Swim ming an d b u rro win g in L im u lu s an d Meso lim u lu s

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1 Swim ming an d b u rro win g in L im u lu s an d Meso lim u lu s DANIEL FISHER Fisher, DC I S : Swimming and burrowing in L imulus and Meso limulus Fossils and Strata, No 4, pp Oslo ISSN ISBN In the swimming of L imulus polyphemus, the development of an unstable, reirulating vortex within the prosomal vault is an important fator de termining swimming orientation, swimming speed, and stro king rate of appendages Experimental evaluation of the harateristis of vortex for mation in Mesolimulus walhi gives us a good estimate of its swimming orientation, speed, and stro king rate The highly vaulted prosoma of Limulus, whih limits its speed as a swimmer, ontributes to it s profiieny as a burrower Similarly, the mehanis of the femoral-patellar joint indi ate greater swimming abilities for Mesolimulus and greater burrowing abilities for Limulus The morphology of eah speeies represents a ompro mise between the onfliting requirements imposed by swimming and bur rowing Daniel C Fisher, Museum of Co mpara tive Zoology, Harvard University, Cambridge, Massahusetts 02138, U SA, 1st june, Present address: Dept of Geo logial Sienes, University of R o hester, R o hester, New York U S A The swimming and burrowing of Reent horseshoe rabs is of speial interest to those of us onerned with the ethology of fossil merostomes and trilobitomorphs As Eldredge ( ) has pointed out, the very general similarities in form between these group s temp t us in to studies of omparative funtional morphology In making suh omparisons, however, it is extremely im portant that we do not simply note speifi orrelations between form and behavior, but rather that we go on to understand the preise, physial reasons for these orrelations This approah leads us to fous diretly on the physial basis of the relationship between form and movement The following analysis of swimming and burrowing is very limited in its goals It will on sider only a few aspets of eah ativity, and only a few sorts of evidene supporting an inter pretation of eah It should, however, have some intrinsially interesting results and also show something of the power of tehniques that diretly investigate the physial onsequenes of ethologial and morphologial patterns The adaptive relationship between form and move ment onstitutes one of the most fruitful approahes to the reonstrution of the behavior of fossil animals In an extended sense, movement is really only another dimension of morphology, one may thus speak of the shape of movement However, movement, with its peuliar evan esene, plaes the burden of its doumentation on statie form It is with this, then, that we must begin STATIC MORPHOLOGY OF LIM UL US POL YPHEMUS AND MESOLIMUL US WALCHI The morphology of the Reent Limulus polyphemus is weu enough known to require little more than a mention of the features whih will be ompared in our two speeies The morpho logial knowledge of the Jurassi Mesolimulus walhi is based on study of material from the S olnhofen limestone, some of whih has been prepared by a speially developed aid tehnique This work is part of a larger sale investigation of the morphology and evolution of horseshoe rabs whih is in preparation by the author Pertinent morphologial details are presented in Fig 1 Of importane for the fouowing disussion are the differene in prosomal width and height, the different angujar relationships of p odomeres when withdrawn into the prosomal vault, and the differene in the robustness of p odomeres 28 1

2 A B Fig 1 Transverse ross setions of L polyphemus (A) and M walhi (reonstruted) ( B ), through the lateral ompound eyes, and perpendiular to a plane defined by the post-ophthalmi branhes of the ophthalmi ridges The plane of the appendages has been rotated somewhat to lie in this transverse plane of the b ody Both are drawn to the same sale and represent animais 45 m in prosomal length P, b ody avity of pro somal arapae; Pv, prosomal vau1t;, oxa; t, trohanter; f, femur; p, patelia; b, tibia; r, tarsus SWIMMING Swimming is probably the most omplex of the ativities in the behavioral repertoire of L polyphemus A full understanding of the preision and oordination of swimming movements and the several phases of swimming behavior would involve a num ber of different sorts of physial analyses However, at present, I wish to onsider only three faets of swimming be havior: ( 1 ) orientation of the body relative to the horizontal, ( 2 ) swimming speed, and ( 3 ) stroking rate of the appendages I shall refer to these as G, v, and fs respetively I will deal with these fators only in the ontext of unaelereated swimming in a horizontal diretion, weu above the surfae of the sediment, and below the surfae