allometry in the placoderm bothriolepis canadensis and its significance to antiarch evolution

9
Allometry in the placoderm Bothriolepis canadensis and its significance to antiarch evolution LARS WEKDtl.lN AND JOHN A LONG LETH A1 A Q Werdelin. Lars 81 Long. John A. 19x6 04 IS: Allometry in the placoderm Borhriolepis cu~iude!isis and its Significance to antiarch evolution. Lerliciiu, Vol. 19, pp. 161-169. Oslo. ISSN “24-1 164. A set of IX measurements of the dermal armour of Bo/hrir/lepi.s ratiuden.7i.f Whiteaves (Placoderrni. Anti- archa) is analyscd with respect to allometric growth patterns. The strongest allometric patterns were found for the orhital fenestra and premedian plate of the head-shield. and the anterior median dorsal plate of the trunk-shield. These are all areas of the greatest importance in antiarch phylogeny and imply a role for ontogcnetic effects such as paedomorphosis in the evolution of antiarchs. It is suggested that this is partly ii result of the severe constraints on growth in a closed box such as the armour of placoderms. and may he generally true of such arrangements. 0 Plucodermi, Anriurrhu, Bothriolepis, ullomerry. onrogeriy, rvoliition. Lim Werdeliii, Dep~irrme~ir of Pulurozoology. Swedish Museum of Nurural Hi.srory. Box 50007. S-1040.5 S/ockholm. Sweden; John A. Long. Depurrmerir of Geology. Ufiiver.siry of Wesrern Aitsrrulia. Nedluiids, We,s/erti Airstraliu MIOY? Aii.s/raliu; 20th February. 19x5. The placodermi is one of the best known of all groups of extinct organisms. Even without the benefit of close living relatives to study, nearly every aspect of the anatomy of the best known of them has been investigated in great detail. Led by the researches of the late Professor Erik Sten- siii of the Swedish Museum of Natural History, Stockholm (e.g. Stensio 1942, 1948, 1959, 1963, IY69), a large number of scientists, many trained by him, have studied these animals, among others Gross (1932), Brvig (1951), Miles (1968) and Denison (1978). One factor accounting for our great knowledge of the placoderms is that they are often well preserved, due to their dermal armour. often protective even against the pro- cesses of post-mortem decay. With the discovery of the spectacularly preserved placoderms from the Gogo Formation, Western Australia (Gar- diner & Miles 1975). still more information on these bizarre animals is coming to light (e.g. Young 1984a). Of all placoderms, those of the genus Both- riofepis are perhaps the most common, both in terms of the number of individual specimens and in terms of the number of described species. This genus has been the subject of several mono- graphs (Gross 1941; Stensiii 1948; Miles 1968) and numerous shorter papers, including the de- scriptions of at least 60 species, with a number of new species from Australia and Antarctica yet to be described. Of the many species of the genus Bothriolepis, the best known is B. canadensis from the Upper Devonian of Scaumenac Bay, Canada. This species is known from many hun- dreds of specimens, including a score with the tail and dorsal and caudal fins preserved. B. cana- densis has been extensively described by Stensio (1Y48), and additional aspects concerning its anatomy and biology have been discussed by Pat- ten (1904), Denison (1941) and Young (1984a). By virtue of its abundance and the detail in which it is known, B. canadensis has in many ways come to form a kind of standard against which other species of the genus are compared. Despite all the information gathered on placo- derms in general and B. canadensis in particular, there is one aspect of their biology which has been largely ignored. This is the study of al- lometric growth patterns. In past work on Both- riolepis, the analysis of growth patterns has been limited to calculations of indices and rather vague statements to the effect that this or that plate in- creases or decreases in length or width during on- togeny. None of these statements is backed up by statistical testing. We have elsewhere (Long & Werdelin in press) stated why we consider indices in many ways to be more obscurant than illumi- nating. In this paper we have instead used re- gression analysis to study allometry, as discussed by Imbrie (1956) and Gould (1966). Allometric patterns in B. canadensis are of considerable interest because of the nature of its 1 I - Lethaia 2/Xh

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Page 1: Allometry in the placoderm Bothriolepis canadensis and its significance to antiarch evolution

Allometry in the placoderm Bothriolepis canadensis and its significance to antiarch evolution LARS WEKDtl.lN A N D JOHN A LONG

LETH A1 A

Q Werdelin. Lars 81 Long. John A . 19x6 04 IS: Allometry in the placoderm Borhriolepis cu~iude!isis and its Significance to antiarch evolution. Lerliciiu, Vol. 19, pp. 161-169. Oslo. ISSN “24-1 164.

