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Analysis of the mero-carpopodite joint of the Americanlobster and snow crab.

II. Kinematics, morphometrics and moment arms

S.C. Mitchell and M.E. DeMont*

Department of Biology, St Francis Xavier University, PO Box 5000, Antigonish, Nova Scotia, Canada, B2G 2W5.*Corresponding author, e-mail: [email protected]

This research reports on the kinematics of lobster and snow crab walking, documents changes in themoment arms of the mero-carpopodite joint during rotation, and examines scaling e¡ects of morpholo-gical and mechanical variables in these crustacean species. Forward walking lobsters and lateral walkingcrabs were recorded and images analysed to describe the kinematics of these animals, and subsequentlymorphometric and moment arm measurements made. During forward walking the lobster maintains¢xed mero-carpopodite joint angles during both the power and recovery strokes, though each of thewalking legs maintains di¡erent joint angles. Legs 3 and 5 are maintained at angles which appear toequalize the £exor and extensor moment arms, and leg 4 joint angle appears to maximize the extensormoment arm. The snow crab has a joint excursion angle of between approximately 508 to 1508 and,during £at bed walking, the leading and trailing legs move through similar excursion angles. The lengthof the meropodite for both species are longer for the anterior two leg pairs relative to the posterior twopairs and the rate of growth of the meropodite is largely isometric for the lobster while consistentlyincreases with positive allometry in the crab. The £exor and extensor moment arms generated as the jointundergoes £exion/extension show two distinct patterns with the extensor moment arm being maximized atrelatively low joint angles (558^1158) and the £exor moment arm reaching a plateau at joint extension withangles between 958 and 1558. The £exor apodeme possesses the largest moment arms in all legs for bothspecies, suggesting the £exors are able to generate greater torques. It appears that, mechanically, theselaterally moving animals may be ‘pulling’ with the leading legs to a greater extent than ‘pushing’ with thetrailing legs.

INTRODUCTION

During walking many adult decapod crustaceans, andother arthropods, adopt a sprawling posture with the legsspread out.This lowers the centre of mass and provides theability to produce large laterally directed forces with whichto counteract any tendency of the body to turn round theroll axis (Alexander, 1971). An integral part of assumingthis posture is the £exion/extension of the legs, particu-larly about the mero-carpopodite and propo-dactylopo-dite joints which function in the vertical planes. Usingthis sprawled posture lobsters walk primarily forward andbackward while crabs move predominantly sideways(Evoy & Ayers, 1982; Clarac, 1984) though each caneasily locomote in either manner (Lockhead, 1960;Chasserat & Clarac, 1983). In forward/backward walkingthe joints providing the majority of power/coordinationare the thoraco-coxal joint (protraction/retraction) andthe coxa-basipodite joint (elevation/depression)(MacMillan, 1975). In this mode of walking, the mero-carpopodite joint contributes little and behaves largely asa ¢xed strut between these proximal joints and the distalparts of the leg (Ayers & Davis, 1977; Ayers & Clarac,1978). In contrast to this, during lateral walking by eithercrabs or lobster, the mero-carpopodite joint contributes tothe driving/pulling power and the spatial placement of

each leg (Ayers & Davis, 1977; Martinez et al., 1998). Oneimplication of this fundamental di¡erence in the use of themero-carpopodite joint between the two styles of walkingis that in forward/backward walking the legs on eitherside of the body are behaving symmetrically, whereasduring lateral walking the leading legs may be pullingthe animal along (or decelerating the forward motion;Blickhan & Full, (1987)) while the trailing legs arepushing (Burrows & Hoyle, 1973).

The forces generated about a joint are functions ofmuscle and joint architecture. The useful force deliveredto a joint system is torque; a product of the muscle forceand its moment arm (Goslow & van de Gra¡, 1982). Themoment arm (i.e. the perpendicular distance from muscleline-of-action to joint point of rotation; Richmond (1998))transforms the linear muscle motion into angular jointrotation (Lieber, 1997), thus allowing forces to be exertedon the external environment. For animals which exert bothpushing and pulling forces during walking, the magnitudeof the moment arms contributing to these actions may helpto clarify through which action (pushing or pulling) thepredominant forces are being generated.