of the water Furtherm ore, I will limit the disussion of investigative tehniques to experiments involving visualization of the pattern of fluid flow about a swimming horseshoe rab, espeially in the region of the ventral prosomal vault The basi motions of horizontal swimming in L polyphemus have been desribed, with various degrees of auray, by numerous authors The most reent desriptions are by Vosatka ( ), Knudsen ( ), and Fisher ( ) The fouowing analysis, however, rests on only a few simple observations, based on work with individuals one to five entimeters in p rosomal length ( Fisher, ) Fig 2 A swimming horseshoe rab Movement is in a horizontal diretion, as indiated by the arrow Swimm ing orientation (Q) is defined as the angle, measured in a vertial longitudinal plane, between the post-ophthal mi branhes of the ophthalmi ridges and the diretion of movement The prosomal appendages have just be gun their power stro ke 2 82

3 ( 1) a During unaelerated horizontal swimming the body m oves in a generally anterior diretion, with the ventrai surfae uppermost b The body is inlined in suh a way that a plane desribed by the post-ophthalmi branhes of the ophthalmi ridges lies at 20 _30 to the horizontal, measured in the diretion of motion ( F ig 2 ) ( 2) Swimming speed usually ranges between 1 0 and 1 5 m se -l ( 3 ) a Swimming i s powered b y the motions o f the prosomal and opisthosomal appendages, whih onsist of p ower and reovery phases of a stroking yle b This yle has a frequeny of se -l (4 ) The opisthosomal appendages and the sixth p rosomal appendages stroke in a metahronal rhythm, the wave of ativation passing anteriorly Prosomal appendages 2-5 m ove in phase with one another, and begin their stroking yle immediately after the sixth pro somal appendages ( 5 ) During their power stroke, the prosomal appendages extend ventrally and move posterior ly During their reovery stroke, they withdraw into the prosomal vault and move anteri orly, their distal elements approximated to the ventral surfae of the prosoma We would now like to investigate the quantitative aspets of the foregoing desription of swim ming, in order to understand the speifi values of G, v, and fs that are observed in L poly phemus and to reonstrut values of eah of these fators for M walhi The qualitative aspets of a similar desription of swimming movements for M walhi, and the rather basi assumption that M walhi swam at all, will be dealt with in detail else where ( F isher, in preparation) Briefly, the argument is as follows Despite the differenes in shape between L polyphemus and M walhi, it an be shown that their arapaes have a similar relative spatial distribution of en ters of m ass-buoyany and lift ( as determined for any swimming position) These observations, oupled with data from the measurement of the fores ating on a swimming horseshoe rab, indiate that if M walhi swam, it also swam on its bak - ie item ( 1 ) a applies to M walhi Similarly, ana tomial and energeti-mehanial onsiderations of appendage movement allow the trans position of items ( 3 ) a and ( 4 ) Furthermore, the best interpretion of suh anatomial details as the ourse and development of the ophthalmi ridges of M walhi (also b ased on fore measurement data not given here) involves the assumption of swimming in M walhi This line of reasoning, together with evidene from trae fossils and details of preservation, supports the assumption that M walhi swam and that its general manner of swimming was similar to that exhibited by L polyphemus Materials and methods It is standard pratie, in studies of fluid mehanis, to simulate the onditions of an objet movmg through a quiesent fluid, by setting up the dynamially equivalent situation of a stationary objet immersed in a flowing fluid For this study, models of horseshoe rabs were mounted in a flume whih supplied a non-turbulent flow, whose veloity ould be regulated between O and 70 m se - 1, through a test setion measuring 45 m by 45 m The flume was built, and is maintained by, the Division of Engineering and Applied Physis, Harvard Universi ty Models of L polyphemus were made by sealing the anterior exuviation suture of dried molts Prosomal and opisthosomal appendages were removed and the resulting openings in to the body avity were plugged For M walhi, a reonstrution of the arapae (without appendages) was sulpted in wax, molded in silione rubber, and ast in polyester resin B oth models have a prosomal length of 45 m The removal of appendages from the models was originally done in order to study how the arapae itself would tend to influene the development of flow patterns It later beame lear that the motion of the appendages during swimming was suh as to reinfore the patterns set up by arapae shape, not obliterate them Unless a mehanism were developed for aurate animation of model appendages, their motionless presene on a model would onstitute more of a distortion of the 'real' situation than their absene We must next raise the question of how aurately a model reprodues the ontrol of flow patterns that the real arapae would exerise In morphologial detail, the models are 283

