological space, mathematical modeling, and cladistic methodology) were orchestrated to develop Ontogenic-Cladistic
Morphospace, a space in which phylogeny and ontogeny harmoniously intermingle to 183 quantify the morphological evolution of a group of organisms. In the development of this synthesis, the following particular conclusions and observations concerning evolution of lambis-like species were made:
i. The generic classification of the family Strombidae is tenuous. The hierarchical classification obtained from a cladistic anaiysis of species of Smmbidae reveaied that, with respect to current alpha-taxonomie classification, the genus Lnmbis is pmphyletic and the genus Strombus is polyphyletic (Figure AVI.1, p 256).
ii. Cmnt subgenenc classification of the genus Lambis is untenable. The hierarchical classification (mentioned above) included a monophyletic clade containing al1 species currentiy classified in Lambis (larnbis-like species, Figure 3.7, p 130) and some species of
Strombus. This hierarchical arrangement is inconsistent with current alpha-taxonomie classification.
iii. Tracks in Ontogenic Morphospace (Figures 5.1-4, pp 152- 155) show that the predominant trend of morphological evolution of lambis-like species consisted of an increase in the vertical dimensions of whorls (apertures).
iv. Contrary to traditional representation, the cladogram for lambis-like species was mapped into morphological space as a three-dimensional branching pattern, forrning
Cladistic Morphospace. Phylogenetic interpretations of these three-dimensional branching patterns (Figures 5.8- 1 1, pp 166-169) reveal that morpholo~calchange was greatest during the early evolutionary history of lambis-like species and diminished thereafier.
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Several constraints prevented field observation and collection of Lambis specimens; instead, museum collections around the world were used. Collections of Lambis specimens are scarce, and lots contain few individuals, pariicularly of rare species. Rior to the current decade, access to rnuseum collections was expensive in terrns of both money and tirne. However, now other means of obtaining specimens are available.
During the past decade, the Advent of the 'Intemet' (the global-wide area network that uses 'Internet Protocol' to interconnect many com puters worldwide; Hahn 1993), and availability of powerful personal cornputers. greatly facilitated rapid msfer of information. Collection catalogues of museums around the world were surveyed via
'gopherspace ' (dl information accessible via the 'gopher, ' an Intemet service that permits access to a wide variety of cornputer data bases worldwide; Hahn 1993) and by 'surfing the World Wide Web* (an Intemet service diat links to information stored in a large number of hypertext-based data bases worldwide; Hahn 1993). Curators were 'emailed' and asked whether specimens could be borrowed. Positive responses came from curators at the Academy of NaW Sciences (Philadelphia, curator G. Rosenberg), Agassiz
Museum of Comparative hlogy (Cambridge, curator T. Kausch), Australian Museum of
Natural History (Sydney, curator 1. Loch), Delaware Museum of Naturd History 21 1 (Wilmington, curator P. Mikkelson). and Peabody Museum of Natural History (E. Lam-
Wasem). Mean acquisition period (the period of time between receipt of email query by a
curator -- determined by time of email response - and the physical receipt of specimen
loan) was 86 days (range 26- 136 days).
In total, 101 lots (693 specirnens) were borrowed (those examined are listed subsequently). All curators generously agreed to permit dissection of specimens (only 1 per lot), provided that al1 materials were renimed upon completion of study. Lists of catalogue numbers, species, numbers of specimens, and comments follow on the next 10 pages. 212
Lots bormwed from the Academy of Natural Sciences. Bodies of specimens from alcohol
preserved lots were exarnined and dissected (* indicates specimens that were examined
only) . S hells comprising dry specimens were radiographed (Appendix III; al1 were figured
in Abbott 1961 (indicated by ").
Alcohol Reserved S pecimens (body and shell)
Catalogue Num ber S pecies Specimens Comments
ANSP 205459 Strombus variabilis
ANSP 20639 1 Ldisscorpius
ANSP 207070 Strombus variabilis
ANSP 207978 Strombus variabilis
ANSP 211097 Strumbus margimtus
ANSP 212429 Mischiragra
ANSP 212698 Strombus plicarus
ANSP 214483 Terebellum terebellum
ANSP 214498 Strombus plicatus
ANSP 229797 Strombus marginatus
ANSP 22987 1 Terebellum terebellum
ANSP 230867 Strombus minimur
ANSP 230869 Strornbus variabilis ANSP 232166 Srrombus vittancs
ANSP 237062 Lambis truncata
ANSP 239413 Srrombus variabilis
ANSP 258009 Srrombus minimus
ANSP 261046 Terebellum rerebellum
ANSP 261645 Strombus plicatus
ANSP 27 1979 Strombus plicatus
ANSP 302623 Strombus margi~fus
ANSP A15610 Strombur gracilior
ANSP A1561 1 Srrombus granulatu
ANSP A 6068 S wombus pug ilis
ANSP A 6073 Srrombus raninus
ANSP A 6074 Srrombus camrium
ANSP A 6075 Strombus thersites labeUed "thersiter"
ANSP A 6279 Srrombus gigas
ANSP A 9307 Strombus luhuanus labelled as 1 specimen Dry Specimens (shell only)
Catalogue Nurn ber S pecies Specimens Comments
ANSP 181794 Sirombus septirnus
ANSP 182563 Strombrrs gigas specimen chipped
ANSP 185442 Strombus urceus
ANSP 185449 Strombus marginatu
ANSP 189133 Strombus farciarirs
ANSP 192937 Lambis vioiacea
ANSP 194550 Strombw tricornis
ANSP 199878 Strombus iubiatus
ANSP 201470 Lambis chiragra specimen chipped
ANSP 203619 Strombus variabilis
ANSP 206999 Strombus pulchellus
ANSP 207068 Strombus gibbemius
ANSP 2073 11 Strombur luhuanu
ANSP 21 11 18 Strombus ruccinctus
ANSP 212819 Lambis crocata labelled as 1 specimen
ANSP 215318 mistruncata
ANSP 223042 Strombur iabiatu
ANSP 223840 Strombus variabilis ANSP 223975 mischiragra lA
ANSP 228924 Lambis millepeda 8*
ANSP 23 IO95 Strombus minimus 4A
ANSP 231549 Sttombus pulchellus 3*
ANSP 232305 Strombus pifus lA
ANSP 234254 Strombus vittatus campbelli 3A Iabelled "S. campbelli"
ANSP 2349 19 Strombus gracilior
ANSP 240155 Strombus thersites
ANSP 242 122 Strombus gibberulus
ANSP 245946 Strombus vittatus
ANSP 24693 1 Lambis lambis specimens chipped
ANSP 252183 Strombus marginatur
ANSP 326151 Srrombus raninus
ANSP 39859 Strombus rypelli
ANSP 39862 S~rombussibbaldi
ANSP 39879 mispseudo scorpia 216
Lots borrowed From the (Agassiz) Museum of Comparative Zoology. The body of a single specimen from lot 288879 was exarnined and dissected.
Alcohol Preserved Specimens (body and shell)
Catalogue Number Species S pecimens Comments
MCZ 288879 Srrombus luhuanus I
MCZ 3 15950 Lambis scorpius 1 217 Lots borrowed from the Austraiian Museum of Natural History. Bodies of specimens
were examined and dissected. Individuals were removed hmshells either by careful manipulation of the body (gentle exmision of the body und the columellar muscle detached from the columella) or by careful peeling of the body whorl (in a manner similar to that executed by crabs), und the body was exposed and easily exmcted. Shells of 13 individuals proved too robust to permit extraction by either methoci. With permission of cwator 1. Loch, shells of these individuals were crushed in a materiais testing machine
(Appendix IV).
Specimens Extracted by Manipulation of Body or by Peeling of Body Whorl
Catalogue Num ber Species Specimens Comments
AMSG CO758 11 Sirombus thersites 1
AMSG C306373 Lambis lambis 2
AMSG C306375 Misrobusta 1
AMSG C306377 Strombtrs dilatarus 3
AMSG C306379 Strombur decorus 2
AMSG C306380 Strombur lentiginosus 1
AMSG C306381 Strombur aurisdiame 1
AMSG C306397 Strornbur dentarus 8
AMSG C306398 Strombur vomer 2 labelled as 1 specimen 218
AMSG C306399 Strornbus epidrumis
AMSG C306401 Strombus huemusforna labe lled "haernastornur "
AMSG C306402 Sirombus bulla
AMSG C306403 Strornbus jkzgilis
AMSG C306404 Strombus microurceus
AMSG C306405 Strombu maculatus
AMSG C306409 Strombus rnutabilis
AMSG C306410 Strombus gibberulus
AMSG C306411 Strombus labiatus Specimens Extracted Using a Materials Testing Machine
Catalogue Number S pecimens Comments
AMSG C30637 1 Lambis millepeda
AMSG C306372 Lambis chiragra
AMSG C306374 Lambis scarpius
AMSG C306376 Strombus campbelli labeiled as "many"
AMSG C306378 Strombus urceus
AMSG C306393 Terebellum terebellum
AMSG C306394 Strombus vittatus
AMSG C306395 Strombus ca~rium
AMSG C306396 Strombus minimus
AMSG C306400 Strombur erythrinus labeiled as "many"
AMSG C306406 Lambis truncata
AMSG C306407 Stromb w plicatus 3 juvenile + 1 1 adult
AMSG C306408 Strombus variabilis 220
Lot borrowed from the Delaware Museum of Natural History. The body of a single specimen was examined and dissected.
Alcohol Preserved S pecimens
Catalogue Number Species S pecimens Comments
DMNH 116760 Strornbus luhuanus 1 sheil + 7 bodies 22 1 Lots borrowed kom the Peabody Museum of Naturd History. Bodies of specimens were examined-
Alcohol Preserved Specimens (body and shell)
Catalogue Number Species S pecimens Comments
YPM 2188 Strombus grandatus 5
YPM 12791 Srnombus fasciatus 5
YPM 12972 Strombus mutabilis 5
YPM 12973 Stromb us gibberulus 5 Appendix II. SCANNING ELECTRON
MICROSCOPE TECHNIQUES USED
The following techniques for specirnen preparation were derived from those described by
Solem (1972).
To determine States of characters associated with each radula examined, the buccal mass was dissected (Appendix 1) and placed beneath a dissecting microscope. Radulae are cornposed of chiton. Therefore, gentle hea~g(in a Stender dish on a hot plate) of a buccal mass bathed in a solution that is approximately 10% potassium hydroxide (KOH) and 90% distilled water (by volume) degraded and dissolved sumunding soft tissues, pennimng isolation of the radula. Time required for complete dissolution of soft tissues ranged between approxirnately 1 and 2 hours and depended on the manner of specimen preservation (in increasing order: freshly preserved. aicohol preserved, and formalin preserved). Radulae were washed in distilled water, then 70% ethyl alcohol, to remove din, traces of soft tissue, and recrystallised KOH. Each radula ultimately was examined under both a light microscope (Olympus mode1 SW,7-5-64 magnification range, fitted with a camera lucida) and a scanning electron microscope (SEM; Hitachi S-2500)
(Hickman 1977). Each SEM stub was wiped clean with tissue dampened with 70% ethyl alcohol,
and the shaft of each snib was pressed into a wad of plasticine on a glas microscope
di&. The surface of each stub was coated with rubber cernent. A drop of 70% ethyl
alcohol was placed on the rubber cement to retard cementation and replenished continually
as it evaporated Using fine forceps, each isolated radula was transferred to the surface of
a stub and placed into the drop of cernent. Whilst viewed under a binocular microscope,
each radula was twist& distorteâ, contorted, discombobulatexi, and disarticulate& using dissecting pins, until some teeth at the postenor (unused) end of the radula ribbon promded completely, as they would be during feeding (Plates AII.1-2; Hickman (1978) proposed another method for protmsion); some teeth remained unprotruded and folded, as they would be during periods of nonfeeding .
Once a satisfactory (maximaily infonnative) configuration (one showing both protruded and folded teeth was achieved) the dissecting pins were withdrawn, and the cernent was allowed to dry. During the first 30 s or so, the radula could be manipulated, and a fibond between radular membrane and stub was assured. Shnnkage of the basal membrane during cementation enhances contortion of the radula and, hence, visibility of teeth. Afier cementation was complete, specimens on stubs were sputter-coated with gold
During SEM examination, numbers of cusps on radular teeth were observed and pho tograp hed. Plate An. 1. Scanning electron micrographs of unused and used ends of a radula.
Unused end of a radula of mistmncata (top; scale bar represents approximately 350 pm). Used end of the same radula (bottom; scale bar represents approxirnately 70pm).
Plate An.2. Manipulation of radulae for maximaily informative examination.
Twisted, distorted contoned, discombobulated radula of Lamois rnillepedo with protmding teeth (top right and Ieft; scde bar represents approximately 400 and 450 Fm, respectively). Disarticulated radula of L. scorpiur with exposed teeth (bottom; scale bar represents approxirnately 400 pm).
