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A NEKTASPID ARTHROPOD FROM THE EARLY CAMBRIAN SIRIUS PASSET FAUNA, WITH A DESCRIPTION OF RETRODEFORMATION BASED ON FUNCTIONAL MORPHOLOGY by

GRAHAM E. BUDD

ABSTRACT. The Sirius Passet fauna from the Lower Cambrian of North Greenland yields a diverse suite of poorly sclerotized arthropods. A new nektaspid from the fauna described here differs from typical naraoiids in having six thoracic segments and in being isopygous. Soft parts are poorly known, but posterior limbs are preserved in some specimens. Although specimens are invariably highly flattened, details of the axial articulation suggest that the animal could enrol. The widths of the articulating half rings can be used to reconstruct both the degree of rotation at each articulation during enrolment and the height at which each point along the half ring is above the fulcrum, and this in turn may be used to make a full three-dimensional reconstruction of the exoskeleton. This method of retrodeformation is in principle applicable to the reconstruction of other taxa, especially trilobites, found in shales.

THE naraoiids s.l. (order Nektaspida Raymond, 1920) are a group of Cambrian–Ordovician, poorly sclerotized arthropods that have elicited interest on account of their suggested trilobite affinities: indeed, they are often referred to as ‘soft-bodied trilobites’ (e.g. Whittington 1977). The first to be described was Naraoia compacta from the Mid Cambrian Burgess Shale (Walcott 1912; Whittington 1977), but since then a variety of similar arthropods has turned up in other Cambrian Lagersta¨tten such as Liwia from the Lower Cambrian of Poland (Dzik and Lendzion 1988); one species of Naraoia from the Early Cambrian Chengjiang fauna of China (Zhang and Hou 1985) and a recently erected genus, Misszhouia (Chen et al. 1997); N. compacta from the Lower to Middle Cambrian of Utah and Idaho (Robison 1984); and from two Ordovician localities: Tarricoia from the ‘Puddinga’ sequence of Sardinia (Hammann et al. 1990) and Soomaspis from the late Ordovician Soom Shale of South Africa (Fortey and Theron 1994). In addition, the poorly known Maritimella from the Cambrian of Russia (Repina and Okuneva 1969) should probably also be included, although it will not be discussed further here (see comments in Fortey and Theron 1994). In this paper I describe a new form from the Early Cambrian Sirius Passet fauna, Buenaspis forteyi gen. et sp. nov., that should probably be referred to the Nektaspida, and discuss certain aspects of its functional morphology, with particular regard to enrolment. THE SIRIUS PASSET FAUNA AND ITS SETTING

The Sirius Passet fauna is a well-preserved Early Cambrian fauna from the Buen Formation of North Greenland (Text-fig. 1; Conway Morris et al. 1987) consisting of a diverse suite of arthropods (Budd 1993, 1995, 1997; Budd and Peel 1998), sponges (Rigby 1986) and other taxa including articulated halkieriids (Conway Morris and Peel 1990, 1995). The siliciclastic sedimentary rocks of the Buen Formation form part of a early Palaeozoic shelf sedimentary sequence deposited after the foundering of a substantial, previously karstified Early Cambrian carbonate platform (Portfjeld Formation). To the north, the Buen Formation grades into the deeper basinal deposits of the Polkidorren Group (see Ineson and Peel 1997 for a recent and thorough description of Cambrian shelf stratigraphy in North Greenland; Budd 1995; Conway Morris and Peel 1995; Budd and Peel 1998 for further discussion of the setting and age of the Sirius Passet fauna). Although the lower part of the Buen Formation is dominated by cross-bedded sandstones, the [Palaeontology, Vol. 42, Part 1, 1999, pp. 99–122, 1 pl.]

䉷 The Palaeontological Association

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1. Locality map for the Sirius Passet fauna (Buen Formation, Lower Cambrian). For details of North Greenland Cambrian shelf stratigraphy, see Ineson and Peel (1997).

Sirius Passet fossils themselves are found in mudstones from the lowermost part of the formation, in its northern outcrop. The presence of the nevadiid trilobite Buenellus higginsi (Blaker 1988; Blaker and Peel 1997), together with stratigraphical considerations, suggests that the fauna is of Nevadella Biozone age of North American usage (Palmer and Repina 1995), and is thus amongst the oldest of the several Cambrian Lagersta¨tten known (for reviews see Conway Morris 1989; Butterfield 1995). SYSTEMATIC PALAEONTOLOGY

Phylum

EUARTHROPODA

von Siebens and Stannius, 1848

Remarks. The original designation of the arthropods, dealing only with living forms is here interpreted as equivalent to crown-group arthropods ¼ Euarthropoda. Although Whittington (1977) and Fortey and Theron (1994) placed Naraoia and Soomaspis respectively in the Trilobita, it is here considered that such placement is premature: more information is needed about the systematics of possibly related taxa such as the tegopeltids and helmetiids. Enlarging the Trilobita to include the Nektaspida whilst still maintaining a monophyletic grouping might otherwise force several other taxa into the clade, some of which might not be particularly trilobite-like (see Chen et al. 1997; discussion in Hou and Bergstro¨m 1997). Order

NEKTASPIDA

Raymond, 1920

Remarks. The order Nektaspida Raymond has been used in various senses, including all ‘soft-bodied trilobites’, a grouping that has been taken to include naraoiids and tegopletids (Shu et al. 1995). As this

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assemblage is almost certainly not monophyletic, the suggestion has been made that Nektaspida should be abandoned (Chen et al. 1997). However, the morphology of Buenaspis allows the provisional recognition of two ‘naraoiid’ families (see below), and thus Nektaspida is revived here to include them in a monophyletic clade, i.e. close to its original usage. It is modified to include only the following taxa: Naraoia, Liwia, Misszhouia, Soomaspis, Tariccoia, Maritimella? and Buenaspis: the relationships of taxa such as Tegopelte would need further investigation if they were to be placed in the order. Evidence for nektaspid monophyly, and thus the characters that define it, are discussed below. The erection of a further ‘naraoiid’-like taxon (i.e. Misszhouia) allows the family Naraoiidae Walcott to be restricted to those nektaspids possessing only a single articulation in the adult, i.e. Naraoia, Misszhouia and Maritimella? The Naraoiidae are probably monophyletic, but, as implied by Fortey and Theron (1994), they may have given rise paraphyletically to those nektaspids with more than one trunk articulation. The subfamily Liwiinae Dzik and Lendzion is herein elevated to the family Liwiidae, containing Tariccoia, Liwia, Soomaspis and Buenaspis gen. nov., and may be defined by those nektaspids bearing more than one trunk articulation. As discussed below, the liwiids may be paraphyletic, and their monophyly may imply that the naraoiids are paraphyletic. Family LIWIIDAE Dzik and Lendzion, 1988 Diagnosis. Nektaspids with more than one axial articulation. Genus

BUENASPIS

gen. nov.

Derivation of name. From the Buen Formation and aspis (Greek), shield. Type and only species. Buenaspis forteyi sp. nov.

