! '' Biomechanics and. Kenneth V. Kardong :~ ;0,. :~{ ;tf. 1. Introduction. 't. .~;

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1 CH. 4. THE IMPORTANCE OF FUNCTIONAL PLASTICITY ith,].l. and Carlson-Kuhta, P. (1995) Unexpected motor patterns for hindlimb muscles luring slope ";alking in the cat']' Neurophys. 74: ith, J.L., Carlson-Kuhta, P. and Trank, T.Y. (1998) Forms of forward quadrupedal JCornotion. III. A comparison of posture, hindlimb kinematics, and motor patterns for!ownslope and level walking. j. Neurophysiol. 79: ne, D. and Shadwick, R.E. (2000) Mechanical power production by internal red muscle at ifferent longitudinal body positions in skipjack tuna (Katsuwonus pelamis) in relation to wimming. Am. Zool. 40: lor, C.R. (1994) Relating mechanics and energetics during exercise. In: Comparative 'ertebrate Exercise Physiology (ed. ].H. Jones), pp Academic Press, San Diego. 'alske, B.W. (1995) Neuromuscular control and kinematics of intermittent flight in the :uropean starling (Sturnusvulgaris).]. Exp. Biol. 198: 'alske, B.W. and Dial, K.P. (1994) Neuromuscular control and kinematics of intermittent ight in budgerigars';' Exp. BioI. 187: son, A.M., van den Bogart, A.]. and McGuigan, M.P. (2001) Optimisation of the muscle ndon unit for economical locomotion in cursorial animals. In: Skeletal Mechanics: From lechanisms to Function (ed. W. Herzog), pp Wiley and Sons, New York. mer, L.M. (1995) The extant phylogenetic bracket and the importance of reconstructing soft,ssues in fossils. In: Functional Morphology in Vertebrate Paleontology (ed. J.J. Thomason), p Cambridge University Press, Cambridge. ledge, R.C., Curtin, N.A. and Hamsher, E. (1985) Energetic Aspects ofmuscle Contraction.,cademic Press, London. ac, F.E. (1989) Muscle and tendon: properties, models, scaling, and applications to bio lechanics and motor control. Crit. Rev. Biomed. Engng. 17: ! '' Biomechanics and. " evolutionary space: a case study : ;0,. f{ :{ ;tf Kenneth V. Kardong 1. Introduction B 't. Biomechanics includes the physical analysis of the geometry of motion (kinematics) and the relation between forces and performance of a biological design (kinetics). The I;' theoretical implications of biomechanics for animal form and function have been ;1' explored (Dullemeijer, 1974). Certainly, the completed biomechanical analysis of animals has been placed within a given phylogenetic context (Weishampel, 1993). But working the other way around, using biomechanics to inform phylogenetic t..; hypotheses (Homberger; Bout, Chapters 13 and 14), has been less frequently attempted. The shortage of such studies in part reflects the difficulties of providing a I".. sufficient biomechanical characterization of complex animals. Examining integrated parts of an organism, functional units (Liem, 1967) or mechanical units (Cans, 1969), - attempts to make such analysis more manageable. But even simplified, the description (:, : of interacting components can become quickly complex (Dullemeijer, 1959) making it "Ii; difficult to use biomechanical analyses in evolutionary studies (Dullemeijer, 1970). But the shortage of such studies also reflects the fact that biomechanics and evolutionary biology have largely grown up independently of one another, with little attempt to develop a formal methodology of relating one to the other. h It is the purpose of this paper to illustrate a possible way in which biomechanics not only informs evolutionary events but also helps explain (Hempel, 1965) evolutionary patterns. I argue that biomechanics may do so by identifying physical features that w limit the success of designs, resulting in the culling of possible phenotypes, The, pocedure will be to apriori evalute, via biomechanics, the limits to modification of a U. particular design. This leaves a population of biomechanical 'species' that represent the extremes of workable designs. These will then be compared with real species to see how-wellbiqmechanics-pr:edices-bo,u.ndaries olevoluxionary_chang.e. Vertebrate Biomechanics and Evolution, edited by Vincent L. Bels, Jean-Pierre Gasc and Adria Casinos BIOS Scientific Publishers Ltd, Oxford. 73