A set of I X measurements of the dermal armour of Bo/hrir/lepi.s ratiuden.7i.f Whiteaves (Placoderrni. Anti- archa) is analyscd with respect to allometric growth patterns. The strongest allometric patterns were found f o r the orhital fenestra and premedian plate of the head-shield. and the anterior median dorsal plate o f the trunk-shield. These are all areas of the greatest importance in antiarch phylogeny and imply a role f o r ontogcnetic effects such as paedomorphosis in the evolution of antiarchs. It is suggested that this is partly ii result o f the severe constraints on growth in a closed box such as the armour of placoderms. and may he generally true of such arrangements. 0 Plucodermi, Anriurrhu, Bothriolepis, ullomerry. onrogeriy, rvoliition.

Lim Werdeliii, Dep~irrme~ir of Pulurozoology. Swedish Museum of Nurural Hi.srory. Box 50007. S-1040.5 S/ockholm. Sweden; John A. Long. Depurrmerir of Geology. Ufiiver.siry of Wesrern Aitsrrulia. Nedluiids, We,s/erti Airstraliu MIOY? Aii.s/raliu; 20th February. 19x5.

The placodermi is one of the best known of all groups of extinct organisms. Even without the benefit of close living relatives to study, nearly every aspect of the anatomy of the best known of them has been investigated in great detail. Led by the researches of the late Professor Erik Sten- siii of the Swedish Museum of Natural History, Stockholm (e.g. Stensio 1942, 1948, 1959, 1963, IY69), a large number of scientists, many trained by him, have studied these animals, among others Gross (1932), Brvig (1951), Miles (1968) and Denison (1978). One factor accounting for our great knowledge of the placoderms is that they are often well preserved, due to their dermal armour. often protective even against the pro- cesses of post-mortem decay. With the discovery of the spectacularly preserved placoderms from the Gogo Formation, Western Australia (Gar- diner & Miles 1975). still more information on these bizarre animals is coming to light (e.g. Young 1984a).

Of all placoderms, those of the genus Both- riofepis are perhaps the most common, both in terms of the number of individual specimens and in terms of the number of described species. This genus has been the subject of several mono- graphs (Gross 1941; Stensiii 1948; Miles 1968) and numerous shorter papers, including the de- scriptions of at least 60 species, with a number of new species from Australia and Antarctica yet to be described. Of the many species of the genus

Bothriolepis, the best known is B. canadensis from the Upper Devonian of Scaumenac Bay, Canada. This species is known from many hun- dreds of specimens, including a score with the tail and dorsal and caudal fins preserved. B. cana- densis has been extensively described by Stensio (1Y48), and additional aspects concerning its anatomy and biology have been discussed by Pat- ten (1904), Denison (1941) and Young (1984a). By virtue of its abundance and the detail in which it is known, B. canadensis has in many ways come to form a kind of standard against which other species of the genus are compared.

Despite all the information gathered on placo- derms in general and B. canadensis in particular, there is one aspect of their biology which has been largely ignored. This is the study of al- lometric growth patterns. In past work on Both- riolepis, the analysis of growth patterns has been limited to calculations of indices and rather vague statements to the effect that this or that plate in- creases or decreases in length or width during on- togeny. None of these statements is backed up by statistical testing. We have elsewhere (Long & Werdelin in press) stated why we consider indices in many ways to be more obscurant than illumi- nating. In this paper we have instead used re- gression analysis to study allometry, as discussed by Imbrie (1956) and Gould (1966).

Allometric patterns in B. canadensis are of considerable interest because of the nature of its

1 I - Lethaia 2/Xh

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dermal armour. In effect, the animal is growing inside a closed box, and this entails considerable restraints on development. If one plate changes its proportions during ontogeny, another must change as well so that the whole still remains closed - a mode of causal relationship between elements which is quite different from that of ani- mals with internal supportive structures. Because of these severe constraints, it is possible that the study of allometric growth may cast light on the phylogeny of Bothriolepb and antiarchs in gen- eral.

