Main articleThe hypothesis that many, if not all, of the South African and Zambian specimens, which have
been regarded as different diademodontine genera and species, actually consitute a taxonomically
homogeneous, ontogenetic growth series is tested. The principles of allometric growth were
applied to this sample of fossils, which varied considerably in size and shape. The approach
which was followed was exclusively morphometric. The results indicate that these specimens do
represent various ontogenetic stages of a growth series of only a single species of Diademodon
Seeley.Non

Grine, F. E.

Hahn, B. D.

Wits Institutional Repository on DSPACE

Palaeont. afr., 21,161-166 (1978) ALLOMETRIC GROWfH IN THE DIADEMODONTINAE (REPTILIA; THERAPSIDA); A PRELIMINARY REPORT by F. E. Grine* and B. D. Hahnt * Department of Anatomy, Medical School, and t Department of Applied M athematio, University of the Witwatersrand, Johannesburg. ABSTRACT The hypothesis that many, if not all , of the South African and Zambian specimens, which have been regarded as diflerent diademodontine genera and species, actually consitute a taxonomi-cally homogeneous, ontogenetic growth series is tested. The principles of allometric growth were applied to this sample of fossils, which varied considerably in size and shape. The approach which was followed was exclusively morphometric. The results indicate that these specimens do represent various ontogenetic stages of a growth series of only a single species of Diademodon Seeley. 161 INTRODUCTION An assemblage of moderately advanced, omnivo-rous-herbivorous, gomphodont cynodonts is well known from the Cynognathus Zone sediments of the Orange Free State and Cape Province, South Africa (Kitching, 1972). The most commonly occurring forms in these deposits are represented by a rather homogeneous assemblage of animals which have been grouped collectively in the subfamily Diade-modontinae by Hopson and Kitching (1972). The fossil remains of these reptiles have been recovered also from the Ntawere Formation, Upper Luangwa Valley, Zambia (Kitching, 1963; Brink, 1963a), the Omingonde Mudstone Formation (Lower Etjo Beds) of South West Africa (Keyser, 1973), and also from the Lincheyu locality, Shansi Province, China (Young, 1961). The Diademodontinae appear to have been late Early Triassic to early Middle Triassic in age (Du Toit, 1954; Cox, 1967; Keyser, 1973). size of the skull; and that the smaller usually possess fewer teeth than do the larger specimens. He sug-gested that rather than the smaller fossils being re-garded (on the basis of tooth number) as specifically distinct from the larger, the smaller specimens should be considered as representing ontogeneti-cally younger stages of development than the larger ones. A plethora of genera and species of diademodon-tines have been named (table 1); but only a few have been based on more than fragmented or distorted specimens, and still fewer have been adequately characterized such that anyone genus or species can be readily distinguished from all others. Hopson and Kitching (1972) have proposed that the vast ma-jority of these names are junior synonyms of Diade-modon tetragonus Seeley. A detailed study of the dentitions of a number of diademodontine spec-imens (Grine, 1976a, 1976b and 1977), which in-cluded the types of Diademodon tetragonus and D. brachytiara as well as remains which had been re-garded as specimens of D. broumi, D. mastacus, D. en-tomophonus and Gomphognathus sp., revealed that these fossils represented a dentally homogeneous group. Grine (1977) noted that the number of postcanine molariform teeth in various diademodontine spec-imens may vary from five to 11, dependent upon the TABLE 1 List of genera and species presently included in the subfamily Diademodontinae. Diademodon tetr(Jf!,onus brachytiara mastacus browni entomophonus platyrhinw