2 74 CH.5. BIOMECHANICS AND EVOLUTIONARY SPACE: A CASE STUDY K.V. KARDONG n This paper is not intended as an extensive review of biomechanics and evolution. Those interested in historical treatments should consult the papers cited herein, others (Thomas, 1979; Wagner and Schwenk, 2000); and this volume. 2. Conceptual setting 2.1 Mechanical machines-straight line P d' One of the first to emphasize that organisms are internally integrated both of anatomy and function was G. Cuvier. He noted that the change of either form or function, necessarily diminishes the performance of the whole organism, constraining if not outright preventing evolutionary change before it begins. Most such evolutionary constraints have been envisioned as developmental constraints on phenotypic variation (Alberch, 1982; Waddington, 1957). Frazzetta was one of the first to provide an extensive evaluation of the significance of mechanics to the evolution of biological designs (Frazzetta, 1975). He too emphasized that biological adaptations are complex and so their modification (=evolution) cannot proceed without soon incurring disruption of their performance, which is based in turn upon the close functional and anatomical integration of their parts. To illustrate, he used an eight-linkage, straightline machine, a mechanism that when moved about its pin connections describes a straight line at one of its points (point P, Figure 1). In practice, this action was given a function of sharpening straight knife blades by placing a suitable grinding stone at point P. Equally, it could have a function in drafting by adding a pen or pencil to this point and using the mechanism to trace a straight line. However, modifications to the machine are limited without disrupting this straight-line action. For example a change in a must be matched by an equal change in a', otherwise it fails to perform the straight-line action at point P. The geometry of its construction limits the modifications it can sustain before it loses its ability to trace a straight line (Frazzetta, 1975, pp. 4-6). The boundaries of its modification are understandably fixed by the mechanics of its design. Certainly, radical transformations of its linkages can be produced, even adding or subtracting components, giving it the ability to now perhaps describe arcs. But so radically changed, the mechanism is no longer part of the family of straight-line machines. To some extent, this was Frazzetta's interest. To examine internal constraints on evolutionary modifications, independent of phylogenetic methods, and to identify such limitations through the use of a biomechanical analysis. 2.2 Biological machines-viperid model The highly kinematic bony, jaw elements of snakes participate in several major functions: drinking, swallowing, predation, defence (Kardong and Bels, 2001). Relative to the braincase, there are chains of linked moveable elements forming kinematic mechanisms of the jaws of snakes. Unlike lizards, the snake kinematic mechanisms of left and right sides are not joined across the midline, thereby permitting independent unilateral, movement of each side (Gans, 1961). Within these kinematic mechanisms there are two units, a --m1lf!'ci ibu-lar-tinit-aoo---a-pa-l-a-to-maxi-ha-ry-trj'tiri-frnzett<r,-i-%6'j;-'flre-marrdihu-l-arurrir includes the mandible, quadrate, and supratemporal linked to the braincase. The palatomaxillary unit includes the palatine and maxilla, although in viperids the palatine provides no significant biomechanicallink during the strike. Elements include the supratemporal. P'./".: ; / L,,/.. ) " /"' Figure 1. Straighi-line machine. The solid grey linkages are joined at pin connections permitting their respective rotation. As the machine is moved down to the position indicated by faint lines, point P moves to position P' and along the way describes a straight-line. After Frazzetta (/975). Complex Adaptations in Evolving Populations. With permission from Sinauer Associates, Inc. quadrate, posterior' pterygoid, ectopterygoid, maxilla and prefrontal, linked to the skull The evolution of venomous snakes from non-venomous ancestors involved the modifi cation of these linkage systems, primarily