Diagnosis. Nektaspid with subequal cephalic and caudal shields; six thoracic segments with pleural facets and axial articulating half-ring. Buenaspis forteyi sp. nov. Plate 1; Text-figures 3–4, 10 v.1987 v.1988

‘isopygous form with cephalon and posterior shield separated by six thoracic segments’, Conway Morris et al., pp. 181–182, fig. 2e. ‘isopygous form with cephalon and pygidium separated by thorax with 6 segments’, Peel, p. 4, fig. 2E [cop. Conway Morris et al. 1987].

Derivation of name. For Dr R. A. Fortey. Holotype. GGU 340103·1715. All type and figured specimens are housed in the Geological Museum, Øster Voldgade, Copenhagen. Type horizon and locality. From the base of the Buen Formation (Nevadella zone, Lower Cambrian), J. P. Koch Fjord, Peary Land, central North Greenland. Other material. Approximately 200 specimens from the same locality in GGU collection 340103.

Diagnosis. As for the genus. Description. A wide size-range is known, with specimens 10–29·5 mm long (Text-fig. 2A). The mean total length is

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TEXT-FIG.

2. Size statistics for Buenaspis forteyi gen. et sp. nov. A, length/width ratio. B, length distribution.

19·6 mm, and the mean width 10·5 mm: lengths fall into an approximately normal distribution (Text-fig. 2B). The exoskeleton is divided into three regions: a cephalic shield, a segmented thorax and a caudal shield (Pl. 1, fig. 1). Overall, the carapace is more or less smooth. However, three surface features, all likely to be taphonomic in origin, are present in some specimens. The most common are concentric crush-marks that are concentrated around the anterior of the cephalic shield and the posterior of the caudal shield (Pl. 1, figs 1–2, 4; Text-fig. 3G – H). Similar crush-marks also commonly mark the pleural extremities. In addition, some specimens (especially the holotype) show traces of two additional features: a poorly developed sagittal ridge (¼ keel in the terminology of Chen et al. 1997) running from just anterior to the rear of the cephalic shield to just posterior to the front of the caudal shield (Pl. 1, fig. 1); and some traces of trilobation within all three regions (Pl. 1, fig. 1). Both of these features are likely to be post-mortem artefacts caused by differential compaction of the exoskeleton, given that they are absent in most specimens. In particular, an artefactual keel is known in some trilobites (e.g. in Kunmingaspis (Reed, 1910); see Jell and Hughes 1997). The variability of this feature in other nektaspids such as Soomaspis (see Fortey and Theron 1994) implies that here too it may be artefactual.

The head shield is sub-semicircular, broader than it is long, and with rounded genal angles. The anterior margin in particular is often heavily marked by the concentric crush marks described above, giving it a stepped appearance and on occasion somewhat obscuring the true anterior margin of the shield. This marginal indistinctness, which also applies to the distal extremities of the pleurae, may indicate compression together of the dorsal exoskeleton and a doublure, traces of which may sometimes be seen (Text-fig. 4A). No evidence for dorsal eyes is present. The thoracic region consists of six tergites (Pl. 1, figs 1, 3–4). Abaxially, the tergites are extended into broad posteriorly directed pleural spines, which are free at their tips. The antero-lateral border of each pleura is delimited by a distinct line running parallel to the pleural margin (Text-figs 4B, E, 6). This border continues to follow the tergite boundary adaxially to form a flange-like structure, soon widening towards the midline of the animal to form a crescentic extension to the anterior of each segment, which appears to underlie the preceding segment (Pl. 1, fig. 1; Text-fig. 3D). The widest overlap is developed between the third and fourth thoracic tergites (Table 1). Although usually poorly preserved, in the occipital region, the holotype appears to show that the head shield overlaps not just a crescentic extension but also part of the tergite itself (Pl. 1, fig. 1; Text-figs 4D, 5). These crescentic extensions are interpreted as articulating halfrings which allowed dorso-ventral flexibility. Close to where the pleural extremities come into contact with the tergites either side of them appears to be developed a distinct posterioriad step in the margin of the anterior tergite (Text-figs 4B, 6) which encompasses the width of the crescentic extensions at this point.

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3. Buenaspis forteyi gen. et sp. nov. A, MGUH 24·548; the largest specimen known, with disarticulated head shield; × 1·0. B, MGUH.24·550; × 1·6. C, F, MGUH 24·546; × 3·6, MGUH 24·551; × 2·8; the two smallest known specimens, showing an already adult morphology. D, MGUH 24·542; details of thorax; × 4·4. E, MGUH 24·547; caudal shield with limb exites visible at exterior; × 3·0. G, MGUH 24·541; cephalic shield, × 3·4. H, MGUH 24·540; cephalic shield; × 9·1.

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The anterior-lateral borders to the tergites are thus exposed, whereas the crescentic extensions adaxial to the steps are under the preceding tergite. The caudal shield is slightly smaller than the cephalic shield, and somewhat more rounded (Pl. 1, figs 1–4). Along its antero-lateral margin are developed identical structures to those in a similar position in the thoracic segments (Pl. 1, fig. 1; Text-fig. 4E). Apart from these structures, and the termination of the sagittal keel discussed above, the shield appears to be featureless. Many specimens show a pair of broad, symmetrically arranged extensions beyond the rear of the caudal shield (Pl. 1, figs 1–4; Text-figs 3B, E, 4C). They are often indistinct, but the holotype and a few other specimens show these structures to consist of series of overlapping lamellae (Text-fig. 4C); in the holotype some traces of these structures are also to be seen within the caudal shield. Although symmetrical, often giving the caudal shield a spinose appearance, these structures are interpreted as limb exites. Apart from these few traces, no other soft parts are known. DISCUSSION

Buenaspis and its relationship to the nektaspids Buenaspis shows little ‘soft-part’ preservation apart from its carapace and the occasional trace of limb exites. Nevertheless, its affinities seem to lie with the nektaspid arthropods, a Cambro-Ordovician group that has often been allied to the trilobites (see Walcott 1912; Raymond 1920; Whittington 1977; Zhang and Hou 1985; Hammann et al. 1990; Fortey and Theron 1994; Ramsko¨ld et al. 1996; Chen et al. 1997; Hou and Bergstro¨m 1997), on the basis of the following polythetic characters (i.e. no attempt is made here to distinguish between plesiomorphic and apomorphic states). 1. Three-part exoskeleton with few thoracic segments (but more than any previously described nektaspid). 2. Small size, typically of 20–30 mm. 3. Length-width ratio of approximately 2:1. 4. Cephalic shield sub-semicircular with rounded genal angles; length (lg.) of cephalic shield approximately one-third that of total body length. 5. Sagittal keel – if this is not an artefact (see above). 6. Articulating half rings. 7. Lack of dorsal eyes (may be absent or ventral). 8. Exopods of limbs bearing long lamellae. These characters are admittedly feeble, and few in themselves are synapomorphies of a monophyletic Nektaspida. Chen et al. (1997) and Fortey and Theron (1994) listed several characters that they consider to support such a concept (their ‘Naraoiidae’); but none of them is particularly strong. It is worth examining these characters in turn to demonstrate the difficulties of phylogenetic analysis with few or poor characters. 1. Trunk narrowed anteriorly relative to head-shield (Chen et al. 1997). This is not a character possessed by Buenaspis, although it is present in other non-nektaspid arthropods such as Fuxianhuia Hou, 1987 and Chengjiangocaris Hou and Bergstro¨m, 1991. As discussed below in the functional morphology section, there is a strong functional constraint on the front of the trunk, as it needs to pass under the broad head shield during the dorso-ventral flexure of which at least some and probably all of these animals were capable. Buenaspis fulfils this functional requirement by possessing broad articulating facets on the most anterior tergite, as do some trilobites.