Lars Werdelin and John A . Long LETHAIA 19 (1986)

Material and methods The data utilized in the analyses in this paper were gathered from the collection of B. cana- densis housed in the Swedish Museum of Natural History (NRM), Stockholm. This material was used by Stensio in his study of the genus, and has been fully illustrated by him (Stensio 1948). The use of the same material makes possible some di- rect comparisons with the results obtained by Stensio from his quite different approach to the problem.

The collection in its present state consists of approximately 650 specimens, of which 104 were complete enough and well enough preserved to be measured with sufficient accuracy.

Terminology in this paper follows Miles (1968). Measurements were taken with Vernier calipers to the nearest millimetre. Greater accuracy was deemed neither possible nor necessary for pres- ent purposes.

The following is a list of the measurements used. The abbreviations within parentheses will be used in the remainder of the paper. The meas- urements are illustrated in Fig. 1.

(1) Length of head-shield (LHs): Midline length of head-shield excluding obtected nuchal area.

(2) Width of head-shield (WHs): Distance from posterolateral corner to midline, multiplied by two (X2). (This system of measurement is used to minimize the effects of preservational distortion, As B. conadensir is relatively flat-armoured, this measure will differ only slightly from the true width of the head-shield. Another benefit is that measuring this way will al- low use of specimens in which only half of the head-shield is preserved.)

(3) Length of the premedian (LPrM): Midline length of the pre- median plate.

(4) Rostra1 width of premedian (WrPrM): Length of rostra1 margin of premedian.

(5) Orbital width of premedian (WoPrM): Length of orbital margin of premedian.

(6) Width of orbital fenestra (WOf): Greatest transverse width of orbital fenestra.

(7) Length of nuchal plate (LNu): Distance from anterolateral corner to obtected nuchal area.

( 8 ) Width of nuchal (WNu): Width of nuchal across lateral cor- ners.

(9) Length of trunk-shield (LTs): Distance from anterior ex- tremity of suture between anterior median dorsal (AMD) and antcrior dorsolateral (ADL) plates, to posterior extremity of suture between posterior median dorsal (PMD) and mixilateral (MxL) plates.

(10) Width of trunk-shield (WTs): Distance from lateral ex- tremity of suture between ADL and MxL to median dorsal ridge x2. (Measurement used for reasons stated above.)

( 1 1) Length of AMD (LAMD): Midline length of AMD

(12) Width of AMD (WAMD): Distance from lateral corner to median dorsal ridge x2. (Measurement used for reasons stated above.)

(13) Anterior width of AMD (WaAMD): Distance between an- terolateral comers of AMD.

(14) Posterior width of AMD (WpAMD): Distance between posterolateral corners of AMD (excluding overlap area).

(15) Tergal length of AMD (LtAMD): Distance from tergal angle to posterior midline extremity of AMD.

(16) Length of PMD (LPMD): Midline length of PMD.

(17) Width of PMD (WPMD): Distance from lateral corner to dorsal median ridge x2. (Measurement used for reasons stated above.)

(18) Anterior width of PMD (WaPMD): Distance between an- terolateral corners of PMD. (Identical to measurement 14 in Fig. 1.)

The regression axes used in this paper are re- duced major axes, for which the slope of the axis (regression coefficient) is calculated as:

where s, and s, are the standard deviations of x and y respectively. The regression coefficients are tested against the null hypothesis H,: a = 1, using the formula:

(Sokal & Rohlf 1981:473), where s, is the stan- dard error of the regression coefficient. A slope

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LETHAIA 19 (1986) Placoderm allometry 163

Fig. 1. Dermal armour of B. conadensis. showing measurements used in the analyses. La = lateral, PNu = paranuchal. PMG = postmarginal. All other abbreviations are given in the text.

significantly lower than unity indicates that the x - variable increases faster with growth than the y- variable, and a slope significantly greater than unity means that the y-variable is the faster grow- ing.

In order to linearize the relationships between the variables, all were transformed into log,, be- fore calculations were carried out.

Results and interpretation As a starting point for the analysis selected vari- ables were tested for normality. It was found that all variables thus selected were normally distri- buted, and no significant skewness and kurtosis

was found. By extension it has been assumed that all variables are normally distributed.

