Bull. geo!. Instn Univ. Upsala: N. S. 4, 6: 81-114, 1974

GROWTH AND VARIATION IN EURYPTERUS REMIPES DEKAY

By

H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

Andrews, H. E., Brower, ]. C., Gould, S. ]., Reyment, R. A.: Growth and Variation in EurypteruJ remipes DeKay, Bull. geo!. Instn Univ. Upsala, Vol. N. S 4, pp. 81-114.

Th e statistic al analysis of two subspecies of Eurypterus remipes shows that both of them display very high integratio:� among all measures considered. The prosomal set of variables are highly integrated with the body set. There is little allometry in bivariate growth sequences. As best known at the present time, trilobites show an analogous leve! of integration; there is therefore reason to suspect that the gr owth relationships here recorded are wide-spread among some arthropods. Ontogenetic growth is analysed for E. remipes remipes, after the establishment of growth stages by a stepwise multivariate technique. Canonical correlation is used to examine the pattern of integration between head and body. This is, again, exceptionally high. Other methods of multi­ variate statistics are applied the analysis of the underlying relationships between variables. The palaeoec ology of the Fiddlersto Gr een Member (Bertie Formation, Upper Silurian) is discussed.

H. E. Andrews, Department of Geology, \'(/ellesley Colle�;e, \'(/ellesley, Mass., U.S.A., S. ]. Gould, Museum of Comparative Zoology, Harvard University, Cambridge, Mass., U.S.A., ]. C. Brower, Department of Geology, Syracuse University, U.S.A., R. A. Reyment, Paleontologiska Institutionen, Uppsala Unit;ersitet. Su,eden.

INTRODUCTION remipes and the E. tetragonophthalmus of Fischer Ever smce Mitchill (1818) recorded the first de Waldheim (synonym E. fischeri) , the other eurypterid from the Upper Silurian of Oneida taxon examined in this paper, became E. remipes County, New York, this group of fossils has fasci­ tetragonophthalmus. nated palaeonrologists. The original Eurypterus Kjellesvig-Waering (1958, p. 1136) , in dis­ remipes DeKay came from the Fiddlers' Green cussing the high degree of likeness between the Member of the Bertie Formation: this stratigra­ two subspecies (for a long time, the European phical leve! is still an abundant source of excell­ one was referred the American remipes), wrote to e:uly preserved specimens. The original specimen that "differences between them are minor and was imerpreted as a catfish of the genus Silurus probably of a geographic or tempora! character" (the appendages of the prosoma were identified and on p. 1137, "E. remipes tetragonophthalmus as the barbels of the fish). Since E. remipes, the is doser to E. remipes remipes than to any other type species of the genus, was first described by American subspecies". He noted that the prosomas DeKay (1825, p. 375, pl. 29), it has been the of the two have the same length-to-width propor­ object of numerous studies. Note-:vorthy are those tions, but the lateral eyes of tetragonopbthalmus of Hall (1859), Holm (1899), and Clarke and appear be larger, the prosomal ornament is to Ruedemann (1912). Kjellesvig-Waering (1958) different, the relative proportions of the sixth grouped several taxa, previously considered as and sevemh segments of the paddle are reversed species, around E. remipes as subspecies. Conse­ and the pre-telson of remipes lacks the epimeral quently, according ro this revision, the E. remipes spines possessed by the other subspecies. More of DeKay, Hall and Clarke became E. remipes recently, StØrmer (1973) has come to the con- 82 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment dusion that differences in the paddles of the indeed: the extreme intensity of integration among European and American forms are great enough nearly all measures is also the primary condusion warrant generic separation and has therefore of Andrews' and Gould's work. Moreover, the few to made tetragonophthalmus the type of his new multivariate studies of trilobites that we know genus, Baltoeurypterus. Kjellesvig-Waering has (Eldredge, 1972, in particular, and references informed us that he is in agreement with StØnner. therein) have independently discovered the exi­ We have Iooked into the grounds for this genus stence of very high correlations and little allometry and Gould and Reyment think that such slight in omogenetic series. W e feel that we may there­ differences can hardly be of more than minor fore be stating a quite general principle of growth taxonomic importance. There is a distinct danger in certain arthropods. Ostracods display a much that we have here a case of the "key character lower leve! of integration (Reyment, 1960, 1963, concept". That is, a certain character is defined as 1966). being of "generic" value (rather than "specific" Gould and Andrews studied a collection of or "varietal") and then one is forced honour eurypterids from the upper Silurian of the Baltic to every variation in this character with a high-leve! island Saaremaa, Estonian S.S.R. The collection taxonomic designation. The variational patterns was made in 1930 by W. Patten (who used them of the European and American eurypterids are to help argue his case for an arthropod origin of very dose indeed. Future study may bring light the vertebrates). Several hundred excellent speci­ to more substantial differences, bur until then, we have mens, ranging fro:n l to 30 cm in length, are chosen a conservative approach by retaining both in the Museum of Comparative Zoology, Harvard taxa as subspecies of Eurypterus remipes. University. The analysis was made on 44 specimens evenly spanning the entire range of size; all had As far as we know, this is the first detailed complete prosomas as well as the first segment of statistical study of a eurypterid appear. Indeed, to the mesosoma and seem to be preserved without Kjellesvig-Waering (1958) observed that the distortion. variability of the eurypterids had yet to be studied. The material studied by Brower and Reyment Qualitative observations occur scattered through­ comes from collections at Colgate University, out the literature, the most comprehensive being Hamilton, N.Y. and Syracuse University, Syracuse, those of Clarke and Ruedemann (1912); most of N.Y. the growth changes they noted in their qualitative appraisal of E. remipes remipes show up dearly in our statistical study. ACKNOWLEDGMENTS The purposes of this work are to study the ontogeny and variation of two dosely related Brower and Reyment are indebted to Colgate eurypterids, to contrast and compare the results University for giving them access a magnificient to obtained, and to attempt a palaeoecological analy­ collection of E. remipes remipes and, in particular, sis for E. remipes remipes. Professor Robert M. Linsley of the Geology to Befare making any general statements about the Department for giving us a set of prosomal nature of functional integration in eurypterids, we measurements on the Colgate specimens. A great must know whether the patterns discovered in one deal of the basic work on the material of E. remi­ species can be detected in related taxa. Thus, pes remipes was carried out as a dass project Brower and Reyment were pleased to learn that by the following students at Syracuse University: Andrews and Gould had done an independent Maurice Cucci, John Douglas, Duane Eppler, Susan mu!tivariate analysis of a European eurypterid. Siwek, John Kennedy, and Ghan Shyam Srivastava. Because the two groups worked in complete in­ Acknowledgment is made in the text for the resu!ts dependence and used different measures and obtained by them. methods, a set of similar results would seem all Measurements on the Syracuse University E. re­ the more compelling. The similarity is striking mipes remipes prosomas and Limulus polyphemus Growtb and Variation in Eurypterus remipes DeKay 83 were made by Edna S. Kaneshiro (1962, un­ ANALYSIS OF EURYPTERUS REMIPES published Master's thesis) who also did much pre­ TETRAGONOPHTHALMUS liminary processing of these data. By The Syracuse University specimens were collec­ Harold E. Andrews and Stephen Jay Gould ted by Adawia Alousi, Nora Kula, Sachiko Naka­ gawa, E. S. Kaneshiro, Ralph Watson, J. L. Craft Twenty seven measurements were made on each and the writers. specimen. We attempted to establish a well-spaced We thank Robert M. Linsley, Erik N. Kjelles­ grid of general lengths, widths and diagonals; vig-Waering (Amoco International Oil Co., Chi­ allometric changes produced by gradients of diffe­ cago, Illinois, USA), C. D. Waterston (Royal rential growth (Huxley, 1932; Gould, 1966) should Scottish Museum, Edinburgh) and D. F. Merriam have a multivariate expression in the clustering (Syracuse University) for reviewing the manu­ of dimensions expressing a gradient. W e also script and making helpful suggestions for im­ constructed a set of measures for anatomical fea­ provement. tures of particular interest (the eyes and the first The identifications of most of the species occur­ mesosomal segment). ring with Eurypterus remipes remipes were kindly We analyzed our 44 X 27 matrix with COVAP made by Professor John W. Wells of Cornell for R and Q mode principal components factor University (lthaca, New York), Dr. Erik Kjel­ analysis with options for varimax and oblique lesvig-Waering, and Professor Robert M. Linsley. rotations. As these techniques assume a linear The text figures were drawn by Mrs. Dagmar relationship between pairs of variables, we trans­ Engstrom and the manuscript typed by Mrs. Eva formed all measures tO their logarithms before Eklind, both of the Palaeontological Department, the analysis. About the only allometric relation­ Uppsala University. The Syracuse University and ship consistently found in arthropods is the nega­ Uppsala University Computer Centers provided tive differential growth of the eyes. Bivariate computer time; James Wilson of the Syracuse plots show that the Saaremaa eurypterids are no Computer Center aided in APL programming. exception to this general trend. Reyment's contribution to the study was made The variables are listed in the explanation to while he was a Visiting Professor at Syracuse Fig. l, the illustration of the variables measured. University, autumn, 1972, in part sponsored by Differential allometric relationships found are: Eye the Mobil Oil Company. length (measure 15) vs. prosoma length (measure 1): EL= 0.64PL0-73, at r = 0.977, COMPUTER PROGRAMS USED FOR THE while for eye width (measure 16) vs. prosoma ANALYSIS OF E. REMIPES length EW 0.46 PL0-62, at 0.907. The computations on E. r. remipes were made = r = Virtually all other bivariate relations are isometric; using standard APL procedures and programs for prosoma width (measure 2) vs. prosoma length, developed by Brower, Reymeot and Wilson. The for example, multivariate analyses were made with BMD PW 1.36 PL0·99, at r 0.998. FORTRAN programs (Dixon, 1970) and FOR­ = = TRAN programs of Blackith and Reymeot (1971) . Because the logarithmic transformation of the Reference is also made tO Veldman (1967) for power function is a standard linear equation, ope­ a program for squared distance coefficients and ration on logarithms of original data removes the average linkage duster analysis. The computa­ potential dilemma of non-linearity due to allo­ tions on E. r. tetragonophthalmus were made with metric power functions. COVAP, a FOR TRAN program (Manson and The first evidence of extremely high integra­ Imbrie, 1964; Gould, 1967). tion comes from the correlation matrix (used to 84 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