EXPLANATION OF PLATE

1

Figs 1–6. Buenaspis forteyi gen. et sp. nov. 1, MGUH 24·545 (holotype); complete specimen showing shields, thorax, articulating facets, articulating half-rings and posterior limb exites (see also Text-figs 4–6); × 5·8. 2, MGUH 24·544; ×1·7. 3, MGUH 24·542; × 2·0. 4, MGUH 24·539; showing distinct bilobed appearance of posterior exites; × 1·7. 5–6, specimens of Buenaspis in association with the nevadiid Buenellus higginsi Blaker, 1988 (5) and paired (6), a common feature of Sirius Passet fossils. 5, MGUH 24·549. 6, MGUH 24·543. Both × 1·7.

PLATE 1

BUDD, Buenaspis, Buenellus

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4. A – E, Buenaspis forteyi gen. et sp. nov.; holotype, MGUH 24·545. A, details of margin of cephalic shield showing crush marks and traces of doublure; × 17·4. B, pleural articulation structures. Note the antero-laterally developed articulating facets and the fulcral structures, where anterior tergites step back over the articulating facets of the preceeding tergite; x 22·5. C, (uncoated specimen) details of limb exites at posterior of caudal shield; × 17·4. D, occiptal region showing posterior margin of head shield and the underlying ahr. In this case, the head shield seems to overlap both the ahr and part of first tergite proper (cf. comments in Fortey and Theron (1994) on a similar arrangement in Soomaspis); × 15·5. E, articulating facets of final thoracic segment and caudal shield; × 11·6.

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TEXT-FIG.

5. Camera lucida drawing of occipital region of holotype (MGUH 24·545), showing interpretation of occipital extension of head shield passing back over the first thoracic tergite: see Plate 1, figure 1; Text-figure 6D. Scale bar represents 4 mm.

TEXT-FIG.

6. Camera lucida drawing of holotype (MGUH 24·545), showing details of the articulation structures on the left side of the specimen. Reference to the ‘anterior’ of a tergite excludes its own ahr. At point A, the posterior of a segment may be seen to overlap slightly the anterior of the segment proceding it; it is assumed that in life the two would normally have coincided. Scale bar represents 4 mm.

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TABLE 1. Length of articulating

half-rings (ahr’s) and corresponding angle of rotation in enroled state in the holotype of Buenaspis (see Appendix 1 for details of analysis). The length of the occipital ahr includes the extra overlap of the cephalic shield onto the first thoracic segment; the ahr itself is 0·5 mm long.

Cephalic shield/1st thoracic tergite 1st tergite/2nd tergite 2nd tergite/3rd tergite 3rd tergite/4th tergite 4th tergite/5th tergitre 5th tergite/6th tergite 6th tergite/caudal shield

AHR LENGTH (mm)

ANGLE TURNED AT ARTICULATION (SEE APPENDIX 1)

0·5 (0·9 total) 0·7 0·8 1·0 0·8 0·7 0·7

35⬚ 27·2⬚ 31·1⬚ 38·9⬚ 31·1⬚ 27·2⬚ 27·2⬚

2. Lack of dorsal eyes (Fortey and Theron 1994; Chen et al. 1997). This lack is shared by Buenaspis, but again caution is needed. The presence of dorsal eyes may not necessarily be in the ground-plan of the euarthropods (although their presence in the most immediate sister-group, the anomalocaridids, suggests that it is; Budd 1997), and in any case several other taxa such as Burgessia Walcott, 1912 (Hughes 1975) and Emeraldella Walcott, 1912 (Bruton and Whittington 1983) also appear to lack dorsal eyes: more critically, in this case, so may Saperion Hou, Ramsko¨ld and Bergstro¨m, 1991 and Helmetia Walcott, 1918, taxa for which there is a prima facie case for consideration in any general study of trilobites and their suspected relatives. Lack of eyes may in actuality be a synapomorphy uniting the nektaspids, but careful analysis of potential outgroups would be needed to prove this. 3. Pygidium longer than head shield (Fortey and Theron 1994; Chen et al. 1997). Whilst it is true that in most previously described nektaspids (but not Buenaspis) the pygidium is longer than the head shield, it is hard to assess the phylogenetic signficance of this feature. In the case of Naraoiidae, this character is certainly valid. However, although in Liwiidae there may be genuine variation in the size of the pygidium, in adults the length of the pygidium is also partly dependent on the degree of segment release from the transitory pygidium during ontogeny. Thus, although all the naraoiids have similar length ratios between the cephalic and caudal shields, the ratio in the liwiids in general decreases in relation to the number of tergites released, so that in Tariccoia (three released) it is approximately 1:2, in Soomaspis (four) it is 1:1·2 and in Liwia (four) and Buenaspis (six) it is approximately 1:1; in the latter two the caudal shield is actually slightly smaller than the cephalic shield. Although the adult pygidial length is to a degree quantized as a result (only integer numbers of segments can be released), whether the pygidial remnant is longer or shorter than the cephalic shield is at least partly contingent upon the degree of segment release. For the character to be compared meaningfully with that in the naraoiids, one might look at the caudal shield length in the degree 0 meraspid (i.e. the stage in ontogeny when the first articulation appears). However, this stage is not known for any liwiid. It should be further noted that degree 0 trilobites may possess a transitory pygidium longer than the cephalon, such as Ceraurinella Cooper, 1953 where the transitory pyigidium takes up 63 per cent. of the total length at this stage (Whittington and Evitt 1953), although this is certainly a derived condition within the cheirurids.