There has been considerable description of lobsterwalking (e.g. Ayers & Davis, 1977; Clarac, 1984; Clarac& Chasserat, 1986; and others) and also for laterallywalking crabs (e.g. Hafemann & Hubbard, 1969; Burrows

J. Mar. Biol. Ass. U.K. (2003), 83, 1249^1259Printed in the United Kingdom

Journal of the Marine Biological Association of the United Kingdom (2003)

& Hoyle, 1973; Hui, 1992; and others), though not for snowcrabs. However, despite the signi¢cance of the mero-carpopodite joint in crustacean walking these descriptionshave not examined the mechanics of this joint in detail,apart from some measurements of joint angle. Thefollowing research was conducted with four goals: (1) toprovide a general description of snow crab kinematicswhich is presently lacking in the literature; (2) toexamine scaling e¡ects of meropodite length and momentarm size on body size; (3) to determine the moment armsof the mero-carpopodite joint in order to assess relativetorque production during leg £exion/extension; and (4) tocorrelate kinematics and moment arm data, andpreviously reported information, in an attempt to assesswhether laterally walking crabs are operating by pushingo¡ the substrate with the trailing legs, pulling with theleading legs, or some combination of the two actions.

MATERIALS AND METHODS

Kinematics

Live American lobster (Homarus americanus) wereobtained through local suppliers, and snow crab(Chionoecetes opilio) from the Department of Fisheries andOceans (DFO). To examine the kinematics of forwardwalking lobster, six animals (four male, two female;carapace length 86.9^152.05mm; mass 0.49^2.87 kg)were motivated to walk on a submerged treadmill(dimensions 1.2�0.52m) in a static seawater tank(2.1�0.55�0.49m) with a viewing window (1.5�0.32m)in the side. The treadmill was made of a horizontal beltwith an active surface (area over which the belt moved)of 1.18m long by 0.41m wide. The belt was a corrugatedvinyl surface painted to provide alternating 50mmpainted and unpainted bands. This was to provide opticalstimulus to the walking animal (see Ayers & Davis, 1977).The belt was powered by a variable speed 13.5 ampLambda LK 341AFM power supply allowing ¢ne controlof belt velocity. The treadmill belt speed was varied withanimal size (based on the length of meropodite of the thirdwalking leg) in order to maintain relatively constantFroude numbers (Fr) and so dynamic similarity acrosssizes. The lobsters were motivated to walk by an illumina-tion gradient, with one end of the tank under bright(250W) light and the other end darkened; preferringdarkness the lobsters attempted to reach the darkenedend. A plastic screen barrier prevented the animal fromreaching that end and maintained them in position forrecording.Walking sequences for each of these six animalswere replicated three times. All animals were allowed aminimum of 10min between termination of one walkingsequence and recording of the next. Recording was onlybegun after a minimum of 10 s of regular forwardwalking; these procedures were to ensure the animal wasmoving in a representative manner when recording tookplace. Belt speed was calculated by recording the movingbelt from an overhead position after each lobster’s threesequences were complete and measuring the displacementof the belt between images. In addition to these movingbelt sequences, ¢ve of the six lobsters (two replicates peranimal) were walked on the treadmill without the beltmoving (i.e. ‘stable bed’ walking). During this recording

an initial interval of 10 s was not possible; recordingbegan as soon as the animal initiated forward walking.This use of a non-moving substrate was to provide astable bed for comparison of treadmill walking with ‘free’walking.