based upon accommodating modifications 0 the maxilla, and within viperid snakes, the incorporation of significant rotation of thi fang-bearing bone (Kardong, 1979, 1980). Certainly other systems accompanied th, evolving bony elements (Kardong, 1982). But the linkage system became the centrepiec' of this evolutionary modification from non-venomous ancestors to viperid snakes. The morphology and function of the viperid jaw apparatus have been described il detail elsewhere, so just a general review is given here. This linkage system in viperi( snakes has been modelled kinematically (Kardong, 1974), summarized in Figure 2 Removal of the skin reveals the underlying venom gland emptying, via a long duct, int( the base of the fang positioned on the maxilla (Figure 2B). Deep to venom gland are th, Mm. protractor pterygoideus and levator pterygoidei muscles (Figure 2C) whos' contractions protract the palato-maxillary arch, and thereby erect the fang (Kardong e al., 1986). The bony elements of the skull are shown in Figure 2D. Based upon thi morphology, and an analysis of the strike (Kardong, 1974), a kinematic model (Figure 3 is proposed that represents the minimum elements required to erect the fang (Figure 4) as occurs during predatory strikes. Although the mandible makes contact with the pre: during the strike (Kardong and Bels, 1998), erection of the fang is based, per side, on si: linkages. Therefore we can simplify the model further by eliminating the mandible ----A-I-rlwuglrrome-di-splrc-emenr-of-rh-dirrka-ges-o'Ccurs-in'""th-e-1atera+-d-i-recti-orrfE-undatl-am Greene, 2000; Zamudio et al.; :WOO), this <jisplacement during the strike can be ignore( without m'uch misrepresentation of the basic kinematic pattern (Kardong, 1974). Thi, leaves us with a seven-bar kinematic model, acting in a two-dimensional plane (FzRure 5) a

3 76 CH.5. BIOMECHANICS AND EVOLUTIONARY SPACE: A CASE STUDY ';/' ;;;;5:;e};,}lll'-lC /:...".1 ( J '\ (.,-.., (.',,/!".)-...,./).t7 -;.,r'j'--' ]... --r. I'..', {",",.L. ' r" y ;... (, \...-.> " 1''"7 '. (' \, \.l.t :c " -'-r- )... -'''(. I i; (. '.r'('- '. _.. / --;...II '\)», :\:L: ::!;= :,; ;.;;::!J;{;:ri /' (Al '<' -"r-"- ( )., K.V. MRDONG quadrate supratemporal V Cl IB) mandible. Figure 3. Biomechanical model ofviperid Jaw apparatus. Based on Figure 2. Strike Kinematics IC) (D) f. / ====> \\ )!. 7' I.. \\j Figure 2. Skins to bones in the head ofa vipend snake, Agkistrodon piscivorus. Successive removal oflayers oftissue from the head ofthis viperid snake (A-D) reveal underlymg positions of venom gland, muscles, and eventually bones ofthe skull. Key to abbreviations: accessory venom gland (ace), braincase (be), ectopterygoid (ec),jang (f), mandible (ma), maxilla (mx), prefrontal (pf), protractor pterygoideus muscle (pp), pterygoid (pt), quadrate (q), supratemporal (st), venom duct (vd), venom gland (vg) :::::::-=.:::' Figure 4. Kinematic displacements ofthe Jaw elements during the strike. Positions ofkinemat elements before (left) and after (right) erection ofthe fang bearing maxilla. The calculations me. to evaluate these displacements are done by the engineering program, Working Model, 2D. Specifically, this viperid model, based on the cottonmouth Agkistrodon piscivorus, includes six linkages related to a seventh, the braincase (Figure 5). Joints between the quadrate, supratemporal and braincase, as well as between the braincase, prefrontal, maxilla and ectopterygoid are represented by pin connections; the pterygoid ec.to.p.te.qcg.oid_j.o.i.nli.s...a...r.es.tr.i.eted..j.oin.t,-al.lowing-vcer.y-limiced-l'ela.tine-i'g-t-a.t.j,g.f.h-1=-ne ends of the quadrate and pterygoid form no joint but instead are tethered by a short ligament, the ligamentum quadrato-pterygoid; upward rotation of the supratemp' on the braincase' is checked by the ligamentum proto-supratemporal; at its poin l. maximum rection, forward rotation of the maxilla is checked by several ligame represented here by a single tether, the maxillary check ligament. The two protrac i mus.c.le.s>-p.lo-tlkt.qlp te[}':goidei and Ievator oidei, are re presemed 0' aspi \ running from braincase to near the pterygold-ectopterygold JOint.