Intra-nektaspid relationships Buenaspis shares with all Liwiidae (as defined above) the presence of few thoracic tergites, and with Tariccoia and Soomaspis the presence of a keel, although this character is, as discussed above, likely to be artefactual (nevertheless, its presence in these taxa may indicate a particularly domed exosketelon, which could be taken as a synapomorphy). However, the monophyly of Liwiidae is not established by these poor characters, for it is difficult to know how to root the group (see Fortey and Theron 1994; Chen et al. 1997). If, for example, a trilobite such as a redlichiid, bearing tergites with articulating devices between them, is

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used as an out-group, then Buenaspis and the Ordovician forms appear to be basal. Conversely, if some other potential arachnate such as Emeraldella (Bruton and Whittington 1983) is used, then Buenaspis and the Ordovician forms appear to be more derived. In the former case, the Naroiidae would have evolved from a tergite-bearing form, and thus Liwiidae is likely to be paraphyletic. If, however, the naraoiids are the more basal forms, they too could represent a paraphyletic grade. As indicated by other studies (Fortey and Theron 1994; Chen et al. 1997), this issue remains at present unresolved, although the balance of evidence must support the monophyly of Naraoiidae over that of Liwiidae. Nektaspid evolution and heterochrony As pointed out by Fortey and Theron (1994) in their discussion of Soomaspis, the outlines of taxa like Naraoia would often conform very closely to that of Naraoia itself if the caudal shield and the thoracic segments were to be treated as a single unit, and this is certainly true for Buenaspis. They suggested that this characteristic came about through heterochronic variation in the degree of segment release from the transitory pygidium in ontogeny. In this model, early-maturing nektaspids would possess few or no free thoracic segments, but large caudal shields, and late-maturing forms would possess more free segments, but smaller caudal shields. Such a suppression of segment release would presumably have needed to have been effected by either terminal progenesis or neoteny (for discussion, see McNamara 1983; McKinney and McNamara 1991). In the case of progenesis, a normal sequence of moults and segment release is abruptly interrupted by the attainment of a precocious adult form, in which case the large caudal shield of the nektaspids would correspond to the ‘transitory pygidium’ observed in trilobites during the meraspid period of ontogeny. In the second case, neoteny, which is considered to be probable by Fortey and Theron (1994) although they refer to the process as hypermorphosis (a peramorphic, not a paedomorphic process; see McNamara 1986), growth rate is slowed, so that relative to the ancestor the descendent is paedomorphic. (The issue here though is complicated. Soomaspis seems to have both slowed its growth rate and delayed maturation, so in size it is a peramorph, but in terms of overall development it is a paedomorph. As Fortey and Theron (1994) stressed the paedomorphic aspects of Soomaspis, it seems correct to discuss its morphology in terms of neoteny rather than hypermorphosis). An implicit claim in Fortey and Theron’s model is that the total number of segments in the adult naraoiids under question is a constant, with only their distribution between thorax and pygidium being affected by heterochrony. There is, however, no particular reason to think that this is true, and the number of segments released into the thorax may not be a reliable guide to heterochronic processes (Hughes and Chapman (1995), in a study of the proetide Aulacopleura konincki (Barrande, 1846) went further and suggested that the ontogenetic dynamics of trilobites may have been decoupled even from the traditional staging of growth based on segment release). Although a ‘giant protaspid’ from the Chengjiang fauna has been described and attributed to Naraoia, too little is known about the ontogeny to be able to ascertain the sequence of segment addition, which in other trilobites is known to be highly variable, with some trilobites apparently having released their full complement of thoracic segments from the transitory pygidium all at once, whereas others both released segments to the thorax more or less sequentially whilst at the same time adding segments to the transitory pygidium. Whilst a neotenic origin for the nektaspids is therefore perfectly possible, too little is known about their ontogeny for this model to be tested adequately: one would really like to know something of the growth dynamics of the ontogeny of nektaspids that possess thoracic segments, i.e. the liwiids. FUNCTIONAL MORPHOLOGY

Buenaspis, in common with many Cambrian arthropods, was probably a member of the vagrant benthos, and by analogy with its close relative Naraoia may have been a predator, utilizing a primitive mode of thoracic feeding (Budd in press; cf. remarks in Walossek (1993) on primitive feeding modes in crustaceans, contra Chen et al. 1995: but see also remarks on naraoiid ecology in Chen et al. 1997, where the predatory nature of all the naraoiids is questioned). Despite the general lack of soft parts, the holotype especially preserves subtle details of the exoskeleton which allow some reconstruction to be

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made of its flexibility. In particular, Buenaspis shows several modifications of the exoskeleton which seem to be related to enrolment. 1. Broad articulating half-rings (ahr’s): the ‘crescentic extensions’ described above. 2. The antero-laterally developed borders to the trunk tergites and caudal shield. Given their position, they are here interpreted as articulating facets, having allowed the extremities of the tergites to pass over each other smoothly during enrolment. 3. Flanges connecting the articulating facets and the axial half-rings, running along the boundaries between adjacent tergites. Their presence implies that a degree of separation could have taken place between the tergites during flexure of the exoskeleton. They are only poorly differentiated from the halfrings themselves, which has certain implications for the three-dimensional structure of the exoskeleton (see below). 4. Possible fulcral structures. Although there is no part of the flange-like structures and ahr’s that is strictly horizontal and transverse, and which could thus act as a hinge, the distinct backward step of each tergite on to the one preceding it may have acted as a fulcral structure; the structure is in a similar position to undoubted fulcral structures in trilobites (e.g. fig. 7 of Bergstro¨m 1973). By reference to similar structures in trilobites (Harrington 1959; Bergstro¨m 1973; Whittington 1996), all of these structures may be interpreted as articulation devices. Articulating half-rings have also been reported from the liwiid Soomaspis (Fortey and Theron 1994), but without comment on the flexibility that they would have allowed the animal; in addition, the animal, possessed articulating facets (R. A. Fortey, pers. comm.). In Buenaspis, the facets, flanges and half-rings run more or less smoothly into each other, suggesting that in this animal and others they all have a common origin, perhaps as a simple half-ring articulating non-trilobed segments (such as those possessed by enroling isopods). In the axial region there is a considerable degree of overlap between the half-rings and the overlying tergite. Unless the animal was enormously domed, such a degree of overlap would allow complete enrolment, and the presence of what may be reasonably interpreted as articulating facets on the caudal shield and thoracic segments supports this interpretation. As well as this common-sense interpretation, this hypothesis may be tested more formally (see below). As Whittington (1996) rightly stressed, an enrolment capacity entails not only articulation devices proper, but the adaptation of the entire exoskeleton to the purpose. The remarkable consequences of this adaptation can be demonstrated by considering how far the three-dimensional morphology of the exoskeleton is determined by the functional requirements of enrolment. Enrolment and convexity in Buenaspis and trilobites Being a sub-isopygous form with few thoracic segments, Buenaspis is likely – if it enroled – to have employed a more or less sphaeroidal form of enrolment as seen, for example, in the rather similar asaphine trilobites, such as Asaphus and the phacopines (e.g. Bergstro¨m 1973; Chatterton and Campbell 1993; Bruton and Haas 1997). In such forms, the thoracic segments subtend an arc through about 180⬚, with the tips of the two shields resting against each other. Whittington (1996) noted several features characteristic of trilobites that were able to enrol sphaeroidally, including the presence of broader and more angled articulation facets on the more anterior segments, which reflects their greater angle of rotation around the genal angle of the cephalon compared with more posterior segments, which lie more flatly along its lateral margin. Such a feature is not present in Buenaspis apart from on the most anterior thoracic segment (the structure is not well preserved in the holotype) where most of the articulation along the cephalic shield was taken up by the similarly sized caudal shield rather than the thoracic segments themselves. In the holotype the ahr’s are not quite equal in length (lg.), but vary in their sagittal length between 0·5 mm and 1·0 mm (Table 1), with the longest articulation being opposite the cephalon/pygidium boundary when the animal was enroled. Given the assumption that the animal had a more or less level thoracic height (in common with many isopygous trilobites), the necessity of the segments to pivot around the fulcral points during enrolment implies that the differing sagittal lengths of the ahr’s are straightforwardly proportional to the angle of rotation at each fulcral point (see Appendix 2). Trilobites in general require ahr’s because during flexure they rotate around fulcral points (or hinges, if the pleurae are