Fig. l. The 29 variables measured Eurypterus remipes tetragonophthalmus Fischer. on

extract eigenvalues in the R-mode analysis). Of are 0.908 for the rwo small and inaccurate mea­ 351 elements in the half matrix of correlarions sures 25 and 27. The factor loadings on principal ( excluding elements of the principal diagonal), components are easily interpreted, bur not very 139 (40 %) are greater than 0.99. The lowesr revealing; all variables load very strongly on the value is 0.70 for posterior lateral eye width (mea­ first axis (the lowest projection is 0.84 for eye sure 17) vs. length of the first mesosomal segment width measure 17). This is clearly a size axis. at its lateral border (measure 23). Only 4 correla­ As the eurypterid grew, all its measures increased rion coefficients are less than 0.80. In one sense, in approximately linear proportion (after loga­ it is remarkable that COVAP was able to make rithmic transformation). This pervasive positive a significant distinction of functional groups correlation produces a size axis that overwhelms within such a monotonous matrix (see below). all other components of variation: there is virrually The theme of right integration is equally evi­ nothing left to load on subsequent axes. dent in the list of eigenvalues; the first eigenvalue We must rotate our axes to detect the fine explains 95.2 % of all information; 3 eigenvalues srructure of variation. The varimax rotation pro­ encompass 97.7 % of the information and provide vides some insights, bur the consrraint that axes the most sensible interpretation (addirional com­ be orthogonal limits its urility. The vectors re­ ponents seem to reflect measurement errors or presenting variables are so tightly clusrered in anomalous single values, while fewer axes clearly m-space that a ser of orthogonal axes cannot Jump separable and meaningful components of achieve a location very near any of them. If we variation). wish to detect clusters of variables by their pro­

The lowest communaliries over three factors jecrions upon axes, we shall need to "collapse" Growth and Varia tion in Eurypterus remipes DeKay 85

Table l. Triaxial obli que factor solution for the The reference axis itself is a width - the most Saaremaa eurypterids; recordered oblique projection posterior width, measure 21 (the choice of refe­ matrix. rence axis is of no particular significance in itself). Measure Now, of the 10 highest projections upon the 21 17 23 num ber reference axis, 8 are widths - and this indudes all the width measures. (The exceptions are length 21 1.000 0.000 0.000 measure 26 and diagonal 10). Moreover, of the 18 0.980 0.025 0.004 26 0.933 -0.013 0.089 first 5 widths, four are posterior widths; the latter 20 0.918 0.061 0.043 three are anterior widths. The remaining 11 vari­ 3 0.906 0.075 0.044 ables are all diagonal or length measures; the 12 0.900 0.074 0.050 diagonals tend to come first ( 4 of the first 5). 19 0.889 0.083 0.052 Thus, we see a stratification of this tight duster lO 0.886 0.047 0.081 2 0.886 0.081 0.060 into four poorly defined but dear aggregations: 13 O.R85 0.102 0.040 posterior widths, anterior widths, diagonals and 4 O.RR2 0.05/l 0.085 lengths. There is same tendency for measures of 7 0.880 -0.006 0.141 a single direction and place to sort together; this 6 0.874 0.052 0.100 must reflect same slight differentiation (by di­ 5 0.869 0.071 0.089 11 0.849 0.045 0.131 rectional gradients or local effects) within the 14 0.838 0.105 0.087 pervasive isometry of integration. l 0.835 0.073 0.124 The second axis indudes the two eye widths 9 0.833 0.115 0.084 and the unsatisfactory measure of prosomal end 8 0.82/l 0.074 0.127 25 0.792 0.157 0.042 width (measure 27 - its projections are low 15 0.747 0.288 0.004 and nearly equal on all three axes; its placement 22 0.482 0.131 0.425 with one of the three demands no special ex­ 17 0.000 1.000 0.000 planation). Eye length (measure 15), though it 16 0.077 0.770 0.185 groups with the general measures, has the highest 27 0.248 0.404 0.392 23 0.000 0.000 1.000 projection upon the second axis of any variable 24 0.064 0.449 0.569 outside the duster of the second axis itself. W e repeat that the separate sorting of eye measures Se e Fig. for the meanings of the measure numbers. l is not, per se, a result of its negative allometry to general size; for a logarithmic transformation was applied to the raw data. The eye shows a our reference space and use an oblique solution partial independence of general size that is re­ with non-orthogonal axes placed within the vector flected in its correlation with measures of the first

swarm itself. COVAP performs an oblique rota­ group (not in the form of its linear regression). tion using actual vectors (at extreme positions in The majority of correlation coefficients lower the swarm) as reference axes. than 0.9 are between measures of eye width and Table l presents a triaxial oblique solution for variables linked with the first axis. the Saaremaa eurypterids; each variable is grouped The third axis encompasses the length (but not with the reference vector of its strongest pro­ the widths) of the first mesosomal segment (the jection. The three groups now have a ready and third length, measure 22, could just as well group interesting interpretation. with this axis as with the first; its projections The first and major duster indudes all the are nearly equal). The width measures for this general dimensions of the length-width-diagonal segment are all firmly allied with the first (gene­ grid; it is this system's expression of a size factor. ral) group. This separation is very revealing: since Nonetheless, there is an interesting stratification the width of the first segment is "moulded" as within it, reflecting same degree of differentiation. a continuous connection with the prosoma (Fig. 86 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

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o. 67 r-

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o. 62 r­ �� ------�------�------,-1 ----,-l ----,-l----,l-----,- 0.62 0.63 0.64 0.65 0.65 0.66 0.67 0.68 FACTOR 1

Fig. 2. Plot of all specimens of Eurypterus remipes sure l greater than 20 mm; circ les represent specimens tetragonophthalmus Fisc he r against the first two van- with measure l less than 20 mm. max axes. The squares represent specimens with mea-

1), its contra! evidently Iies with the general factor malizes all samples (individual specimens this m determining prosomal size. But its lengths are case) befare the analysis by dividing each element potentially independent of this contra!, since by the vector length of its sample. This has the posterior extension (or curtailment) of the seg­ effect of scaling all specimens to a common size. ment does not disrupt the continuity of its lateral The first eigenvector encompasses an overwhel­ margins with the prosoma. ming 99.9 percent of all information: the speci­ Thus, each of the three axes has an interesting mens are morphometrically very similar to one biological interpretation: general prosomal size another indeed! (with directional gradients and local effects within Fig. 2 shows a plot of all specimens against it), eye size, and mesosomal lengths (but not the first two varimax axes. There is a clear separa­ widths). tion by size into groups for small and large speci­ The Q-mode analysis is of less interest, but it mens. This would be of no particular interest if does display o ne significant point. COV AP nor- size had remained as an explicit variable in the Growth and Variat ion in Eurypterus remipes DeKay 87

analysis. Bur normalization has removed size per mann (1912, pp. 71-113). These discussions 111- se. lf the plots still show separation by size, this dicate that euryprerids occur in sediments of nor­ must reflect the differences in shape rhat correlate mal marine salinity that were deposited at various to it. Despite the overwhelming similarity of depths, and in brackish and hypersaline environ­ shape among all samples, we can still detect a ments near, and perhaps in, the intertidal zone. small allometric componenr (due primarily the Same euryprerids may have lived in fresh-warer to negative allometry of eye size). environments although we are not convinced by Both R and Q analyses Iead us to the same the river hypothesis of O'Connell (1916). conclusion. The integrarion of variables is ex­ Our specimens come from the Fiddlers Green ceedingly srrong; it dwarfs that of any comparable Member of the Upper Silurian Bertie Formation ser (of measures and ontogenetic range in size) from the well-known Passage Gulf occurrence on known us either from aur own experiences or Spohn Road, in Passage Gulf, 0.3 miles south of to from the literature. We do not doubt that it re­ the junction wirh Brewer Road, about l.S miles flects a general principle of arthropod growth. southeasr of Elizabethtown, Millers Mills 7 1/2' Nonetheless, multivariare methods can still detect Quadrangle, New York (see Rickard, 1962, 1969 small bur clearly significanr (statistically and bio­ for reviews of the srratigraphy). Depositional en­ logically) distinctions wirhin rhis pervasive system vironments of the sequence are summarized by of integrarion. In the R made, eye size and first Treesh (1972) and Leurze (1964). segment Iengths gain separate expression, while Eurypterids are numerous in several thin beds the general duster srrarifies by directional gra­ in the uppermost metre of the Fiddlers Green dients and local influences. In the Q made, allo­ member. A prominent mud-cracked zone occurs metric consequences of increasing size separate above the euryprerid beds. The Fiddlers Green large and small specimens by their shape. is a thinly laminated, at least partly clastic, high magnesium rock. The associated materials include ANALYSIS OF EURYPTERUS REMIPES detrital quartz, clay minerals, and organic matter. REMIPES The organic matter is concentrated in certain beds which could represenr algal mars. The grain frac­ by tion of typical Fiddlers Green sediment contains James C. Brower and Richard A. Reyment silt-sized quartz, dolomite, calcite and, or, high magnesium calcire. The matrix consists of a mix­ P ALAEOECOLOGY ture of clay minerals, organic matter, calcite, high Speculation on the palaeoecology of eurypterids magnesium calcite and perhaps dolomite. The has been rife. Kjellesvig-Waering (1958) con­ most common sedimentary structures are fine !ami­ cluded thar eurypterids of the genus Eurypterus nations, mudcracks, and crossbedding, Graded preferred calcareous muds, high in magnesium, bedding, scour-and-fill structures, and current and he referred to these sediments as waterlimes. ripples are also present. The fine laminarion de­ This terminology and inrerpretation derives from monstrates that most sediment has not been re­ views on the chemistry of the Fiddlers Green worked by burrowing organisms. A few extensively member of the Bertie Formation, the type horizon burrowed beds are known, bur eurypterids are not for E. r. remipes. found in them. The fauna associated with Euryp­ Previous work on the palaeoecology of eurypte­ terus remipes remipes includes the eurypterids rids is vast, confusing, and aften conflicting; we Acutiramus macrophthalmus (Hall), Pterygotus have no intention of reviewing the Iirerature. juvenis Clarke & Ruedemann, and Dolichopterus Good summaries are available in Caster and Kjel­ herkimerensis Caster & Kjellesvig-Waering, scor­ Iesvig-Waering (1964), Kjellesvig-Waering (1964), pions, leperditid ostracodes, Tetrameroceras accola Brooks (1957, an annotated bibliography), StØr­ (Ruedemann), "Gomphoceras" ruedemanni Feer­ mer (1934, pp. 58-69), and Clarke and Ruede- ste, a species of gastropod, a phyllocarid, plants, 88 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