Appendix III. RADIOGRAPHIC TECHNIQUES USED
S pecirnens (Appendix 1) were raàiographed to obtain morphometric shell data (Appendix
W) to which equations of form (Appendix VII) were fit (Stone 1995a). The radiographic procedures followed were derived from those described by Stone (1995a). Specimens were placed on either an opaque plastic bag or radiographic plate containing a sheet of photographic emulsion (Kodak Xndustrex SR). Specimens were maintained in approximate life orientation, apertures flush with the surface of the imaging platform. Radiographs were made using a Hewlen Packard Faxinon Mode1 43805N X-Ray machine. Radiation voltage ranged between 50 keV and 90 keV, and times ranged between 240 and 300 S. Appendix IV. MATERIALS TESTING TECHNIQUES USED
SheUs that were too robust for manual extraction of contained soft bodies were subjected to compression tests using an Instron Mode1 1 130 materials tesring machine. The mshing device consisted of a tension load ce11 fitted with compression jigs. Compression speed was 0.5" per minute (0.02 mm s-'), and chart speed was 10" per minute (0.4 mm s-
) Full scale readings of force used were 100, 200. 500, and 1ûûû Ibf (pound force; 445,
890,2224, 4448 N). Appendix V. INFORMATION MATRIX
Infoxmation conceming species of Lambis. 26 species in the genus Strombur, and the single species in the genus Terebelium is stored as binary code in a manix on the next 23 pages (Symbols: O = absent; 1 = present; ? = unobserveci; gr/a = greatly reduced or absent). species central lateral teeth teeth f orrnula formula
212 313 414 5 1 5 12 13
T ter O 1 1 O O O
S can O 1 1 1 O 1 S the O 1 0. O O O S urc 1 1 0 O 1 1 S lab 1 1! O O 1 1 S mic 1 0 1 O O 1 O S mut 1 1 O O 1 O S mac 1 O O O 1 O S ery 1 11 O O O 1 S hae 1 1 O O O O S den 1 O O O 0 / 1 s fra 1, O O 0 ! O I 1 S pli 1 1 1 O O O 1 S di1 1 O O O O O s rnar 1 11 O O 0 1 1 S var 1 1 1 O 1 1 S min 1 1 O O 1 1 S epi 1 1 O O O, O Svit l 11 1 i O O 1 1 s v cam O 11 O O 1 1 S len 1, O O O O 1 s aur 1 1 I 11 1 O O 1 S bu1 1 0 1 O O O 1 S vom 1 0 1 O O 1 ------O - S luh 1 1 O O O 1 S dec 1 1 O O O 1 S gib O 1. 1 0, O 1 i L lam 1 1L tru 1 L dia
L vio L chi 2: species lateral ! teeth formula
1 14 15 16 !1 7 18 19
T ter O 1 O O O O s can I 1 1 11 1 1 S the O 1 1 1 0 1 O O S urc O 0 0 1 O 1 O O S lab O O, 0 1 0 ( O O S mic 0 0 0 0 1 O 0 S mut 0 0 0 1 O i 0 O S mac O O O 1 O 1 O O s ery O O O i O i O O S hae O O O 1 0 1 O O S den O O, O ' 0 1 O O S fra O O / O' O 1 O O S pli 1 O / 1 ; O i O O S di1 O O I O 1 0 1 0: O S rnar 1 O! 0 1 0 / 0 1 0 S var 1 1 0 1 0 1 O 1 O O S min 11 O l O 1 O 1 O O S epi II 11 O 1 0 1 O O S vit 01 O [ O i 0 1 O O S cam 11 0 1 O i O 1 O O S len 1 0 1 O i 0 O O S aur 1 0 I 0 ' 0 i O O S bu1 O' 0 1 0 1 O O O s VO~ O O f 0 i O O O S luh 1 1 1 0 1 0; O O S dec 1 1) 0 / 0 1 O O S gib 1 O O 1 0 1 O O l ! L lam 1 0 1 0 1 0 1 O O L tru 1 O O 1 O O O L cro O 0 1 O ( O O O L mil 1 O 1 O 1 O O O L dig .? ? (? !? ,? ? L rob O 1 O l O i O 0 1 O L SC0 1 i O] 0: O. O O L vio ? j? I? ? ? ? L chi 1 1 0 1 0 i O 1 O O species lateral 1 denticle inner 1 teeth lof I marqinal) formula lateral teeth teeth formula I
1 1 1 T ter 0 1 o ( 0 o 1 0 0 I 1
S urc S lab I 0 S mic 1 0 - -- smut I 0 - - s mac 1 0
S den S Era 0 S pli 0 0 0 0 0 0 S dil l? 0 0 0 1 S mar 0 1 0 0 0 0 S var 0 1 i 0 0 0 1 1 S min 0 1/ 0 I 0 0 1 Sepi , 0 1 1 0 0 0 0 S vit 0 0 1 0 l 1 / 1 1 S cam o! 1 I 11 0 0 0 s len I I 1 o l o i o o I I o o S aur [ 0 0 I 0 1 0 0 1 S bul 0 0 1 0 1 0 0 1 S vom 0 0 I 0 1 0 0 0 S luh 1 0 0 1 o! 0 0 1 S dec 0 1 0 0 0 I S gib 0 0 0 0 0 0
L lam 0) o I o 1 0 I o L tru i o / 0 0 I 0 1 0 L cro I 0 0 0 0 0 L mil 0 0 0 0 0 L dig ? O? ? ? L rob 0 o! 0 0 0 L sco 0 0 0 I 0 0 L vio ? 0 ? I? ? L chi 0 0 1 0 1 0 0 species inner ' outer marqinal + marginal 1 / teeth 1 ! 1 teeth I formula ' ! formula ! 5 6 i 7 9 2 3 i 1 I I T ter 0 f 1 i 1 I 0 I O O 1 S can O 0 i 0 1 O 1 1 0 S the O 11 0 1 11 O O s urc 1 1 1! 0 l 0 1 0 1 0 S lab O O i 0 / 0 1 0 1 O S mic 1 0 i O 1 0' O 1 O S mut 1 0 1 0 1 O 0 1 O S mac 1 O i O O O O s ery 1 1 O! 01 O! O O S hae O 1 I O 1 O ( O' O S den 1 1: O l 0 1 0, O S fra 1 O' O 1 O] O O s pli 1 O. 11 0 1 O O S di1 O 0 ! O I O 1 O I O I I s rnar 1 O. O i O i O 1 O S var 1 O 1 0 1 O! O O S min I O i O 1 0 O O 1 i 01 01 O O S vit O O i 0 1 O 1 O O s cam 0 I 1. 0 1 O! O 1 S len 11 1, O i O i O i O S aur 1 I 0 0 1 0 1 0 1 O S bu1 0 / O' O i 0 1 O 1 O S vom 1 l O, 0 1 0 1 O O S luh 11 1. 0 1 0 1 O O S dec 1 1 O i 0 1 0 ) O O - S gib O ( 1 i 1 i O O O I i 1 L hm 1 1 / O 0 f O O L tru I O 1 1 O 1 O O L CL0 1 O 1 O 0 1 O O L mil 1 1 i 0 1 O 1 O O L diq ? ? i? !? /? !? L rob 1 1 O i O! 0 i O O L SC0 O. 1 i O! 0 1 O O Lvio I? \? !? i? i ? ? L chi 1 1 O i O 1 0 1 O O species 'outer marqinal teeth formula
4 5 6 7 8 9
T ter O O 1 0 1 O 1 S can 1 1 O O O O O S the O O O 1 1 O S urc O 1 _ 1 1 1 O lab S 1 11 O O O O s mic O 11 0 1 1 O O S mut 0. I j 1 O O O s mac 0 I l! O O O O S ery O 1 1 1 O, O O S hae O O O O O I S den 0 1 1 1 O O O S fra 0 1 1 1 0 O O S pli O O O O 1 1 S di1 O O 1 O O O S mar O O 1 O O O
S var 1_ 1 1 1 1 O S min 0 1 1 1 1 O, O S epi 0 1 O 1 O, 1 O S vit 1 i 1 O 0 1 O O S cam 1 11 1 0 / O 1 1 O S len 0 1 I 1 1 1 ( O 1 O s aur 1 O l 1 / 1 1 I 0 l O S bu1 0 ! 1 O 0 1 O O S vom O 1 1 O O O S luh O O O, 1 1 O S dec O I 1. O O O S gib O 1 O O 1 1 O O t L larn 1 1 1 O O O L tru O O 1 1 1 O L cro j 0 1 0 0 1 O 0 L mil O O 1. O O O L dig ? ? ? ? ? ? L rob O O! 1 1 O O L SC0 O 1 1 O! O O L vio ? ? 1? ? I? ? L chi O. O 1 1 11 O 0-
Lspecies 1 type 1 radular 1 opercu- / 1 - rows I 8lof 1 1 I luml 1 cusps 1 serra- tion plica- vitat- toid toid O 2 3.
I I iI I T ter O O 35 O O O
S can 0 1 O 40 - 45 0 1 O O S the O O? 1 O O S urc O O 38 O 0 ! O S lab O O 381 O O O
S mic O O 2 9 ' O O O S mut O O 36 - 42 O 0 1 O S mac O O? O 0 / O S ery O O/? 0 l 0 l 0 S hae O O 34 ? ? ' ? S den O O 4 6 0, O O S fra O 0138 - 43 O O O S pli 1 / O/? I O O O S di1 O O 3 1 O 0 / O S mar 1 O O 35 1 O 0 1 O s var O O 1 42 J O O l O S min O 01 33 1 O 1 0 1 O Sepi 1 O O 55 - 60 1 O O O Svit O 1 25 - 26 1 O O O S cam O O 27 I O O O S len O 0145 - 47 ! O 1 1 1 1 S aur [ O 0140 - 50 1 O O O S bu1 i? ? 421? ? ? S vom O 0 l 44 O O f O S luh O 0142 - 46 O 0 ( 1 S dec I? ? ? 1 O 0 1 O S gib O O 32 - 46 1 O O O
1 1 I i1 1 I L lam 0 01' 1 1 01 0 L tru 0 O! 55 1 O 1 0 L cro ? j? 40 1 0 1 O L mil 0 ( O)? 1 0 O L dig ? ? I? i? ? ? L rob O Ol? 1 1 O 1 O
1 1 L vio I? /? /? j? l? I? L chi 1 O 1 O/? I O 1 O 1 O species opercu- lurn serra- tion 1 f 1 I 1 I 4 5 1 6 1 7 1 8 9 1 T ter 1 O O 1 O O O
S can O O 0 f 1 1 O S the 0 1 O O 1 O 1 O O S urc O O 1 0 1 0 1 O O S lab O O! 0 ! 0 1 1 1 S mic 0 1 0 l 0; I 1 O O S mut O 1 O l 01 0 1 0 O S mac 0 1 0 l 0' 0 1 0 O s ery 0 I 0 l Oi 1I 1 1 S hae ? ? j? I? /? ? S den O 0 1 O 1 O ' O O S fra O 0 I 01 1 O O s pli O I 0 1 Oi O O 1 S di1 0 1 0 1 O' 0 1 1) O s mar j 0 l O l 0 I O / 0 l 0 s var O I I I Os 11 1 I O S min 0 1 O 1 0, O j O 1 S epi 0 I O l O i 0 1 O O S vit 0 1 0 1 O, 1 I 0 1 1 S cam O ! O l O' 1 ' O O S len 1 O 1 O 1 O' O i O O
S aur O 1 O I I I l! O O S bu1 ? l? i? ? I? ? S vont O 1 0 1 0 1 11 1 O S luh 1 i 1 1 0 / O 1 1 O Sdec 1 O 1 0 1 11 1 ( O O S gib O 1 0 1 O 1 i O O 1 1 4 L lam 0 1 0 1 O i O ( O O L tru 0 1 O l O 1 O 1 O O
1 L mil O 1 0 1 0 1 O O O L dig ? !? 1.1 I? ? ? L rob 0 1 O i 0; 0 1 O I O,
L vio ? 1? j? i? I? I? L chi O ! O 1 0 : 0 1 O 1 O 237 species opercu- lum serra- tion
10 11 12 13. 14 16
l T ter O O O O O 1 O I ! S can 0 1 O ' O O O O S the 0 1 O O O O O S urc O' O 1 1 O O O S lab O O O O O O Smic 1 O 0 I O O O O 1 S mut 1 1 .. O O O S mac 1 1 0 0 0 0 0 S ery 0 / 0 0 0 0 0 S hae ? !? /? ? ? 3 S den O 1 0 / 1 O O O S fra O 0 1 O O O O S pli , 1 I 0 1 O O O O S di1 0 1 O O O O O S mar O 1 1, O O O O S var 1 0 1 O! O O O O s min 0 l O 1 O O 1 0 0 s epi 0 I 0 l 1 1 1. O S vit O I 0 / O O O O S cam i 0 1 0 1 O O O O S len j O i 0 1 O 0 / O O S aur i O 1 O / 0 O 1 O O Sbul /? !? !? ? i? ? S vom O O O / O O O S luh 0. O 0 1 O 0. O S dec O O O 0 1 O .- O S gib O O 0 1 O O O I L lam O O 0, O, O O
L tru O ~ O O 1 O 0 1 O L cro O O / 0 1 O O O L mil O O O O O O L dig ? ? ? .? /? ? L rob 0. O. O 0 / O O L SC0 1 lt O 1 O ' O l O O L vio I? II ? 1? i? ? 4L chi 1 O 1 O 0 1 Ut O 1 238 species verge form
simple broad with a iwith iplicat- margin- simple procesç !procesç lbroad i oid( atoid
l j l T ter 1 0 1 O 1 0 / O 0 1 S can 0 0 1 1 I O O 0 S the j? ? i? /? 1 O O S urc 1 O ! O 1 O O O S lab ? ? i? ! ? O O s mic 1 1 O 1 O / O O O S mut 1 I O 1 0 1 0 1 O 1 O s rnac I? l? 1'1 !? O I O s ery I 1 I 0 l O 1 O I O l O S hae j? ? l? ; ? 1 O 1 O S den O O 1 1! O 1 O O s fra ? ? ;? 1? i O O s pli O O i 0 l 0 1 1 O S di1 ? ? l? i? 1 O i O S mar O 0 1 O I 0 1 O 1 S var i 1 0' O i 0 1 O O S min 1 O' O i O i 1 I O O S epi 1 0 1 O i O 1 O ' O O S vit ! 11 0 i 0 1 0 i O 1 O S cam I 11 O i O i O 1 O 1 O s len i 0 1 1 i O 0; 0 1 O S aur i 1 I 0; O 1 0 1 O l O , S bu1 !? ? 13 j ? I 0 I O S vom 1 O i 0 i O l O O S luh , 0 1 1j 0 1 0 1 O O S dec 1 0 1 11 O i O O O S gib 11 O! O O O j O I1 1 l i L lam 1 1 O i O i O / O O L tru ! O O 1 1 I O O O L cro 1 1 0 1 0 O 0 0 L mil 1 0 1 0 1 O O O L dig -? ? !? 1 ? O O L rob 1 I O 1 0 1 O! O O L SC0 1 0 1 O 1 O / O O L vio ? (? /? O, O .1? - - - - - 1 - - - - .- chi / 1 I O; 0 i O 1- 01 O species verqe poster- mouth form ior type anal canal I epidro- 1 strom- epidro- luhua- moid tapered 1 boid elongate! moid noid
T ter O O 1 O, O O 1 I S can 0 0 - O 1 O 1 1 1 O i S the O 0 1 1 0l O O S urc O 0I 1 O ( 0 I O S lab O 1) O 11 O 1 O S rnic O _ O 1 1 O 1 O O s mut O I, 1 / O! O O S mac O 01 l! O / O O S ery 0 O 1 1 / 0 1 0 0 i S hae 0 1 li? 11 /? ? S den 0 1 1/ 1 1 O! O O S fra 0 1 1 1) 0 1 O O S pli , O 1 i 11 O 1 O O S di1 O O / 0 1 11 O O S mar O O i O 1 1 I O O S var 0,0/1 I 1 I 1 j O O S min O 01 1 / 0 1 O O S epi I 1 / I I O) O / 1 O 5 vit 1 0 1 O i 1 / O 1 O O S cam O / O 0 1 1-1 O O S len 0 1 11 1l 0 l O O S aur O 1 O 1 1 !' 0 1 O O S bu1 O? i? ? i? ? S vom O? i O 1 \ O O S luh O 11 O 0 1 O 1 S dec O? I 1 i 01 O O S gib O. O 1 0 1 11 O O i I I 1 I i 1 I 1 I 1 L lam O 0 1 O O O L tru O O!? ? ? ? L cro i O? j? ? ? ? L mil O 1 I 1 O O O L dig O? j? ? ? ?