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7. Reconstruction of the enroled Buenaspis sectioned through the fulcral plane. It should be noted that the cephalic and caudal shields did not necessarily possess surfaces that lay in this plane in life.

horizontal and transverse) located on the pleurae (see analysis in Bruton and Haas 1997). When the animal is (sphaeroidally) enroled therefore, the sagittal line lies along the arc of a larger circle than that formed by drawing an arc through the pleural hinge points, so, without ahr’s, the segments would separate along the dorsum. This point may be explicitly tested by an analysis of an enrolment ‘paradigm’ (sensu Rudwick 1964) set up for Buenaspis, based partly but not fully on its known morphology: the fit of the rest of the known morphology to the enrolment paradigm may then be assessed (see Appendix 1 for details). In this case, calculating from the known cephalic and caudal lengths (measured in the fulcral plane), and assuming that the ahr’s are fully utilized in enrolment delivers a thoracic segment length of 1·2 mm, compared to the measured value of 1·28 mm – a good agreement. This analysis thus suggests that the exoskeleton of Buenaspis was indeed well-adapted to enrolment, and that from the paradigmatic model, the angles of rotation at each articulation may be calculated (Table 1), with the proviso that this assumes that the six thoracic tergites were of approximately equal height – a reasonable assumption given the large size of the caudal shield and the otherwise identical appearance of all six tergites including their width (tr. and lg.). The animal, as sectioned through the fulcral plane, may thus be reconstructed (Text-fig. 7). However, a great deal more information is available by considering other requirements of enrolment including the reconstruction of dorsal convexity.

Reconstruction of convexity Soft-part preservation of arthropods is most common in shales, where the animals are unfortunately often found in a highly flattened state. Part of the challenge of reconstructing such animals, therefore, is trying to replace the missing third dimension. In some cases, such as when a variety of different preservational orientations are known, the animal can be reconstructed with a fair degree of confidence (see e.g. Whittington 1971; Briggs and Williams 1981). However, in faunas such as the Sirius Passet fauna, where almost all of the fossils are preserved parallel to the bedding plane, the task is made much harder: in such cases study of functional morphology may assist in the reconstruction. In the case of Buenaspis, knowledge of the shape of the ahr’s in dorso-ventral projection allows the reconstruction of the dorsal convexity of the animal, although some caution is required. The requirement for space-filling ahr’s discussed above naturally applies not just to the dorsum, but to every point along an articulation that lies adaxial to the fulcral point. Further, there is a precise relationship between the angle turned through during enrolment, and the amount of ‘extra tergite’ required for each height above the fulcral point (Text-fig. 8). In many trilobites, the three-dimensional shape of the exoskeleton is known. However, in specimens found flattened in shale, which are rarely enroled, for whatever reason (Bergstro¨m 1973, p. 17; Chatterton and Campbell 1993), knowledge of the shape of the ahr’s can be used to reconstruct

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the dorsal convexity, if it is assumed that there is no ‘excess capacity’ in the ahr’s, in other words that they are minimally covered by the tergites when the animal is at maximum flexure, i.e. when enroled. Unfortunately, as noted by Bergstro¨m (1973), study of the ahr’s has been relatively neglected. Some authors, such as Stitt (1983) have commented on the different angles turned at each articulation, but without relating this to possible differences in ahr morphology along the trunk axis, nor to trunk convexity. In advanced trilobites, such as the phacopines, the ahr’s may be specialized into two fields, only one of which is exposed during enrolment (Bruton and Haas 1997), but in other forms, such as the Early Cambrian Crassifimbra walcotti (Resser, 1937) which also exhibits sphaeroidal enrolment and of which the articulation is known in considerable detail (Palmer 1958), the ahr’s are much simpler. Whilst a small portion of the ahr’s may have remained covered during the enrolment of Buenaspis, there is no evidence for their division into distinct fields. There are two ways of calculating the dorsal convexity, one by totalling the sagittal length of the ahr’s and assuming an approximation to a sphere, and the other by calculating the angle turned through by any particular articulation: however these two methods are equivalent and give the same result (see Appendix 2 for analysis). The maximum dorsal height above the fulcral points may thus be calculated to be 1·47 mm. Assuming that the tips of the pleurae close to form an enclosed box during enrolment (which may or may not be correct, and cannot be correct unless the pleurae are free and angled downwards abaxial to the

TEXT-FIG.

8. Fulcral point rotation in Buenaspis and trilobites. The length of exposed articulating half-ring (l) is proportional both to its height (in the plane of rotation) above the fulcral point and to the angle of rotation (v). When enroled, the angle of rotation is fixed for each articulation, and thus l is directionally proportional to v. See Appendix 2 for further details.

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TEXT-FIG.

TEXT-FIG.

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9. Reconstruction of the enrolled Buenaspis with dorsal height restored.

10. A, digitized and smoothed outline of the articulating half-ring between tergites four and five. B, reconstruction of the cross section of Buenaspis. C, posterior view of enroled Buenaspis showing elevation of rachis.

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fulcral points (cf. Whittington 1996)) this gives a total height of the exoskeleton of c. 4·3 mm, most of which is taken up by the downwardly-flexed pleural regions adaxial to the fulcral points (Text-fig. 9). This analysis may be extended to every point along an articulation, not just along the sagittal line. This allows the conversion of the shape of the ahr’s into a corresponding cross section of the animal. To investigate this, the outline of the third ahr was digitized and converted into a series of x-y co-ordinates. The resulting set of data and the corresponding graph were then treated in the same way as the sagittal line above, and the results replotted to give a profile of the animal (Text-fig. 10). As may be seen, the animal had a moderately flattened rachial region, with more or less uniformly sloping pleural regions down to the presumed fulcral points. The shape of the exoskeleton abaxial to the fulcral points is less clear, as beyond these points there is no obligation for successive segments to remain in contact during enrolment, whilst the exoskeleton can still vary in three dimensions. Nevertheless, some constraints may be placed on the overall shape. First, the extremities of the tergites show a considerable preservational variation, suggesting that they are highly angled to the plane of flattening. In the holotype, for example, the anterior extremities are small and show crush marks, whereas the posterior ones are large and smooth, a distinction not seen in all specimens. One explanation for this variety is that the extremities are angled, and during flattening may either be crushed or rotated into the plane of preservation (Text-fig. 11A). In theory, this difference could be used for reconstructing the original angle of the extremities (Text-fig. 11B), but it is rather unreliable as both known extremes are probably a mixture of both compaction and rotation. Nevertheless, some constraints can be placed on the disposition of the distal extremities of the pleurae.