parringtoni laticeps rhodesiensis Cynochampsa laniaria Gomphognathw kannemeyeri polyP. minor haughtoni grossarthi broomi (Diastemodon) dimorphodon Ocl(Jf!,omphw woodi Cyclogomphodon platyrhinw Protacmon brachyrhinw reubsameni Sysphinctostoma srnithi gracilis Cragievarus kitchingi Tilanogomphodon crassw Ordosiodon lincheyiiensis Trirachodon browni Seeley 1894 Seeley 1894 Seeley 1894 Seeley 1894 Seeley 1908 Broom 1913 Brink 1955 Brink 1955 Brink 1963 Owen 1859 Seeley 1895 Seeley 1895 Broom 1911 Broili and Schrooer 1935 Broili and Schroder 1935 Broili and Schrooer 1935 Seeley 1908 Broom 1919 Broom 1919 Watson 1920 Broom 1950 Broili and Schroder 1936 Broom 1950 Brink 1965 Keyser 1973 Young 1961 Broom 1915 162 Brink (1963b) recorded and illustrated four spec-imens which had been recovered from a single "fossil pocket" on the farm Cragievar, near Burg-hersdorp, Cape Province. He regarded these as im-mature individuals of Diademodon browni, and noted that there "is some individual variation which could partly be accounted for in terms of growth" (1963b, p. 109). The hypothesis entertained in this study is that many, if not all, of the 12 genera and 26 species which have been recognized for the Diademodonti-nae (table 1) may possibly constitute an ontogenetic, sexually dimorphic series of but a single species, Di-ademodon tetragonu5 Seeley. This paper constitutes a preliminary report of a much more detailed study (see Grine, Hahn and Gow, 1978). MATERIAL AND METHODS A series of 55 specimens (table 2) was examined. The material ranged from relatively undistorted, complete skulls (i.e. BPI. FN. 4669) to fragmented dentaries. The principles of relative (allometric) growth were applied to this sample of fossils, which varied considerably in size and shape. The approach which was followed was exclusively morphometric. Figure 1. Diademodontid skull measurements (see opposite page) A large number of variables of both the cranium and dentary were designated for measurement (fig. 1); but, due to the oftentimes fragmentary nature of the available material, there was no single specimen on which all 52 metrical characters could be re-corded (see table 2). All measurements were taken with either a sliding Vernier caliper (in the cases of smaller dimensions) or the top segment of an an-thropometer, and recorded to the nearest milli-metre. The variables which were selected for measurement generally reflected the overall shape of the skull and its various parts rather than the confi-guration of individal bones or pans of bone devel-oped from specific ossification centres. In order to assess and describe quantitatively the processes of skull growth, the measurements were fitted to the bi-parametric power function (the equation of simple allometry): y = axP (1) where y is the variable whose increase relative to that of another variable is considered, x is a different di-mension of the same skeletal complex, a is a numer-ical constant and ~ is the slope of the rectilinear plot (or simply the ratio of the specific growth rates of A, norma verticalis; B, norma basalis; C, norma lateralis; D, norma occipitalis; E, nonna venicalis of delllary; F, norma lateralis 01' lower jaw. Variable Description 1 Basal skull length 2 Total skull length 3 Pre-orbital length 4 Pre-orbital basal length 5 Pre-orbital total length 6 Cranial masticatory length Cranial postcanine masticatory length 8 Hard palate length 9 Temporal fossa length 10 Cranial length to back of jugal flange 11 Cranial length to posterolateral edge of jugal 12 Total dentary length 13 Dentary length of coronoid process 14 Dentary length to angle 15 Mandibular masticatory length 16 Mandibular postcanine masticatory length 17 Symphyseal length 18 Total o-anial width 19 Cranial width across jugal flanges 20 Interorbital width 21 Least snout width 22 Greatest snout width 23 Parietal width coincident