4 probably exellent representations of the real animals The molt of L polyphemu:s gives us as near perfet a model, in this respet, as ould be desired In fat, flow visualization experiments on plasti models representing progressively more simplified abstrations of the arapae mor phology of L polyphemus show that it is its general shape, rather than minute surfae details, whih is signifiant for explaining the flow patterns that will be dealt with here S ome attempts to model organisms for hydrodynami study are onfounded beause of the diffiulty of reproduing the elasti and textural properties of biologial surfaes F or the present stu dy, this problem is of minimal importane For our purposes, the smooth, stiff, hitinous exoskeleton is effetively simulated by rigid plastis The models were supported in the flume on the end of a brass rod, one quarter inh in diameter, mounted on the ventral surfae of the model The rod was held in a brae whih ould be rotated about the animal's enter of mass ( F ig 3 ) This varied the orientation of the model relative to the diretion of fluid movement, without displaing the model within the test setion The similarity of the flow patterns, using this method of supp ort, to those de veloped using other methods (not involving strutures within the prosomal vault) indiates that the presene of the rod do es not signifiantly affet flow p atterns within the prosomal vault In order to trae the patterns of flow about the models, hydrogen bubbles were gene rated upstream of the models through the eletrolysis of the flume water The eletrodes were fine wires mounted p aradiametrially aross a plexiglass hoop In most ases, the athode was platinum and the anode opper, resulting in a single linear soure of H2 bubbles The results of bubble traking are obviously most signifiant when the terminal veloity of bubble asension is very muh less than the veloity of fluid flow In these experiments terminal asension veloeity of the bubbles was usually 5-1 0% of the flow veloity As bubbles were generated from a linear soure, a planar sheet of bubbles was propagated downstream In the presene of an obj et suspended in the flow, this sheet was deform ed in a m anner losely approximating streamline deformation around the objet, thus giving a visible reord of flow patterns Flow patterns developed for eah of the models, at speified orientations and flow veloeities, were reorded on 3 " x 5" Polaroid film and on 16 mm ine film Frame by frame analysis of the eine film provided a means for measuring the periodi struture of these patterns Results The flow p atterns illustrated by these experiments are aused solely by the interation of arapae morphology and the moving fluid medium The details of the flow p attern whih are most informative onerning the aspets of swimming that we have hosen to analyse + Fig 3 M el mount and eletrode for flow visualization experiments The to ps o f the vertial supports were attah ed ng!dly to the top of the flume hannel Diretion of flow is fro m right ba kground to left foreground 2 84

5 Fig 4 Flow pattem near the prosoma (shown in longitudinal setion through the interophthalmi region) of a swimming L imulus polyphemus Vetors on the veloeity profiles indiate diretion and magnitude o f the flow veloeity at their origins on a vertial baseline The urve b represents a streamline whih, above the prosoma, marks the upper ex tent of the boundary layer The urve v represents the lous of points with a veloeity equal in magnitude to the maximum flow veloeity in the anteriorly moving portion of the vortex v may be taken as the size and shape of the fuhy developed vortex ( orientation, speed, and stroking rate ) are those oneming flow in the prosomal vault and in the wake behind it When fluid approahes the anterior prosomal margin, it either moves over the dorsal sur fae of the arapae or passes ventrally aross the prosomal doublure Fluid moving along this ventral path experienes an abrupt disontinuity in surfae onformation, resulting in a flow separation at this margin ( The physis of flow separation are disussed in any fluid dynamis text What onems us here is only the resulting pattem of flow ) This fluid is de fleted fudher ventrally in a smooth ar and then p asses bak into the wake The spae be tween this defleted flow and the ventral surfae of the prosoma is oupied by a reirulating vortex whih, when intat within the prosomal vault, has a roughly resentoid shap e The 'dorsal ' portion of this