TEXT-FIG.

11. A – B, flattening taphonomy of Buenaspis to explain variability in appearance of pleurae in, for example, the holotype: the pleurae in dorso-ventrally crushed specimens will have a shorter preserved length than those in slightly angled specimens, where the pleurae may rotate into the plane of preservation rather than be flattened into it. C, theoretical reconstruction of pleural disposition in life. On the (questionable) assumption that the pleurae adaxial to the fulcral points were planar structures, the angle of downward deflection may be calculated from the variation in their preserved length.

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First, as the enrolment appears to be more or less sphaeroidal (based on the evidence of the size distribution of the ahr’s), the pleural extremities must project a minimum length in the plane of enrolment for them to form a closed box during enrolment (trilobites that simply folded flat during enrolment, such as Cryptolithus, may not have formed a closed box at all, but rather a cylinder (Bergstro¨m 1973)). Second, the presence of a narrow flange between the segments abaxial to the fulcral points suggests that the segments remained more-or-less in contact during enrolment in this position, so that the parts of the pleurae closest to the fulcral points were more-or-less horizontal. Third, the distribution of crush marks suggests that only the tips of the pleurae were very strongly angled. When allied with the requirement of pleural closure during enrolment, a reasonably accurate reconstruction of the pleurae can be made. Once a reconstruction of the enroled animal has been made, it can be ‘unrolled’ to produce the normal life position (Text-figs 12–13). It is clear that if the ventral surfaces of the two shields were parallel to the sea-floor, the ahr’s at the back of the cephalic shield and at the front of the caudal shield would, all things being equal, be permanently exposed. The occipital extension of the cephalic shield over the back of the first segment (a similar state to that in other liwiids and some trilobites), however, suggests that the halfring here was covered, both when the animal was and was not enroled. However, no such extension (from the last trunk tergite) is known, and the final ahr was therefore probably permanently exposed except for when the animal arched its back (Text-fig. 12A). The fact that in preserved specimens the last ahr appears

TEXT-FIG. 12. Reconstructions

of Buenaspis forteyi gen. et sp. nov. A, the presumed normal life position, demonstrating occipital cephalic extension to cover the 1st ahr. B, reconstruction of probable normal preservation of Buenaspis, showing how the two shields rotated to bring their long axes into the plane of flattening.

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13. Dorsal view of Buenaspis forteyi gen. et sp. nov. in life position (i.e. dorsal view of Text-fig. 12A).

not to be exposed may be explained by the early taphonomic history of the animal: death and burial would lead to compressional forces acting upon the exoskeleton, tending to force the long axes of the two shields to rotate to lie in the plane of flattening (Text-fig. 12B). This point should be applicable to all trilobites with subequally sized ahr’s: when the ventral surface of the cephalon and pygidium were parallel, as they were when the animal was enroled and when it was completely straightened out, both cephalic and pygidial ahr’s must have been at least partially exposed, unless the occipital ahr was concealed by an occipital extension of the cephalon. Such a degree of flexibility was advantageous, however, as when the animal straightened out, it was still possible for it to move the head and tail upwards: such flexure might have been useful in, for example, moulting the exoskeleton or righting the animal if it came to lie on its back. CONCLUSIONS

Buenaspis forteyi is a new nektaspid-like arthropod from the Early Cambrian exceptionally preserved Sirius Passet fauna, with well-preserved articulation devices. Consideration of these structures allows a well-constrained three-dimensional model of the animal to be reconstructed, which is of particular importance in an animal preserved two-dimensionally in shales. Analysis of the articulation structures provides insights both into what the animal looked like when enroled, and also into other aspects of its functional morphology: for example, suggesting that even when not enroled there was considerable upwards flexibility of the head, and that both the first and last articulating half-rings would have been permanently exposed, were it not for the presence of an occipital extension of the cephalic shield. These considerations are equally valid for trilobites with large shields and subequally sized ahr’s. The techniques used to reconstruct Buenaspis are in principle also applicable to trilobites found only in shales, although careful adaptation to the animal in question would be required. This work suggests that careful study of articulating half-rings in trilobites would yield interesting insights into their morphology and mode of life which, especially for those taxa known only from shales, may have hitherto eluded description.

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Acknowledgements. I thank J. S. Peel for reading a previous draft of the manuscript, R.A. Fortey for discussion, and N. C. Hughes in particular for a constructive review. This work was funded by the Swedish Research council (NFR), and specimen collection by the Geological Survey of Greenland (GGU), the Carlsberg Foundation and National Geographic, all of whom are thanked. This is a contribution to IGCP Project 366 (Cambrian ecology). REFERENCES ¨ M, J. BERGSTRO BLAKER, M. R.