and several burrows, tracks and trails constructed cracks). Eurypterids lived in the subtidal areas by unknown organisms and fragments of black where mudcracks are lacking. The environment material. Although these have not been analyzed, probably tended to be hypersaline, as indicated they appear to be carbonaceous and might be by several factors such as the lack of normal marine remains of algal mats. organisms (all groups found could have tolerated The fact that the eurypterids are restricted hypersalinity which is consistent with the low almost entirely to the upper part of the member fauna! diversity); the association of the unit with suggests that the rock at this leve! could reflect, known evaporites - certainly the gypsum and per­ in its chemical composition, favourable ecological haps the dolomite. The lagoons seem to have conditions for them. The chemical variability of been similar to those associated with the sebkhas the sediment at the Passage Gulf exposure was of the Persian Gulf (Friedman and Sanders, 1967, therefore studied. Seventeen samples were taken pp. 284-286; Sugden, 1963; Illing, Wells and at half-metre intervals beginning at the contact Taylor, 1965). between the Bertie Formation and the underlying The dolomite is primary, penecontemporaneous, Camillus Formation. The samples were analysed or both. This is indicated by several lines of evi­ by atomic absorption spectrophotometry by Mauri­ dence. The grain fraction commonly bears rounded ce Cucci and John Douglas. Taking the standard sand and silt-sized quartz. Sedimentary structures, precautions against interference, they determined such as crossbedding, indicate that these grains nickel, manganese, iron, copper, sodium and zinc were transported. The origin of such grains must on a Perkin-Elmer Model 403 atomic absorption predate their deposition. It is possible they were spectrophotometer and magnesium and calcium transported by wind into the lagoons. Dolomite of on a Phillips Unicam SP-90. other beds exhibits most!y euhedral dolomite The elements, with the exception of iron, show rhombs; abraded grains are lacking. Virtually all little variation. Most of the elements are present the dolomites are finely laminated. This indicate> in very small amounts, particularly copper. The that the material was either originally deposited strata rich in eurypterids at the top of the section as aragonite, or perhaps high magnesium calcite, (about l from the top) do not show any and dolomitized soon after deposition (for ex­ m remarkable differences from the other strata of ample, see Skinner, 1963; von der Borch, 1965; the sequence. The topmost bed of the section has Illing, Wells and Taylor, 1965). a calcium to magnesium ratio very different from In summary, we believe that the Fiddlers Green all the other samples, probably due to its partial is a primary or penecontemporaneous do.Jomite, absorption into the soil profile. The occurrence which formed in environments ranging from the of eurypterids is not correlated with any of the supertidal to the shallow subtidal zone. Quiet elements considered in this investigation. water conditions prevailed in the subtidal lagoons The Fiddlers Green member consists on the inhabited by the eurypterids, as witnessed by the average of 23 % calcium (range 20.4%- 30.9%) fine-grained clastic sediment with a silt-sized and 8.2 % magnesium (0.69 %-10.6 %). If grain fraction and a clay-sized matrix. The waters the anomalous topmost sample is excluded, the were probably somewhat hypersaline. ranges are, for calcium, 20.4 %-24.8 %, and for It is possible that the occurrences represent magnesium 7.0 %-10.6 %. The rock is hardly mass deaths of eurypterids living near the shore. a pure dolomite but rather a magnesium-rich ar­ The fact that the assemblages consist of moul­ gillaceous limestone. Other values are: copper ted carapaces, adults, and individuals of all growth (0.0456 %-0.0069 %), iron (0.39 %-0.13 %), stages, showing appendages, argues for this m­ sodium (0.028 %-0.021%) , manganese (0.022% terpretation. This could be analogous to the -0.0'13 %), and zinc (0.0037 %-0.0016 %). mass mortality of crustaceans in the modern in­ The habitats ranged from shallow water subtidal tertidal environment as a result of sudden, heavy lagoonal to supertidal flats (denoted by the mud- storms. After a sudden storm had struck south- Growth and Variation in Eurypterus remipes DeKay 89 western Denmark (Ho Bay) on June 13th, 1971, 76). When swimming, the paddle appendages Reyment observed great numbers of dead, largely could have functioned as paddles, as suggested by juvenile crabs spread widely just below the high Clarke and Ruedemann, or as guide planes, as tide line. R. M. Linsley has drawn our attention proposed by StØnner (1934) (in Norwegian, StØr­ to two specimens in the Colgate collection which mer uses the term svømmefØtter). Most authors demonstrate the interment of the eurypterids. One have assumed that Eurypterus was either predatory, is completely disarticulated, but all the segments and ate worms, small arthropods, "soft-shelled" are aligned and all the appendages are preserved, pelecypods, etc., such as does Limulus, or that thus evidencing the absence of post-mortem distur­ the animals were scavengers. The food could have bances by currents and scavengers. The second been raken from the surface or grubbed from within specimen is oriented upside down on the bedding the sediment. In the case of E. remipes remipes, plane, with its telson penetrating the underlying "soft-shelled" pelecypods are lacking in the sedi­ sediment. It seems to have been buried while in ment, but the large leperditid ostracods could the act of righting itself. have provided a comparable diet. Tracks, trails, The eurypterids seem have been rapidly and burrows testify to the presence of "worms" to buried in a catastrophic fashion, which is indicated and other soft-bodied creatures. Such feeding in several ways. The complete preservation of habits are consistent with the nature of the leg same entire specimens with all appendages and bases and the small chelicerae of E. remipes their eye integuments intact (see later discus­ remipes. E. remipes remipes was a flat-bodied sion) which apparently represent dead individuals. form. It probably spent much time resting on the These views conflict with those of Clarke and bortom, covered by a thin layer of sediment, like Ruedemann (1912, p. 25) and StØrmer (1934, flounders, skates, and rays of the present day. p. 57) . We also point to the lack of any traces of scavenging activity. Dead Limulus are scavenged almost immediately by crabs, shrimp, microbes, STATISTICAL RECOGNITION OF MOULT STAGES and other creatures. Same of the eurypterids are obviously moults. lntroduction These include the loose prosomas, aften with the In arthropods, such as many ostracods, the moult first abdominal segment attached, the loose seg­ stages are discrete and these can be easily deter­ ments, isolated telsons, and pieces of appendages. mined by direct inspection of size-frequency Probably the complete or nearly complete speci­ graphs, bivariate scatterplots, scatterplots of princi­ mens with damaged eyes are also moults. pal component scores, scatterplots of principal coordinates, etc. Examples of such discrete moult Inferred made of life stages include trilobites: Hunt ( 1967), Robiso n Turning to the living habits of Eurypterus remt­ (1967) and Whittington (1957, figs. 20, 21); pes remipes, we follow the ideas of Clarke and ostracods: Reyment (1960, 1963). Not all arthro­ Ruedemann (1912, pp. 71-85) and StØrmer pods moult with such distances between stages (1934, pp. 58-67) in general outline. The pre­ and for these, the moult stages are therefore not sence of well developed walking legs shows that clearly discontinuous. Both the living Limulus and the animals spent same of their lives crawling Eurypterus remipes remipes are cases in point; along and digging in the bortom; this is dso although several of the larger moult stages are in consistent with the general body shape, size and fact discontinuous, the smaller stages tend to inter­ position of the eyes, and the Limu!us-like telson. grade. In such examples, the selection and identi­ The paddle appendages may have served in both fication of moult stages may become subjective. grubbing and swimming, as do similar legs in the Any procedure for the selection of moult srages crabs, Platyonichus ocellatus and Callinectes hasta­ must be operational and applicable by the average tus (Clarke and Ruedemann, 1912, pp. 71, 75, non-mathematical palaeontologist. Therefore, it 90 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

the first sample. We have checked Kaneshiro's work on Limulus polyphemus and Eurypterus re­ mipes remipes, same of which is included for comparative purposes. Most of the eurypterids are preserved with the dorsal side uppermost, which means that few specimens could be sexed. The measurements were thus made on the dorsal side and these have G been pooled into a single group comprising im­ mature individuals and adult males and females. Inspection of the univariate and bivariate plots of all variables failed disclose significant sec­ to ondary sexual dimorphism in these dimensions.

Moult stages recognized on single variables

In the first phase, moult stages were selected by trial and error using histograms for prosomal length in Eurypterus and Limulus in connexion with which, we attempted to maximize the between groups variances in relation the within groups to variances. Several frequency graphs were plotted using various dass widths and end-points. Nu­ merous groupings were tried for both Eurypterus and Limulus. Such a method was necessary because the moult stages, with a few exceptions, do not width �l fall into discrete groups. The moult stages finally Fig. Variables measured on the prosoma of Euryp­ 3. inferred with respect length are shown in terus remipes remipes DeKay (above) and Limulus po­ to lyphemus (below). Figures 4a and 4c; these are mutually exclusive and there is no overlap. The pertinent statistics for Eurypterus remipes remipes and Limulus polyphemus are listed in Tables 2, 3, 4, 5. seems that the methodology should begin with The data on L. polyphemus are incomplete. simple graphics and be followed by univariate, Moult stages I through VII are relatively conti­ bivariate and then multivariate statistics (cf. Rey­ nuous (Fig. 4c). The wide gaps between Stages ment, 1971). VII, "VIII", and "IX" suggest that there are The following samples were examined in this several missing stages, not represented in the study (see Fig. 3 for measurements): data. l. E. remipes remipes. Colgate collection, 127 Student's t tests were performed between adja­ prosomas, measured by Colgate University stu­ cent moult stages for both the limulid and euryp­ dents. 2. Limulus polyphemus. A total of 233 spe­ terid data. In all cases, these are significantly eimens; measurements were made, and the pre­ different. Most of the probabilities of larger values liminary moult stages defined, by Kaneshiro of t are less than 0.001, which indicates that the ( 1962). The animals were obtained from North null hypothesis may be rejected with a very Falmouth, Mass., USA and from the supply room minimal risk of O.l %. at the Marine Biological Laboratory at Wood's In the second phase, we examined the moulr Hole, Cape Cod, Mass., USA. stages inferred above with respect to the univariate Most of the following discussion is based on distriburion of prosomal width for Limulus and Growth and Variation tn Eurypterus remipes DeKay 91

remipes remipes mulus polyphemus 40 E Colgale collection LFolmouth, i Cape Cod 80 16

30 IV 10 29 Ill •• �50 •• VI " � "' I�20

lO

Prosomo length (mm)

@ f'rosomo l�ngth (mm)

remipes rem1pes E Colgole collectlon

Limulus polyphemus Falmoulh, Cape Cod IV JO 29 80 10 16 20 ;:-;60 � 50 �40 10 30 � 20 10 10 ow�����,.w��um����m•m•mm=M @ Prosoma width Post�rior widlh of ptosomo (mm) (�,�m) d Fig. 4. Size fr equency gr aphs for E. r. remipes and Li­ th e number of specimens in th at stage. Roman numerals mulus polyphemus. The endpoints for the moult stages stand for the num ber of the moult stage, Ar abic nu­ ar e the maximum an d minimum values for that moult merals show the number of specimens in the moult stage. The dashed vertical line is Iocated at the mean stage. Overlapping ar eas ar e stippled. of the moult stage and the height of the peak denotes

posterior width of the prosoma in Eurypterus is discussed further in the subsequenr section on (Figs. 4b, d). The moult stages now begin to over­ discriminant analysis of two or more variables. lap, as indicated by the stippled parts of the fig­ As for the prosomal length, t tests were per­ ures. For the eurypterids, 14 out of 127 specimens formed on the prosomal widths for the adjacent overlap to the extent of 11.0 %. The same Limu­ moult stages. The t values, though highly signi­ lus values include 25 out of 233 specimens and ficant, are slightly lower than those calculated for an overlap of 10.7 %. In general, one would equiva!ent moult stages based on prosomal length; expect the degree of this overlap to be inversely this ref!ects the amount of overlap for the prosa­ proportional to the correlation coefficient between mal widths, whereas moult stages are mutually the two variables. The amount of overlap should exclusive for prosomal length. The probabilities decrease as the correlation increa�es. For E. remi­ of higher t values are still mostly less than 0.001 pes remipes, the correlation coefficient for prosa­ for the prosomal widths. mal length versus posterior width of the prosoma is 0.987 and we see 11 % overlap in the width Comparison of frequency distributions for Limu­ of the prosoma for the moult stages defined lus and Eurypterus. The frequency graphs for lim­ relative to the length of the prosoma. This idea ulids are right-skewed; young specimens predo- 92 H. E. Andrews, ]. C. Brower, S. ]. Goulcl, and R. A. Reyment

Table 2. Basic statistics for the moult stages of Euryp- Table 4. Ba sic statistics for the moult stages of Limulus terus remipes remipes, DeKay (Colgate collection) . polyphemus. Data modified fr om Kaneshiro (1962). Me asur em en ts in mm .