vortex is appressed to the ventral surfae of the prosoma and the 'ventral' portion of the vortex grades into the body of defleted flow, oasionally inorpor ating some of this flow into its own reirulation ( Fig 4) Another important feature demonstrated by the flow visualization experiments is that the vortex formed in the prosomal vault is not ontinually present or ative there Rather, vorties are periodially formed and shed in to the wake behind the horseshoe rab This may be expressed as a strong periodiity in the energy distribution of fluid moving in the separated region This periodiity is superimposed on the more randomly variable energy distribution of turbulent flow in the wake ( the unstable range of vortex hedding, in Roshko's terminology, ) This allows the period of individual formation-shedding yles to vary somewhat, but does not obsure the strong periodi struture of the wake ( Figs 5 and 6 ) Fig 5 A single frame o f the 1 6 mm eine film o f flow visualization using a model o f M walhi Bubbles moving below the mod el are 2, formed at a platinum anode H2 bubbles formed at the athode are of a sm ah and a large (due to partiulate matter in the water) size dass The former are useful for traeing flow patterns, while the latter rise onspiuously A vortex has just b een shed, and the defletion in b ubble paths whih is seen just posterior to the opisthosoma represents a portion of its reirulating flow 285

6 Fig 6 A single frame of the 1 6 mm eine film of flow visualization using a mode! of L polyphemus (details as for Fig 5 ) Vorte x formation and shedding i n and from the prosomal vault i s harateristi o f any generally horseshoe rab-like shape, at any of the orientations or flow veloities under on sideration However, a doser look at these flow p atterns shows that the preise size and shape of the vortex is dependent on the orientation of the model and the veloity of the fluid This dependeny is illustrated in Figs 7 and 8, matries of orientation-veloity variation for eah model Dependeny is mappable on a finer sale than the divisions of this matrix might suggest However, the most unambiguous signifiane an be assigned to variation of this sale Now, of what importane to a swimming horseshoe rab is the formation of a vortex of a partiular size and shape? One aspet of effiient swimming is effiient prodution of thrust This, in turn, requires effiient appendage funtioning in both p ower and reovery phases of the stroking yde It is during the reovery stroke that the vortex omes most diretly into play Effiient reovery means reduti on of the drag fores ating on the appendages during reovery movements, sine these fores would be oriented opposite to the diretion of motion One important way in whih horseshoe rabs effet this drag redution is to redue the veloity L i m u l u s Ro l YJh e m u s v 0 _ 1 0 e m/se m/se m/s e m/s e "-!?I < q; Q/ q; ,/ y ;; ;/ fl )J y - Fig 7 Matrix showing variation in vortex size and shape eorresponding to different values of Q and v for L polyphemus The heavily fram ed square indieates the value of Q and v whieh results in the most effiient reeovery stroke for the prosomal appendages Flow is indieated by arrows whieh eorrespond to eurves b and v in Fig 4 286

7 e v 5-10 m/s e m/s e l11;s e 0 _ 1 0 oy m/se M e s o l i m u l u s wa l h i --- V a-/ / - /' / ,/ )' --- ;Jf ---- ;7 Fig 8 Matrix showing variation in vortex size and shape orresponding to different values of Q and v for M walhi (detaiis as for Fig 7 ) o f prosomal appen dages re! ative t o their surrounding fluid during the reovery, and o n e import ant I? ethod for domg this IS to exeute the reovery stroke via the 'dorsal' anteriorly moving port o of the prs? mal vortex Therefore, the vortex arrangemen t whih would be most auspilous for efficlent reovery stroking would be one in whih there was a oherent bakflow extending from the p osteriormost p ortion of the exursion range of the p rosomal appendages, forward t? the nt riormost p rtion of their exursion - the edge of the prosomal doublure ThIS onfiguratlon IS best obtamed, for the models, under the onditions represented by the h aily framed squares of Figs 7 and 8 These same onditions therefore onstitute our pre ditlon of G and v values for the swimming animals Indeed, for L polyphemus these onditions of orientation and flow veloity are just those under whih horizontal swimming ours This behavioral observation onstitutes onvenient and enouraging orroboration of our preditions of G and v based on the experiments How ever, the preditions an be made just as strongly in the absene of observed values for these haraters The oini dene of the path of movement of the prosomal appendages with the flow patterns observed on the L polyphemus models, and the oinidene of observed values of G and v with the