1973. Organization, life, and systematics of trilobites. Fossils and Strata, 2, 1–69, pls 1–5. 1988. A new genus of nevadiid trilobite from the Buen Formation (Early Cambrian) of Peary Land, central North Greenland. Rapport Grønlands geologiske Undersøgelse, 137, 33–41. —— and PEEL, J. S. 1997. Lower Cambrian trilobites from North Greenland. Meddelelser om Grønland, Geoscience, 35, 1–145. BRIGGS, D. E. G. and WILLIAMS, S. H. 1981. The restoration of flattened fossils. Lethaia, 14, 157–164. BRUTON, D. L. and HAAS, W. 1997. Functional morphology of the Phacopinae (Trilobita) and the mechanics of enrolment. Palaeontographica, Abteilung B, 245, 1–43, pls 1–14. —— and WHITTINGTON, H. B. 1983. Emeraldella and Leanchoilia, two arthropods from the Burgess Shale, British Columbia. Philosophical Transactions of the Royal Society of London, Series B, 300, 553–585. BUDD, G. 1993. A Cambrian gilled lobopod from Greenland. Nature, 364, 709–711. BUDD, G. E. 1995. Kleptothule rasmusseni gen et sp. nov.: an ?olenellinid-like trilobite from the Sirius Passet fauna (Buen Formation, Lower Cambrian, North Greenland). Transactions of the Royal Society of Edinburgh: Earth Sciences, 86, 1–12. —— 1997. Stem-group arthropods from the Lower Cambrian Sirius Passet fauna of North Greenland. 125–138. In FORTEY, R. A. and THOMAS, R. H. (eds). Arthropod relationships. Chapman and Hall, London, 383 pp. —— and PEEL, J. S. 1998. A Xenusion-like lobopod from the Lower Cambrian Sirius Passet fauna. Palaeontology, 41, 1201–1213. BUTTERFIELD, N. J. 1995. Secular distribution of Burgess-Shale-type preservation. Lethaia, 28, 1–14. CHATTERTON, B. D. E. and CAMPBELL, M. 1993. Enrolling in trilobites: a review and some new characters. Memoir of the Association of Australasian Palaeontologists, 15, 103–123. ¨ LD, L. and ZHOU, G.-Q. 1995. Head segmentation in Early Cambrian Fuxianhuia: CHEN, J.-Y., EDGECOMBE, G. D., RAMSKO implications for arthropod evolution. Science, 268, 1339–1343. —— —— —— 1997. Morphological and ecological disparity in naraoiids (Arthropoda) from the Early Cambrian Chengjiang fauna, China. Records of the Australian Museum, 49, 1–24. CONWAY MORRIS, S. 1989. The persistence of Burgess Shale-type faunas: implications for the evolution of deeper-water faunas. Transactions of the Royal Society of Edinburgh: Earth Sciences, 80, 271–283. —— and PEEL, J. S. 1990. Articulated halkieriids from the Lower Cambrian of North Greenland. Nature, 345, 802–804. —— ——1995. Articulated halkieriids from the Lower Cambrian of North Greenland and their role in early protostome evolution. Philosophical Transactions of the Royal Society of London, Series B, 347, 305–358. —— —— HIGGINS, A. K., SOPER, N. J. and DAVIS, N. C. 1987. A Burgess Shale-like fauna from the Lower Cambrian of Greenland. Nature, 326, 181–183. COOPER, B. N. 1953. Trilobites from the Lower Champlainian formations of the Appalachian Valley. Memoirs of the Geological Society of America, 55, 1–69, pls 1–19. DZIK, J. and LENDZION, K. 1988. The oldest arthropods of the East European Platform. Lethaia, 21, 29–38. FORTEY, R. A. and THERON, J. N. 1994. A new Ordovician arthropod, Soomaspis, and the agnostid problem. Palaeontology, 37, 841–861. HAMMANN, W., LASKE, R. and PILLOLA, G. L. 1990. Tariccoia arusensis n.g. n.sp., an unusual trilobite-like arthropod. Rediscovery of the ‘phyllocarid’ beds of Taricco (1922) in the Ordovician ‘Puddinga’ sequence of Sardinia. Bollettino della Societa` Paleontologica Italiana, 29, 163–178. HARRINGTON, H. J. 1959. General description of Trilobita. O38-O117. In MOORE, R. A. (ed.). Treatise on invertebrate paleontology. Part O. Arthropoda 1. University of Kansas Press, Lawrence, Kansas, 560 pp. HOU, X.-G. 1987. Three new large arthropods from Lower Cambrian, Chengjiang, eastern Yunnan. Acta Palaeontologica Sinica, 26, 272–285. [In Chinese, with English abstract] —— and BERGSTRO¨M, J. 1991. 179-187. In SIMONETTA, A. M. and CONWAY MORRIS, S. (eds). The early evolution of Metazoa and the significance of problematic taxa. Cambridge University Press, Cambridge, ix þ 296 pp. —— —— 1997. Arthropods of the Lower Cambrian Chengjiang fauna, southwest China. Fossils and Strata, 45, 1–116. —— RAMSKO¨LD, L. and BERGSTRO¨M, J. 1991. Composition and preservation of the Chengjiang fauna – a Lower Cambrian soft-bodied biota. Zoologica Scripta, 20, 395–411. HUGHES, C. P. 1975. Redescription of Burgessia bella from the Middle Cambrian Burgess Shale, British Columbia. Fossil and Strata, 4, 415–435, pls 1–13.

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and CHAPMAN, R. E. 1995. Growth and variation in the Silurian proetide trilobite Aulacopleura konincki and its implications for trilobite palaeobiology. Lethaia, 28, 333–353. INESON, J. R. and PEEL, J. S. 1997. Cambrian shelf stratigraphy of North Greenland. Bulletin of the Geology of Greenland Survey, 173, 1–120. JELL, P. A. and HUGHES, N. C. 1997. Himalayan Cambrian trilobites. Special Papers in Palaeontology, 58, 1–113. McKINNEY, M. L. and McNAMARA, K. J. 1991. Heterochrony: the evolution of ontogeny. Plenum Press, New York, 437 pp. McNAMARA, K. J. 1983. Progenesis in trilobites. Special Papers in Palaeontology, 30, 59–68. —— 1986. A guide to the nomenclature of heterochrony. Journal of Paleontology, 60, 4–13. PALMER, A. R. 1958. Morphology and ontogeny of a Lower Cambrian ptychoparioid trilobite from Nevada. Journal of Paleontology, 32, 154-170, pls 25–26. —— and REPINA, L. N. 1993. Through a glass darkly: taxonomy, phylogeny, and biostratigraphy of the Olenellina. Paleontological Contributions from the University of Kansas, New Series, 3, 1–35. PEEL, J. S. (ed.) 1988. Cambrian–Jurassic trace fossils and stratigraphy from Greenland. Rapport Grønlands geologiske Undersøgelse, 137, 1–159. ¨ LD, L., CHEN, J.-Y., EDGECOMBE, G. D. and ZHOU, G.-Q. 1996. Preservational folds simulating tergite junctions in RAMSKO tegopeltid and naraoiid arthropods. Lethaia, 29, 15–20. RAYMOND, P. E. 1920. The appendages, anatomy and relationships of trilobites. Memoirs of the Connecticut Academy of Arts and Sciences, 7, 1–169, pls 1–11. REPINA, L. N. and OKUNEVA. O. P. 1969. Cambrian arthropods of the Maritime Territory. Palaeontologischeskii Zhurnal, 1969(1), 95–103. RESSER, C. E. 1937. Third contribution to nomenclature of Cambrian trilobites. Smithsonian Miscellaneous Collections, 95, 1–29. RIGBY, K. J. 1986. Cambrian and Silurian sponges from North Greenland. Rapport Grønlands geologiske Undersøgelse, 132, 51–63. ROBISON, R. A. 1984. New occurrences of the unusual trilobite Naraoia from the Cambrian of Idaho and Utah. Palaeontological Contributions from the University of Kansas, 112, 1–8. RUDWICK, M. J. S. 1964. The inference of structure from function in fossils. British Journal of the Philosophy of Science, 15, 27–40. SIEBOLD, C. T. W. VON and STANNIUS, H. 1848. Lehrbuch der vergliechenden Anatomie der Wirbellosen Tiere, Teil 2. Veit, Berlin, xii þ 482 pp. STITT, J. H. 1983. Enrolled late Cambrian trilobites from the Davis Formation, southeast Missouri. Journal of Paleontology, 57, 93–105. WALCOTT, C. D. 1912. Middle Cambrian Branchiopoda, Malacostraca, Trilobita and Merostomata. Cambrian Geology and Paleontology, II. Smithsonian Miscellaneous Collections, 57, 145–228. —— 1918. Geological explorations in the Cambrian Rockies. Smithsonian Miscellaneous Collections, 68, 4–20. WALOSSEK, D. 1993. The Upper Cambrian Rehbachiella and the phylogeny of Branchiopoda and Crustacea. Fossils and Strata, 32, 1–202. WHITTINGTON, H. B. 1971. Redescription of Marrella splendens (Trilobitoidea) from the Burgess Shale, Middle Cambrian, British Columbia. Bulletin of the Geological Survey of Canada, 209, 1–24. —— 1977. The Middle Cambrian trilobite Naraoia, Burgess Shale, British Columbia. Philosophical Transactions of the Royal Society of London, Series B, 280, 409–443. —— 1996. Sphaeroidal enrolment and thoracic characters in Beltella depressa and other olenid trilobites. Palaeontology, 39, 377–388. —— and EVITT, W. R. 1953. Silicified Middle Ordovician trilobites. Memoir of the Geological Society of America, 59, 1–137, pls 1–33. ZHANG, W.-T. and HOU, X.-G. 1985. Preliminary notes on the occurrence of the unusual trilobite Naraoia in Asia. Acta Palaeontologica Sinica, 24, 591–595. GRAHAM E. BUDD