4 78 79 BIOMECHANICS AND EVOLUTIONARY SPACE: ACASE STUDY K.V. KARDONG CH. 5. / /'--/ muscles / ligament ligament ligament Figure 5. Biomechanical model ofviperid jaw apparatus, with mandible removed. Mechanically, ligaments represented by cords; muscles (protractor and levator pterygoideus) represented by spril1;g. 3. Methods of procedure 3.1 Testing the viperid model This viperid model was tested in 'Working Model, 2D ' an engineering software application used to evaluate the performance of engineered machines (Knowledge Revolution, San Mateo, CA). It does so by resolving forces on elements of the machine, calculating the consequences on linked components of the machine, then moving the machine elements accordingly through the stepped motions that result. from the resolution of forces, producing a dynamic animation of the machine. The viperid model (Figure 5) was graphically brought into Working Model's visual display, represented as a machine, and run. The result was to protract the palatomaxillary arch, erect the fang bearing maxilla, and draw the various check-ligaments taut (Figure 6). This simulated result from the model closely matched the actual events during fang erection in striking snakes (Kardong, 1974). This was accomplished quickly, within 10 calculated steps, and used to establish the performance criteria for the 'evolved' model snakes tested next. 3.2 Evolving the viperid model To 'evolve' the model, each of the six linkages (but not the braincase), in steps, were changed one at a time in length and the resulting modified model tested in Working Model. The length of the braincase linkage distance was used as the standard. Each element in turn was set to this same distance, 1.5 times this distance, and two times this ";\';--?1 -+ "?" g;,c"j L-=f Figure 6. Performance criteria, fang erection. it, 1 t ;,t ;ly distance; correspondingly it was set to half and to one-quarter the braincase length. This produced up to five different modifications of the model. Combinations of linkage changes were not examined. Each linkage was modified separately. However, the criterion of connectivity was observed, namely following each change of a link, its connection to immediately adjoining links was maintained. Therefore a change in linkage length never resulted in breaking the seven-bar linkage train. But occasionally an adjoining link or ligament was lengthened or shortened just enough to maintain connectivity with the modified link. Performance criteria. Full erection of the fang was used as the criterion to evaluate the performance of each modified model. This had to be accomplished within 20 steps, instead of the 10 steps of the model, thereby reducing time bias in evaluating performance. By visually comparing the performance of the modified model to the original model, it was easy to detect failure fully to erect the fang. Further, Working Model represents slack ligaments as such, further betraying failure to erect the fang. For example (Figure 7), the supratemporal was set at a length equal to the braincase linkage length (lx), and run in working model, producing full fang erection. It was then set to 1.5x and 2x, succeeding at 1.5x but failing at 2x. Similarly it was shortened to 'I2X (successful) and '/4x (failing). Therefore the extremes of modification of the supratemporal could be determined, before failure occurred. This was done for each of the other linkages (but no[.rhe braincase), producing a population of biomechanical 'species' that worked, met the performance criteria. / 'r;< -+ :'fie L1 i?-'-e1. 1!--=::--"'.' i" '(A)..-=.=.:=--=::-. 'f f.' /. (8) 1.5x Y,x J == Ix ;.- t:r,.tj#: If,;; D\'==-' "i, -"J:!., - -:_ E '''-.''._-o=:.::j - j j' ),.' -_.._= 'r 1;4 X -.,. I '-"" z; Figure 7. Modification (evolution) ofthe supratemporal, (A) performance criterion. (B) Res ulting mechanical result when the supratemporal is changed from one-quarter ofthe braincase linkage length to twice that length. Note that beyond about 1.5x and II, x the erection ofthe fangfails..". :.'

5 3.3 Morphometries and statistical analysis Morphometrics and statistical analysis were performed on these 'surviving' biomechanical species, as well as upon actual species. This was begun by measuring the lengths of the six moveable linkages (supratemporal, quadrate, pterygoid, ectopterygoid, maxilla, prefrontal). To eliminate size as a factor, all measurements were standardized to braincase length (linkage length). In the biomechanical species, this was done by first projecting all species to the same bricase length, then measuring linkages. In the real species, all linkage measurements were divided by the length of the braincase linkage. These standardized measurements were then examined with principal components analysis (SAS V8 statistical software). Included in the real species of vipers measured were eleven species of various genera (Agkistrodon, Azemiops, CalLoseLasma, Crotalus, Deinagkistrodon, Vip era). An attempt was made to measure a relatively large and small member of each species. Linkage lengths of 21 species of colubrid species were similarly measured. This produced three data sets: biomechanical vipers, real vipers, colubrids. This represented the examination of snakes from the viperids and from the paraphyletic group the colubrids, but not from the elapids (Figure 8). 