That the variables should be normally distri- buted was not an expected result, and merits dis- cussion quite apart from the regression analysis. It has generally been assumed that Bothriolepis grew more or less continuously for an extended period of its lifespan, and if this is correct the dis- tribution of the measured variables stands in a di- rect relationship with the distribution of speci- men ages in the population being measured. Taken at face value this would mean that the dis- tribution of specimen ages in the population is normal, which is not expected whether mortality is normal or catastrophic (Kurttn 1983), unless juvenile mortality was abnormally low in Both-

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riolepis, a possibility which seems most unlikely. Two alternative explanations for the observed pattern can be proposed: (1) That all the speci- mens are adults of an extremely variable species. As a corollary this would mean that individuals of Bofhriolepis grew for only a short period of their lifespan, and stopped growth at a given time, per- haps when their dermal armour fused up. This explanation is contrary to what is known of anti- arch biology, as it appears that the plates of Bofh- riolepis grew from clearly defined centres of os- sification (Graham-Smith 1978), and must be re- jected for that reason. (2) The second possible explanation is that there is a preservational bias against small specimens. Such a bias should be of a probabilistic nature, i.e. the likelihood of pre- servation should be a monotonically decreasing function of decreasing age, rather than one which has a cut off point beneath which no specimens are preserved (but see below). The function should also be such that it approximately coun- teracts the greater number of small specimens (juveniles) expected in the living population, thus producing in the fossil material a size distri- bution which does not differ significantly from a normal distribution function. It should be em- phasized that this second explanation, while seemingly more plausible than the first, is en- tirely ad hoc and based on negative evidence only; there have been no studies of the post-mor- tem processes acting on placoderms which have provided data to support or reject this hypoth- esis. It is clear, however, that the specimens of B. canadensis from Scaumenac Bay are not ran- domly distributed. The collection of entire indi- viduals complete with tails and caudal fins de- scribed by Patten (1904) and now in the Amer- ican Museum of Natural History, New York, apparently all comes from a single horizon, and consists of specimens which are almost identical in size, perhaps representing a school of medium sized adults buried by a mud slide.

The observed normal distribution of sizes also has another implication, that the largest observed specimen of B. canadensis is near to the maxi- mum possible for the species. If this were not the case we should, barring further preservational biases, expect to see a truncation of the large end of the size range and thus a skewed distribution. No such skewness has been detected, and the lar- gest specimen in the sample, NRM P2130 (Sten- sio 1948, Figs. 11 1, 159), with a dorsal Hs + Ts length of 178 mm, and a WTs of 132 mm, is near to the maximum for this species.

Lars Werdelin and John A . Long LETHAIA 19 (1986)

The minimum size of B. canadensis, i.e. the size at hatching, is not clear. The smallest meas- urable specimen, NRM P2747 (Stensio 1948, Fig. 88), had an LTs of approximately 17 mm. There is, however, a still smaller specimen, NRM P4175 (not figured by Stensio) which is too poorly pre- served to be measured. The dermal armour of this specimen is very thin and i t may be that this specimen is either a recent hatchling or that smaller individuals had not developed the dermal armour to such an extent that it increased fossil- ization potential significantly. Very small speci- mens of Bothriolepis sp. from Mt Howitt, Vic- toria, Australia (e.g. Museum of Victoria P157162, with an armour length of 18 mm) show that the dermal armour was very thin and partly flexible, as plates appear to be crinkled and folded over one another. The dorsolateral and ventrolateral ridges are extremely well developed in these small specimens, giving strength to the trunk-shield when the laminae of bone were very thin. The minimum observed Hs + Ts length of B. canadensis is thus some 20-25 mm and is not likely to have been much less at hatching.

The results of the regression analyses are pre- sented in Table 1 . Of the 16 variable pairs for which regression coefficients were calculated 9 showed isometric growth patterns (a not signifi-