range of those values predited from flow visualization, argue that flow patterns are an important ontrol of swimming orientation and speed In reality, there are other physial relationships whih share in this ontrol The most important of these is the dependene of lift and drag fores on G and v In the final analysis, though, these other ontrols simply serve to loate the atual values of G and v within the range presribed by' flow patterns As noted above, and as shown in Fig 8, the values of G and v whih result in the most 'helpful' vortex onfiguration for M walhi are 0 _ 1 0 and m se -l These results give us an experimental estimate of these haraters for this fossil speies Vortex shedding frequeny ( fv ) is dependent on the same variables as vortex shape and size Thus, for the optimum onditions speified above, eah model has a harateristi fv ' In order for the relative veloities of prosomal appendages and their surrounding fluid to be minimized during their reovery stroke, it is obvious that the prosomal vortex must be in tat and in plae during reovery exeution If this relationship is to be preserved throughout onseutive stroking yles, stroking frequeny ( fs ) must equal fv and vortex shedding must our during the power phase of the stroking yle This is not to say that stroking is absolutely onstrained to oinide with vortex sheddmg as observed in the legless models The energy input of appendage motion is great enough to 28 7

8 overome the periodi energy distribution assoiated with the vortex In fat, within ertain limits, stroking frequeny is probably able to ontrol the atual rate of vortex shedding in the swimming animal This is why there is no problem in oordinating phases of these two yles, one their periods are equal The point is simply this: when vortex shedding and stroking are oordinated, there is a savings of appendage energy whih would otherwise be invested in setting up a periodi distribution of urrent energy different from that distribution whih is potentially (ie independent of appendage motion) in fore For the L polyphemus model, the measured f v is about 2 se-i This orresponds losely to the fs noted above, lending support to the hypothesis of ontrol that has been set fodh This hypothesis would also argue that the measured f v for the M walhi model (1 7 se -I ) indiates for that speies a normal f s during horizontal swimming of 1 7 se-i Again, we have an experimental determination of a swimming harater for a fossil speies that is independent of our knowledge of the value of that harater in the Reent speies To summarize this look at swimming, experiments involving the visualization of flow pattems around models of swimming horseshoe rabs allow one to explain or reonstrut swimming orientation, swimming speed, and stroking rate M walhi swam at a smaller angle to the horizontal, swam faster, and swam with a lower stroking rate than L polyphemus The full signifiane of the values for eah of these haraters will take form only in the light of other investigations on the swimming of horseshoe rabs However, even at this point, the differenes between M walhi and L polyphemus suggest greater swimming ability and endurane for the former If the arapae morphology of M walhi is more speialized for swimming, what is the reason for the more highly vaulted arapae of L polyphemus? Part of the answer beomes lear when we look at the burrowing behavior of horseshoe rabs BURROWING The disussion of swimming has involved a onsideration of the diret interation between the dome-like prosoma of a horseshoe rab and the extemal environment; here, let us look at a more indiret interation During burrowing, the ventral surfae of the prosoma and the substrate de fine a losed spae, the prosomal vault, within whih the prosomal appendages operate The ventral surfae of the prosoma orresponds preisely to the surfae form of an abstrat three-dimensional body defined as the lous of all appendage positions This relationship means that during burrowing, the limb elements of M walhi annot obtain the aute angulation of those of L polyphemus (see Fig 1) During burrowing, part of the first phase of propulsive movements of the prosomal appendages onsists of flexion at the femoral-patellar artiulation This flexion takes plae about an axis defined by two points of artiulation on the dorsal surfae of the joint It is aomplished largely by musles in the femur whih insert on an aruate slerite embedded in the ventral arthrodial membrane of this joint (Ward, 1969) As an be se en in Fig 9, the moment arm of these musles ating about the femoral-patellar artiulation is greatest when the angle between the femur and patelia is small When the length of this moment arm is maximized (holding other variables onstant), so is the fore whih an be generated, at the distal end of the