with pineal foramen 24 Temporal fossa width 25 Bicondylar breadth 26 Post-temporal breadth 27 Width between post-temporal foramina 28 Greatest breadth of maxillary tooth rows 29 Least breadth of maxillary tooth rows 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Maxillary bicanine breadth Dentary thickness Minimum intercorporal breadth Minimum symphysial breadth Maximum symphysial breadth Mandibular bicanine breadth Maximum post-temporal height , Maximum height of mid-temporal crest above maxillary base Maximum height of postorbital above maxillary base Maximum height of maxilla Maximum height of corpus of delllary Projected rameal breadth Orbital breadth Orbital height Nasal aperture length Foramen magnum height Foramen magnum breadth Mesiodistal diameter of maxillary canine (or socket) Buccolingual diameter of maxillary canine (or socket) Mesiodisl<!l diameter of mandibular canine (or socket) Buccolingual diameter of mandibular canine (or socket) Maximum height of jugal Pterygoid width I I ~ BP - M Fig.IA Fig. IF • 11 I t. ~2 I '-5 I I J I I I • ... 13 Fig. IB 26 Fig.ID 163 36 164 TABLE 2 List of specimens measured. Y, number of mensurable parameters recorded; BPI.FN., Bernard Price Institute for Palaeontological Research Field Number; C.S., Ceological Survey, Pretoria; N.M., National Museum, Bloemfontein. Specimen Specimen Museum No. Previous taxonomic designation description Y I BPI.FN.3754 Diademodon grossarthi Cranium 36 2 BPI.FN.3639 Diademodon rhodesiensis (type) Skull 42 3 BPI.FN.2522 Diademodon mastacus Cranium 29 4 BPI.FN.3757 Diademodon haughtoni Snout 14 5 BPI.FN.4669 Diademodon sp. Skull 46 6 C.S. R.322 TitanogomjJhodon crassus (type) Cranium 7 7 BPI.FN.1695 Diademodon sp. Snout 13 8 BPI.FN.1195 Diademodon broami Cranium 18 9 C.S. R.530 Cranium 17 10 BPI.FN.3758 Diademodon browni Skull 40 II BPI.FN.1177 Diademodon sp. Skull 14 12 BPI.FN.3756 Diademodon mastacus Skull 40 13 BPI.FN.3769 Diademodon browni Skull 39 14 BPI.FN.3773 Diademodon browni Cranium 34 15 BPI.FN.3772 Diademodon browni Cranium 33 16 BPI.FN.4528 Diademodon sp. Snout, dentary 13 17 BPI.FN.2519 CyclogamjJhodon jJlatyrhinus Snout, dentary 21 18 C.S. R.531 Cranium 17 19 BPI.FN.4647 Diademodon sp. Cranium, dentary 25 20 BPI.FN.377I Diademodon sp. Skull 25 21 BPI.FN.3776a Cragievarus kitchingi (type) Skull 25 22 BPI.FN.4658 Diademodon browni Skull 40 23 BPI.FN.3511 Diademodon browni Skull 36 24 BPI.FN.4529 Diademodon sp. Snout, dentary 9 25 BPI.Fn.1169 Skull 8 26 C .S. R.483 Skull 19 27 C.S. R.327 Diademodon tetragonus Dentary 13 28 C.S. R.321 Diademodon tetragonus Dentary 29 C.S. R.321a Diademodon tetragonus Dentary II 30 C.S. R.321b Diademodon tetragonus Dentary II 31 C.S. R.321c Diademodon tetragonus Dentary • 15 32 C.S. R.321d Diademodon tetragonus Dentary 3 33 C.S. R.319 TitanogamjJhodon cf crassus Symphysis 7 34 BPI.FN.2666 Diademodon sp. Demary 10 35 N.M. C2707-30 Diademodon entamojJhonus Demary 12 36 N.M. C2707-31 Diademodon entamojJhonus Demary 12 37 N.M. C2707-32 Diademodon entamojJhonus Dentary 7 38 N.M. C2705-33 Diademodon entamojJhonus Demary 15 39 N.M. C2705-34 Diademodon entamojJhonus Dentary 3 40 N.M. C2706-35 Diademodon entamojJhonus Dentary 10 41 N.M. C2705-36 Diademodon entamojJhonus Dentary 15 42 N.M. C2707-37 Diademodon entamojJhonus Dentary 3 43 N.M. C2707a Diademodon entamojJhonus Dentary 9 44 N.M. C2707b Diademodon entamojJhonus Demary 10 45 N.M. C2707f Diademodon entamojJhonus Dentary 9 46 N.M. C2707h Diademodon entamojJhonus Demary 14 47 N.M. C2706-50 Diademodon entamojJhonus Dentary 8 48 N.M. C2706-51 Diademodon entamojJhonus Dentary 13 49 N.M. C2707-1 Diademodon entamojJhonus Demary 13 50 N.M. C2707-2 Diademodon entamojJhonus Demary 12 51 N.M. C2707 Diademodon entamojJhonus Dentary 6 52 N.M. C2705-8 Diademodon entamojJhonus Dentary 9 53 N.M. C2705-12 Diademodon entamojJhonus Dentary 15 54 N.M. C2709 Diademodon