L rob O? 1 1 1 O - O O I L SC0 O 0/1 I 1 l 0 1 O O L vio O? i? !? I? ? L chi 1 O 0/1 I 1 1 01 O O species ctenidi- 1 i 1 ommato- al phore: filament 1 tentacle form 1 length 1 I I 1 fine moderate 1 coarse i < 4 4 to 10 > 10 I 1 I 1 1 t 1 1 T ter 1 O O 1 O! O I
I I 1 l S can 1 1 O 1 11 O O S the O 1 O i 1 1 O O S urc O O 11 1 1 O O S lab O 1 O i 1 1 O O S mic O 11 O i 11 O O S mut 1 1 1 O 1 1 t O O s mac O I O ! 11 O O S ery 1 1 O 1 11 O O S hae 1 0 1 O!? I? ? S den O 1 i O i 1 j O O S fra O 1 1 O i 1) O O S pli O O] 1 i 1 I O O S di1 O 1 1 0 i 1 / O O S mar O 1 / O 1 1 1 O O s var 1/ II O i 11 01 - O s min j 11 1 i O 1 11 O i 0 S epi 1 1 I I 0; 1 j O ( 0 Svit I O l 1 ! 0 i 1 i O 1 O S cam 1 0 / 11 0s 1 i 0 1 0 ------S len I O I O 1 I ! II O i O s aur O I- I O i 1- O O I I I! S bu1 j? I? I? ? i? ' ?
ç vom /? I? ? I ? I? ? 3 luh O 1 O! 1 1 O O 5 dec I? ? ? ' ? I? ? 3 gib 0 ! 11 O i 11 O 1 O
Llam 1 O 1) O I O 1 O L tru O 1 11 1 i O 1 O L cro ? ? I? I 0 I 1 O L mil O 1 1 0 l O 1 0 L dig ? ? 1? \? ? ? L rob ? ? (? 1 0 1 1 O L SC0 1 1 I 01 0 l 1 O L vio ? ? /? . ? ;? ? L chi 1 0 1 1 ! 1 i O I 1 1 O 24 1 species 'mantle apical whorl filament sculp- sculp- I 1 length ture ture 1 1 smooth 1 cords lines lribs I T ter long 1 1 0 1 0 0 I I S can short 1 0 1 1) 1 1 S the ? I 0 / 0 1 0 1 S urc 3 mm 0 0 1 0 1 1 S lab 2-2.5 mm 0 1 0 1 1 I 1 S mic ? 0 1 0 0 1 0 S mut 2 rnm I 0 i 0 1 1 1 0 S mac ? 1 0 1 0 l 1 1 I 0 s ery ? 0 I o 1 1 I I I S hae ? I 0 1 0 1 0 0 ! 1 S den long 0 1 0 1 0 1 1 1 S fra shrt/ lng 0 ! 0 1 0 1 I 0 S pli ? ? I 0 1 0' 0 1 1 S dil ? 1 1 0 1 0 11 1 S mar short 0 1 0 1 0 f 0 ( 1 s var ? I? I 0 I O 0 O S min long 0 1 0 1 0 0 1 0 I S epi I? I 0 I 0 I 1 0 I 1
S vit /short /? I 0 1 1 1 1 1 S cam /? i? 0 1 0 1 I 1 I S len j3-4 mm I? ! 0 f 1 I 0 / 0 S aur /4 mm I? I 0 I 1 0 i 1 S bul /? I? I 0 1 1 0 1 1 S vom I? 0 I 0 I 0 - 0 I 0 S luh ? 0 1 0 i 0 / 0 ! 1 i S dec ? i 0 1 0 I 0 1 1 I 1 S gib I? 0 0 1 0 1 1' 0 I I L lam qr/a 0 0 1 01 0 0 L tru gr/a ? 0 I 1 0 , 0 L cro gr/a 0 0 / 0 o ( 0 L mil gr/a 0 0 i 0 0 1 0 L dig 1gr/a ? /? I ? ? I? L rob Igr/a I!? ;? ? Lsco lgr/a OI? I? ? I? L vio gr/a ? 0 t 1. 0 i 0 L chi qr/a I? 1 0 1 1 I O! 0 lspecies lwhorl 1 1 ! columel- 1 i 1 I Isculp- 1 t la / ! I I turel sculp- i i I ! 1 1 turei i I I I I 1 1 j threads i beadç i smooth / lirae 1 rugae I IT ter I O I OI? I? t? I
S can O 1 11 O 1 O S the 0 1 0 1 0 1 11 0 1 O s urc O 1 O! 1 i 1 i 1i O S lab 0 1 0 1 O / 0 1 1 O S mic l i 0 1 O i O l 1 1 O S mut 11 11 O 1 0 1 1 j O S mac 1 O 1 O 1 1 i 1I l! O S ery 11 1; 0 0 1 1i O S hae 1 I 11 O! 01 1 1 O S den 0 1 O 1 O 1 1 [ 11 O S fra 11 1I O 1 1 1 \ O
S pli 1 O 1 1 I O l O 1 11 O Sdil 1 0 1 O 1 O 1 I 1 O 1 O S mar i f il 1! 1 f il 0 S var i i 1 11 O 1 i i O 1 O S min 1 I 1 1 O 1 1 I 1 1 IS epi I O l O I O 1 11 O l O S vit O l 1 I 0 1 O 1 1 1 1 S cam 1 O 1 O i O ' O 1 I 1 1 Sfen O l 1 i O l i O! O S aur i O 1 11 O 1 I 1 1 O S bu1 1 O I 11 O i 1 0 1 O S VO~ 1 O! 1, 1 i O 1 I O S luh Il 1 ' 01 1 0 O S dec 1 11 O ' O!? ? ? S gib 1 1 11 0 1 1 O O 1 I l I ! L lam O 1 i Il I i O O L tru 0, 1 1 O 1 1 O O ï, cro 0 ! 11 O i 1 O O L mil O 1 O 1 1 1 O 1 O L diq ? I? l? O 1 O Lrob I? I? '? '? ? ? ,L SC0 I? I? ' ? ' O I O L vio 0 / 1 ' Or? ? ? ,L chi O I 11 0 i 0 ( 1 0, 243 species columel-1 columel-1 1 la1 la sculp- Jcolour ture1I
teeth white black orange yellow brown 1 T ter ? ? ? ? ? ?
S can 0 I I 0 0 0 0 Sthe 1 0 / I 0 1 0 0 0 s urc 0 I 1 1 / 1, 1 O S lab 0 1 0 1 0 1 1 0 S mic 1 I 0 0 1 I 1 S mut 0 I 0 0 0 0 1 S mac 11 I 0 0 0 0 S ery I 1 0 0 0 1 1 S hae 0 1 0 0 0 0 1 S den 01 1 0 0 0 1 1 S fra 0 / 0 0 O! 0 1 S pli 0 / 1 0 1 0 I 0 0 S dil 1 / 1 ! 0 1 01 0 0 S mar I 11 1 I 0 1 0 t 0 0 S var f O 1 1I O! 0 I O 1 S min 0 1 I 0 ! 0 I 0 0 S epi 0I I 0I 0 1 0 0 Svit 0 1 1 0 1 0 1 0 1 0 s cam 0 1 1 I o / 0 1 0 0 S len 0 i 1 I 0 1 0 1 0 0 S aur 0 i 0 1 0 1 01 0 0 S bul I 0' 1 I 0 ( 0 i 0 0 S vom I I 0 1 0 1 1 I 0 1 S luh 1 0 0 I 11 0 1 0 1 S dec ? I 1 i 0 / 0 I 0 1 S gib 0 1 1 0 1 01 0 1 0 I I I L lam 0 I O 1 0 I O I- L tru O(? ? ? I? ? L cro I OI? ,? ,? I? ? L mil 0 1 0 l 0 l 0 I 0 - -- - 1 L diq 0 1 0 I 0 I o! 0, 0 L rob ? I 0 1 0 0 1 01 0 L sco 0/ 0 I 0 0 I 0 1 Lvio I? I? I ? I? I? I? L chi 0 1 0 1 0 1 0 / 0 ! 0 species columel- 1 la colour 1 I ,I I
L I I i 1 purple red ipink !tan /mauve lcrearn I 1 I 1 T ter ? i? ' ? I? [? 1 I 1 1 1 ! ! i i s can [ 0 0 O l 01 01 O '8O O i O l 0 / O S urc 0 0 1 0 i 0 1 0 1 O S lab O 0 1 O 1 0 ! 0 1 O s mic 1 0 1 0 i 0 0 i 0 S mut O 0 1 1 i O 1 l O s mac 0 0 1 0: 0 1 0 1 0 S ery I O 1 01 0 / 0 ! 0
S hae O 1 ! 1 ' 0 1 0 1 O S den O 0 1 0 : 0 / O 1 O S fra O O l 01 0 1 01 O S pli O O i O. O i O! O S di1 O 0 i O i O 1 O 1 O
S mar O ' 0 / 0: 0 / 01 O S var O O 1 0 ! O 1 0 1 O S min O 0 1 O 1 0 1 0 i O
, Seip O* Oi 0, 0 1 0 1 0 s vit 1 0 1 0 l O i O 1 O 1 O s cam i 0 1 01 0 O 1 O) O S len 1 O i O i O O 1 O 1 O s aur [ O 1 O i O , 1 i O' 1 s bu1 1 0 i O 1 O O! O O s vom 1 O l O 1 0 ! 0 l O O S luh 1 O, 0 1 0 1 O O O ,S dec O O l O 1 O O O S gib 1 0 1 O 1 0 1 O O I I I ï, lam O 0 1 0 1 O i O O L tru ,? ? I? !? j? ? L cro /? ? I? i? l? ? IL mil j L dig 1 O 0 1 O i O 1 11 O L rob 1 O O 1 O ~ 0 1 O 1 L SC0 1 0 1 O' O / O O L vio ? l? I? ? i? ? [L chi 1 i O 1 1. O I O I O 245 species aperture I I colour 1 I I
white yellow , black purple pink brown
l 1 T ter 1 0 1 O 0 1 O O I l S can 1 O 1 O O 1 O O S the 1 0 1 O 0 1 O O s urc 1 1 t 11 1 I O 1 S lab 0. 0 1 O 1 / O O S mic O 1 1 O 11 O, 1 Smut ! O, O 1 O, 0 / 1, O s mac 1 0 i 0 O 1 0 O S ery O 0 1 O I O 1 S hae 1 O 1 O O O O S den O 11 O O( O O S fra O 01 0 1 0 0 1 S pli 1 O O 1 O 0. O S di1 1 O l 0 ( 1 0, 1 S mar 3 ? j? I? ? ? S var 1 0 1 O / O 1 0 0 S min O 1 I O 0 1 O O S epi 1 0 i O, 0 I O O S vit 1 O 1 O! O O O s cam ? ? i? ( ? ? ? s len 0 I O O l O 1 O S aur 1 0 1 O I O 1 O O O S bu1 0 1 0 1 0 / 0 1 01 O S vom O 1 0 l 0 1 O / 0 l O S luh 0 1 0 1 0 1 01 O O S dec O i 0 1 0 1 O 1 O O S gib 1 1 O 1 O 1 1 O O I ~lam 1 O O ( O O 1 O O L tru 1 01 0 1 1 0 0 L cro O 0 1 O O O O L mil O O O O O 1 L diq O O f O 1 1 O O L rob 0 1 1 i O O 1 O, O L SC0 0 1 O 1 O 1 I O O L vio 0 ) O 1 0 1 11 O O -L chi I 1 1 O 1 0 1 0 1 O O 246 species aperture1 1 s iphonal 1I 71 colour I canal 1 length I I ! rose tan 1 mauve ! cream 1 orange short l 1 I I T ter 1 O 0 / O 1 0 1 O? I i S can 0. 0 ! O 0 1 O 1 S the 0 1 0 1 O 1 0 1 O? s urc O O l O / 0 1 O O Slab 1 O 0 1 O 1 0 1 O 1 s mic 0 1 O i O / 0 O? S mut O O i 0 I O O 1 S mac. 1 O, 0 1 0 1 O O? S ery O 1 O i 0 i 0 1 O(? S hae O! 0 1 0; O 1 O? S den 1 1) 0 ( O O 1 O? S fra 1 O 1 0 i 0 1 0 1 O? S pli O O i O i 0 O I S di1 0. O 1 0 1 0 1 O O Smar I? ? )? i? ? ? S var O O / O 1 O O/ 1 S min O O i O 1 0 1 O'? Sepi j 0 1 O / 0 1 O i O 1 ,S vit O 0 I O i 0 I O 1
S cam )? ? l3 . ? ;? ?
S len O O 1 0 ; O i O 1 S aur i O O! O i 1 l Il?