Recording of the lobster walking was done from aposterior perspective which allowed the best view of themero-carpopodite (M-C) joint of the last three walkinglegs (numbered 2 to 5 from anterior to posterior; thechelae form leg 1). Unfortunately the ¢rst pair of walkinglegs (leg 2) were blocked by the posterior three pairs fromthis angle and so the kinematics of this pair could not beinvestigated with this experimental procedure. Recordingwas conducted using a mirror at 458 to the plane of thecamera to re£ect the image through the tank window to aRedlake Motionscope high speed camera (framing rate60Hz), with a sequence of 3^4 s per replicate beingcollected then downloaded to a computer (Figure 1).Images were analysed using image analysis software(IMAQ# Vision for LabVIEW1) and consisted ofmeasurement of the M-C £exion angle at the approximatemid point of both the power and return strokes (i.e. whenthe leg was normal to the anterio-posterior axis of thelobster).

Four male snow crabs (carapace width 95.0^124.4mm;mass 0.37^0.89 kg) were videotaped walking laterally on astable bed for kinematic analysis. Taping was conductedusing standard video equipment utilizing two cameras,one placed overhead and the other frontal (Figure 1), andan American Dynamics AD1470A beam splitter to allowsimultaneous analysis of two images on a single screen.As the crabs were not as easily motivated as the lobster,and move in a much less stereotyped manner, taping wasinitiated and the animal allowed to move at its discretion.This resulted in 5 to 15 min of tape per replicate with indi-vidual short sequences of movement in the sequence. Eachanimal was taped for three replicates. Individualsequences in which the crab walked laterally across thescreen were analysed.

Images of legs 2, 3 and 4 were analysed by directmeasurement of the joint angle from the monitor (over-head view) using a protractor, accuracy is estimated as�58. The timing in the step cycle of maximum extensionand £exion is based on the frontal lateral view. Maximumextension was de¢ned as the M-C angle when the dactylo-podite contacts the substrate and maximum £exion whenthe dactylopodite lifts o¡ the belt. Leg 5 was not analyseddue to the plane of the M-C joint for this leg being signi¢-cantly out of the planes of both the overhead and lateralcameras. Selected sequences were examined in greaterdetail with the leg extension and £exion being measuredat every ¢fth tape frame (framing rate 30 frames persecond) in order to document angle excursion patterns ofthe leading and trailing legs.

Morphometrics

Morphometrics of these crustaceans were examined bymaking external measurements on 26 lobsters (9 female, 17male; carapace length 75.2^152.05mm; mass 0.30^2.87 kg) and 30 snow crabs (4 female, 26 male; carapacewidth 53.0 to 129.9mm; mass 0.06^0.79 kg). Body size wasestimated using the linear measurements (mm) of

1250 S.C. Mitchell and M.E. DeMont Crustacean joint structure


carapace length (lobster) and carapace width (crab).Dimensions of the walking legs (mm) were measuredalong the length of the meropodite, carpopodite, propo-dite and dactylopodite of each of the four legs. Meropoditelength was measured from the ischial-meropodite suture tothe end of the meropodite at the mero-carpopodite jointalong the dorsal surface of the leg. All linear measure-ments were made using vernier calipers (�0.05mm).

Moment arm

To examine the length of the moment arm within theM-C joint, legs 2 to 5 of 14 lobsters (seven each male andfemale; carapace length 72.45^152.05mm; mass 0.30^2.87 kg) and 20 snow crabs (eight male and 12 female;carapace width 53.0^122.9mm; mass 0.06^0.79 kg) weredissected. Dissection followed the procedures outlined in

Crustacean joint structure S.C. Mitchell and M.E. DeMont 1251


Figure 1. Experimental set up for ¢lming of lobster walking kinematics (A�overhead view) and snow crab (B�frontal and sideviews). The same tank is represented in both ¢gures. v, video cameras.