Num ber of Num­ Stagc Me an Std. dev. spe cimens ber of Variable Stage Mean Std. dc v. �- ! speci- Length of prosoma men s 7.2 0.07 2 Il 9.2 0.73 17 Pr osomal length 8.9mm l Ill 12.7 0.75 13 Il 14.6mm 1.14mm 76 IV 16.7 1.18 29 Ill 18.9mm 0.82mm 50 V 20.7 0.80 22 IV 26.5 mm 1.76mm 6 VI 25.3 1.10 14 V 36.0mm 2.30mm 30 VII 31.1 1.65 23 VI 44.8mm 1.79mm 45 VIII 4Ul 1.84 5 VII 53.8mm 2.19mm 7 IX 50.5 2.33 2 "VIII" 120.3mm 11.30mm 11 "IX" 189.1mm 11.20 mm 7 Posr er io r width of pro so ma 9.4 0.71 2 Pr osomal width 12.0 mm Il 11.6 1.45 17 Il 19.3mm 1.69 mm 76 III 16.8 1.10 13 Il l 24.5mm 1.18mm 50 IV 21.6 2.00 29 IV 33.6mm 2.47mm 6 V 26.9 1.68 22 V 44.3mm 3.31 mm 30 VI 32 9 1.83 14 VI 54.3mm 3.45mm 45 VII 40.8 3.47 23 VII 68.3mm 6.31mm 7 VIII 54.8 2.29 5 "VIII" 147.0mm 13.10mm 1.1 IX 60.6 1.70 2 "IX" 225.0mm 9.30 mm 7

Table 3. Euryptertts remipes remipes: co m parison of obser ved moult stage means wirh predicted values, as­ suming that the animals moulted each time the volume was doubled.

Pr edicted va- 1 Moulr Moult lue, i.e., ean Degrees � Student's Prababiliry of t value Variable stage stage l of pr evwu s l of wirh gr eater magnitude mean std. dev. moult stage fr ec dom X 1.26 --�---- Pr osoma length Stage Il 9.2mm 0.73mm 9.0mm 0.22 16 above 0.50 Ill 12.7mm 0.75mm 11.6mm 1.45 12 between 0.20 and 0.10 JV 16.7mm 1.18 mm 16.0mm 0.62 2H above 0.50 V 20.7mm 0.80mm 21.1mm -0.47 21 above 0.50 VI 25.3 mm 1.10mm 26.1mm -0.73 13 between 0.50 and 0.40 VII 31.1mm 1.65mm 31.8 mm -0.45 22 above 0.50 VIII 41.8 mm 1.84mm 39.2 mm 1.30 4 between 0.40 and 0.20

Posterior width of pr osoma Stage Il 11.6mm 1.45mm 11.8mm - 0.12 16 above 0.50 Ill 16.8mm 1.10mm 14.7mm 1.85 12 between O.l O and 0.05 IV i 21.6 mm 2.00mm 21.2 mm 0.20 28 above 0.50 V 26.9mm 1.68mm j 27.2mm -0.16 21 above 0.50 VI 32.9mm 1.83mm 1l 33.9mm -0.51 13 above 0.50 VII 40.8mm 3.47mm 41.5 mm -0.21 22 above 0.50 VIII 54.8mm 2.29mm l 51.3 mm 1.37 4 between 0.40 and 0.20 Growth and Variati on in Eurypterus remipes DeKay 93

Table 5. Comparison of observed moult stage means for prosomal size of Limulus polyphemus with pre­ dicted values, assuming that each time the animals moulted, the volume was doubled.

Predicted l value Moult Moult Degrees robability of t value 1- =m ean) of Srudenr's p Variable stage stage of with higher previous t mean std. dev. freedom magnitude moult stage X 1.26 - l Prosomal length Stage Ill 18.9mm 0.82mm 18.3mm 0.66 49 a bove 0.50 IV 26.5mm 1.76mm 23.8mm 1.40 5 b etween 0.40 and 0.20 V 36.0mm 2.30mm 33.4mm 1.13 l 29 b etween 0.40 and 0.20 VI 44.Smm 1.79mm 45.4mm -0.31 44 bove 0.50 l VII 53.8mm 2.19mm 56.4mm -1.14 6 ab etween 0.40 and 0.20

Prosomal width Stage Ill 24.5 mm 1.18mm 24.3mm 0.15 49 bove 0.50 IV 33.6mm 2.47mm 30.9 mm 1.02 5 ab etween 0.40 and 0.20 V 44.3mm 3.31 mm 42.3mm 0.58 29 a bove 0.50 VI 54.3mm 3.45 mm 55.8 mm -0.44 44 a bove 0.50 VII 68.3mm 6.31 mm 68.4mm -0.02 l 6 a bove 0.50 Growth stages represented by insufficient specimens were omitted.

minate and adults are relatively rare (Figs. 4c, d). Size interval between adjacent moults. According In Limulus polyphemus, young specimens hatch and to "Dyar's Law" (Thompson, 1942, p. 165), the live in or near the intertidal zone. Larger speci­ average linear dimensions of successive moult mens are generally found furrher offshore and in stages of many arthropods increase at a geometri­ deeper water; for the Jiving habits of Limttlus, ca! rate that is constant throughout ontogeny. see Waterman (1953), Owen (1872), Fowler "Przibram's rule" is a special case of Dyar's more (1907), Agassiz (1878), Packard (1871), Laverock general "law". Przibram ( 1931) noted that same (1927), Goto and Hattori (1929), Shuster (1957, crustaceans moulted each time the body weight 1960). Sexually mattue animals (the final moult) doubled. Assuming a constant bulk density for migrate shoreward during the spring and summer the animal, a doubling of weight yields a doubling reproduce and spawn. Our limulid sample of volume. Under these conditions, an ideal linear to comes from both nearshore and offshore habitats. dimension should increase by a factor of 1.26, i.e., Although there are numerous gaps in these data, by the cube rom of 2.00, each time the animal the curves seem to represent, roughly, the entire moults. Growth of approximately this sort has size-frequency distribution, including the moul­ been documented by Hunt ( 1967) for an agnostid ting history and morrality of most of the whole trilobite and by Kesling (195 1, 1952, 1953) and population. The Eurypterus remipes remipes cur­ Reyment ( 1963) for various ostracods. Other ves are less asymmetrical than these and young arthropods show different geometrical growth specimens are under-represented. Frequency dia­ ratios; for example, Palmer (1957, pp. 110-114, grams of more mature limulids collected from 1962, pp. 89-92) calculated the following growth offshore areas resemble those of the eurypterids. ratios for three trilobite species: Olenellus gilberti Thus, we believe that the eurypterid collections 1.13; Paedeumias clarki 1.16; Aphelaspis sp. = = are mainly composed of more mature animals, 1.08. = possibly from offshore habitats. Growth of E. r. remipes and L. polyphemus has 94 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

remipes remipes 200 60 E. Co lgete collection Limulus polyphemus

50 175 .o

40 150 E E . <> 'E 125 .s o

20 c 100 � "'� o .9"·· li:_ o

. o E o� · ··· 75 ' ' . · ·· · · ti li:_

.• ' 0 50 . ·· o��--�I I--7.1 I�I --!IV�-L--�V �I --V�I I---VLII_I�IX · o "' · Moult stage number · - � · 25 � a 0 ··Ø o��--���--�II�I--�IV�-L--�V�I--V�I�I �VLII�I �IX__ I -L �__ 70 rem ipes re mipes X E. Colgate collection Moull slage number

60

E �5E 0 250 mu lus polyphemus L i o eV\ E 200 a_ � L 40 .. L o "O

"O:!: 30 � 150 o ·� E o V\ o 20 å:.o 100 � . . · ·o · V\ . o . o a_ 10 50 .,.. @> Q. · · · · · · · ø. · · . . �···· IV o o Il Ill Moult stegeVI numVII berVIII IX Il IllMoult IV stege V number VI VIl Vlll IX

b d Fig. 5. E. remipes remipes and L. polyphemus. Graphs showing growth of prosomal size in relation to moult stages.

been te3tecl with respect to the Przibram hypo­ None of the means differs significantly from the thesis as follows. The mean of a moult stage is preclictecl values. In most examples, the probabili­ tested against a preclictecl value, assuming that ties of larger t values are above 0.50. Conse­ the animals moulted each time the volume doublecl, quently, it is concludecl that the animals moultecl this value being the mean of the previous moult each time the volume doublecl. stage multiplied by 1.26. The results, which were These conclusions were checkecl by calculating tested by Student's t, are listecl in Tables 3 and 5. the observed rates of size increase between aclja- Growth and V ariation in Eurypterus remipes DeKay 95

Table 6. Regression statistics for the growth of instars spectively. Following this, curves were fitted to in Limulus polyphemus and Eurypterus remipes remipes. observed Stages I thraugh VII and the predicted Independent variable Dependent Std. esti- Stages IX and XI. Initial variable mate of X Slope inter- Numerous observations indicate that Limultt.r (=moult stage error for y cept polyphemus does not attain sexual maturity unril number) (logarithms) slope the last moulr. The smallest eurypterid with genital E. remipes remipes prosomal length 0.105 0.772 0.00256 appendages that we have seen is a female from E. remipes remipes prosomal width 0.104 0.891 0.00362 Stage V in the Syracuse callection, which suggests Limulus polyphemus prosomal length 0.129 0.879 0.00424 that E. remipes remipes became sexually mature Limulus polyphemus prosomal width 0.124 1.000 0.00384 lang befare the Jiving Limulus. In sexing aur eurypterids, we have used the criteria summarized by Kjellesvig-Waering (1958) and StØnner and cent moult stag es, i.e., (mean of moult stage) / Kjellesvig-Waering (1969) . (mean of previous moult stage), for Limulus and Moult stages recognized on multivariate data E. remipes remipes. These growth indices are for E. remipes remipes, 1.27, for Limulus polyphemus, The mault stages were initially base:.! on the 1.29. Neither differs significantly from the ideal length of the prosoma (G); these moult stages value of 1.26. are mutually exclusive and there is no overlap Least squares regression analyses were performed between adjacent stages. When examined with for development of the prosomal size parameters respect the width of the prosoma (Limulus), or to versus the moult stage numbers. The prosomal posterior width of the prosoma (B) (Eurypterus), size measures were represenred by average values the adjacent mault stages overlap to the extent for particular moult stages. The graphs are illustra­ of about 11 % of the total number of individuals. ted in Fig. 5; the regression details are listed in W e may also investigate the num ber of mis­ Table 6. In all cases, prosomal lengths and widths idenrifications ("misclassifications" of same statis­ grew geometrically with respect to moult stages; ticians) with respect the joinr distribution of to as previously noted, the rate of increase of prosa­ two or more variables. This was done with the mal size does not differ significantly from a factor BMD 07M computer program for generalized and of 1.26 times the prosomal size of the previous stepwise discriminant analysis (Dixon, 1970, pp. moult. The analysis of variance of regression shows 214a-2 14t) for the Colgate collectian. that the best fit equations are of the form (see The variables are entered into the discriminant data in Table 6) log Y=a+ bX, where Y= analysis in stepwise order. The first variable the prosomal size parameter, X = moult stage maximizes the between-groups variance with re­ number; a= log Y when X= O, i.e. the initial spect to the paoled within-groups variance in the intercept, and b = slope on semi-logarithmic plot. form of a one way analysis of variance. The The curvilinear relationship between the two second variable entered is the one that maximize3 variables implies that growth rates of the prosomal the between-group differences, acting in conjunc­ size measures increased throughout ontogeny with tion with the first variable. The process continues respect to moult stages. until all variables that make a significant conrri­ For Limulus polyphemus, the situation is more bution to between-group differences have been complex. As previously menrioned, there are seve­ enrered. The F-ratio is ca]culated for the differen­ ral missing moult stages between VII and "VIII" ces between all the groups. An F-ratio array with and "IX". Consequently, equations were fitted to constant degrees of freedom reflecting the "distan­ the complete data sets for moult stages I through ces" between groups is constructed for all passibJe VII. These were then used to predict the "best" pairs of groups. Two group discriminant functions moult stages for the observed Stages "VIII" and are calculated for all groups. For example, the "IX"; the "best fit stages" are IX and XI, re- first group is tested against all other groups 96 H. E. Andrews, ]. C. Brower, S. ]. Go uld, and R. A. Reyment