S bu1 1 0 1 O 1 O 1 l? S vom O 0 1 O 1 O 1 1 O S luh I 1 0 / 0 1 O / II? S dec 1 O ! O ! 0 1 1 O O 1 oi 01 O . 1 ' 1 l [ L lam 1 I î 0 l 1! 1 0 L tru O I 1 O t O O 1 L cro O O f O 1 O 1 O L mil O 0 i 1 i O O 1 L dig O O 1 1 I O O 1 L rob O O 1 O i 1 O O L SC0 O 0 1 O / 0 l O, O Lvio 1 O O i O i O l O! 0 L chi 1 O O 1 O 1 O 1 0 (? - - - species siphonal 1 1 siphonal 1 1 outer ( circcum- canal 1 canal / lip I apertur- I length I i 1 i al 1 I (projec- I i I I tions lmoderate long Itwisted /curved Jflared 1 1 l i 1 l 1 I - 1 I 1 l l I T ter ? 2 1 2 I ? I O I O I I
S urc 0 1 1 - 11 O O O S lab O 0 1 O O O O s mic ? ,? /? ? 1 0 i 0 s mut 0 I O l O O O I O s mac (? I? ? 1 2 0 t 0 s ery I? l? 1'1 ? 1 0 1 0 S hae ? ? ,? ? 0 I O S den ? ? ? ? 0 1 O S ira ? -? ) ? ? 0 1 O S pli 0 1 O 1 O 1 O! 0 1 O S di1 O 1 1 I O 1 1 1 1 1 O IS mar 11 I? I? I? O I O I s var I O ( O 1 01 0 I 11 O [S min i? I? O i I 1 0 i O] S epi I O 0 I O 1 0 l 1 I O S vit 1 0 1 O 1 O 1 0 1 1 0 S cam I? (? i? !? 1 O O s len i 0 1 0 1 II 0 1 O 1 0 s aur /? l? It 0 i 1 1 0 ! 1 S bu1 ]? 1 ? ? 11 1 1 O 1 S vom l 0 i 1 i O 1 1 1 1 S luh I? !? j? !? O O Sdec ' 1 1 0 1 0 1 O O O S qib 0 i O 1 0 1 O O, O l I L lam O I 1 1 O 1 O L tru 0 O 1 0 - O 1 ( 0 L cro O 1 ' O 1 1) O L mil O O 1 O 11 O O'l O/ II O O L rob 0 1 1 1 O 1 1 ( O 1 L SC0 O 1 I O 1 1 O L vio 1 O 1i il O 1 0 ,L chi 1? l? 1'2 !? i 1 O, species circum- l 1 l apertur- I 1 I l I l al i l I Ipro ject- i j I l tions i 1 2 3 I 5 1 6 1 a i 9 1 I 1 I I I ! I l I T ter 1 0 ( 0 l 0 O l 0 l O l l I I 1 1 I i l I s can 0 0 1 0 1 0 1 0 1 O S the O / O 1 O 1 0 1 0 1 O s urc O O 1 O I 0 1 O! O S lab O 0 1 0 1 O O O S mic O O 1 0 1 O- O O Smut , O l O i O 1 O l O O mac O l O i O 1 O 1 O 1 O IS 1 1 IS ery O! O 1 O 1 O 0 1 O S hae O O 1 O 1 O - O O S den O O 1 0 1 O O O -S fra 1 O O 1 O 1 O O] O S pli O, O 1 0: 0 l 0 l O S di1 O 1 0 l O 1 0 1 O O S mar O 1 O i 0 1 O O O S var O O i 0 O O O S min O O l O1 O O O S epi O O i O / O 1 O O S vit O 1 O 1 O i 0 1 O O S cam O 1 O i O 1 0 I O O S len ! 1 i 1 I 0 i O 1 O, O Saur 1 O l O r O 1 0) O 1 O S bu1 0 ( O i O 1 0 1 O O S vom ' O 1 01 0 l O O O S luh 0 1 O' 0 1 O O O Sdec / O r O 0 1 0 0 ! O S gib 1 O! 0 i O 1 O O O
1 I I I I L lam O O t O 1 1 O O L tru O O i O) 1 O O L cro L mil O. 0' 0 1 O O 1 L dig O O i 0 1 O 1 1 L rob O 0 1 0 1 1 O O L SC0 O O 0 l 1 O O L vio 0 1 O 0 1 O O O - - IL chi 1 O 1 O l! O Ï O 1 O] species circum- peri- 1 strom- apertur- ostracum boid al notch l projec- develop tions ( ment 10 11 thin moderate thick poor
1 l T ter O 0 - - - -
I 1 S can O O O O 1 1 S the O O 1 O O - O S urc O O 1 O O 1 S lab O O 1 O O 1 S mic O O 1 O O O S mut O O 1 O O 1
S mac O O O O 1 - 1 S ery O O 1 0 1 O S hae O O? ? ? S den O O 1 O O S fra O O O O I S pli O O 1 O O S di1 O O 1 O O S mar O O 1 O O S var O O 1 O O S min O O 1 O 1 O S epi O 0 1 1, O O S vit O 0 1 1 ( O 1 O S Cam 0 1 O 1 I O O? S len O O 1 O O O S aur O O 1 O O? S bu1 O O 1 O O? S vom O O 1 O O O S luh O O O O 1 O S dec O O 1 O O O S gib O O? ? ? ? I
-. -- L tru O 0 I O 1 O O L cro O O O O 1 O L mil O O 1 O O O L dig O O O O 1 O L rob O O 1 O O O L SC0 O O 1 O O O L vio 1 l? ? ? O L chi O O 1 O O O species strom- whorl whorl boid number number
, notch develop- 1 ment moderate well 6 7 8 9
I T ter - - O 11 O O
L 1 I S can O O 1 O O 1 S the O 1 O O O O S urc
S mic O 1 O 1 1 O S mut O I O O 1 1 S mac O O, O O 1 1 S ery ? ? O O O O S hae ? ? O 1 1 O S den ? ? O O 1 1 S fra O O O / O O 1 S pli 1 O O O O O S di1 O 1 O O O O S rnar O O O O O 1 S var ? ? O O O 1 S min O O O O O 1 S epi 0 ( 1 O O O O S vit O O O O O O S Cam ? ? O O 1 1 S len O I O O O 1 S aur ? ? O O O 1 S bu1 ? ? O O O 1 S vom O 1 O O O O S luh O 1 O O 1 1 S dec 1 0. O O O 1 S qib ? ? O O O O f 1 1 1 L lam O 1 O O O ( O L tru O 1 O O O ( 1 L cro O 1 O O 0 1 O, L mil O 1 O . O O O L diq O 1 O O O O L rob O 1 0 1 O O 1 L SC0 O 1 O O O I L vio O 1 O O O I L chi O 1 O O O O 1 I T ter O O O
L lam 1 1 O L tru 1 O O L cro 1 1 O L mil O 1 O -- L dig 1 O O L rob O O O L SC0 1 1 O L vio O O O Appendix VI. CLADISTIC CODING TECHNIQUES USED
Traditiondy, the radula has played an important dein gastropod systematics.
Cuspidation of radular teeth may affect feeding performance by snails. In particular,
nurnbers of cusps rnay determine the efficiency with which 'algavorous' species rasp
surfaces. Some species of snails have plastic radula morphologies, and revenible changes
in radular form can be induced by changes in food consurned or feeding environment
(e.g., Lmum; Padilla, pers. corn.). Nevertheless, the radula remains a source of
rnorphological information for gasaopod s ystematics (e-g., Reid 1996). Therefore,
numbers of cusps of the various teeth in rows of radulae were considered as characters
and coded as character States.
The number of cusps of lateral teeth is variable both within and among strombid
species. Most specimens exarnined have a single cusp on the edge proximal to the cenaal
tmth and one of 12 configurations of smaller cusps extending to the edge proximal to the
inner marginal teeth: 2, 3, 4, 2 or 3, 2 to 4, 3 or 4, 3 to 5, 5, 3 or 4 or 6, 3 to 9, 4 or 5, or 5 or 6. Two species have lateral teeth with 4 equivalent cusps (Strornbus huemastom and S. dilatanu), and one species has either a single cusp with 3 smaller cusps extending to the edge proximal to the inner marginal teeth or 4 equivalent cusps (S. dentatus).
There are 14 different configurations in total. However, of the 14 configurations, 7 are 253 autapomorphic (Le., 4, 5, 3 or 4 or 6, 3 to 9, 4 or 5, 5 or 6, and the combination found in
S. denrazus are unique to single species) and cannot function as synapomorphies (i.e.,
cannot effect cladogram topology). Therefore, state coding is resnicted to only putative
synapomorphies (Le., states comrnon to multiple species), and al1 autapomorphies except
one are coded as unobserved (Le.. as ?, pp 108-1 15). Such restriction affects summary
measures (such as lengths and consistency and retention indices) of cladograms resulting
from analyses but not cladogram topologies (pp 110-1 11). Thus, states of the charmer
'number of cusps of lateral teeth,' which establishes 7 hypotheses (each coded as a state),
may be defined: 2 coded as 2, 3 as 3, 2 or 3 as 5, 2 to 4 as 6, 3 or 4 as 7, 3 to 5 as 8, or
4 equivalent cusps as 9. One of the 7 autapomorphies (4 cusps) is found in the ingroup
species Wismillepeda and is coded as 4. The numencd values of codings are inconsequential, provided that states are unordered during analysis (Le., changes between any two states count as one step on the cladogram), and are chosen for convenience (Le., most codings are sums of states used in definitions: 2 = 2, 3 = 3, 4 = 4, 2 + 3 = 5, 2 + 4
= 6, 3 + 4 = 7, 3 + 5 = 8; 4 equivaient cusps coded as 9 is incidental). Each hypothesis proposes that there are strombids that possess a pariicular number of cusps to the exclusion of other members of the Strombidae (p 56).
The number of cusps of inner marginal teeth dso varies greatly both within and among strombid species. Specimens examined have one of 13 configurations: 4, 4 or 5,
4 or 6, 4 to 6, 5, 5 or 6, 5 or 7, 6 or 7, 1 or 6, 2 to 4, 3, 6, or 6 or 9. However, of the 13 configurations, 6 are autapomorphic (Le., 1 or 6. 2 to 4, 3, 4 or 6, 6, or 6 or 9 are unique 254 to single species) and cannot function as synapomorphies (i.e., cannot effect cladogram topology). Therefore, as with the coding of the number of cusps on lateral teeth (pp 252-
253), state coding is resaicted to only putative synapomorphies (i.e., states common to multiple species), and al1 autapomorphies are coded as unobserved. Again, such restriction affects summary measures (such as lengths and consistency and retention indices) of cladograms resulting from analyses but not c1adogm.m topologies. Thus, states of the character 'number of cusps of inner marginal teeth,' which establishes 7 hypotheses
(each coded as a state), may be defined: 4 or 5 coded as 1, 4 to 6 as 2, 5 or 6 as 3, 5 as
5, 4 as 7, 6 or 7 as 8, or 4 or 6 as 9. One of the 6 autapomorphies (4 or 6 cusps) is found in the ingroup species Lambis scorpiur and is coded as 9. Again, the numerical values of these codings are inconsequential, provided that states are unordered during analysis (i-e.. changes between any two states count as one step on the cladogram), and are chosen for convenience (i.e., codings are chosen so that putative synapomorphies of ingroup species receive the lowest values: 4 or 5 as 1, 4 to 6 as 2, 5 or 6 as 3, 5 or 7 as
4, and 5 as 5; 4 as 7 and 6 or 7 as 8 are found in outgroups, whereas 4 or 6 as 9 is incidental). Each hypothesis proposes that there are strombids that possess a particular number of cusps to the exclusion of other members of the Strombidae.
The number of cusps of outer marginal teeth also varies greatly both wiîhin and among strombid species. Specimens exarnined have one of 18 configurations: 5, 5 or 6,
6,6or7,4to6,6to8,4or5,5to7,7or8,3to5or8,4to8,5or7,5to8,6or8.6 or 9, 7, 8 or 9, or 9. However, of the 18 configurations, 11 are autapomorphic (Le., 4 to 255 6,6to8,3to5or8,4to8,5or7,5to8,6or8,6or9,7,8or9,and9cuspsa~ unique to single species) and cannot function as synapomorphies (i.e., cannot effect cladogram topology). Therefore, once again, state coding is restricted to only putative synapomorphies (i.e., states common to multiple species), and all autapomorphies except two are coded as unobserved. Once again, such resniction affects summary measures
(such as lengths and consistency and retention indices) of cladograms resulting from analyses but not cladograrn topologies. Thus, the character 'number of cusps of outer marginal teeth,' which establishes 7 hypotheses (each coded as a state), may be defmed:
5 coded as 1, 5 or 6 as 2, 6 as 3, 6 or 7 as 7, 4 or 5 as 5, 5 to 7 as 6, or 7 or 8 as 4.
Two of the six autapomorphies (4 to 6 cusps and 6 to 8 cusps) are found in ingroup species (Lambis lambis and mistruncata, respectively) and are coded as 8 and 9. The numerical values of these codings are inconsequential, provided that states are unordered during analysis (i.e., changes between any two states count as one step on the cladogram), and are chosen for convenience (i.e., codings are chosen so that putative synapornorphies of ingroup species receive the lowest values: 5 as 1, 5 or 6 as 2. 6 as 3; 7 or 8 as 4, 4 or
5 as 5, 5 to 7 as 6, and 6 or 7 as 8 are found in outgroups, whereas 7 or 8 as 4 is incidental). Each hypothesis proposes that there are smmbids that possess a particular number of cusps to the exclusion of other members of the Strombidae.
Analogous schemes were used to code other characters (descriptions on pp 116-
127; states in Table 3.1, p 129; analysis of data in Table 3.1 contained in Figure AVI.1). Figure AVI. 1. Cladograrn of species of S trom bidae.
The results of a cladistic analysis of data contained in Table 3.1 (output from the cornputer program Hennig86 (Farris 1988)). A consensus cladogram of the 1246 equally parsirnonious cladograms. A clade within the ciadogram, including aii species currently recognised and narned as Lambis (the ingroup) is presented in Figure 3.7 (p 130). procedure lambisc-ben * xread Lambis body and shell data. Run outgroup = 0.26;~~- /.; mhennig length 227 ci 51 ri 49 trees 1 bb file O from mhennig 1 tree bb length 225 ci 52 ri 50 trees 1246 nelsen file O £rom bb 1246 trees tplot file O from nelsen 1 tree
log a:\lamcmhbb.out - Appendix VII. MORPHOMETRIC SHELL DATA
Morphomehic data for sheil specimens used in this study are contained on the next 20 pages. The &ta are reformatted output from Marhematica (Wolfram Research, Inc. 1996) and are presented in the form filemme (usually a derivative of species name) = ( {8, r, z. h, v 1, ... }, for various values of 8 (Stone 1995a). Smarginatus (ANSP 185 44 9) = 258
{{IO Pi, 0.5, 5., 0.25, 0.251, {Il Pi, 0.5, 650.5, 0.5),
(12 Pi, 0.75, 7., 0.5, 1.(13 Pi, l., 8., 0.5, 2.1,
(14 Pi, l., 9., 0.75, 2.51, (15 Pi, 2,, Il., 1.25, 4.251,
116 Pi, 2.5, 13., 1.5, 6-25}, {17 Pi, 3., 16., 2., 8.51,
118 Pi, 4., 20., 2.5, 10.51, (19 Pi, S., 24., 2.75, 16. 1,
(20 Pi, 7., 26., 3., 17.))