Mitchell & DeMont (2003). After removal of the overlyingmuscle^apodeme complex a small wire marker wasclamped to the apodeme of the remaining in situ compleximmediately adjacent to the apodeme attachment to thecarpopodite (Figure 2). This marker was used to ensureconsistent measurements to the same point on theapodeme between legs and between individual animals.A pin was then inserted from the distal to the proximalend of the carpopodite, through the exoskelton wall, inorder to extend the carpopodite. This extension allowedmore accurate placement of the carpopodite segmentalong established angles. The meropodite was pinned to atemplate marked at 158 increments between 08 and 1808.The carpopodite was then manually moved through itsrange-of-motion (ROM) with images of the muscle^apodeme complex and joint architecture captured via anoverhead video camera at 158 increments of M-C joint£exion from 258 to 1658 and digitized (Figure 2). Themagni¢cation of the image was calculated from the scaleat the bottom of the image once for each series. All sub-sequent measurements were made using the image analysissoftware listed previously. The collection of images from asingle apodeme of a single leg as the carpopodite wasmoved through its ROM produced a series of images. Foreach series, the di¡erence between the angle of theinserted pin relative to the ‘true’ carpopodite angle (asmeasured along a plane through the longitudinal centreof the carpopodite) was measured and all subsequentjoint £exion values in this series corrected for this ‘pinplacement’ error. Within each individual image the

£exion angle (from the midline of the meropodite to theinserted pin) was measured and the point of rotationdetermined by triangulation of three of the converginglines on the template fulcrum hole (Figure 2). Distance(dp in pixels) and angle (ym) was measured from this esti-mated point of rotation to the wire marker on theapodeme. The distance dp was then converted to mm(dmm) using the scale determined for that series.

The moment arm (L1 in mm) for each image was calcu-lated as:

L1 ¼ cos ym � dmm (1)

Due to the moment arm being calculated as a functionof angle and length from the fulcrum to the apodememarker, maximum moment arms could occur with longlengths at low angles; to exclude these only measurementsin which the moment arm was within �458 of normal tothe meropodite midline were used.

Statistical analysis

Equivalence of mean M-C joint £exion angles betweenpower and return stroke, and moving belt and stable bedruns for the lobster was tested using one way analysis ofvariance (ANOVA; for this and all subsequent tests,a¼0.05). The data were tested for normality via normalprobability plots and determined to come from a normal



Figure 2. Experimental set-up to measure moment arm ascarpopodite moves through joint £exion excursion. ep, pinplacement error; cp, carpopodite; mp, meropodite; a£, £exorapodeme; f, fulcrum; m, marker; ym, angle of marker from 08;dp, distance of marker from fulcrum; ma, moment arm.

Figure 3. Mean £exion and extension angles for (A) thelobster during forward walking and (B) the snow crab duringlateral walking. Error bars are one standard deviation.Numbers associated with columns represent number ofmeasurements. Large di¡erence in sample size between leadingand trailing legs due to the animal walking out of the ¢eld ofview; leading legs leave ¢rst and can often record anothertrailing leg cycle once the leading legs are out of view.

distribution, justifying the use of parametric procedures.The snow crab data were likewise normally distributedand comparison of mean £exion and extension anglesbetween leading and trailing sides for each leg wereconducted using Student’s t-tests.

The length of the meropodite relative to total leg lengthand carapace size was assessed as a proportion of these totallinear measures.The length of themeropodite of a given legas a proportion of leg length or carapace size was deemedsigni¢cantly di¡erent from other legs if the mean value fell

outside the 95% con¢dence intervals of the other legs. Toassess scaling e¡ects over the size ranges, allometricanalyses were conducted on measured meropodite lengthand maximum moment arm as functions of carapace size(length for lobster; width for crab). Data were log10 trans-formed and ordinary least squares (OLS) regressionconducted. Reduced major axis (RMA) slopes were calcu-lated (appropriate when values of the independent variableare measured with error; LaBarbera, 1988; McCardle,1989) and compared. Regression slopes were tested for



Figure 4. Time course and associated moment arms along step cycle for leg 3 of the snow crab. The leading leg with £exorapodeme moment arm is illustrated in (A) and the trailing leg with extensor moment arm in (B). The two panels are taken fromdi¡erent sequences of the same animal and are not occurring simultaneously, therefore are not directly comparable.

isometry (Ho: b¼1.0), and slopes and elevations of regres-sion lines were tested for di¡erences between legs. Slopeand elevation testing follow Zar (1999).