Typescript received 18 October 1997 Revised typescript received 15 June 1998

Department of Earth Sciences Historical Geology & Palaeontology Uppsala University Norbyva¨gen 22 Uppsala S-752 36 Sweden e-mail [email protected]

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APPENDIX 1

Geometrical analysis of enrolment in Buenaspis: analysis of angle of rotation at each articulating half-ring The animal can be considered, when enroled, as an irregular octagon, with sides made by the six thoracic segments sectioned through the fulcral points, and the projection of the two shields into the plane of the fulcral points (Text-fig. 14): all these lengths may be directly measured on the fossil: lengths w, y, z and a are construction lines.

TEXT-FIG.

14. Geometrical analysis of enrolment in Buenaspis forteyi gen. et sp. nov. For details, see text.

Given that the segmental lengths are equal, DABF, GAC, DBH are all isoceles triangles, and thus the angles opposite the apex (h, f, etc.) are equal in each triangle. To solve for the angles of rotation, let the (unknown) angle of rotation at each articulation be proportional to the length of the appropriate ahr: then, the angles are distributed as follows. As the sum of external angles of a closed polygon are equal to 360⬚, 7 8 10 8 7 7 b þ b þ b þ b þ b þ b þ b þ a ¼ 360⬚ 9 9 9 9 9 9 56 ⇒ b þ a ¼ 360⬚ 9 As ⬔g ¼∠d, w ¼ y

½1ÿ

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As the sum of internal angles of a triangle is equal to 180⬚

Similarly, ⬔l ¼

1 10 5 ⬔h ¼ ð bÞ ¼ b 2 9 9

7 b 18

7 8 5 b¹ b¹ b 18 9 9 7 8 5 Similarly, ⬔k ¼ 180 ¹ b ¹ b ¹ b ¼ ⬔e 18 9 9

And thus ⬔e ¼ 180 ¹

As w ¼ y and ⬔e ¼ ⬔k, the quadrilateral ABCD is therefore a parallelogram, so that z jja. But if so, then ⬔m ¼ ⬔v Then, considering the angles at C and D: 7 b ¹ v ¼ ⬔v 18 18 7 ⬔v ¼ 180 ¹ b ¹ b ¹ r 9 9 7 7 7 ⬖180 ¹ b ¹ b ¹ v ¼ 180 ¹ b ¹ b ¹ r; 18 18 9 4 ⇒v ¼r¹ b 18

⬔m ¼ 180 ¹ b ¹

½2ÿ

But as S of internal angles of triangle ¼ 180⬚ v þ r þ ð180 ¹ aÞ ¼ 180; i:e: v þ r ¼ a 56 b ðfrom ½1ÿÞ 9 4 56 ⬖2r ¹ b ¼ 360 ¹ b 10 9 58 ⇒ r ¼ 180 ¹ b 18

a ¼ 360 ¹

½3ÿ

and v ¼ 180 ¹

62 b 18

ðfrom ½2ÿÞ

½4ÿ

DCDE of Text-figure 14 may now be fully resolved, as two sides are known, and all angles known in terms of each other. From the Law of Sines,       58 62 112 b ¹ 180 sin 180 ¹ b sin 180 ¹ b sin 18 18 18 ¼ ¼ b c a From standard trigonometric identities,  sinð180Þ cos ⇒

         58 58 62 62 b ¹ cosð180Þ sin b b ¹ cosð180Þ sin b sinð180Þ cos 18 18 18 18 ¼ b c

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i.e.

    58 62 b b sin sin 18 18 ¼ b c   62 b sin c 18  ⇒ ¼  58 b sin b 18

121

½5ÿ

But from measurement, c ¼ 5·96; b ¼ 6·38 Eqn |5] may be solved by graphical means to give b ¼ 35·0⬚, and from [1], a ¼ 142·3⬚ It should be noted that the angles of rotation have been found without reference to the thoracic segment length, which must therefore be determined by the system. Its value (in this system, with the given shield lengths) may be found as follows. First , the various angles in Text-figure 14 may be calculated from the equations (see values given in Table 1): these values have been substituted appropriately below. From [3], [4] and [5], 2x2 cosð141:1Þ ¼ 2x2 ¹ w2 ½6ÿ 2x2 cosð152:7Þ ¼ 2x2 ¹ y2

½7ÿ

(both by application of the Law of Cosines) And a ¹ w ¼ 2z ⇒ 4:23 ¹ w ¼ 2z

½8ÿ

z cosð64:7Þ ¼ y

½9ÿ

Also

[6], [7], [8] and [9] are a system of four simultaneous equations with four unknowns which may be solved: w2 ½6ÿ⬅ ⬅ cosð141:1Þ ¼ 1 ¹ 2 2x w ⇒ ¼ 1:886 x Similarly, y ½7ÿ⬅ ¼ 1:943 x substituting y for z in [8] gives 2y cosð64:7Þ ¼ 4:23 ¹ w; substituting x for w gives 2y cosð64:7Þ ¼ 4:23 ¹ 1:886x But from [7], y ¼ 1·943x ⇒ 1:66x ¼ 4:23 ¹ 1:886x ⇒ x ¼ 1:20 mm

½10ÿ

The theoretical segmental length can thus be calculated by knowing the shield lengths as projected into the fulcral plane (i.e. as preserved) and the relative lengths of the ahr’s. The calculated thoracic segmental length is in excellent agreement with the observed length of 1·28 mm, a difference of 6 per cent. The paradigm of the various exoskeletal features being enrolment devices thus receives support from this analysis.

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PALAEONTOLOGY, VOLUME 42

APPENDIX 2 Convexity analysis of Buenaspis The length of an articulating half-ring is proportional to the height above the fulcral point and to the angle turned (Text-fig. 8): v l ¼ 360 2ph   v ⇒ l ¼ ph: 180

½1ÿ

Therefore, the height of the exoskeleton above the fulcral point at any point along an articulation, h, is given by:   1 180 h¼ p v Where v is fixed at each articulation (see Appendix 1 and Table 1 for calculation of its value at various articulations). For the fifth articulation, v ¼ 31·1⬚, so that h ¼ 1:84l ½2ÿ Along the axis, l ¼ 0:8 mm ⇒ h ¼ 1:47 mm This gives the maximum height of the exoskeleton above the fulcral points. From the profile given in Text-figure 10A, the corresponding value h for various points along the ahr may be calculated from [2] and replotted to give a corresponding convexity (Text-fig. 10B).