Surceusl (ANSP 185442) =
{{IO Pi, 0.5, 0.5, 0.25, 0.51, (11 Pi, 0.5, 2-, 0.25, 0.5),
(12 Pi, 0.5, 2.5, 0.5, 0.51, (13 Pi, 0.75, 4., 0.75, 1-51,
{14 Pi, l., 5., l., 2 (15 Pi, 1.5, 7., 1.25, 3.1,
{16Pi, 2,, B., 1.5, 4-51, {l7Pi, 2.5, 5,2., 7.1,
{lSpi, 3., IS., 2., 9 {19Pi, 3., 21.5, 2.5, 13.1,
(20 Pi, 4,, 28., 2.5, 11.5))
Svariabilisl (ANSP 203619) =
((10 Pi, 0.5, 2.5, 0.25, 3.51, {II Pi, l., 3., 9-25, 0.251,
{12Pi, 0.75, 4., 0.25, 0.25}, {13PF, l., 5.5, 0.5, l.},
{14 Pi, l., 6., 0.5, 2 {i5?i, 1.5, 8., 0.75, 2.51, {16Pi, 2., 10., l., 4.), {17Pi, 2.5, 12., 1.5, 6-51,
{18Pi, 3., 16., 2., 9.1, (19Pi, 4., 21., 2.5, 12.1,
(20 Pi, 7., 23., 3.5, 13.})
Spulchellusl (ANSP 20 6999) = {{9Pi, 0.5, 1.5, 0.25, 0.251, {lOPi, 0.25, 2., 0.25, 0.251,
{il Pi, l., 2.5, 0.5, 0.251, (12 Pi, l., 4., 0.5, 1.5},
{13 Pi, l,, 4.5, 6.75, 5 (14 Pi, 1., 6., 0.75, 2.), (15Pi, 1.5, 7., 0.75, 2.{16Pi, 1.5, 7., 0.75, 2.51,
{17Pi, 1.5, 8.5, 1., 3.}, {18Pi, 2., ll., l., 5-1, 259 (19 Pi, 2.5, 17., 1.5 7.51, (20 Pi, 3., 17.5, 2.5, 9.1,
{12 Pi, 0.5, 3., 0.25, 0.251, (13 Pi, 0.25, 3., 0.25, 0.251,
{14Pi, l., S., 0.25, 0.5}, (15Pi, l., 6 0.5, 0.51,
{16Pi, 1., 8., 0.75, 2.51, {17Pi, 2., IO., l., 4-51,
{la Pi, 2., 12., 1.25, 5 (19 Pi, 3., 15, 1.5, 7-51, (20 Pi, 3., 6 2.5, 7.))
SseptimusI (ANSP 181794) =
{{8 Pi, 0.5, 2., 0.25, 0.251, (9 Pi, 0.5, 3., 0.25, 0.51,
(lOPi, 0.75, 3.5, 0.25, 0.51, (11 Pi, 0.75, 4., 0.5, 1.1,
{12Pi, l., 5., 0.5, 1 {13Pi, 1., 6., 0.75, 2.1,
(14 Pi, S., 8., l., 2-51, (15 Pi, 2., 10., 1, 4-51,
(16 Pi, 2.5, 12.5, 1.5, 2 (17 Pi, 3., 15., 1-75, 9.1,
(18 Pi, 3.5, 17., 2., 9-51, (19 Pi, S., 24., 2.5, 13.},
(20 Pi, 6., 27., 3., 3 (10 Pi, 0.5, 3., 0.25, 0.251,
(11 Pi, 0.5, 3.5, 0.25, 1.(12 Pi, 0.75, 4.5, 0.5, 1.51,
{13Pi, I., B., l., 2.51, {14Pi, 1.25, 8., l., 3.1,
(15 Pi, 2., IO., 1.25, 5.51, (16 Pi, 2.25, 13., 2., 6.5!,
(17 Pi, 3., 17., 2., 9.51, (18 Pi, 4., 20., 2.25, Il.},
(19 Pi, 4.5, 25, 2.5, 5 (20 Pi, 7., 27., 3., 15.11
Sfasciatus (ANSP 189133) =
I(9 Pi, 1., 4., 0.5, 0-51, (10 Pi, l., 4.5, 0.75, 1.1,
{ilpi, 1.5, 7., l., 2-25}, {12Pi, 1.5, 8., 1., 3-51,
(13 Pi, 2.5, 10-5, 1.5, 5 (14 Pi, 3., 13., 1.75, 5.51,
(15 Pi, 4., 17.5, 1.75, 8-25}, (16 Pi, 5., 22., 2.25, 11-1,
(17 Pi, 6., 28.5, 2.5, 12.5}, (18 Pi, 8.5, 33., 3.5, 15.},
(10 Pi, 0.5, 3., 0.5, 0.75), (11 Pi, l., 4.5, 0.75, 1.51, (12 Pi, 1.5, 6., l., 8 (13 Pi, 2., 8., 1.5, 5.1, 260
{14 Pi, 2.5, IO., 1.5, 5.51, 115 Pi, 3.5, 14., 2-, 8-1, {16Pi, 4.5, 18., 2.5, O,{l8Pi, a., 30., 3., 15-11
Lviolacea (ANSP 192937) =
{{Spi, 1.5, IO., 0.5, 1 19 Pi, 2.5, 12.5, 1.5, 33,
{lOPi, 2.5, 16,, 1.5, 6,(11 Pi, 4., 18., 2., 7.5L
(12 Pi, 4.5, 22.5, 2., 9.51, (13 Pi, 6.5, 27.5, 3-5, 12-51,
(14 Pi, 7., 34.5, 3.5, 16.51, Il5 Pi, 8., 45.5, 4., 22-51,
{16 Pi, 9.5, 52., 4.5, 19-51, (17 Pi, Il., 62.5, 4.5,
25.51, {18 Pi, 18., O,6., 40.1)
(specimen probably is L. digitata -- unused in morphospatial analyses)
Surceus2 (ANSP 185442) =
((13 Pi, l., 3.5, 0.5, 1.251, Il4 Pi, l., 4., 0.75, 1-51,
{15 Pi, 1.5, 7., l., 3.51, Il6 Pi, 1-5, 8., 1-25, 4-75),
{17Pi, 3., 11., 2., 7.51, {18Pi, 3.5, 12.5, 2.25, 8.75L
{19Pi, 3.5, 19., 2.5, 1 IZOPi, B., 22.5, 2.5, 10.511
Sseptimus2 (FXSP 181794) =
((13 Pi, i., 6, 0.5, 2 {14 F, i., 6. l., 2-1,
{15 Pi, 2.5, 9., 1.25, 4.51, {16 Pi, 2., IO., 1.5, 5.51,
(17 Pi, 3.5, 14.5, 2., 9 (18 Pi, 4., 16., 2.5, lO.Si,
(19 Pi, 5.5, 20.5, 2.75, 5 {SO Pi, 7., 21.5, 4., 15.5))
Lchiragral (ANSP 201470) =
({9Pi, l., 3.5, 0.5, 0.751, {IOPi, i., 4.5, 1., 1.1,
{Ilpi, 2.5, 5.5, 1.25, 1.251, {12Pi, 2.5, 8., 1.5, 5.1,
{13Pi, 3., Il., 2., 7.5}, {14Pi, 4.5, 15., 2.25, 9.51,
(15 Pi, 6., 19., 3., 3,(16 Pi, 7., 25, 4., 14.51, *
a 4 4
4 Ln e M 4. r (V
C ln a Ln
4 -4 Pc O (V w
4 A. (V rl
C
O C?
4 a CV (V 4. Tl'
C -4 [1i
0, rl + 4 A. N
4 ln r 0 0
cn4 u'- rl
4 - 4 [L C3 -#-I
4 * m 0 Q
C m * 0
4
M 4. l-i
4 -4 04 N rl L-C {19pi, 4., 22., 3., 8.751, {13Pi, 0.75, 3., 0.5, 1-25), 263
{14 Pi, 0.5, 3.5, 0.75, 1.251, {15 Pi, 2., 6., l., 3.1,
- (16 Pi, 1.5, 7., 1.5, 4.1, (17 Pi, 3., 10.5, 2., 5-51,
(18 Pi, 3., 12.5, 2., 8.51, (19 fi, 4.5, 17., 3., IO.), {20 Pi, S., 21., 2.5, 9 (11 Pi, 0.5, 4., 0.25, 0.51,
{12Pi, l., 4.5, 0.5, 0.51, {13Pi, l., 5., 0.75, 1.1,
{14Pi, l., 6.5, 1., 2.5), {15Pi, 1.75, 9., 1.5, 3.51,
{16Pi, 2., 10.5, 1.25, 5 {17Pi, 3., 14., 2.5, 6-51,
(18 Pi, 3.5, 17., 2.5, 8 (19 Pi, 4., 21., 2.5, lL5},
(20 Pi, S., 26., 2.5, 11. ))
Svittatus (ANSP 245946) =
((13 Pi, l., 6 0.25, 5 {14 Pi, l., 8., 0.5, 1-51,
{15Pi, 1.5, 9., 0.75, 2.51, {16Pi, 1.5, IO., l., 2-51,
(17 Pi, 2.5, 13., 1.5, 4.51, (18 Pi, 2., 16., 1.5, 5.51,
{19 Pi, 3., 20., Z., 8.1, (20 Pi, 3., 22., 2.5, 9.51,
121 Pi, 3.5, 29., 3., 4 . , (22 Pi, 4., 34., 3., 15.1,
(23 Pi, 6., 42., 3.5, 8,(24 Pi, 9., 46., 4.5, 18.5},
(13 Pi, 1.5, 5,, 0.75, 1.5, (14 Pi, 0.5, 6.5, 0.5, 1.5},
{15Pi, l., 9., 1., 2,{16Pi, l., IO., l., 2-51,
(17 Pi, 2., 14., 1.25, 4-51, (18 Pi, 2., 16., 1.75, 5. },
{lSPi, 2.5, 19.5, 2., 6.51, {20Pi, 3., 23., 2.5, 8.1, (21 Pi, 3.5, 28.5, 2.5, IL),
{22Pi, 4.5, 33., 2.75, 11.5},
{23 Pi, 5, 39., 3.5, 6,{24 Pi, 9., 40., 4., 18.5))
Lcrocatal (ANSP 212819) =
{{il Pi, 0.5, 3., 0.25, 0.251, (12 Pi, 0.5, 3.5, 0.5, 0.751,
{13Pi, l., 4.5, 0.75, 1,{14Pi, 1.5, 6., l., 2.51, 264 (15 Pi, 2.5, 8.5, 1.5, 4 (16 Pi, 3., IO., 1.5, 5.5},
(17 Pi, 4., 12.5, 2., 7.51, {18 Pi, 5., 16., 2.5, lI.S},
{19 Pi, 6., 22., 2-75, 14.}, (20 Pi, B., 31., 3.5, 14.1,
(21 Pi, 7., 37., 4., 5 (22 Pi, 12.5, 40., 4., 27-51,
111 Pi, 0.5, 3.5, 0.25, 0.51, (12 Pi, l., 4., 0.5, 1.1,
(13 Pi, 1.25, 5.5, 0.75, 1-25}, (14 Pi, 1.75, 6.5, l., 2.1,
{ISPi, 2., 8.5, 1.5, 4 {16Pi, 2.75, 10.5, 1.5, 5.1,
(17 Pi, 3., 12.5, 2., 8.), {18 Pi, 4.75, 17., 2.5, 15.1,
{19Pi, S., 24., 2.5, 5 {20Pi, 5., 31.5, 3.5, 15.51,
(21 Pi, 6., 35.5, 5.75, 15.1, (22 Pl, 14.5, 36., 4- 26.1i
Slubuanus (MSP 207311) =
((14 Pi, 1,, 15, 5 6 (15 Pi, 3.5, 20.5, 1-75, 8-51,
{16Pi, 4.5, 23., 2., O.{17Pi, 8., X.,2.5, 17-51,
(18 Pi, 9.5, 28.5, 3., 7,{gel, i., 2.5, 0.25, 0.51,
{lOPi, 0.5, 3., 0.5, OS), {11Pi, 1.5, 4.5, 0.75, 1-75},
{12 Pi, 1.5, 6 1.,2 {13 Pi, 2.5, 8.5, 1-25, 4.1,
{14ei, 3., 11.5, 1.75, 6 {iSPi, 4., 16.5, 2-, 9.51,
(16 Pi, S., 23., 2., 1.5, Il7 Pi, 6527., 2.5, 17-1,
{lapi, 8., 31., 3., 9 {8Pi, l., 2.5, 1-25, OS},
{9Pi, 0.5, 3., 0.25, 0.51, {lOPi, 1.5, 3.5, 0.5, 0.751,
(llPi, 1.5, 5.5, 0.5, 2 {12Pi, 2., 8., 0.75, 3.1,
(13Pi, 2.5, 9.5, 1., 3.51, {14Pi, 3.5, 13., 1., 6.1,
{15Pi, 4., 17., 1.75, 9.{16Pi, 5., 22.5, 2., 12,},
(17 Pi, 7., 26.5, 2.5, 19.5}, (18 Pi, IO., 27., 3.75, 20.1,
(8Pi, 0.75, l., 0.25, 0.25}, {9Ti, l., 1.5, 0.25, l.},
{IO Pi, l., 3., 0.5, 1.1, 111 Pi, 1.75, 4., 0.5, 2.1, (12 Pi, Z., 6.5, 0.75, 4.1, El3 Pi, 2.5, 9.5, 1.1 4-51, 265
{14Pi, 3., 13., 1.5, 6.51, I15Pi, 3.5, 16.5, 2., 8.1,
(16 pi, 4., 22., 2., 9.1, (17 Pi, 6., 27., 2.5, 16.1,
{18Pi, 7.5, 31., 3., 18. {8Pi, 0.5, 3., 0.25, 0.25),
(9 Pi, 0.5, 4., 0.25, û.75}, (10 pi, 0.75, 4.5, 0.5, 1.51,
(11 Pi, 1.5, 5.5, 0.75, 2-25}, (12 Pi, 1.75, 7., l., 3.1,
{13Pi, 2.5, 8., l., 5 {14Pi, 2.75, 11.5, 1.5, 6-51,
(15 Pi, 3., 15., 2., 9.5}, (16 Pi, S., 18., 2-, Il.},
{17Pi, 6., 27- 2.5, 18.1, {18Pi, 7.5, 30., 3., 20.},
{9 Pi, l., 3., 0.25, 1 El0 Pi, 0-5, 4., 0.5, 1.1,
{Il Pi, 1.25, 6., l., 2.51, (12 Pi, 1-25, 7.5, 1,, 2-51,
{13 Pi, 2.5, Il., 1.25, 4.251, (14 Pi, 2-5, 13., 1.5, 5.1,
{15Pi, 4., 16., 1.5, 7.51, {16Pi, 4., 22., 2., 8.51,
(17 Pi, 7., 26., 2.5, 6.5 (18 Pi, 7.5, 31., 3.5, 20.))