RESULTS

Kinematics

The kinematic analysis of forward walking Homarus

americanus indicates that the M-C joint £exion angle forany of the legs 3, 4 or 5 is not statistically di¡erentbetween power and return strokes either on a movingtreadmill belt or on a stable bed (ANOVA; Leg 2P¼0.326; Leg 3 P¼0.308; Leg 4 P¼0.15). Thereforepower and return strokes for the stable bed and movingtreadmill belt are combined to provide estimates of thelobster M-C joint £exion angle of (Figure 3A) 57.98�1.48(SE) for leg 3, 91.48�1.48 for leg 4, and 55.18�1.48 forleg 5. The Fr of the walking lobster ranged from 0.006 to0.016, a range of 2.7 times. The distribution of Fr was notuniform over this range, four of the lobster had Fr of*0.008 while two of them had higher Fr of 0.14. Thisinconsistency in Fr was a result of having to increase thebelt speed for two of the animals in order to motivatethem to walk; the di¡erences in Fr represent a di¡erenceof 0.05m/s in belt speed from the target speed.

Preliminary analysis indicated that the snow crab(Chionoecetes opilio) uses a complex walking motion inwhich legs 2, 3 and 4 are maintained at an acute angleto the substrate rather than perpendicular as commonin other crustaceans. While walking, the angle ofthe plane of leg 2 through the mero- and carpopodite isbetween approximately 208 and 508 with respect tothe horizontal, leg 3 between 308 and 408 and leg 4in the range of 508 to 608. Leg 5 is maintained approxi-mately perpendicular to the horizontal. These acuteangles prevent accurate M-C joint angle measurementsfrom a lateral perspective, and the overhead cameraprovided the best view.

The time course of two to three step cycles by the snowcrab are plotted in Figure 4. The physiological range of



Figure 5. Proportion of total leg length (A) and carapace size(B) represented by the meropodite for legs 2 to 5 of the lobsterand snow crab. Error bars are one standard deviation.Numbers associated with columns represent number ofmeasurements.

Table 1. Summary of regressions of meropodite length on carapace size for lobster and snow crab. Common slopes are included for thoselegs with common allometric relationships. Asterisks indicate statistical signi¢cance of slope di¡erent from isometry (isometric conditionb¼1.0; departures from this indicated by *, P50.05; **, P50.005; ***, P50.001).

Leg EquationBOLS95%

con¢dence intervals r2 N bRMA

BRMA 95%con¢dence intervals

Lobster2 Y¼0.952*X70.247 0.873^1.032 0.944 36 1.008 0.928^1.0963 Y¼1.04*X70.458 0.951^1.129 0.941 36 1.105* 1.015^1.2024 Y¼0.981*X70.401 0.899^1.064 0.945 35 1.038 0.955^1.1285 Y¼0.978*X70.476 0.904^1.052 0.954 36 1.026 0.952^1.106

Equivalent slopes (OLS)Leg 2¼Leg 4¼Leg 5 Bcommon¼0.970Leg 3¼Leg 4 Bcommon¼1.011

Snow crab2 Y¼1.562*X71.156 1.379^1.746 0.904 33 1.728*** 1.543^1.9363 Y¼1.508*X71.046 1.331^1.685 0.904 33 1.669*** 1.490^1.8704 Y¼1.403*X^0.874 1.198^1.609 0.862 32 1.628*** 1.418^1.8695 Y¼1.373*X71.007 1.230^1.515 0.923 33 1.487*** 1.344^1.645

Equivalent slopes (OLS)Leg 2¼Leg 3¼Leg 4 Bcommon¼1.496Leg 4¼Leg 5 Bcommon¼1.387

OLS, ordinary least squares; RMA, reduced major axis.