VARIABLE B

69.75 - \ 65.25 - \ \

60.75 - \ \ \ 56 .25 - \ \ \ \ 51 . 75 � \ \

47.25 \ � \ \ 1 111 1 42 .75 2 1 \ 1- \ 1 11 11 \ 38.25 \ 1- \ 1 1 2 \ �\, 11 \1 1 1 1 33 . 75 \ � \ 1� \ 1\1 1 \ \ � \ 1 1 29. 25 1 1 \ r- \ 11 � 11 \ 2 2 \ \ 24 .75 - \ � 12\ ::: \ 2 \ \ 111�: : \ 20.25 - \ � \ 23132 \ \ 1 12 2 \111 15.75 - � \ 2211 \ \ \ 1 1 4 4: \ 11.25 \ 111 \ _, \ 1�1 1 \ - \ 6.75 \ l l l l \ l l 4.50 14.50 24 .50 34 . 50 44 .50 54 .50

VARIABLE G Fig. 6. Bivariate graph for the variables B and G of me rals de note moult stages, the Arabic nume rals the E. remipes remipes (Colgate collectio:-�) showing the moult number of specime ns at a particular plotting point. stages Sc!bdivided by the dashed lines. The Roman nu-

pooled together, then the ,;econdgroup is similarly differences between growth stages ( this was ex­ tested and so on. Finally, each individual is placed pected as the moult stages were based upon in the group with which it has the highest pro­ length). The posterior width of the prosoma was bability of membership. This is summarized in an also entered, which indicates that this variable identification array showing the group assignments makes some contribution to between-group dif­ of all individuals. Lastly, canonical variables are ferences. computed with a plot of the scores for the first The discriminant functions only misidentified two canonical variables. These illustrate, graphi­ two specimens. A Stage Il animal with a relatively cally, the relationships between the various groups narrow prosoma was placed in Stage I and one and individuals. Stage VII individual was assigned to Stage VI, In the first stage, two variables, prosomal length that is, two out of 127 individuals, relative to the (G) and posterior width of the prosoma (B), moult stages defined on prosomal length alone. were investigated. The groups used were the Inasmuch as there are only two variables, there moult stages established on prosomal length. A is only ane canonical variate, which 1s: graph of these two variables is depicted in Fig. 6. y= 0.11 B+0.73 G. The program first entered length, thus indicating that this variable is associated with most of the The score plot (Fig. 7) shows that the canonical Growth and V ariation in Eurypterus remipes DeKay 97

-14 -12 - 0 -4 -2 o 2 4 6 8 10 12 14 16 18 20 22 24 26 1 -8 -6 Canonical variable Fig. 7. Histogram of the scores for the first canonical G. The moult stages are denoted by Roman numerals; variate of E. remipes remipes for the variables: posterior every second stage is filled in with black for ease of length of the prosoma B, and the length of the prosoma interpretation.

variate is a general size factor, with larger speci­ first two eigenvalues, 69.20 and 0.29, are signifi­ mens having higher scores. The larger coefficient cantly greater than zero and account for 99.5 and for prosomal length in the canonical variate 0.5 % of the dispersion. reflects the greater discriminating power of this The scores show that the first canonical variable variable. Fig. 7 illustrates that the boundaries represents overall size increase during ontogeny. between adjacent moult stages correspond to low As before, prosomal length constitutes the most frequency areas on the first canonical variate important variable. The second canonical variable scores. Although not shown on the plot, there contrasts the two prosomal width measurements is no overlap between the canonical variable and tends to separate the two individuals in Stage scores for the different moult stages. Thus, the IX from the other stages. Animals with low scores bivariate analysis sharpens the difference among for the second canonical variable have relatively growth categories. rectangular prosomas, while those with higher An increase in the number of variables in the scores tend to have prosomas with more strongly stepwise analysis reproduced the same results as rapering sides. Adding one variable, the width found for two variables, without adding essential anterior to the eyes, results in relatively little new information, apart from the loadings of the va­ information, especially with respect to identifica­ riables in the discriminant functions, which give tion of individuals. a relative idea of the contributions of the variables Ten variables (N 77) were also analyzed = to the discrimination. with the discrimination program. The coefficients For the three variables, prosomal length (G), of the first two canonical variates are shown in posterior width of the prosoma (B), and width Table 7. The results are the same as for two of the prosoma anterior to the eyes (C), the first variables, but this time there were no misidenti­ two canonical variates are: fications of specimens. The !argest first coefficient of the first canonical y1 =0.75 G+0.18 B-0.09 C variate, 0.96, is the prosomal length; the magnitude Y2 = 0.30 G-0.93 B+0.75 C. of the other coefficients is 0.36 or less. Clearly, As before, the differences between all stages, prosomal length is by far the best separator. The except Stage I versus Il, are highly significant; other variables have much lower coefficients in the same two specimens were misidentified. The canonical variable I because all are highly correlated 98 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

Table 7. Canonical variables for E. remipes remipes are discussed in detail in subsequent sections on the Canonical Stepwise regression analysis of the prosoma. variate order of Variable coefficients entry into Summary ----·--- the discri- minant In both Eurypterus remipes remipes and Limulus li analysis polyphemus, moult stages are not discrete and ------A Prosomal width anterior l their identification is best accomplished by a to the eyes -0.36 -0.41 5 trial and error procedure. lnitially, we based the B Posterior width of the 1 moult stages upon the length of the prosoma. prosoma 0.35' 0.59 2 Nine moult stages were identified for E. remipes i C Length from posterior and for Limulus polyphemus. margin of prosoma to J The moult stages, defined by prosomal length, anterior of eyes - o. 0.053 4 were then examined with respect to prosomal G Total length of prosoma 0.96 - o.n 1 width. The adjacent moult stages begin to over­ U Prosomal width poste- 1 lap, and the overlap percentage includes about rior to the eyes 0.12 l -0.13 9 11 % of all individuals for both Limulus and V Length from eyes to an- l Eurypterus. The low percentage of overlap partial­ teriorma rgin of prosoma -0.12 -0.98 7 ly reflects the high correlation between the two W Length from posterior variables, 0.987 for. E. remipes remipes. In general, margin of prosoma to overlap of this type should decrease as the corre­ posterior margin of eyes 0.14 0.71 8 lation between the two variables increases, although

X Distance from eyes to same overlap could exist, even with perfect corre­ lateral margin of pro- lation. The distributions of the two variables are som a -0.13 1.31 6 also important in dictating the amount of overlap. Y Anterior distance be- 1 Student's t-tests between adjacent moult stages tween the eyes 0.24 -0.19 3 show that they differ significantly with respect Z Posterior distance be­ to both length and width. Both Limulus poly­ tween the eyes -0.22 -0.44 10 phemus and E. remipes remipes moulted each 1 - Percentage of trace 98 % l 1.2 % time the body volume doubled. Growth in size relative to moult number was geometric in both Colgate collection, N = 77. the limulids and eurypterids. The size-frequency distributions of E. remipes remipes resemble those of living Limulus polyphemus from offshore habitats. Palaeoecological analysis also suggests that the eurypterids lived in environments below with the prosomal length; the pertinent correla­ the intertidal zone. tion coefficients range from 0.94 0.98. Conse­ All prosomal variables of E. remipes remipes are to quently, most of the information carried by these highly correlated, the correlations ranging from variables is redundant - they could be predicted 0.99 to 0.94; therefore, adding new variables to with reasonable accuracy, solely from length of the discriminant analysis produces little new the prosoma. information about differences between moult The second canonical variable is a complex stages. When dealing with highly correlated shape factor that separates the two Stage IX ani­ variables in arthropods, satisfactory identifications mals from the rest. The variables involved are of growth stages can be made on a single variable prosomal widths, A and B, and a whole series of indicative of overall size. For 127 eurypterids, the variables that deal with eye size, shape, and posi­ best multivariate identifications of the moult tion, V, W, X and Z. These changes in shape stages only improve the identification based on Growth and V ariation in Eurypterus remipes DeKay 99

c

Fig. 8. Photographs of some of the specimens of E. 157 (X 1.1); c) Syracuse KWM 20 (X 1.8); d) Syracuse remipes studied: a) Colgate 221 (X 1.1); b) Uppsala NAr. KWM 22 (X 1.3). 100 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

VA RIABLE A

64 .50 -

. . · _ _ 60 . 00 - ,

55 . 50 -

51 .00 -

46. 50 -

42. 00 - , _ . · 37. 50 . · 1 z . . . , � . . _, . ,, 33 .00 - , 1 1 , .. ·'2 z 28. 50 ,. � 1 24. 00 .1 _,.,. � 1 z ··i 1 1 . . ·1Z3 1 11-Z'I 1 19.50 r- -�·i 1 1 .·fl _, .. 1 15.00 . � ".. z · . .··2 , , · 1 10. 00 . - r- 2 ,.3 1 .· i ,• 1 6.00 � lL l l l l l 4. 50 14. 50 24. 50 34. 50 44 .50 54.50

VARIABLE G Fig. 9. Plot of the relationship between variables A and G for the prosoma of E. remipes remipes.

prosomal length from about 0.0 about 6.5 per­ square anterior prosomal outline while the other to cent ( depending on the data set and method example is more rounded. The topographic re­ used). This level of er ror is easily tolerated. ference points or coordinates for this grid were then plotted on marure specimens. The deforma­ RELATIVE GROWTH OF THE PROSOMA tion of the adult grid illustrates changes in pro­ Ten measurements were used in the ontogenetic porrions. Full discussion of the method is available study of prosomal shape. The measurements are in D'Arcy Thompson (1942). A word of caution illustrated in Fig. 3 and a representative suite is in order. In relation arthropods, these grids to of specimens is shown in Fig. 8. Complete data have been usefully applied to trilobites (Palmer, sets were obtained from 77 individuals with a 1957); trilobite cephalons possess many topo­ range in prosomal length of 7.2 to 52.2 mm. A plot graphic reference points so that the grids are of one equation for relative growth is given in easily defined and transferred from young to adult Fig. 9. Graphs were made of all of the variables specimens with reasonable objectivity. Eurypterid of Fig. 3 against G. Since the plots do not differ prosomas are comparatively featureless, with only essentially, we offer Fig. 9 for A against G as a a few good topographic reference points, namely, specimen. the eyes and the margin. Nevertheless, the eurypte­ Growth grids (Fig. 10) were made by plotting rid grids presented here do portray the main square grids on two small specimens. These were changes in shape occurring during ontogeny. These selected to include the range of variation seen in include reduction of the length and width of the small individuals; one prosoma has a relatively eyes compared to the the total size of the prosoma, Growth and Variation in Eurypterus remipes DeKay 101

�-.....