Svariabilis2 (ANSP 22384 0) =
{{liPi, 0.75, 4., 0.25, 1.{lîpi, i., 4.5, 0.5, i.5},
{13Pi, 1.5, 5.5, 0.75, 2 (14Pi, 1.5, 8., l., 3.1,
{iSPi, Z., 10., l., 4.51, (16Pi, 2.25, 12.5, 1.25, 6.5),
{17 Pi, 3., 16., 2., 9 (18 Pi, 3.5, 22., 2.5, 12.},
{19Ci, 5.5, 27., 2.75, 6 {SOPi, 7,, 30., 3.25, 17.5),
{Ilpi, l., 4.5, 0.5, 0.751, {12Pi, 0.5, 5., 0.5, 0.75),
{13 Pi, 1.5, 7., 1.25, 2.51, (14 Pi, 1.5, 8., l., 3.51,
{15Pi, 2., 11., 1.25, 4 {16Pi, 2.5, 13., î., 4.1,
(17 Pi, 3., 16.5, 2., 9 (18 Pi, 4., 23.5, 2., ll.],
(19 Pi, 5., 28., 3., 16,), (20 Pi, 7.5, 30., 3., SO.),
{il Pi, i., 4.5, 0.25, 1.(12 Pi, 0.5, S., 0.5, lœ},
(13 Pi, 1.5, 7., l., 2.51, (14 Pi, 1.5, 8., 1., 3.1, 266 {lS Pi, 2., IO., 1.25, 4 (16 Pi, 2.5, 13., 1.5, 6.5),
(17 Pi, 3., 16.5, 2., 9 {18 Pi, 4., 22.5, 2., 11-1,
{19 Pi, 4.5, 27.5, 3., 6 (20 Pi, 7., 33., 3.5, 17.5},
{13Pi, 1.25, 6.5, 0.75, 1.5 {14Pi, l., 7., l., 2-51,
(15 Pi, 2., IO., 1.25, 3. 1, (16 Pi, 2., 1.5, 1.25, 3.75},
{17 Pi, 3., 15., 1.75, 7-51, {18 Pi, 4., 19., 2., 10.1,
{i9 Pi, 4.5, 24., 2.5, 12.51, (20 Pi, .S., 30., 3., 16-11
Ltruncatal (ANSP 215318) =
{{IO Pi, 1.25, 8., 1.25, 5-51, (11 Pi, 4.5, 9.5, 1.5, 7.1,
{12 Pi, 5.5, 12., 2.5, 3 (13 Pi, 8.75, 6 3., I8.S), {14 Pi, 1.22., 4.5, 24.51, U5 Pi, Il., 33., 6.5, 32.51,
(16 Pi, 6 41., 7., 40.51, {17 Pi, 18., 58., 8.5, 48. ),
(18 Pi, 16., 102., 8.5, 60.1, {19 Pi, 26. , 99., 12.5, 56. 1,
(20 Pi, 33., 134., 18.5, 101.5) 1
Lmillepedal (ANSP 228924) =
{{9 Pi, 0.25, 1.5, 0.25, 0.251,
{IOPi, 0.5, 2., 0.25, 0.251,
(11 Pi, 0.75, 2.5, 0.5, 0.51, il2 Pi, 1., 3., 0.75, l.},
{13 Pi, 1.25, 4., l., 2 {14 Pi, 5 5.5, 1.25, 4-1,
(15 Pi, 2., 7., 1.5, 6.25), (16 Pi, 2.5, 9., 2., 6.51,
(17 Pi, 4., 11.5, 3., O,(18 Pi, 4.5, 14., 3., 13.51,
fi9 Pi, 6.5, 19., 3.5, 8.1 (20 Pi, 7.25, 25., 4., 22.51,
(21 Pi, 9., 35., 4.25, 9,(22 Pi, 13., 52., 9., 38.1,
{9Pi, 0.25, l., 0.25, 0.25), (10Pi, 0.5, 1.5, 0.25, 0.2s),
{Il Pi, 0.75, 2., 0.25, 0.25), (12 Pi, 0.75, 3., 0.5, 0.51, {13Pi, 1.25, 4., 0.75, 1.1, (14Pi, 1-75, 5., l., 2-51, 267
(15 Pi, 2.5, 7.5, 1.75, 4 {16Pi, 3., 9.5, 2., 7-51, {17Pi, 4., 12.5, 3., 1 {18Pi, 6.5, 16., 3., 14.1,
{19Pi, 6.5, 23., 3.5, 15.51, {20Pi, 7.5, 33., 4., 20.51,
{21 Pi, 8.75, 41., S., 9 (22 Pi, 6 44., 8.5, 41.1,
(11 Pi, l., 3., 0.25, 0.25), (12 Pi, 0.5, 4., 0.25, 0.251,
(13Pi, 1.25, S., 0.75, 1 (14Pi, l., 6., 0.5, 3.51,
(15 Pi, 2., 7.5, l,, 4.1, (16 Pi, 3., 9.5, 1.5, 6-51,
(17Pi, 4., IS., 2., 9 {18 Pi, S., 14., 2.5, 13.},
{IgPi, 7., l8., 3., 12{20Pi, 8.5, 25, 3.5, 19.1,
(21 Pi, 9., 35., 3.75, 18.5}, {22 Pi, 18., 27., 8.5, 37.51,
(10 Pi, 0.25, 2., 0.25, 0.251, Cl1 Pi, l., 3., 0.25, 0.51,
{12Pi, l., 4., 0.25, 0.51, {13ei, 1-25, 4., l., l.},
(14 Pi, 1.25, 5.5, 0.75, 2 (15 Pi, 2.5, 7., l., 4.1,
{16 Pi, 2., 9., 1.5, 4.75}, (17 Pi, 4., 11.5, 2., 8.51,
(18 Pi, 4., 14., 2.5, 10.5), {19 Pi, 6., 19., 3., 12.51,
(20 Pi, 7., 25., 3., 16.5}, (21 Pi, 8., 34.5, 3.5, 16.}, (22 Pi, 14., 28.5, 7.5, 31.)) -
MlJep&a2_(mSp223924)=------
({il Pi, 0.5, 2., 0.25, 0.251,
(12 Pi, 0.75, 2.5, 0.25, 0.25), (13 Pi, l., 4., 0.75, OS), (14 Pi, 1.25, 4.5, l., 1.51,
{lSPi, 2., 6, 1.5, 3-25}, {16Pi, 3., 7.5, 1.5, S.},
(17 Pi, 4., 10., S., 8.5}, Il8 Pi, 5., 14., 3., 12.51,
{19Pi, 5.5, 18., 3., 17.1, {2OPi, 7.5, 24., 3., 21.1,
(21 Pi, 8.5, 31., 3.5, 18.51, (22 pi, l8., 16., 9.5, 37-51,
(11 Pi, 0.5, 2., 0.25, 0.251, {12 Pi, 1.5, 3., 0.25, 0.51, (13 Pi, 1.5, 4., 0.5, 1.251, (14 Pi, 1-75, S., l., 3.1,
(15 Pi, 2.5, 6 1.5, 4.251, (16 Pi, 3.5, 8., 1-75, 7.1,
(17 Pi, 4.5, 10.5, 2., 1 (18 Pi, 6., 13., 3.5, 15.1,
{19Pi, 7., 18., 3.75, 9 (20P1, 8., 28., 4., 25.1,
(21 Pi, 9.5, 37., 4.5, 20.51, (22 Pi, 20., 20., 20.5, 36.1,
{il Pi, 0.5, 3.5, 0.25, 0.251, (12 Pi, l., 4., 0.25, 0.25),
(13 Pi, l., S., 0.75, 1 (14 Pi, 1.5, 6 l., 2.1,
(15 Pi, 2.5, 8., 1.5, 4.51, (16 Pi, 3., 9.5, 1.5, 7.1,
{17Pi, 4., 12.5, î., 10.251, {18Pi, 5.5, 15.5, 3., 13*},
{19Pi, 6 21., 3.5, 17.75), {SOPi, 7.5, 25.5, 3.5, 23.1,
(21 Pi, IO., 33., 3.5, 9 (22 Pi, 19., 30., 4., 34-51}
Scampbelli (ANSP 234254) =
((9 Pi, 0.5, 4.5, 0.5, 1.5 (10 Pi, 1., 5., 0.5, 1.51,
{IlPi, l., 7., i., 1.51, {12Pi, 1.5, 8., 1., 2-51,
(13 Pi, 2., 10.5, 1.25, 3.51, {14 Pi, S., 13., 1.5, 5-51,
(15 Pi, 3., 16.5, 1.5, 7 (16 Pi, 3., 19.5, 2., 7.751,
(17 Pi, 4., 24.5, 2.5, 1.{18 Pi, 4., 3O., 3., 12.25},
{19Pi, 5.5, 37., 3., 17{20Pi, 8., 39., 3.5, 17-},
(7 Pi, 0.5, 3., 0-25, 0.251, (8 pi, 0.75, 3.5, 0.25, 0.251,
(9 Pi, 1., 4.5, 0.5, 1.(lOPi, 1.25, 5., 0.5, 1.251,
(11 Pi, 1.5, 6.5, 0.75, 2.1, {12 Pi, 1.5, 8.5, l., 2.25),
{13Pi, 2., 10.5, l., 3-51, {14Pi, 2., 12., l., 3.51,
(15 Pi, 3., i5., 156 (16 Pi, 3., 18., 1.5, 6.1,
{17Pi, 4., 23., 2., 9.51, {18Pi, 4., 27., 2.5, 10.5),
(19 Pi, 5.5, 32., 2.5, i3.}, (20 Pi, 7.5, 37.5, 3.5, 14.1,
(9 Pi, l., 4.5, 0.5, 1.25), (10 Pi, l., S., 0.5, 1.251, {liPi, 1-5, 7., 1., 5 {12Pi, 1.75, g., l., 2.1, 269
(13 Pi, 1.75, Il., 1, 3.51, (14 Pi, 2., 13., l., 4.1,
{15~i,2.5, 6.5 1.5, 5.51, {16Pi, 3., 19., 1.75, 6-25),
(17 Pi, 3.5, 23.5, 2,, 9 (18 Pi, 4-, 27., 2., 10.251,
(19 Pi, 5., 33., 2.5, 13.51, (20 Pi, 8., 35., 3.5, 15.))
Ssibbaldiplicatus (ANSP 3 98 62) =
((14 Pi, 0.5, 7.5, OS, 1-75}, (15 Pi, 2., Il., l., 2-51,
{16Pi, l., 12., 1.25, 3 (17Pi, 3., 14.5, 1.5, 6-1,
{18Pi, 2., 17,, 1.5, 7 {19Pi, 3.5, 20.5, 2., 8*},
(20 Pi, S., 23., 3., 9.) 1
Srupellierythrinus (ANSP 39859) =
((12 Pi, l., 4,, OS, 0.751, (13 Pi, 1.5, 6., l., 2-51,
(14 Pi, S., 7.5, l., 3.5}, (15 Pi, 2.5, IO., 1.5, S.},
(16 Pi, 2-5, 13., 1.5, 6-25], (17 Pi, 3-, IL, 2., 7.51,
{18Pi, 4., 24., 33, C14Pi, 2., S., l., 24,
(15Pi, 2., 8., l., 3-}, {16Pi, 2.5, IO,, 1.5, 5.1,
{17pi, 3,, 12.5, 1.5, 4.5}, (18Pi, S., 16., 3., 6.))