Table I . Results of the regression analysis of selected variable pairs. a = regression cocfficient. s, = standard error of a, t, = result of 1-test of slope against null hypothesis of a slope of I . df = degrees of freedom. N = number of observations, NS = not significant. * = significant at S%-level. * * = significant at 1%- level, * * * = significant at 0.1%-level. Variable abbreviations are given in the text.

~~~~~~

Variables II s, f, df Significance W Y ) (N-2) level

WHdLHs I ,042 0.0577 0.728 21 NS LHslLTs 1.161 0.08421.912 12 NS W H s N T s 1.283 0.0619 4.572 29 * * * WTslLTs 1.044 0.0380 I . 158 30 NS LPrM/WrPrM 0.856 0.0667 2.159 23 * WrPrMlWoPrM 0.658 0.0972 3.519 21 * *

WOVWHs 1.337 0.0865 3.896 30 * * * LHslLPrM 1.059 0.0717 0.823 21 NS WTslWAMD 1.057 0.0203 2.808 44 * * LAMD/WAMD 1.065 0.0324 2.(M 54 ' LtAMDlLAMD I.008 0.0180 0.444 54 NS WaAMDl

WpAMD 1.135 0.0740 1.824 54 NS LAMDlLPMD 1.048 0.0532 0.902 20 NS LPMDlWPMD 1.055 0.0459 1.198 23 NS WaPMD/WPMD 0.905 0.0351 2.707 32 *

LNu/WNu 0.949 0.0492 1.037 so NS

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LETHAIA 19 (1986) Placoderm allometry 165

Fig. 2. This figure shows graphically the differences between a small (A) and a large (B) B. canadensis. Note especially the largc eyes, short PrM and narrow AMD and PMD of the former. 0 A . Redrawn after Stensio (1948, Fig. 98). 0 B. Redrawn after Sten- siii (194X. Fig. 1x2). Abbreviations as in Fig. I . except csl. csll. cs12 = central sensory lines; otr = oblique transverse ridge; dlgl. dlg2 = anterior and posterior sensory line grooves.

cantly different from unity) and the remaining 7 TWO variable pairs, WrPrMIWoPrM and WTsI showed some degree of allometry. This propor- tion is, of course, not representative, as the vari- ables used d o not represent a random sample. Nevertheless, it does indicate that many, if not most, of the plate proportions in B. canadensis remained constant during ontogeny.

Two variable pairs, WOUWHs and WHs/WTs, showed the greatest degree of allometry (p < 0.001, Table 1 ) . The former pair was considered by Stensio (1948:233), who arrived at the same conclusion, that the orbital fenestra decreases considerably in relative size (in the present paper only width is considered) during ontogeny. The latter pair of variables was not considered by Sten- sio. and represents somewhat of a surprise. It shows that the trunk-shield grew considerably faster in width during ontogeny than did the head-shield. This result has not been reported previously, but is clearly to be seen on the speci- mens and in the figures published by Stensio (e.g. 1948, Figs. 90, 134).

WAMD, show the next highest degree of allo- metry (p < 0.01, Table 1) . The first of these is, of course, closely related to the first pair discussed in the previous paragraph, where it was found that the orbital fenestra decreased in relative width during ontogeny. In this situation we would expect that the orbital margin of the PrM would grow more slowly during ontogeny than the rostra1 margin, and this is exactly what we find. This result was also noted by Stensio (1948:239-240). The PrM thus becomes more flared during ontogeny. From the second vari- able pair we can see that the trunk-shield as a whole increased more slowly in width during on- togeny than did the A M D alone. This means that the A M D successively made up a greater propor- tion of the dorsal armour as the animal grew larger. As a corollary it should be realized that the dorsal laminae of the A D L and MxL plates would decrease in relative size to compensate for the growth of the AMD. Due to the dearth of

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well preserved A D L and MxL plates this result cannot be derived directly.

Of the three final variable pairs to show signifi- cant allometric relationships two, LPrM/WrPrM and LAMDWAMD, give results that were also noted by Stensio. For the first pair the analysis shows that the PrM grows faster in length than in rostral width. In the second case the analysis shows that the A M D increased faster in width than in length. This last growth pattern is only weakly significant, however, and the effect is not as pronounced as it would appear to be from Stensio’s statement (1948:287): ‘The A M D (breadthAength ratio) .. . is clearly somewhat larger in large individuals than in smaller ones’. When the width of the A M D was measured, those individuals exhibiting the ‘Remigofepis- type’ overlap relationships of the A M D (Stensio 1948) were set aside, as it was thought that they might show a different growth pattern from indi- viduals with the usual Bothriofepis overlap pat- tern. Upon analysis, this seems to be the case. Small specimens showing the Remigofepsis-type pattern (it is not exclusively confined to large in- dividuals as previously thought) have WAMD of nearly the right magnitude for specimens of their size, whereas large specimens with this pattern have a much wider A M D than expected. The anomalous overlap type thus seems t o lead to a shift in the slope of the regression axis, and rep- resents a release from the rigorous constraints of the normal overlap pattern of Bothridepis.