4. Results [n the principal component analysis, the first three eigenvalues (Prin1, Prin2, Prin3) lccounted for 92% of the variation, 56%, 21 %, 15%, respectively. These three were plotted on a three-dimensional axis and rotated to find the projection providing the greatest resolution of points. This proved to be right angle, Prin1 vs. Prin2. The plot of biomechanical species is shown in Figure 9a, which group in the right-hand side of the MODEL Basal snakes Viperi Colubrids Elapids rt It,..',. 19 :s 1I' :t if::,lit:,.{.. "' rf :1 :i.,.,,1.' -,ft,' Ir,.B ".$;, projection. The plot of real viper species, added to this, is shown in Figure 9b, which overlaps the biomechanical species. Inclusion of real colubrid species is shown in Figure ge, which are non-overlapping to the other two data sets. 5. Discussion The plot of biomechanical species falls within a well-defined cloud (Figure 9a). The two greatest outliers, top-right and bottom-right, represent biomechanical species produced by extreme lengthening of the supratemporal and of the ectopterygoid, respectively. The performance criteria required only that the maxilla be fully erected, and its check ligaments taut within 20 steps. These criteria were met formally in the extreme lengthening of the supratemporal. However, note that the check ligament to the supratemporal (Figure 1, 1.5x) is slack, suggesting that the posterior elements of the kinematic chain were still not in place. If this criterion had been added to the performance measures, then extremes of supratemporal modifications would have narrowed, and this point moved closer to the rest of the cluster. Lengthening or shortening of the ectopterygoid, in fact, is a trivial modification. This is because the ectopterygoid articulates to the middle of the pterygoid through a restrictive joint, permitting little rotation. As a consequence, the ectopterygoid and pterygoid essentially form mechanically a single, solid bar. Lengthening (or short.ening) the ectopterygoid, and. maintaining the condition of connectivity, produces changes in internal representation of the eciopterygoid within this bar, bu t it does not affect the oraillengthof the bar, pterygoid plus ectopterygoid. The plot of real species lies largely within the predicted boundaries of the biomechanical model (Figure 9b). This supports the interpretation that the model, despite its simplicity, does reasonably capture the limits to design of a viperid jaw system. Even those species that lie outside (to the left of) the model's polygon are instructive, because most of these are primitive or basal viperids. For example, the data point closest to the colubrids is of Azemiops, that on the basis of morphological (Liem et al., 1971) and'molec,ular (parkinson, 1999) data, is usually placed basally within vipers or a sister group of crotalines. The adjacent data points are for the members of the genius GLoydius, a basal group of crotalines (Parkinson, J999). Neither real nor model species of viperids overlap with the colubrid polygon (Figure 9c). This outcome is consistent with the view that the viperid jaw design represents a distinct bauplan (Valentine, 1986), a distinct design within the morphospace (McGhee, 1999) of at least macrostomous snakes. Certainly these initial results must be taken cautiously, given the restrictive conditions of the model. The criterion of connectivity is reasonable, and keeps the model closer to the real biological situation. If a modified linkage resulted in dismemberment of the kinematic chain, then the model would immediately fail, biasing the results to overly restrictive outcomes. Keeping the criterion of connectivity requires that modification of one element be accompanied by adjustments of linkage partners. But this now identifies and invites examination of coordinated changes. Analysis is in only two dimensions. Had more than one change been permitted per model modification, then mqre accommodation to modification might have been possible, and more biomechanical species 'survived', extending the polygon of workable possibilities. The analysis of the model was restricted to two dimensions. While advisable to exlenclthis_ analysis to three-dimensions, this may not be expected significantly to alter outcomes