Smarginatus (ANSP 252183) =
{{IlPi, 1.5, 3.5, 0.75, 1.751, Il2 Pi, l., 4.5, l., 3.1,
(13Pi, 2., 6.5, l., 4 {14Pi, 2., 8., 1.5, 5.51,
(15 Pi, 3., IO., 1.5, 7-51, (16 Pi, 3.5, 13., 2., 9. 1,
(17 Pi, 4., 18.5, 2., 5,(18 Pi, 3., 19.5, 2,, 7.75})
Llambisl (ANSP 246931) =
((9 Pi, 0.75, 3., 0.25, 0.5},
{lOPi, 0.75, 3.5, 0.25, 0.25),
{II pi, I., S., 0-5, 1-1, {12 Pi, 1-25, 1-, 2.51,
Il3 Pi, 2.5, 7.5, 1.5, 4.1, (14 Pi, 3., 9., 1.5, 5.5}, (15Pi, 4.25, 11., 2., 8.51,
(16 Pi, 4.75, 15, 2.75, llS},
{17 Pi, 6., 18.5, 3., 12.S}, (18 Pi, 8., 21., 3., 19.1,
(19 Pi, 9.5, 28., 4.25, 20. }, (20 Pi, 11., 43., 5., 27.51,
(21 Pi, IB., 43., 5.5, 27.51, (22 Pi, 28., 53., 9.5, 43.1)
Stricornis2 (ANSP 194550) =
((11Pi, 1.5, 5.5, 0.75, 2 (12 Pi, 1.25, 6, l., 3.1,
(13 Pi, 3., 7., 1.5, 5 (14 Pi, 2.5, 10.5, 1.5, 6.1,
{15 Pi, 4.5, 13.5, 2., 10. ), (16 Pi, S,, 16., 2.5, 12.51,
{17 Pi, 6.5, 22., 2.5, 16-51, {18 Pi, 7., 24.5, 2.75, 18.1,
Il9 Pi, 8.5, 53., 3.5, 24.51, (20 ?i, 15., 29., 5., 22,511
Lpseudoscorpia (ANSP 3 9 87 9 ) =
((8 Pi, 0.5, 5.5, 0.75, 1.1, (9 Pi, 1.25, 7., 0.75, 2-1,
{IOPi, 2.5, 8.5, l., 4.{llpi, 3., 11., 1.5, 6-51,
(12 Pi, 4.25, 14., 2., 9.51, (13 Pi, 6, 17., 2.5, 13-51,
El4 Pi, a., 22., 3.5, 19(15 Pi, 5., 43., 6., 20. 1,
(16 Pi, 7., O., 4.5, 20.1, (17 pi, 21., 42., 5., 37,5})
(specimen probably is L. scorpius -- unused in morphospatial analyses)
Lchiragrafemale (ANSP 223 975) =
((7 Pi, 0.5, 2.5, 0.5, 1.251, (8 Pi, 1.75, 3., 0.5, 1-51,
(9 Pi, 2., 6., l., 1.751, (10 Pi, 2.5, a., 1-25, 2.1,
(Il Pi, 4.5, IO., 2.5, 7.51,
(12 Pi, 4.5, 13.5, 2.5, 11.75),
{13 Pi, 7., 18., 3.5, 13.5}, (14 Pi, 7.5, 22., 4.25, 17.5}, 27 1 (17 Pi, 18., 47.5, 7., 32.1, (18 Pi, 27., 67.5, 14., 50.1) (unused in morphospatial analyses)
Sthersites (ANSP 240155) =
{{10Pi, 0.5, 6.5, 0.25, 0.51, (Ilpi, 2., 9.5, 0.25, 0.51,
(12 Pi, 1.75, 12., 0.5, 0.75),
(13Pi, 2.5, ls., 1.25, 3.51,
{14 Pi, 2.5, 17.5, 1.5, 4-51, Il5 Pi, 4., 22-, 1.75, 7.1,
{16Pi, 3.5, 29., 2.25, O {17Pi, 6., 33., 2.5, 13.1,
(18 Pi, 6., 41., 3.5, 17.5), (19 Pi, IO., 47., 4., 21.51,
(20 Pi, 80, 63., 4.5, 26.), {21 Pi, 13., 72.25, 6., 31.51,
{22Pi, 26., 93., 7., 55-51, {12Pi, l., 9., 0.5, l.s},
113 Pi, 2., 11.5, 0.75, 3.1, (14 Pi, 2.5, 15., 1.25, 3-51,
{15Pi, 3.5, la., 1.5, 6.1, {16Pi, 4.5, 23., 1.75, 7.751,
(19 Pi, 9., 40., 3.5, 19.75}, {20 Pi, IO., 47.5, 4., 22.1,
(21 Pi, 14.5, 57., 5.5, 27.1, {22 Pi, 15, 72., 6., 48-11
Srninimus (ANSP 231095) =
{{9 Pi, 0.25, 4., 0.25, 0.25}, 110 Pi, 0.5, 4.5, 0.25, O.s),
(11 pi, I., 5.5, 0.5, 1.1, (12 Pi, 0.75, 6., 0.5, 1.251,
{13Pi, 1.25, 7.5, 0.75, 1-75),
{14Pi, 1.25, 8.5, 0.75, 2.51,
{iSPi, 2., 9.5, l., 2.1, I15Pi, 2., 12.5, 1-25, 4-5L
{17 Pi, 2.5, 16., 1.5, 7.L (18 Pi, 3.5, 18.5, 2., 7-25},
{lOPi, 0.5, 3., 0.25, 0.751, {Il Pi, l., 4., 0.25, 1.1,
(12 Pi, l., 5., 0.5, 1.5}, (13 Pi, 1.5, 6., 0.5, 2.1,
{14 Pi, 1.5, 7.5, l., 2.51, Il5 Pi, 2., g., 1., 4-}, {16 Pi, 2., 11.5, 1.5, 5.}, (17 Pi, 2.5, 14., 1-75, 7-1, 272
(18 Pi, 3.5, 20., 2.5, 7.5))
Spulchellus2 (ANSP 23154 9) =
{{9Pi, 0.25, l., 0.25, 0.25},
{lOPi, 0-5, 1.5, 0.25, 0.25},
(II Pi, 0.75, 2.5, 0.25, 0.51,
{lZPi, 0.75, 3., 0.5, 0.75),
(13 Pi, l., 4., 0.5, 1.5, (14 Pi, l., 4.5, l., 1-75},
{lSPi, 1.5, 6.l., 3 {16Pi, 1.5, 8., l., 3-51,
(17 Pi, 2., 10.5, 1.5, 7,{18 Pi, 2., 12., 1.5, 6.},
{19 Pi, 3.5, 16., 1.75, 8.5), (20 Pi, 4., 18., 3., 9.51,
(11 Pi, 0.5, 2.75, 0.2s, 0.25),
El2 Pi, 0.75, 3., 0.25, 1-51,
(13 Pi, 1., 4., 0.25, 1.75), (14 Pi, l., 5., 0.5, 1-75},
(15 Pi, 1.25, 5.5, 0.75, 2.51, (16 Pi, 1.5, 8., l., 3-51,
(17 Pi, 2., 10.5, l., 5.5}, (18 Pi, 2., 13.5, 1.25, 6.1,
(19 Pi, 3., 16.5, 1.75, 8 , (20 Pi, 3., 20., 2.5, 9.))
Lcrocata2 (ANSP ROM Acc 1987-043) =
{{IlPi, 0.5, 3.5, 0.25, 0.25}, (12 Pi, l., 4.5, 0.25, l.},
(13 Pi, 1.25, 5.5, 0.75, 2 Il4 Pi, 1.25, 7., l., 3.1,
(15 Pi, 2., 8.5, 1.75, 4.51, (16 Pi, 3., 10.5, 2., 6.1,
(17 Pi, 3.5, 14., 3., 8.}, (18 Pi, 4.5, 17., 3., 11.5},
{19 Pi, 6., 21.5, 3.5, 5 } (20 Pi, 6., 32., 3.75, 18.75),
{21 Pi, 6.75, 38.5, 4., 16.5),
(22 Pi, 13., 39., 5.5, 30.5),
(11 Pi, 0.5, 3., 0.25, 0.51, (12 Pi, 0.5, 4., 0.5, 1.1,
(13Pi, l., S., 1.25, 2.{14Pi, 1.5, 6., 1-25, S.}, 273 (15 Pi, 2., 8., 1.25, 4.1, {16 Pi, 3., IO., 1.5, 5.51,
{17 Pi, 3.5, 12., 2., 8.51, {18 Pi, 4., 15., 3., ILS},
119 Pi, 5.5, 20.5, 3.25, 1.(20 Pi, 4.5, 35., 3.5, 18.1,
{SI Pi, 7., 35.25, 4., 16.1,
{22 Pi, 14.5, 35.5, 5.5, 28.51,
{12Pi, 0.5, 2.5, 0.25, l.), {13Pi, l., 4., 0.5, 2.1,
{14Pi, l., 5., 1., 3 {lSPi, 2., 6., 1.5, 5.1,
(16 Pi, 3., 8., 2., 6.1, (17 Pi, 4., 10.5, 2.25, 10-5),
(18 Pi, 4., 15.5, 3., 2 {19 Pi, 6., 18.5, 3., 17-51,
(20 Pi, 6 27., 3.5, 9 (21 Pi, 8., 33., 4., 17-51,
(22 Pi, 16.5, 35., S., 29-51, {13 Pi, i.., 3., 0.25, 1-1,
(14 Pi, l., 4.5, 0.5, 15(15 Pi, 1.5, 6 l., 3.1,
{16Pi, 2., 7.5, 1.5, 4.1, {S'Pi, 2.5, IO., 2., 6.1,
(18 Pi, 2.5, 12.5, 2.25, 8 (19 Pi, 6.5, 14., 3.5, 12.1,
(20 Pi, S., 18., 4., 6,{21 Pi, 8., 33., 4., 19.},
(22 Pi, 13.5, 37.5, 5., 30.1, (12 Pi, 0.5, 3.5, 0.25, la),
{i3 Pi, 0.75, 4.5, l., 1.51, {14 Pi, 1.5, 6., 1.5, 34,
{15 Pi, 2.25, 7.5, 1.75, 4 (16 Pi, 2.5, 9.5, 2., 6.1,
(17 Pi, 3.5, 12.5, 2.5, 8-51, (18 Pi, 4., 14., 3., ILS),
Il9 Pi, 6.5, 18., 3.5, 16.1, (20 Pi, 5., 33., 4., 19.51,
{SI Pi, 8., 35., 5., 17.1, (22 Pi, 13.5, 37., 5.5, 30.1 1
LlAmhis2 (ROM Acc 1990-039) =
{Il2 Pi, 0.75, 3., 0.5, 0.751, (13 Pi, 1.75, 5.5, l., 2.5!,
{14 Pi, 1.75, 6.5, 1.25, 4-75}, {15 Pi, 3., 8.5, 1.75, 7.1,
(16 Pi, 3.5, 12.5, 2., 9.751, (17 Pi, 5.5, 16., 3., 12-51,
{la Pi, 7., 19., 3.25, 15.51, (19 Pi, 9., 25., 3.75, 21.1,
(15 Pi, 12-5, 22., 3-25, 17.751,
{16 Pi, 13.25, 30., 7., 26.1,
(17 Pi, l6., 45., IO., 31.1, {18 Pi, 22., GO., Il., 46.1,
(19Pi, 26., 92., 15., 55.1,
(20 Pi, 54.5, 100-, 30., 110.))
Ssinuatua (author's collection) =
({ilpi, 1.25, 4.5, 0.25, 1.1, {12Pi, 1.25, 6., 1., 2.51,
(13 Pi, 2., 8., 1.25, 3.251, {14 Pi, 2.5, Il., l., 4-75},
il5 Pi, 3,, 12.5, 1.75, 7.51, {16 Pi, 4.5, 17., 2.5, lO.},
(17 Pi, 65SI., 3., 15(18 Pi, 6.5, 21-, 3., 15.1,
Il9 Pi, 9.5, 32.5, 4., 23.), {20 Pi, 13., 55., 4.25, 23.1,
(21 Pi, IO., 60., S., 23.751, (22 Pi, 20-, 51., 8.5, 44.11
Lchiragra2 (M. Telfordrs collection) =
({ilPi, 2.5, 5., 1.5, 3.51, {12 Pi, 2.5, 6., 1.5, 5.51,
(13 Pi, 5.5, 8., 2.5, 7.5), {14 Pi, 5-5, 13., 3.5, 11.5},
(15 Pi, 8., 17., 3.75, S.} (16 Pi, 8., 28-, S., 19Jf
{17 Pi, 8.5, 35., 6., 22.51, (18 Pi, 14, 47., IO., 37.5)}
Lscorpius (authorfs collection) =
((13 Pi, 0-5, 3.5, 0.5, 1.251, {14 Pi, l., 4., l., 2.1,
{15 Pi, 1.5, 6., 1.25, 4 (16 Pi, 2.5, 7., 1.5, 5Jf (17Pi, 3.5, IO., 2., 9.{18Pi, 4., 12., 2.5, lo.},
(19 Pi, 5.5, 15.5, 3-, 16.51, (20 Pi, 6 29., 3.5, 20.51,
{21 Pi, 6., 41., 4., 17.51, (22 Pi, 12-, 33., 3.75, 32-51)
Ldigitata (ROM 945) =
({IOPi, 0.5, 7.5, 0.75, 1.751, {llPi, 2-25, 9.75, 1., 3.1,
(12 Pi, 1.5, 11.75, 1.25, 4-51, (13 Pi, 3.5, 14., 1.75,
(21 Pi, 10.5, 51.5, S., 29. 1, (22 Pi, 12., 59., 5.5, 354} (estimated from illustrations, following Saunders and Swan 1984)
Svomer = {{Il Pi, 0.8, 4.5, 0.25, 1-25},
{12Pi, 1.25, S., 0.8, 1.751,
(13 Pi, 1.75, 6.25, 1.25, 2-25},
{14Pi, 1.75, 9., 1-25, 3-51, {15 Pi, 2.25, 11.25, 5,5 (16 Pi, 2.5, 14, 2-25, 5-1,
{19 Pi, 6.25, 30., 3.25, 18.1, (20 Pi, 7.75, 34., 4.25, 20.1,
(estimated from illustrations, following Saunders and Swan 1984)
Sdilatatus =
(111 Pi, 0.5, 2.75, 0.15, 0.751, {12 Pi, 0.75, 3., 0.5, 1.1,
{17 Pi, 2., 10.75, 1.5, 6.1, {18 Pi, 2.5, 14.75, 1.75, 8.1, (19 Pi, 3.75, 18.25, 1.75, 10.8), Pi, Pi,
(estimated from illustrations, following Saunders and Swan 1984) Appendix Vm. CODING AND USING SHELL
PARAMETERS CLADISTICALLY
Shell parameters cm be coded and used in cladistic analyses. SheU parameters used to analyse lambis-like species were coded in a manner denved from that presented by Stone
(1997b). Coordinate positions ({r, z}, Figure AVIII.l) and linear dimensions ({h, v),
Figure AVIII.1) of the shell aperture at one whorl intervals, according to atlornerric equations of form, were determined for each species. Parameter values that transform the mathematical description of Strombus variabilis shell form ({O, T) and {H, V), respectively) into that of each lambis-like species were determined.
Parameter values of 1.00 leave the mathematical description of shell form unchanged. The outgroup taxon. by definition (Stone 1997b1, has parameter values of
1.00. A member of the ingroup that has a value of 1.00 for a given pararneier (0,T, H, or V) is similar to the outgroup species in that particular aspect of shell fom (r, z, h, or v) (Stone 1997b). Values greater than 1.00 indicate that that aspect of shell fom in a member of the ingroup is greater than that of the outgroup; values less than one indicate that it is less than that of the outgmup.
Because sample sizes were very small, polarisation of parameter values was Figure AVIII. 1. Variables and parametee used in analyses of larnbis-like species.
280 detexmined algebraically instead of using overlapping confidence intervals (Stone 1997b).
Parameter values were rounded to the integer N when their values were within the range
(N- 1) +0.10SNIN+0.10.
Raw data (unrounded parameter values) for larnbis-like species are presented on the next 8
pages (as ( (species narne abbreviated as in Figures 5.14-17, ( {parameter values}, ... } } 1).