The last significant allometric relationship is WaPMDWPMD, which shows that the anterior width of the PMD increases more slowly than the greatest width of that plate. As a result, the PMD will appear more triangular in large specimens than in small ones, where it is more rectangular (cf. Stensio 1948, Figs. 138, 139).

In a few of the 9 cases where no significant al- lometry was found (specifically WTs/LTs, LNu/ WNu and LPMD/WPMD), this result is in con- trast to the assertions of Stensio (1948), illustrat- ing the dangers of using intuitive assessments of indices. Thus, the trunk-shield does not widen relative to its length during ontogeny, the Nu is not relatively broader in small specimens, and the PMD does not become relatively wider dur- ing ontogeny.

The difference between an adult and a juvenile B. canadensis is shown graphically in Fig. 2.

Lars Werdelin and John A. Long LETHAIA 19 (1986)

Evolutionary significance As we have seen, the strongest allometric pat- terns within B. canadensis were shown by the PrM and orbital fenestra in the head-shield, and the width of the trunk-shield, especially the width of the AMD. We propose that, in general, growth of external plates of bone in a closed-box arrangement should result in the strongest al- lometry occurring in anatomical regions of phy- logenetic importance. In other words, the great- est amount of change exhibited in the phylogeny of a largely homogeneous group such as both- riolepids will occur on plates with the most geno- typic potential for variation. Species of Both- riofepis have previously been defined largely on the basis of proportional indices of plates, with notes of unusual morphological features and characterization of dermal ornament. The results of our biometric study indicate that many species of Bothriofepis warrant revision if plate indices used in their definition either fall within the range of interspecific variation or show signifi- cant ontogenetic variation.

The PrM is perhaps the most variable plate in the head-shield of antiarchs (Fig. 3) and is intim- ately associated with the rhinocapsular division of the neurocranium (Young 1984a). Slower growth of the PrM at the orbital margin than the rostral margin, as demonstrated above for B. canadensis, is explained by the close association between the bothriolepidoid preorbital recess (of the PrM) and the orbital fenestra, through which the eyes and nares open externally. Preorbital re- cess shape varies considerably within the genus, ranging from simple semilunar types to trifid shaped ones bearing well defined median and lat- eral horns. Similarly, as the preorbital recess with a ventral lamina flooring the rhinocapsular is B bothriolepidoid synapomorphy, the development of a long PrM plate is seen only in certain species of Bothriolepis. The significance of these two fea- tures to antiarchan phylogeny has been discussed by Janvier & Pan (1982), Long (1983) and Young (1984a, 1984b). A few further points may be made. Firstly, the homology between the trifid preorbital recess of bothriolepidoids and the tri- fid preorbital depression of yunnanolepidoids im- plies that a semicircular preorbital recess is apo- morphic within Bothridepis (Janvier & Pan 1982). Young (1984a) has proposed that this ho- mology is only partly correct, as the anterior or preotbital division of the depression is unor- namented in yunnanolepidoids, which indicates

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LETHAIA 19 (1986) Placoderm allometry 167

Fig. 3. Head-shields of representatives of the different antiarch groups mentioned in the text. 0 A. Borhriolepis, a bothriolepidoid. 0 B. Asvrolepis. an asterolepidoid. 0 C. Yunnanolepis. a yunnanolepidoid. 0 D . Sinolepis, a sinolepidoid. A, Dafter Long 1983, B after Karataiute-Talimaa 1963. C after Zhane 1980. La = lateral, PNu = paranuchal, PMG = postmarginal, PP = postpineal. All

meorbital recess n

- other abbreviations are given in the text.

that if the rhinocapsular was housed below and slightly in front of the orbit, the shape of the rhi- nocapsular would be of a simple crescentic type. Long (1983) proposed that the trifid preorbital recess is apomorphic for bothriolepids by asso- ciation with other derived characters (such as large size in B. maxima and B. gigantea). It is now clear that a very elongate PrM is also de- rived for bothriolepids, although species possess- ing both semicircular and trifid preorbital reces- ses are known with elongate PrM plates (B. cul- lodenensis, Long 1983, B. shaokuanensis, Liu 1973). The strong allometry of the PrM in B. can- ademis, both in rostraVorbital width and in lengthlwidth, is indicative of the phylogenetic sig- nificance of these characters to antiarch evolu- tion.

The orbital fenestra of B. canademis was pro-