/:V V � E E /; l -' E ....CD E [\ !\ � \ ."· l \ ( \ u

-.::::::t:::::..._-

E E E E .., �

T

E E E "' E � �

Fig. l O. Growth grids illustrating the ontogeny of the tion. The numbers list the specimens used in making prosoma in Eurypterus remipes remipes. All but one the grids, in the order of left to right: KHC 17, 8 5, specimen (Syracuse KHC 17) from the Colgate collec- 401/KHC 17, 401/85, 90/KHC 17, 90/85.

rotation of the axe3 of eye length and develop­ for prosoma and body shape and power functions ment of a prominent "brim" in front of the eyes. are not required. The analysis of variance for several selected In this analysis, the slope is considered as the equations demonstrates that linear equations pro­ growth rate of Y with respect to unit increments vide adequate first-approximation fits to the data of X. For a linear equation, this growth rate is 102 H. E. Andrews, }. C. Brower, S. }. Gould, and R. A. Reyment

constant throughout ontogeny. The initial inter­ the eyes U. Many adult specimens have more cept, i.e., Y when X O, is a location parameter equal prosomal widths at the anterior and poste­ a, = for the line. Regardless of the growth rate, if rior eye levels, which produces a more subquadrate the intercept is zero, development is isometric outline of the prosoma. Both types of individuals and the shape of the two dimensions remains can be seen at all ages. However, subquadrate constant throughout ontogeny. If a finite initial specimens predominate among adults while most intercept is introduced, growth becomes allometric juvenile prosomas are rounded. Regardless of age, and the shape changes. The amount and nature the prosoma is widest at its posterior margin of the shape changes depends on the signs of and tapers toward the anterior. the growth rate and initial intercept and the The differential growth patterns of prosomal magnitude of the growth rate compared the in­ widths are best illustrated by the ontogeny of to tercept. The growth rate and intercept interact widths in the area of the eyes, A and U, relative to produce the dunges in shape described by to the posterior width, B (Table 8, equations 10, the equation. Here, the shape changes are ex­ 11). The A/B ratio increased from 0.83 to 0.93 pressed as shape ratios, calculated for the smallest while the U/B ratio increased slightly from 0.91 and !argest specimens: Shape ratio (Y predicted to 0.96. The growth rates for A and U were = from the equation)/(X observed). almost the same, 0.94 or 0.95 mm per l mm in­ In the eurypterids examined here, all the slopes crease in posterior width B, bue A has a greater or growth rates are positive. With a negative negative initial intercept. initial intercept and a positive growth rate, the above shape ratio (Y/X) increases with growth. Ontogeny of eyes relative to prosoma With a positive initial intercept, the shape ratio During growth of the prosoma, the main shape declines in larger animals. A useful account of changes occurred in the size and position of the these relationships is given in Gould (1972). eyes. Due to their smallness and curved outline, The following discussion emphasizes the smal­ the eyes could not be measured with accuracy. lest and !argest observed values of the independent Approximate measures of eye size can be obtained variable, X, and the corresponding predicted or by the subtractions C-W; for the length and equation figures for the dependent variable, Y. [A-(Y+2X)]/2 for width. Hopefully, this approach shows the ontogeny of The most important omogenetic trend is a the "average" individual. Two-dimensional shape decrease in eye size relative to prosomal size. changes are depicted by the ratios of Y (predicted) / Small specimens, distributed over the prosomal X (observed). length interval of 7 .O to 8.0 mm, have eyes ranging from about 2.5 to 3.0 mm in length and 1.5 to Proportions of the prosoma 2.0 mm in width. The same values for the !argest The development of prosomal widths A, B and U available adult are at a prosomal length of 40.4 with respect to length was nearly isometric and mm; eye length, 7.9 mm; eye width, 3.5 and 3.7 shape remained roughly constant throughout onto­ mm. The juvenile eye length is almost 3 7 % of geny (Table 8, equations 1-3). The U/G ratio the prosomal length; the equivalent value for was stabilized at 1.2, regardless of age and size. The large specimens is only 20 %. The absolute size quotient A/G increased slightly from 1.1 to 1.2, of the eyes increased throughout growth, although while B/G declined from 1.4 to 1.3. These differen­ the size of the prosoma increased relatively more tials ref!ect a slight shift of prosomal shape with rapidly. (This was detected qualitatively by Clarke progressive age. Young specimens aften show and Ruedemann (1912)). E. remipes tetragonoph­ prominent rounding of the anterior part of the thalmus shows the same trend. prosoma, which begins just posterior to the eyes. The decline of relative eye length also affected Consequently, the prosomal width anterior the the overall geometry of the prosoma. Ontogeny to eyes A is often less than the width posterior to of length from the posterior prosomal margin to Growth and Variation in Eurypterus remipes DeKay 103

Table 8. Regression statlsttcs showing relative growth of the prosoma in Eurypterus remipes remipes DeKay from the Colgate collection (X and Y meamred in mm).

-- "' l Q).eaio - � - E c. ��f� ·-c:: Independent Initial Pre- Pre- Std. est. o "'.... -=�-�� -..cg 8 variable Dependent variable intercept e x dicted dicted Y/X Y/X Correl. for error � E O':> O>- E b Xmin Y min X max Y max min max coeff. for b � c:: X y a b ��-- --

l G Prosomal length A Width ant. to - 0.52 1.19 7 .2 8.06 52.2 61.7 1.12 1.18 0.96 0.040 eyes

2 G B Posterior width 1.09 1.25 10.10 66.4 1.40 1.27 0.97 0.034 " " ' " 3 G U Width posterior 0.40 1.20 9.07 63.3 1.24 1.22 0.97 0.036 " " to eyes ' " 4 G X Distance from -0.85 0.28 1.14 13.6 0.16 0.26 0.94 0.011 " " eyes to lateral ' " margin

5 G Y Ant. distance -1.28 0.48 2.20 24.0 0.31 0.46 0.97 0.015 " " between eyes ' "

6 G Z Post. distance -0.43 0.53 3.36 27.0 0.47 0.52 0.96 0.017 " " between eyes ' "

7 c Length from post. 1.99 0.59 6.26 32.9 0.87 0.63 0.97 0.018 " " to ant. of eyes ' " 8 G V Length from eyes -1.31 0.38 1.40 18.3 0.19 0.35 0.97 0.011 l " " to ant. margin ' "

9 G w Length from post. -0.39 0.43 2.70 22.0 0.38 0.42 0.98 0.010 " " of eyes to post. ' " margin lO B Posterior width of A Width ant. to -1.38 0.95 9.9 8.18 61.3 57.1 0.83 0.93 0.98 0.02 1 prosoma eyes

11 B u Width post. to -0.47 0.94 9.00 58.6 0.91 0.95 0.96 0.016 " " eyes ' "

12 B X Distance from -1.07 0.22 1.12 12.6 0.11 0.21 0.96 0.007 " " eyes to lateral ' " margin

13 B y Ant. distance - 1.57 0.38 2.21 22.0 0.22 0.36 0.98 0.008 " " between eyes ' "

14 B Z Post. distance -0.75 0.42 3.36 24.9 0.34 0.41 0.98 0.010 " " between eyes ' "

15 c Length from post. V Length from eyes -2.02 0.60 5.2 1.08 31.9 17.0 0.21 0.53 0.95 0.02 3 margin to ant. of to ant. margin eyes l

16 c w Length from post. -1.38 0.69 2.23 20.7 0.43 0.65 0.97 0.019 " " of eyes to post. ' " margin

17 y Ant. dist. between X Dist. from eyes -0.03 0.56 2. 3 1.27 25.8 14.5 0.55 0.56 0.96 0.019 eyes to lateral margin

18 y Z Post. distance 1.05 1.08 3.53 28.9 1.53 1.12 0.99 0.020 " " between eyes ' " l ll 104 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment the anterior of the eyes, C, length from the eyes to the anterior margin of the prosoma, V, and the length from the posterior of the eyes to the 1i ® posterior edge of the prosoma, W, relative tO tOtal : prosomal length, G, was allometric and the shape ratios increased or decreased throughout ontageny ® (Table 8, eqns. 7-9). Shape ratios for the ® youngest and oldest specimens are: C/G, 0.87 and 0.63; V /G, 0.19 and 0.35; and W /G, 0.38 and Q) 0.42. These changes were caused both by the relative decrease in eye length and a shift in eye CD position with growth. The shape ratios disclose that the change was !east marked for W; this suggests that eye position relative to the posterior margin of the prosoma was roughly constant during ontogeny. Compared with prosomal length, V rose and C declined markedly in larger specimens. Therefore, most of the change in eye position Fig. 11. Measurements made on whole specimens of involved the anterior margin of the eyes. The Eurypterus remipes remipes. eyes seem to have grown more slowly tawards the anterior margin than towards the posterior. Young specimens have comparatively large eyes with a small anterior "brim", whereas adults have rela­ one another. The eyes grew faster taward the tively small eyes with large "brims". posterior margin of the prosoma than wward the anterior edge. These growth trends caused Major changes also occurred in eye widths allometric changes in the prosoma, the most and the measures of eye position relative to proso­ noticeable being the development of a "brim" mal width. The relative decrease in eye width anterior to the eyes. is best seen in the ontogeny of distance from the eyes to the side of the prosoma, X, distance between the anterior ends of the eyes, Y, and RELATIVE GROWTH THE ENTIRE distance between the posterior margins of the OF BODY eyes, Z, with respect to prosomal length, G, and Due to differences in preservation, only ten posterior width of the prosoma B (Table 8, eqns. measurements (Fig. 11) were made. The sample 4-6, 12-14). All shape ratios increased during comprises 19 specimens, ranging from 5.0 to 35 growth as tabulated for the smallest and !argest mm in prosomal length. Several specimens are specimens: X/G, 0.16 and 0.26; Y/G, 0.31 and pictured in Fig. 12. 0.46; Z/G, 0.47 and 0.52. The same patterns Development of abdominal length J was allo­ characterized X, Y, and Z relative to the posterior metric with respect to the standard measure of prosomal width, B (eqns. 12-14). size, prosomal length, G, and total body length, In summary, development of prosomal shape K (Table 9, eqns. 3, 4). Throughout ontogeny, was approximately isometric. The main allometric the abdominal length became relatively greater. changes involved decrease in length and width The shape ratios for the youngest and oldest of the eyes relative the size of the prosoma Epecimens are: J/G, 2.8 and 3.3; K/G, 3.8 and to and a shift in the orientation of the eye-length 4.3. In K/G, higher ratios denote a relatively axes. The immature eye-length axes converge shorter prosoma and a longer abdomen. strongly taward the anterior margin of the proso­ The abdomen is divided into two parts, a ma, but the mature axes are roughly parallel to preabdomen including the anteriormost seven seg- Growth and Variation m Eurypterus remipes DeKay 105

a b Fig. 12. Eurypterus remipes remipes DeKay. a) a young KWM 18) - the left tip of the paddle and the telson individual (Colgate 121); b) a large specimen (Syracuse are broken.