6 .. N II:.) Model //'.. -4 I I i i Plinl Model + Vipers 0 J,6,.)..I I I /' , I I I I i Ponl Model + Vipers + Colubrids /'. lj o t. : ',,J.).-. I I I, I i i I I Ponl Figure 9. Statistical plots, principal components, ofthe distribution ofspecies. (a) Biomechanical ---"'sp"'e,..,c""ie"'s'-;-'.(}z) Biomechanical s/li!i.e5-/zoo...lealviperijls.j,.c';jj.iomechauicalsp.ecies.,_r.eawipe0dsr and selected colubrids. '. 11 'f.: " " ';I because including lateral components of motion do not seem to be the basis for failure of fang erection, the performance criterion. The jaws participate in other functions, such as swallowing. During swallowing, these same linkages are involved, but their displacements, relative to the braincase, are generally similar during swallowing to those during fang erection (Cundall, 1987). The palato-maxillary bar protracts (Kardong, 1977) and may partially or even completely erects the fang-bearing maxilla (Kardong, 1982), just as during the strike. Certainly the external events of whole head lateral displacements carry the protracting bones in a sweep over the prey (Kardong, 1977). But, the internal kinematics of swallowing, relative to the braincase, are not radically different from. the displacements accompanying fang erection during the strike. Both exhibit the common kinematic event of protraction of the palato-maxillary arch. The mandibular arch was not included in examination of the viperid model, even though it shares the quadrate and supratemporal elements with the palata-maxillary arch. The mandibular arch, specifically the tip of the mandible, participates in prey capture, often being the first part of the jaw apparatus to make contact with the prey (Kardong and Bels, 1998). During swallowing, especially in macrostomous snakes, the mandibular arch seems to have lengthened as a way of accommodating the intraoral transport of relatively large prey (Cundall and Greene, 2000; Kardong and Bels, 2001). This could conceivably impose limits on the lengths of the quadrate and supratemporal, and this in turn imposes limits on their modifications within their functions in fang erection. Individual elements may serve in multiple actions, requiring a compromise in their designs rather than an optimal design for one dedicated function. Measurements of increased numbers of colubrid and viperid species would be helpful in deciding if these polygons fairly represent the diversity of jaw designs in these snake groups. The vipers included in this study include sister species/basal groups (e.g. Azemiops, Gloydius) as well as derived vipers (e.g. Crotalus). Within the colubrids, a range of species was included indicated by the length of the polygon (Figure 9c). Therefore, while the number of viperid species is small, the species examined represent a broad range of species. The special attention on basal species helps clarify possible transitional steps and reduces effects of derived specialists. Overall, the species included represent a reasonable diversity of taxonomic and ecological types. Certainly relaxing restrictive assumptions of the model, examining consequences in three dimensions, including other functional roles, and increasing the sample size are desirable next steps. But what stands out is that even with the simple assumptions of the current biomechanical model, it produces biomechanical survivors close to the real group of vipers, and helps illustrate one approach to a search for causes of evolutionary diversification. 6. Conclusions As with a straight-line machine, the restricted geometry of the viperid kinematic jaw system limits its evolutionary possibilities. Out of imaginable phenotypes, the geometry of the jaw apparatus determines the kinematic combinations that will meet the performance criteria, namely the function of completing fang erection to inject venom into prey. Modifications of the jaw apparatus that fail fang erection, fail to bring survival benefits, and natural selection eliminates the individual from the population of ),2ossibilities. The biomechanical model allows us, a priori, to identifx the kinematic combinations that will fail. In so doing, the biomechanical analysis explains, in part,

7 84 CH.5. BIOMECHANICS AND EVOLUTIONARY SPACE: A CASE STUDY K.V. KARDONG 85 the culling of viperid phenotypes by providing an explanation for the limited suite of phenotypes that characterize viperids. Within this suite of possible biomechanical species, the viperid model does not explain why some possibilities are realized in nature and others are not. The reasons for this would have to do with other factors affecting evolution such as historical constraints, genetic drift, biogeographic factors, developmental features, and so on. In addition, selective factors related to other bioloical roles will also exert a culling effect upon the population of possible viperids. Outside this suite of possible biomechanical species however, the viperid model does, in fact, explain the absence of reallzed vipers in nature. As an independent methodology, it accounts for some of the overall pattern of evolutionary diversification. The viperid model does so by examining the causes of the culling process that eliminates phenotypes, and thereby explains some of the process behind the pattern of evolution within viperids. Illustrated here with the viperid model of jaw kinematics, biomechanics not only informs us about evolution, but biomechanics helps explain evolution. Biomechanical analyses can take us beyond the limited descriptive hypotheses of phylogenetics, to hypotheses of explanation of the processes behind the patterns. Although not developed in this paper, it is worth noting that biomechanics may also contribute to more formal analysis of evolutionary possibilities. The viperid model, illustrating the use of biomechanics in