appendage, against the substrate Thus, the prosoma of L polyphemus allows greater fore prodution, in this respet, than that of M walhi We may also look at the shape of podomeres themselves The femur and patelia of L polyphemus are muh deeper dorso-ventrally and of greater ross-setional area than those of M walhi Besides being able to aommodate a larger musle mass, this means that at any possible limb orientation the aruate slerite is loated farther from the femoral-patellar artiulation in L polyphemus Again, this represents an inrease in the moment whih an be developed for flexion at this joint These observations are only brief examples of the sort of differenes that exist between the mehanial system of burrowing in L polyphemus and M walhi Other indiations of speializations for burrowing behavior in L polyphemus have be en noted by Eldredge (1970) and will be dealt with further elsewhere Before leaving the matter of appendage morphology, it is important to note that the joint mehanis of M walhi are not without their advantages The shorter moment arm of musles ating at its femoral-patellar joint means that for a given rate of displaement of the musle insertion, the appendage tip will move at a greater linear veloity This is important beause flexion at the femoral-patellar joint also ours during the power stroke of the 288

9 swimming yle of the prosomal appendages, and beause the propulsive fore generated by the appendage varies as the square of its linear veioity In general, the appendages of M walhi are 'designed' for quik ation against relativ'eiy small fores of resistane, while those of L polyphemus are 'designed' for more powerful ation against larger resistane These alternate strategies may be interpreted as speializations for swimming and burrowing respe tively CONCLUSIONS A hydrodynami and mehanial analysis of swimming and burrowing in horseshoe rabs an help to explain and reonstrut preise details of their morphology and behavior This dis ussion has dealt with only a few aspets of eah of these ativities Many ativities ( eg walk ing, suttling, feeding, enrolling, righting) have not even be en mentioned However, further work on these and other ativities supports the speifi determinations made here, the im portane of swimming and burrowing to eah of the speies onsidered, and the general view of relative swimming and burrowing profiienies It is interesting that eah morphologial harater disussed (general prosomal shape, appendage angulation, and appendage robustness) is influened, in eah speies, by onfliting seletive pressures that are related to the divergent mehanial requirements of two important ativities The state of any one of these morphologial haraters thus reflets a ompromise representative of the relative importane of the ativities Certainly there are instanes of morphologial hange, in the evolution of horseshoe rabs, that are related to real innovations in their behavioral repertoire However, at least some of the differenes between M walhi and L polyphemus seem rather to be the result of a shift in the balane of importane between two mehanially ompeting ativities - swimming and burrowing Fig 9 Moment of a femoral-patellar flexor (musele represented by dash ed lines) Axes or points of artiulation are shown as small ireles f, line of fore prodution, or line of musele ation in a flexed position (A); f', line of musele ation in a more extended position (B) ; m, moment arm of musele ating in the flexed position (A) ; m', moment arm for the more extended position ( B ) ; a, aruate selerite 289

10 ACKNOWLEDGEMENTS - Part of this work was ompleted during tenure of a National Siene Foundation Graduate F ellowship I am partiularly grateful to Rihard 1 Land and D J arnes B aker for advie and equipment pertaining to tehnial aspets of the experimenta tion I have also appreiated disussions of the material presented here with Niles Eldredge, Stephen J Gould, Thomas A MMahon, Jane A Peterson, and Leif S tørmer RE FERENCES Eldredge, N : Observations on burrowing b ehavior in Limulus polyphemus ( Chelierata, Merostornata ), with impliations on the funtional anatomy of trilobites A merian Museum Novitates 2436 [ Fisher, D C : Funtional morphology and evolution of the Limulaea Unpublished AB thesis, Department of Geologial Sienes, Harvard University pp ] Knudsen, E I : Musular ativity underlying ventilation and swimming in the horseshoe rab, L imulus polyphemus ( Linnaeus ) Biologial Bulletin 1 44, Roshko, A : O n the development o f turbulent wakes from vortex streets National A dvisory Com m ittee for A eronau tis, Report Vosatka, E D : Observations on the swimming, righting, and burrowing movements of young horseshoe rabs, Limulus polyphemus Ohio Journal of Siene 70, Ward, D V : Leg extension i n Limulus Biologial Bulletin 136, U