entamojJhonus Demary 14 55 N.M. C2709a Diademodon entamojJhonus Dentary 14 variables x and y). If equation (1) is converted to log-arithms, then curvilinear growth relationships be-come linear, and the problem is reduced to the fit-ting of a straight line, thus: log y = log a + ~ log x (2) Equation (2) may be rewritten as Y=a+~X (3) where Y = log y, X = log x and a = log a. With the establishment of linear relationships any line-fitting technique may be used to determine the slope. The slope of the "best straight line" through the data is regarded as the allometric coefficient. Kermack and Haldane (1950) and Kermack (1954) have cautioned against the use of regression models which assume error to be related to only a single variable. The fitting procedure utilized here was that of Bartlett's best fit (Bartlett, 1949). This method has been recommended for analysis of allometric growth by Simpson, Roe and Lewontin (1960) and has been so used by Kidwell and Chase (1967) and by Dodson (1976). 5-80 1 • 5·40 .3 5·00 .2 co 4·60 I~ ~ 0 12 .22 -l 4·20 • .13 3·80 3-40 .23 3·00 3·00 3-40 3·80 4·20 4·60 5·00 5-40 5·80 LOG 1 Figure 2 Specimen No. Log X Log Y X Y 23 3,85 3,33 47 28 12 4,30 4,19 74 66 13 4,52 4,17 92 65 22 4,62 4,62 101 71 14 4,72 4,53 112 93 10 4,90 4,74 134 115 15 4,96 4,74 142 115 5 5,18 4,87 177 130 2 5,44 4,97 230 144 1 5,62 5,53 275 253 3 5,66 5,33 287 207 f3 = 1,005 ±0,21 a = -0,303 ±O,IO 165 If the estimates of a and ~ are to be of any value, confidence intervals must be calculated. Formulae for the calculation of these, and of the values of a and ~, have been presented by Simpson et at. (1960) and will not be repeated here. In all results pre-sented below, the upper and lower 95 per cent confi-dence limits for a and ~ have been calculated. Further analysis of our data will be approached through the utilization of multivariate techniques (see Grine, Hahn and Gow, 1978). RESULTS As most of the fossil specimens consisted of less than complete skulls, more than one mensurable character was used as the comparative base value x. The following parameters were used as x values: ( 1) Basal skull length (3) Pre-orbital length (4) Pre-orbital basal length ( 14) Dentary length to angle ( 1 7) Symphysial length (21) Least snout width 5·80 5-40 5·00 r<l ~ 4·60 0 -l 4·20 3·80 12 • 3-40 23 • 3·00 3·00 3-40 3·80 4·20 4 ·60 LOG 1 Figure 3 Specimen No. Log X Log Y 23 3,85 3,14 12 4,30 3,66 20 4,43 3,58 13 4,52 3,81 22 4,62 3,66 14 4,72 3,87 10 4,90 4,01 15 4,96 4,06 5 5,18 4,42 2 5,44 4,58 1 5,62 4,87 3 5,66 4,95 ~ = 0,964 ± 0,09 a = -0,625 ±0,04 5·00 5-40 5·80 X Y 47 23 74 39 84 36 92 45 101 39 112 48 134 55 142 58 177 83 230 98 275 130 287 141 166 All of the available measurements for each spec-imen were compared and plotted in a bivariate manner with each of the above base values. Due to limitations of space, only two bivariate plots are presented here (figs. 2 and 3). Comparisons of variables 18 (Total cranial width) and 3 (Pre-orbital length) with variable 1 (Basal length) for some 11 and 12 crania respectively, indicate isometric or near isometric growth (allometric coefficients of 1,0 and 0,96 respectively). The logarithmic values of x and y, and the a and ~ values for each plot are pre-sented. The amount of variability appears to be somewhat higher for cranial width than for pre-orbital length. Although the allometric coefficient for pre-orbitallbasal length (0,96) appears to indicate isometric growth, Dodson (1975) found that for Alli-gator mississifJiensis coefficients as close to isometry as 0,98 were significantly different from 1,0 at p = 0,05. For convenience, the specimen numbers (see table 2) have been placed next to their respective points on the plots. Both comparisons indicate a growth series extending from the smallest Diademo-don specimen known (No. 23, BPI.FN. 3511) to the third largest fossil in the