These are points of ontogenic tracks in morphospace. T, 8, V Ontogenic Morphospace Tracks = ({Ltru, {{2.26148, 4.44415, 10,08171,
(2.61798, 4.69893, 8.09885}, (2.96773, 4.92877, 6.71351),
(3.31174, 5.13899, 5.69756) } ), {Lmil, ((0.47517, 0,955372, 0.6496621, I0.711554, 1.03544, 0,7615571, (0.744277, 1.10934, 0.8726121,
(0.774129, 1.17829, O. 982945)} },
(Ldig, ((2.68754, 2.93537, 4.51039}, (2.44542, 2,45957, 3.46047},
(2.25544, 2.11382, 2.75776},
(2.10141, 1.8515, 2.26118} ) 1,
{Lchi, ((1.62863, 3.54328, 3.874 },
11.76864, 3.43363, 3.694761,
(1.89811, 3.3424, 3.547831,
12.01909, 3.2646, 3.42411) }},
{Lvio, { (5,69682, 5.00521, 9.63588 1, (4.74662, 4.17772, 7.11166},
(4.09156, 3.57857, 5.48234),
(3.57999, 3.12541, 4.36643) ) ),
{Llam, { (0.954067, 1.3357, 1.373031, {0.960955, 1.34301, 1.33455), {0.966895, 1.3493, 1.30245), (0.97212, 1.35483, 1.27501))},
{Lsco, { (0,374203, 1,06524, 0.859279), (0.469639, 1.05135, O .9Ol4Ol), {O -570526, 1.03959, O. 939lZZ), (0.676384, 1.02942, 0.973407)}},
{Lcro, { (0.699734, 0.945988, O.895257), (0.748942, 1.00604, 0.915292), (0.793837, 1.0605, 0.93281), C0.835305, 1.11055, 0.948407))},
{Lrob, { {1.5067, 3,82922, 6.323441, (1.66455, 3.06698, 4,86933), {1.81285, 2.53591, 3,892751, (1.95336, 2.14738, 3.20058))),
{Sdil, { (0.684743, 0.672216, 1.1119) , {O.686223, O .715682, O. 9433891, (0.687494, 0.755145, 0.819505),
{O. 688608, 0.79144, 0,7245631 11,
{Sbul, ( (1.51485, 1.95305, 2.089381, I1.5189, 1.76061, 1.80405), (1.52067, 1.61092, 1.590831, (1.52221, 1.49047, 1.4251))),
{Svom, { (2.11263, 1.40196, 1.80875), {1.13049, 1.36969, 1.52771}, (1.14601, 1.34264, l.32197),
(1.15976, 1.31942, 1.16486) )) ) O, E, V Ontogenic Morphospace Tracks =
( {Ltru, { (4 ,51291, 4.44415, l0.0817),
(5.03775, 4.69893, 8.098851, (5.53561, 4.92877, 6.713511, (6.01123, 5.13899, 5.69756)11,
(Lmi.1, ({0.90191, 0,955372, 0,6496621, (1,03816, 1,03544, O ,7615571, {1.17113, 1 .10934, 0 -8726121, (1.30132, 1.17829, O. 9829451 11,
{Ldig, { (1,97735, 2,93537, 4.510391, I2.08606, 2.45957, 3.46047 1, (2.18392, 2.11382, 2.75776), E2.27327, 1.8515, 2.261181 11, {Lchi, ((3.10347, 3.54328, 3.8741, {3.14483, 3,43363, 3.694761, {3.1807, 3.3424, 3.547631, (3.2124, 3.2646, 3.42411)) 1, {Lvio, {{5.11917, 5.00521, 9.635881, {4.71915, 4,17772, 7.111661, (4.40143, 3.57857, 5.482341, {4.14113, 3.12541, 4.3664311),
{Llam, { (1.23006, 1.3357, 1.373031, (1.35946, 1,34301, 1.334551, (1.48108, 1.3493, 1.302451, (1.59635, 1.35483, 1.27501}}1, {Lsco, {{O.419374, 1.06524, 0.859279), {0.56408, 1.05135, O. 901401), {O .727l44, 1.03959, 0.9391221, (0.90798, 1,02942, 0.973407}}), {Lcro, ((0.718542, 0.945988, 0.895257), (0.839927, 1.00604, 0.915292), {O. 960066, 1.0605, 0,932811, {1.07915, 1.11055, 0,948407))),
{Lrob, { {2.60522, 3.82922, 6.323461, {2.60562, 3.06698, 4.869331, (2,60597, 2,53591, 3.892751, (2.60628, 2.14738, 3.20058})),
{Sdil, { (0.681071, 0,672216, 1.1119), {0.709001, 0.715682, 0.9433891, {O ,733834, 0 -755145, 0.8195051,
I0.756267, 0.79144, 0.724563)) ),
{Sbul, ( (1.8809, 1.95305, 2.089381, (1.77219, 1.76061, 1.804051, Il. 68408, 1.61092, l.590831,
1.61061, 1.49041, 1.4251))),
{Svom, { (1.24946, 1.40196, 1.80875), (1.24463, 1.36969, 1.527711, (1.24051, 1.34264, 1.321971, I1.23691, 1.31942, 1.164861 1)) O, T, V Ontogenic Morphospace Tracks =
( (Ltru, { (4.51291, 2.26148, 10.0817},
{S. 03775, 2.61798, 8.098851, {5.53561, 2.96773, 6.71351), (6,01123, 3.31174, 5.69756) )),
{Lmil, { {O. 90191, 0.67517, 0 .649662), (1.03816, O .711554, 0.7615573, {1.17113, O ,744277, O. 8726121,
(1.30132, 0.774129, O. 982945))1,
{Ldig, { (1.97735, 2.68754, 4.51039 1, (2.08606, 2.44542, 3.460473,
(2.18392, 2 -25544, 2.75776 j, (2.27327, 2.10141, 2.26118))),
(Lchi, {{3.10347, 1.62863, 3.874 ), f3.14483, 1.76864, 3.69476), (3.1807, 1.89811, 3,547831,
t3.2124, 2.01909, 3.42411) }),
{Lvio, { (5.11917, 5.69682, 9.63588 j,
{4.7191!jf 4.76662, 7.11166},
(4.4Ol43, 4.09156, 5,482341,
{4.14113, 3,57999, 4.36643111,
(Llam, ( (1.23006, 0.954067, l.37303), (1.35946, O. 960955, 1.334551, {l.48lO8, O. 966895, 1.30245), (1.59635, 0.97212, 1.27501))),
{Lsco, {{0.419374, 0.374203, 0.859279),
{O ,56408, O. 469639, O. 9Ol4Ol), (0,727144, 0.570526, 0.939122},
{0.90798, O. 676384, 0.9734071 }), {Lcro, ((0.718562, 0.699734, 0.895257), (0.839927, O. 748942, O. 9l5292),
{0.960066, 0.393837, O. 932811,
(1.07915, 0,835305, O. 948407)) ),
{Lrob, { (2.60522, 1.5067, 6.323461, (2.60562, 1.66455, 4 - 869331, (2,60597, 1.81285, 3.89275), (2.60628, 1.95336, 3.20058})},
{Sdil, { {O. 681071, 0.684743, 1.11193, (0.709001, 0.686223, 0.943389), (0.733834, O. 687494, O. 8195O5),
(0.756267, 0.688608, 0.724563) )),
(Sbul, { (1.8809, 1.51685, 2.089381, (1.77219, 1.5189, 1.80405), (1.68408, 1.52067, 1.59083}, (1.61061, 1,52221, 1.4251))},
{Svom, { (1.24946, 1.11263, 1.80875), (1.24463, 1.13049, 1.52771), (1.24051, 1.14601, 1.32197),
(1.23691, 1.15976, 1.16486) } } } O, T, ff, Ontogenic Morphospace Tracks =
{ {Ltru, { (4,51291, 2.26148, 4.444151,
(5.03775, 2-61798, 4,69893),
(5 ,53561, 2.96773, 4 92877 1, (6.01123, 3,31174, 5.13899))},
{Lmil, {{0.90191, 0,67517, 0.955372),
(1.03816, 0,711554, 1.03544}, (1.17113, 0.744277, 1.10934),
(1.3013Zf 0. 774129, 1.17829) ) ),
{Ldig, { { 1.97735, 2.68754, 2.935371,
(2,08606, 2.44542, 2,459571,
(2.18392, 2,25544, 2.11382),
(2.27327, 2.10141, 1.8515)) ),
{Lchi, { (3.10347, 1.62863, 3.54328 1,
(3.14483, 1.76864, 3.43363),
(3.1807, 1.89811, 3.34241,
- (3.2124, 2.01909, 3.2646)) ), {Lvio, ((5.11917, 5,69682, 5.00521),
(4,71915, 4.76662, 4.177721,
(4 .OOl43, 4.09156, 3.578571,
{4.l4ll3, 3.57999, 3.12541) ) ),
(Llam, { (1,23006, 0.954067, 1.33571,
{ 1.35946, O. 960955, 1.34301 ) ,
(1.48108, O. 966895, 1.34931,
(1.59635, 0.97212, 1.35483))),
{Lsco, { {O ,419374, 0.374203, 1.065241,
(0.56408, 0.469639, 1.051351, (0.727144, O .570526, 1.03959},
(0,90798, 0.676384, 1.02942) } },
{Lcro, { {O, 718562, 0.699734, 0 ,94S9881,
(0,839927, 0 -748942, 1,00604),
{O. 960066, 0.793837, 1-06051,
(1,07915, 0.835305, 1. 11055) ) ),
(Lrob, { (2.60522, 1,5067, 3.829221,
(2.60562, 1.66455, 3.066981,
(2.60597, 1.81285, 2.535911,
{S.6O6S8, 1.95336, 2.14738) 1 ),
{Sdil, { { 0. 681071, 0.684743, O.672216},
{0.709001, O, 686223, 0.7156821,
{O. 733834, O, 687494, 0.755145),
(0.756267, 0.688608, 0.79144})),
{Sbul, ( {1,8809, 1.51685, 1.953051,
(1.77219, 1.5189, 1.76061},
{1.68408, 1.52067, 1.61092),
I1.61061, 1.52221, 1.49047}}},
{Svom, { (1-24946, 1,11263, 1.40196),
(1.24463, 1.13049, 1.36969),
(1.24051, 1.14601, 1.342641,
(1.23691, 1.15976, 1.31942)) ) ) Appendix IX. ASYMMETRIC COILING
The accretion of a gasmpod shell is an asymmeaic process: a matrix of inorganic
material is secreted at the rnantle edge and accretes onto only one end (the aperture) of a
pre-existing shell. Arnong gasmpod shells, four types of developmental asymmetries can
be distinguished: dextrai onhosmphy, sinistrai onhosmphy, dextrai hyperstrophy, and
sinistral hyperstrophy. The distinction among these four types of asymmetry concems the
direction of shell accretion. often considered with respect to an imaginary mis, the coiling
mis.
'Handing' out Morphological 'Trophies'
A shell that is accreted around a coiling axis in a direction that is known
conventionally as 'right handed' is called 'dextrai;' one that is accreted 'left handed' is
'sinistral.' Viewed apically, the whorls of a dextral shell coi1 in a direction that follows the movement of the hands on the face of a clock or the motion of the sun viewed from above the North Pole. These distinctions, 'right handed,' 'clockwise, ' 'eas t to west, ' etc., are human consmcts but here repre sent different manifestations of calcium carbonate in nam. In his provocative book The Curves of Life, Cooke (19 12) invited readers to consider a metaphor in which a shell is a spiral staircase, the aperture serving as an 290 entrance at the bottom. if a 'Lilliputian' were to ascend the staircase and fmd the outer wall on the right, the spiral would be dextral; if the outer wall were on the left, the spiral would be sinisnal. A shell that accretes dong its coiling axis in a direction that is known conventionally as 'downward' (i.e., hmthe top of the staircase to the bottom) is orthostrophic; one that accretes 'upward' (îe., from the top to the bottom of an inverted spiral staircase) is h yperstrop hic.
nie relation between dexd and sinistral is one of reflective symmetxy (wherein the two types are reflected about a plane between them and paralle1 to their coiling axes;
Figure AIX.l), whereas that between onhostrophy and hyperstrophy is one of topologically invened symmetry (wherein the two types are reflected about a plane between their body whorls and perpendicular to their coiling axes; Figure AM.1). Both cases of each symmetry can be accommodated readily by mathematical conchology and cornputer-graphical simulation (e-g., by exchanging Cosines and Sines or by changing a negative sign to a positive sign in equation 4.2). Considering the intricacies of the processes involved in generating coiled shells, this is an arnazing exarnple of the power of mathematical modeling!
During development, gastropod zygotes undergo spiral cleavage, a process of division wherein a zygote cleaves in planes that are oblique to one another (detexmined by the orientation of spindles of the third cleavage), and blastomeres become spirally arrangeci. Unlike many animals whose zygotes undergo spiral cleavage but which exhibit Figure AIX. 1. Coiling symmeiries.
The relation between dextrai and sinisual is one of reflective symmetry (wherein the two types are reflected about a plane between them and parallel to their coiling axes; shell in centre and shell at right), whereas that between onhosaophy and hyperstrophy is one of topologically invened symmetry (wherein the two types are reflected about a plane between their body whorls and perpendicular to their coiling axes; shell in centre and shell at bottom).
292 bilaterally syrnmeaic larvae and adults, gastropods retain asymmehic structure throughout
their lives, in their shells. Furthemore, the asymrnetry of a cleavage pattern is related to
the asymmetry of shell accretion.
Coiling of Lymmea: hheritance and 'Genetic Assimilation'
Much of the work conceming coiling asyrnmeaies has been investigated using shells of the genus Lymmea. The direction of coiling is determined by a single gene, of which the dextral allele is dominant, and cm be determined as early as the fmt cleavage of the femlised egg (Freernan and Lundelius 1982).
Early in this century, the inhentance of coiling asymrnetry was examineci and found to exhibit matemal inheritance, or delayed segregation, that is, the direction of accretion is detexmined by matemal phenotype (Boycott et al. 1930). Thus, the phenotype of a particular genotype inherited by one generation (FI) is expressed in the subsequent generation (F2). Occasionally, Lymmea offspring possessing dextral shells are produced in sinisaal breeding lines. Some of these dextrals breed me (Le., as dextrais). When first observed, the production of these anomalous individuals with dexaal shells was vexing, but modifier genes piver and Andersson-Kotto 1938) and an elaborate cross-over model that accords with empirical data (Freernan and Lundelius 1982) have been proposed to explain these observations. In the cross-over model, the dexaal gene is reconstituted hm previously dissociateci parts, during meiosis or mitosis of the female genn line, or a dextrai gene is created by means of a position effect
Recently, the direction of coiling of sinisaal shelled stock Lymnaea individuals was countered by injection of (various quantities) of cytoplasm from eggs of dextral coiling individuals (at various stages) into uncleaved eggs of the sinisaals (Freeman and
Lundelius 1982). Cytoplasm hmsinistrai eggs injected into uncieaved eggs of dextrds produced no change in the direction of coiling (Freemm and Lundelius 1982). The simplest explanation of these data is that the dexaal gene specifies a cytoplasmic product which influences cleavage properties; sinistral eggs cleave sinistrally because of the absence of this product (Freeman and Lundelius 1982).
Mor to his work in psychology, coiling of Lymnaea shells was investigated by
Piaget, who proposed the concept of 'genetic assimilation' (described in Waddington
1973). Piaget found that particular shell phenotypes resulted when individuals of
Lymrzuea sfag~liswere grown in different environments. Snails in turbulent wave-action regimes tended to contract their columeilar muscles to adhere fmly to substrats whenever waves threatened to dislodge the animais. As a biomechmicd consequence of continued contraction, these snaiis developed shells that were shorter than those of snails in aanquil ponds. When reared in laboratones or tranquil ponds, the shorter varieties retained their shorter forms. Piaget surrnised that the shorter fom, which presumably resulted as a reaction to the stress of wave-action, had been assimilated via naturai selection into the genetic program of the snails. 294 The concept of genetic assimilation was endorsed and clarified by Waddington,
late in his life (1973). Genetic assimilation probably is a pleiotmpic phenornenon. With
respect to varieties of Lymea stagnnlis, many genes probably participate in the
development of the shorter phenotype, and selection for the shorter phenotype would
promote selection of that particular combination of genes. Even when environmental
stress was removed, therefore, the combination of genes sufficd to produce the shorter phenotype. IMAGE EVALUATION TEST TARGET (QA-3)
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