(i) 70

60 60 ® o o

50 o 50 o o 00

40 40 o

w o o I -' • 30 (IJ 30 LU <( o _J a: (IJ o o o <( o <( > a: o <( 20 20 > o o

o 10 10 o o

o o o 10 20 30 40 ® o 20 40 60 VARIABLE G VARIABLE H ®

Fig. 13. Plots for the pairs of variables H against G, remipes to show bivariate relationships in whole in­ and I against H (see Fig. 11) for Colgate E. remipes dividuals. 106 H. E. AndrewJ, ]. C. Brower, S. ]. Gould, and R. A. Reyment

Table 9. Regression statistics for the relative growth of whole spccimens of E. r. remipes from the Colgate collection.

' C: 15. ·- ' · ;;.. a 3o l a >< lo l Independent vari­ Depender:! variable Initial Pre l Pre- Std. est. - l l di ete Y/X able (in mm) (in mm) intercept 8] 5 d dicted l Y/X Correl. of error ��]]l Xmin Ym In X ax min l max coeff. for b X y a l 10 ; til ----·- i ·�-;---- m�-�m Prosomal length Length of pre­ il G - 2.65 1.65 5.0 5.6 l 35.0 55.2 1.12 l 1.58 0.945 0.139 H abdomen l

2 G Length of post­ -0.39 1.74 8.3 3 60.6 1.67 1.73 0.975 0.096 abdomen " 'l 3 G ] Length of ab­ -3.04 3.40 13.9 o 116.0 2.79 3.31 0.972 0.200 domen "

4 G K Total length -3.04 4.40 18.9 o 151.0 3.79 4.31 0.983 0.200 " 5 G L Anterior width of -0.21 1.35 6.54 47.0 1.31 1.34 0.984 0.059 abdomen "

6 G M Abdomen width 0.42 1.47 7.78 51.9 1.56 1.48 0.982 0.068 at segment 3

7 G N Abdomen width 0.90 0.28 2.31 10.7 0.46 0.31 0.797 0.052 at last segment 8 L Anterior width M Abdomen width 0.80 1.09 8.0 9.49 47.0 51.8 1.19 1.10 0.992 0.032 of abdomen at segment 3 9 I L N Abdomen width 0.85 0.21 2.55 10.8 0.32 0.23 ! 0.824 0.035 at last segment 1 Length of ab­ l O l Length of pre­ -1.66 0.49 18.0 7.24 122.0 58.6 0.40 OAS 0.988 0.019 J domen H abdomen 11 I Length of post­ 1.66 0.50 10.80 63.4 0.60 0.52 0.988 0.019 J abdomen

12 J L Anterior width of 2.02 0.38 8.88 i 48.5 0.49 0.39 0.972 0.023 abdomen 13 M Abdomen width 2.65 0.42 10.20 0.022 iJ 53.8 0.57 0.44 0.977 l at segment 3 i 14 l ; N Abdomen width 1.46 0.08 2.86 11.0 0.16 0.09 0.772 0.015 at last segment i 15 Length of pre­ I Length of post­ 4.86 58.0 61.3 1.51 1.06 0.951 0.076 ·�Habdomen abdomen 1 ! -- _!_____ ----�--�--- l ------� ments, and a postabdomen made up of the last isometric with respect to the prosomal length, G, five segments (Figs. 11, 12). These two parts of and the I/G shape ratio was stabilized at 1.7 the abdomen exhibit conrrasting developmental throughout growth (Table 9, eqn. 2). This shows patterns. Relative prosomal length, G, the that all relative lengthening of the abdomen resul­ to preabdomen, H, became langer in progressively ted from allometric changes of the preabdomen, larger animals (Table 9, eqn. l); the shape ratios not the postabdomen. Specimen plots of relation­ for the smallest and !argest animals are: H/G, ships between variables are shown in Fig. 13. 1.1 and 1.6. Onrogeny of the postabdomen, I, was Development of the two preabdominal widths, Growth and Variation in Eurypterus remipes DeKay 107

Table 10. Regression statistics for growth of the paddles of Eurypteru.r remipes from the Colgate collection. ---1

· re- Std. est. c Initial � 2 p p o .... -� dicted di Y/X Y/X Correl. of error � E Independent variable Dependent variable intercept 8 � � 15 for b """ Xmin Ymin X max Ymax mm max coeff. r::r :::> l l l e":) �� � l·c� c X b u y l a j l l l l l J G Prosomal length O Total paddle 2.87 0.912 7.0 9.25 l 35.0 34.8 1.32 0.994 0.907 0.0848 mm l length mm 2 G P Maximum width 0.639" 0.407 7.0 3.49 35.0 14.9 0.499 0.426 0.908 0.0377 of paddle mm 3 O Total paddle length P Maximum width 0.333 0.398 7.0 3.12 35.0 14.2 0.445 0.407 0.891 0.0406 mm of paddle mm l -- -- l l

anterior width, L, and width at the third and entire body included the relative lengthening of widest segment, M, was almost isometric, relative the abdomen, mainly preabdomen compared to to the prosomal length, G (Table 9, eqns. 5, 6) . the prosoma. The abdomen tended to become The L/G ratio is 1.3, regardless of age, but M/G progressively more slender, the most intense change decreased slight!y from 1.6 to 1.5. Growth of occurring in the last segment. abdominal width at the last segment, N, was allometric with respect to prosomal size and N/G GROWTH OF THE PADDLES declined from 0.46 to 0.31 throughout ontogeny The ontogeny of two padd!e dimensions, total (Table 9, eqn. 7). length, O, and maximum width, P, was smdied Changes in abdominal shape are best shown for 27 specimens, ranging from 7.0 to 35.0 mm by development of the widths, L, M and N, relative in prosomal length. The measurements are shown to the total length of the abdomen, J (Table 9, in Figs. 11 and 12 and the regression results eqns. 12-14) and the ontogeny of abdominal are listed in Table 10. widths compared to one another (Table 9, eqns. The two paddle dimensions, total length, O, 8, 9). The proportions of the anterior width of and maximum width, P, also decreased relative to the abdomen, L, and the maximum width of the overall size, G (Table 10, eqns. l, 2). The shape abdomen, M, decreased somewhat relative to the ratios for the youngest and oldest animals are: length of the abdomen, J; shape ratios for the 0/G 1.3 and 0.99; P/G 0.50 and 0.43. Allo­ = = smallest and !argest specimens are: L/J, 0.49 and metry is indicated by the large positive initial inter­ 0.40; M/J, 0.57 and 0.44. Development of L and cepts in conjunction with relatively small positive M was almost isometric with respect to each other growth rates. The decrease of overall paddle di­ (Table 9, eqn. 8). The main shape change in mensions relative to body size suggests that adults abdominal widths occurred in the relationships could have shown less swimming ability and of the last segment, N, with the other abdominal perhaps spent more time on the bortom than the widths, L and M, and the abdominal length, J younger specimens. A similar phenomenon occurs (Table 9, eqns. 9, 14). In both cases, N declined in Limulus, where immature animals swim more relative to the other measures. Shape ratios of the actively and more frequently than the !argest smallest and !argest animals are N/L 0.32 and individuals. During ontogeny of padd!e shape, = 0.23; N/J 0.16 and 0.09. width decreased somewhat compared to length = In summary, the major shape changes in the (Table 10, eqn. 3). 108 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

INTEGRATION BETWEEN THE BODY Table 11. Vector loadings for the first canonical AND PROSOMA correlation for Eurypterus remipes remipes. Response Predictor The intuitively most satisfying model for studying Variable Variable weightings weightings the strength of correlation between two sets of l Un- Un- variables is that of canonical correlation. Although Adjusted Adjusted adjusted adjusted this method is one of the older ones, it has not l been widely applied, as the main interpretations M 0.56 1.00 L -1.13 0.93 of the analysis Iie with the sizes of coefficients N 0.26 0.96 G 2.14 0.93 of the pairs of equations for each set and it has o 0.16 0.85 0.00 0.90 in practice turned out to be difficult to judge p l CORRELATION = 0.95 H 0.02 0.93 the significance of these (cf. Blackith and Rey­ ---·-- ment, 1971). Recently, psychometricians have succeeded in deepening the theoretical background of canonical correlation analysis with an improved means of producing the characteristic equation required interpreting the roles of the elements. These im­ for finding the correlations between sets). provements have been made in the light of ex­ Submatrices R11 and R2 2 contain the correla­ perience arising of recent years in developing the tions for the two sets, predictors and responses, statistical foundations of factor analysis. respectively. Submatrices R1 2 and R2 1 contain Five of the variables were judged as response the correlations linking the variables across the variables and two of them as predictors, for a two sets. The purpose of this analysis is present to total number of 27 individuals from the Syracuse these interrelationship in paired linear combina­ and Colgate collections. The predictor set com­ tions of the variables. The rank of the smaller prises the width of the prosoma at its base L and of the submatrices R11 and R2 2 determines the the length of the prosoma G, in that order. The number of paired combinations. response variables are the width at the base of the We shall begin the analysis of the 27 indi­ third segment M, the width at the base of the viduals by briefly considering the direct rela­ last segment N, the length of the paddle O, the tionships between the elements of the cross-cor­ width of the paddle P, the length from the prosoma relation matrices. Practically all ·of the variation to the base of the seventh segment H. The loca­ in the negative definite matrix R12 resides in tions of these measures are illustrated in Fig. 11. one eigenvalue. Only the first eigenvalue is signi­ We shall first consider the matrix of correla­ ficant (Bartlett's test yields 53.3). In effect, xio= tions for the seven variables considered together. virtually all of the information contained in the It is: observations is localized to the first eigenvalue and its associated vectors. L G M N o p H L 1.00 0.96 ; 0.99 0.96 0.85 0.89 0.93 A comparison of the raw loadings and the R21 G 0.96 1.00 • 0.95 0.95 0.79 0.91 0.91 improved "factorial" estimates is presented in M 0.99 0.95 : 1.00 0.83 0.88 0.93 Table 11. It will be seen that the raw loadings : 0.96 N 0.96 0.95 0.96 1.00 0.71 0.83 0.88 (unadjusted) are meaningless. If only these were o 0.85 0.79 0.83 0.71 1.00 0.85 0.83 available for interpretation, the analysis would R 0.89 0.91 0.88 0.83 0.85 1.00 0.89 21 p be rejected out of hand by any quantitative biolo­ H 0.93 0.91 0.93 0.88 0.83 0.89 1.00 gist, for they are at complete variance with all With such high correlations, it is to be ex­ other information. For example, we have the pected that most of the variation will Iie with the completely misleading zero coefficients for P and first pair of canonical variates. H. The adjusted coefficients give, however, a The dashed lines in the correlation matrix completely different picture. All weights are denote its partitioning into four submatrices (for roughly the same and, with the canonical correla- Growth and V ariation in Eurypterus remipes DeKay 109

o. 2oo .-��- -�

•'

o. 165 22 .

o. 130 r-

0.095

•' 0.060 ·"

o. 025 •'

- o. 010

27 . -0.045 " 6 " . . . 15 21 . . o 17 •" • 7 -0.080 r- 20 16.2 . •' 13 -o. 115f- .