present sample (No.3, BPI.FN. 2522). This series includes crania which have been regarded as specimens of D. browni, D. Mastacus and D. (GomfJhognathus) rhodesiensis (the type specimen). Clearly, all of these crania can be accom-modated in a single growth series according to these two (and at least some 25 other) bivariate cranial plots. DISCUSSION The preliminary results of this investigation lend support to the contention that many, if not all, of the South African and Zambian specimens which have been regarded as different diademodontine genera and species may constitute a taxonomically homogeneous growth series. The fossils from South Africa and Zambia probably represent various onto-genetic stages of a growth series of only a single species, Diademodon tetragonus. The possibility that this animal evinced sexual dimorphism will be ex-amined fully in a later study (Grine, Hahn and Gow, 1978). Perhaps those specimens from South West Africa and China may be part of a phylogenetic growth series. The confirmation or refutation of these hypotheses, however, must await study of a larger series (including the type specimens) of these animals. This quantitative approach, combined with detailed morphological observations, may help to alleviate the taxonomic confusion which currently prevails in the literature on this group of Triassic mammal-like reptiles. ACKNOWLEDGEMENTS Grateful acknowledgement is made of the kindness extended by Dr. J. W. Kitching, Dr. A. W. Keyser and Mr. J. van Heerden, in the loan of specimens in their care. Dr. C. E. Cow was of in-valuable assistance in the recording of some 960 measurements. All computing and plotting was done on the I.B.M. 370/158 of the Computer Centre, University of the Witwatersrand, Johan-nesburg. We thank Professor P. V. Tobias for reading this man-uscript, and for his invaluable criticisms and advice. REFERENCES BARTLETT, M. S. (1949). Fitting a straight line when both var-iables are subject to error. Biometrika, 5, 207-212. BRINK, A. S. (]963a). Two cynodonts from the N'tawere For-mation in the Luangwa Valley of Northern Rhodesia. Pal-aeonl. afr., 8, 77-96. ---- (]963b). Notes on some new Diademodon specimens in the collection of the Bernard Price Institute.Palaeonl. afr. , 8, 97-11l. COX, C. B. (]967). Changes in terrestrial vertebrate faunas dur-ing the Mesozoic. The Fossil Record, a Symposium with Documen-tabon. Geo!. Soc. Lond., 77-89. DODSON, P. (1975). Function and ecological significance of relative growth in Alligator. j. Zool. Lond., 175, 315-355. ---- (1976). Quantitative aspects of relative growth and sexual dimorphism in Protoceratops. j. Paleonl. , 50, 929-940. DU TO IT, A. L. (954). The Geology of South Africa. Oliver and Boyd, London. GRINE, F. E. 0976a). 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Organic correlation and allometry. Biometrika, 37, 30-4 l. KEYSER, A. w. (973 ). A new Triassic vertebrate fauna from South West Africa. Palaeont. afr., 16, 1-15. KIDWELL, J. K. and CHASE, H. B. (967). Fitting the allome-tric equation - a comparison of ten methods by computer simulation. Growth, 31, 165-179. KITCHING, J. w. (963). The fossil localities and mammal,like reptiles of the Upper Luangwa Valley, Northern Rhodesia. S. Afr. j. Sci., 59, 259-264. --.:-- (972). On the distribution of the Karroo vertebrate fauna with special reference to certain genera and the bear-ing of this distribution on the zoning of the Beaufort beds. Ph.D. Thesis, University of the Witwatersrand, Johannes-burg. 1-127, 1-256. SIMPSON, G. G., ROE, A. and LEWONTIN, R. C. (960). Q.uanlitative Zoology. 2nd ed. Harcourt, World and Brace, New York. 1-440. YOUNG, C. C. (]96!l. On a new cynodont from NW Shansi. Vert. palasiat., 1961(2), 111-114. 

Allometric growth in the Diademodontinae (Reptilia; Therapsida); a preliminary report

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