portionately considerably larger in the juvenile head-shield than in adult individuals. The signifi- cance of the orbital fenestra to antiarchan phy- logeny is evident in the small orbital size of primi- tive antiarchs (yunnanolepidoids and sinolepi- doids, Fig. 3). It must be pointed out, however, that the orbital fenestra of yunnanolepidoids is really a suborbital fenestra, as part of the pre- orbital depression housed the eyes and nares (Young 1984a). The real size of the orbital fen- estra was still relatively small with respect to overall head-shield area. As in other placoderm groups (petalichthyids, paleacanthaspids, actino- lepidoids, Denison 1978) the occiput of primitive antiarchs is long. A shortening of the occiput in asterolepidoids made possible an enlargement of the orbit. This sequence of events also occurred in bothriolepidoids, although subsequent devel-

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opment of the preorbital recess restricted orbit size, presumably as olfactory sensation increased in importance at the expense of vision. The re- gression analysis presents some evidence that heterochrony (possibly paedomorphosis) was partly involved in the evolutionary change in or- bit size, as adults of the derived group (asterole- pidoids and bothriolepidoids) have a character state (large orbit) more similar to the situation seen in juveniles of the primitive group (yunna- nolepidoids and sinolepidoids), than to the adult state in the latter group.

The increase in width of the trunk-shield of B. canadensis is to a significant degree due to the ra- pid increase in width of the AMD. This is also an important region in antiarchan evolution, al- though one susceptible to convergence. Primitive antiarchs (yunnanolepidoids, Zhang 1978) have long trunk-shields with separate posterior lateral plates, as do actinolepidoid euarthrodires (Deni- son 1978). The posterior lateral plate may be primitively retained in certain higher antiarchs, such as some asterolepidoids (Remigolepis, Bys- sacanthus, Denison 1978), but in general this plate is fused to the posterior dorsolateral to form a mixilateral plate in most advanced anti- archs (bothriolepidoids, many asterolepidoids). A shortening of the trunk-shield relative to the head-shield first occurred at an early stage of antiarchan evolution, as Sinolepis shows this fea- ture whilst retaining a primitive yunnanolepi- doid-type head-shield. Certain asterolepidoids retain the primitive trunk-shield condition but have apomorphic characters of the head-shield such as shortened occiput, large orbital fenestra (see above) and narrow lateral plates (e.g. As- terolepis, Remigolepis, Denison 1978). All both- riolepidoids show the derived trunk-shield condi- tion in conjunction with specialized head-shield features. Although not significant, the allometric pattern of LHs/LTs suggests that the trunk-shield became relatively longer during ontogeny (Table 1, with more data this pattern is quite likely to become significant). Thus, juvenile B. cunudemis once again present a more derived condition than adult individuals.

Lars Werdelin and John A . Long LETHAIA 19 (1986)

great number of other variables for which al- lometric relationships would be of considerable interest. This is especially true of the pectoral fin. There is no reason to doubt Stensio’s (1948) con- clusion that the anterior segment grew faster in width than in length during ontogeny, but just how much faster? What is the relationship be- tween the lengths of the two segments of the pec- toral fin, and between the fin as a whole and the trunk-shield? Other areas not considered here in- clude the lateral and ventral armours. The rela- tionship between the height of the lateral wall and its length would be of considerable interest to both phylogenetic and functional studies of Bothriolepis, but sufficient material is at present not available.

For purposes of phylogeny reconstruction and recognition of species, a consideration of the growth patterns of various plates is clearly of the first importance. Indeed, these can be very useful taxonomic characters (cf. Long & Werdelin in press).

The strongest allometry shown by B. cana- densis was found to occur in anatomical regions of phylogenetic importance. Further studies of the biometry of closed-box systems, such as pla- coderm armours, may determine whether this observation is true in general.

Acknowledgements. - We thank Gavin Young, Bureau of Min- eral Resources. Canberra. and Wolf-Ernst Reif, Geological In- stitute. Tiibingen, for comments which improved the quality of this paper. For permission to study material in their care we thank Tor Brvig and Valdar Jaanusson, Swedish Museum of Natural History, Stockholm and John Maisey, American Mu- seum of Natural History, New York. This research was sup- ported by grant numbers 1629-100 and 162%101 from the Swedish Natural Science Research Council to LW, and by a Rothman’s Postdoctoral Fellowship at the Australian National University to JAL.

Concluding remarks The variables used in this regression analysis study of B. canadensis are those that could be ac- curately measured on a large enough sample that statistical analyses were possible. There are a

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