evolutionary studies, marks the predicted boundaries of jaw designs that work. This llmited suite of biomechanical possibilities stands apart from non-venomous colubrids (Figure 9c). If these possibilities could be plotted against possible environments, then we would produce for biomechanics a representation of evolution similar to adaptive landscapes (Wright, 1932), wherein genetic possibilities are plotted against environmental success. This has already been proposed for morphologies (McGhee, 1999), and one step up from this would be to do so for biomechanical models that include morphologies (jaw apparatus) together with the consequences of function (fang erection to inject venom). In this paper, I have also noted where a few real vipers fall outside the predicted boundaries of the kinematic model (Figure 9b). It is provocative that these species are primitive members of the vipers, suggesting that we are seeing the way in which the evolutionary transition in form/function occurs between non-venomous and venomous vipers. At the very least, such a biomechanical analysis identifies the particular species, the outliers, which invite closer study. This, together with the use of biomechanics in modelling morphological and functional change, should encourage more frequent use of biomechanics in evolutionary studies. In particular, biomechanics may be one methodology by which we can study the processes behind evolutionary patterns. Acknowledgements For comments on the manuscript, my sincere thanks go to P Dullemeijer, T.H. Frazzetta, and Tamara L. Smith.. Refer_ences Alberch, P. (1982) Developmental constraints in evolutionary processes. In: Evolution and Development (ed. J.T. Bonner). Springer-Verlag, Berlin, pp it, R '" f,. illf'.flt. i ;11). '':'i:;' Ii 'i:::' :; :1:,." t Cundall, D. (1987) Functional morphology. In: Snakes - Ecology and Evolutionary Biology (eds R.A. 5eigel,].T. Collins and 5.5. Novak). Macmillan Press, New York, pp Cundall, D. and Greene, H.\ (2000) Feeding in snakes. In: Feeding in Tetrapod Vertebrates: Form, Function, Phylogeny (ed. K. Schwenk). Academic Press, San Diego. Dullemeijer,; P. 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8 Wagner, G. and Schwenk, K. (2000) Evolutionarily stable configurations: functional integration and the evolution of phenotypic stability. In: Evolutionary Biology (ed. M. Hecht)/ Academic/Plenum, New York, pp Weishampel, D.B. (1993) Beams and machines: modeling approaches to the analysis of skull form and function. In: The Skull (eds J. Hanken and B.K. Hall). The University of Chicago Press, Chicago, pp Wright, S. (1932) The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proceedings ofthe XI International Congress ofgenetics 1: Zamudio, K.R., Hardy, D.L., Martins, M. and Greene, H.W. (2000). Fang tip spread, puncture distance, and suction for snake bite. Tox/con 38: II Respiration in elasmobranchs: new models of aquatic ventilation l Adam P. Summers and Lara A. Ferry-Graham it ;-,;;.,1;,. -. } l.. if "';; ;l' '. I'" '. {IJ ' t.!ji; Qi',\lMj.: ',t. 1. Introduction Aquatic vertebrates have two options for the mechanical process of ventilation: they can either move their gills through the water (ram ventilation), or actively pump water across their gills (oropharyngeal pumping). From the mechanical point of view ram ventilation is simply swimmil).g with the mouth held open, however oropharyngeal pumping is more complex. The currently accepted model of oropharyngeal pumping was described over 40 years ago by Hughes (1960a), and has been incorporated into textbooks and physiological literature alike. It was suggested that alternating 'suction' and 'pressure' pumps allowed for the continuous (or nearly continuous; Evans, 1993), unidirectional flow of oxygenated water over the gills. This unidirectional flow of water is important because it allows for a counter-current oxygen exchange mechanism thought to be prevalent in fishes. A counter-current exchange facilitates effi ciem ttansfer of oxygen to the blood, and allows more oxygen to be extracted from the water than cquld be if the flow were not continuous or unidirectional (Piiper and S'cheid, 1977). However, in elasmobranch fishes there is evidence that the pressure and suction pump do not always work in perfect phase, leading to periods of higher pressure in the parabranchial than the oropharyngeal chamber (Ferry-Graham, 1999; Hughes, 1960a; Hughes and Morgan, 1973; Summers and Ferry-Graham, 2001). This pressure differential, a reversal of the normal pressure profile, may mean that water flows back across the gills and into the oropharyngeal chamber during that portion of the respiratory cycle. In other words, for some period of time the water flow is potentially co-current with the blood flow rather than counter-current. Pressure reversals have now been clearly demonstrated through experiments on three species of shark and one skate species (Ferry-Graham, 1999; Hughes, I 960a; Summers and Ferry-Graham, 200la,b). Vertebrate Biomechanics and Evol;;;ion, edited by Vmcent L.BelS,}ean-Pierre Gasc and Adria Gs;nos BIOS Scientific Publishers Ltd, Oxford. 87 ';':'.