- o. 1 50 -0.1'---90---- '--0.1' -'--46�� -0-'--. 102��-'-�� -0.058 -0l__.014� ___j0.0L__30� ___J.0.'�074 �__L��_j_��_L��_jo. 118 o. 162 0.206 0. 250

Fl RST VA R lATE Fig. 14. Plot of the scores for the canonical variates 4, 5, 22) are the !argest specimens of the sample, those of the first canonical correlation for E. r. remipes. The falling in the lower corner (points 25, 13 and 3) are points fall ing in the upper part of the plot (points l, the smallest individuals.

tion of 0.95, the exceptionally high imegration redundancy coefficients are 0.77 for predictors and between body and head is manifest. responses alike, and also for both total coefficients Another instructive result arising from the of redundancy. adjusted weightings is the equal contributions of There is virtually nothing left over for the the predictor variables L and G. In the unadjusted second canonical correlation, which is a low 0.14. coefficients they are in a negative relationship The raw vector elements give high and apparently which is misleading. meaningful loadings, but these are artifacts. All The "transformed canonical scores" for the of the adjusted coefficients are dose to zero, with two sets of vectors were plorted (Fig. 14). only the length of the paddle approaching a mea­ ningful leve!. This variable was the most difficult The most obvious thing arising from this plot is the spread of the values, according to size, across of all measure, and we suspect that its high to the field, with the smallest falling in the bortom coefficient is a reflection of measurement error. left quadrant and the !argest in the upper right quadrant. As a result of the high level of integra­ R AND Q MODE ANALYSES tion, both axes reflect size variation, although the horizontal axis also includes a shape-differentiating The same seven prosomal and abdominal measure­ element over part of the field (i.e. among more ments as used in the canonical correlation as well mature specimens). as the full set of prosomal measures were subjec­ A redundancy analysis can hardly be expected ted to an R-mode principal components analysis. to furnish any surprises. All variables correlate Although we consider the canonical correlation highly with the original data (0.88 L, 0.88 G) and model be more appropriate to the biological to (0.95 M, 0.91 N, 0.81 O, 0.85 P, 0.89 H). The problem at hand, it is well known, that an in toto 110 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

a"

5.0

" 4.0

3.0

2 0 . 1.0 14

20

o .o 21 16 13 -1.0 17

- 2.0

- 3 0 o .

Q: ,__ 22 r - 4 .o

-5.0 "

-6.0

-7.0

-e.o

9 0 - . - - 35.2 29.l -22.8l -16. 6 -10. 4 - 4.2 o SECONO VA RIATE

Fig. 15. Graph of the scores of the secood and third plot of the canooical correlation scores of Fig. 14. Oh­ priocipal compooencs for Eurypterus remipes remipes. serve the locations of the sexable specimeos. The oumberiog of the poiots is the same as for the

consideration of the data often yields useful in­ deviate from the mean by the appropriate standard formation that might otherwise be overlooked. deviation; this would have given much the same Should the matrix of correlations or the matrix result as the correlations. of covariances serve as a base for the eigen­ The first principal component of the correlation analysis? There are several arguments that speak matrix is connected to more than 90 % of the in favour of the former. Firstly, we are interested total variation. All of its elements are dose in in examining the morphological integration of value (0.39, 0.39, 0.39 0.38, 0.35, 0.37, 0.38), , the eurypterid. The correlations are clearly, then, showing the remarkably even contriburions of the obvious starting point. Secondly, the correla­ each of the variables and, consequently, the excep­ tions are in themselves a form of standardiza­ tionally close-knit integration. The second princi­ tion. In the present study, this is a necessary con­ pal component, including only 5 % of the varia­ sideration, as the variables have widely differing tion, comrasts mainly the width of the paddle ranges of variation. In fact, the first eigenvector with the width of the base of the last segment; of the covariance matrix turns out to ref!ect, this is possibly a dimorphic characteristic. This faithfully, the sizes of the respective standard principal componem has the structure: deviations. W e could have standardized our ob­ servations by the usual method of dividing the 0.2 G-0.2 M-0.5 0+0.8P+0.3 H. Z2 = Growth and V ariation in Eurypterus remipes DeKay 111

0. 250 xxlx 0X X X X X X X X X XX 0.173 - o o

o o • o • • o o • 0.096 - • • • l:. O • • l:. l:. • • l:. 0 . 019 - l:.

l:. l:. l:. l:. • • l:.t:; - 0.058 - • l:. • l:. • IJ) • • • >< -0.135 - l:. • • • • Stage VI ; • o o • -0.366 - <> Stage VIl ; <> o o Stage VIll; <>

; -0.443 a Stage IX r- L7 L7

-0.520 l l l l l l l l l l -0.080 -0. 067 -0.054 -0.041 -0.028 -0.01 5 -0.002 0.011 0.024 0.037 0.050

FIRST AXIS Fig. 16. Plot of the first two sees of coordinates for degree of correlation between the variables of the proso­ the principal coordinates analysis of prosomas of E. ma, in part indicatory of a quadratic relationship be­ remipes from the Colgate collection. This plot gives r.a tween the first and second eigenvecrors of the association remarkably good ordination into moult stages. The matrix. parabolic form of the plot is in part a result of the high

The plot of the first two transformed scores fore, appear to rece1ve a measure of support in also reflecrs a growth-size relationship, as one the graphical analysis. The third principal com­ might expect. The grouping of the observations ponenr (2 % of the variance) has the structure: inro two fields found in our data is difficult z3 -0. L+0.2 G-0.3 M -0.2 N to explain, bur it might bear some relationship = -0.40+0.8 P. to sexual dimorphism. Too few sexed specimens were available for a detailed analysis, bur these do It is mainly a measure of shape variation m seem to have a tendency to segregate. This is most the paddle. clearly indicated on the plot of the second and The principal componenrs of the correlation third transformed variables, shown in Fig. 15. matrix of the ten prosomal measurements were The second and third eigenvalues represenr to­ extracted (the first three componenrs are shown gether almost 7 % of the total variation. The in Table 12). The first componenr is a growth possible indication of dimorphism suggested by facror, the second and third componenrs reflect the paddle to pre-telson relationship does, there- shape differences, particularly in the shape and 112 H. E. Andrews, ]. C. Brower, S. ]. Gould, and R. A. Reyment

Table 12. Principal components for the prosoma of of his type. After "size variation" had been remo­ Eurypterus remipes remipes from the Colgate collection. ved from the observations, using the principal components model, the plots of the new set of Principal component principal coordinates yielded a completely hapha­ Variable Il III zard picture, reflecting largely random variability. A Prosoma width anterior 0.319 0.04 1 -0.197 A few points forming an attenuated duster away to the eyes from the main body could not be interpreted B Posterior width of the 0.318 -0.058 -0.171 meaningfully. prosoma 1 C Length from posterior 0.312 -0.515 0.597 margin of prosoma to anterior of eyes REFERENCES G Total length of prosoma 0.318 -0.135 0. 142 Agassiz, Alexander. 1878. Note on the habits of young Limulus. Am. Sei., ser. 3, V. 15, 75-76. U Prosomal width posterior 0.317 0.016 -0.160 ]. Banks, H. P. 1972. The stratigraphic occurrence of early to the eyes land plants. Palaeontology, 15, 365-377. V Length from eyes to an­ 0.315 0.423 0.218 Blackith, R. E. and Reyment, R. A. 1971. Multivariate terior margin of prosoma Morphometrics. Academic Press, London and New W Length from posterior 0.317 -0.163 0.234 York, ix+412 pp. margin of prosoma to Borch, C., von der. 1965. The distribution and preli­ posterior margin of eyes minary geochemistry of modern carbonate sedi­ ments of the Coorong area, South Australia. Geo­ Distance from eyes to la­ 0.312 0.674 0.219 X chim. Cosmochim. Acta, 29, 781-799. teral margin of prosoma Brooks, H. K. 1957. Chelicerata, Trilobitomorpha, Y Anterior distance be­ 0.317 -0.057 -0.404 Crustacea (exclusive of Ostracoda) and Myriapoda. tween the eyes Annotated bibliography in Mem. geol. Soc. Am., 67, vol. 2; Treatise on Marine Ecology and Paleo­ Z Posterior distance be­ 0.316 -0.221 -0.465 tween the eyes ecology: Paleoeco�ogy. Edited by ]. W. Hedgpet:1, ------1 ------� - pp. 895-930. Percent of correlation matrix 0.8 % 0.5 % Caster, K. E., and Kjellesvig-Waering, E. N. 1964. trace associated with the Upper Ordovician eurypterids of Ohio. Palaeontogr. listed component Am., 4, 32, 297-358. Clarke, ]. M., and Ruedemann, R. 1912. The Eurypte­ rida of New York. Mem. N.Y. St. Mus. nat. Hist., 14, 628 pp. positioning of the eyes. This agrees with the results DeKay, ]. E. 1825. Observations on a fossil crustaceo·Js for E. r. tetragonophthalmus. animal of the Order Branchiopoda. Ann. N. Y. Lye. Nat. Hist., 375-377. The prosomal observations on 77 prosomas in l, Dixoa, W. ]. (ed.). 1970. BMD biomedical computer the Colgate collection were analysed by the Q­ programs. Ur:iv. Cal. Publ. in autom. Computation, mode technique introduced by Gower (1966). 2, X and 600 pp. (2nd ed.). For biological interpretations, see Blackith and Eldredge, R. N. 1972. Systematics and evolution of Reyment (1971). This analysis succeeds in ordina­ Phacops rana (Green, 1832) and Phacops iowensis Delo, 1935 (Trilobita) from the Middle Devonian ting the individuals into successive size classes, of North America. Bull. Am. Mus. nat. Hist., 147, 45 which represent moult stages. The graph of value3 -114. of the principal coordinates for the 77 individuals, Fowler, H. W. 1907. The King Crab fisheries in Dela­ shown in Fig. 16, has a paraboloid form, a re­ ware Bay, New Jersey. Ann. Rep. St. Mus. (1907), flection of the very high correlations between 113-116. variables and a quadratic relationship between Friedman, G. M. and Sanders, ]. E. 1957. Origin and occurrence of dolostones; Devs. in Sedimentology: the eigenvectors forming the first and second 9/i, Carbonate Rocks. Chap. 6, 267-348; Edited axes. The residual, after two eigenvalues had been by G. V. Chillingar, H. ]. Bissell, and R. W. Fair­ extracted, was only 31.8 %, a low value for studi es bridge, Elsevier, Amsterdam. Growth and V ariation in Eurypterus remipes DeKay 113

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