M-C joint angle used by the snow crab during lateralwalking is between approximately 508 (£exion) and 1508(extension). Mean angles of the joint extension and£exion for legs 2 to 4 on both leading and trailing sidesare illustrated in Figure 3B. Neither the mean £exion norextension angles are signi¢cantly di¡erent (P40.05)between the leading and trailing side of the body in legs2 or 3. Leg 4, however, does show signi¢cant di¡erenceswith the mean £exion angle of the leading legs being lessthan the trailing legs (0.025P50.05) and the meanextension angle of the leading legs being greater thanthe trailing legs (0.025P50.05). Examination of thecoe⁄cient of variation (CV¼ s= �xx � 100) of thesemeasured angles, initially only for the trailing legs forwhich the sample size is reasonably large, indicates thatthe joint angles during extension are more consistent(CV¼98^118) than during £exion (CV¼198^278). Theleading leg measurements utilized a much smallersample size, yet the CV indicate similar patterns (58^138for extension; 148^278 for £exion) to that of the trailinglegs. This is suggestive of two things: (1) the extension ofthe leg occurs to a much more regular ¢nal joint anglethan £exion; and (2) the measurement of this variable isnot highly sensitive to sample size.

Morphometrics

The meropodite in both the lobster and the snow crabforms a constant proportion of total leg length betweenthe four legs within a species; comprising between0.32�0.001 (SE) and 0.35�0.002 of the leg length in thelobster and from 0.41�0.002 to 0.45�0.002 in the crab(Figure 5A). As a proportion of carapace size, indicativeof meropodite length compared with body size, thelobster shows a trend of decreasing meropodite lengthfrom leg 2 to leg 5 (Figure 5B). Allometric analysis ofmeropodite length on carapace size indicates that meropo-dite length increases in an isometric manner (i.e. b¼1.0)for legs 2, 4 and 5 of the lobster (Table 1), and with positive



Figure 6. Mean moment arm as a function of M-C joint£exion angle for leg 3 of (A) the lobster and (B) the snow crab.X and Y error bars represent standard errors. Arrows indicateapproximate range of motion of M-C joint during lateralwalking. <, Extensor; ., £exor.

Table 2. Curves describing pattern of mean moment arm length(Y¼mm) to mero-carpopodite £exion angle (X in degrees) forfour walking legs of the lobster and snow crab. See Figure 6 forillustration using leg 3.

Leg Apodeme Equation r2

Lobster2 Extensor Y¼70.0003X2+0.0577X70.3411 0.867

Flexor Y¼70.0002X2+0.063X70.8493 0.798

3 Extensor Y¼70.0004X2+0.0782X70.501 0.870Flexor Y¼70.0003X2+0.104X71.9727 0.916

4 Extensor Y¼70.0004X2+0.0605X+0.7789 0.787Flexor Y¼70.0005X2+0.1215X72.249 0.935


Snow crab2 Extensor Y¼70.0002X2+0.0222X+2.4877 0.640

Flexor Y¼70.0005X2+0.1427X71.9081 0.956




Table 3. Range of M-C joint £exion angle through whichmaximum moment arms occur. See text for description.

Leg Apodeme Lobster Snow crab

2 Extensor 758^1158 558^858Flexor 1158^1458 1058^1558

3 Extensor 758^958 558^858Flexor 1158^1458 958^1258

4 Extensor 758^1158 558^858Flexor 1158^1358 958^1558

5 Extensor1 558, 858, 1108 458, 758, 1058Flexor 1258^1458 1058^1358

1, maximum moment arms occurred over a large range of £exionangles rather than forming a single peak.

allometry in leg 3 (0.0255P50.05). However, due to thelow statistical signi¢cance, and the strongly isometricpattern if the OLS slope is used in place of the RMA,concluding that the positive allometry indicated by leg 3is real may not be supported. As further evidence of this,comparison of slopes between the four walking legs withina species indicates that the lobster leg 3 has an RMA slopesigni¢cantly greater than legs 2 and 5, but equal to leg 4,which is isometric with carapace length. For the snowcrab, all four legs show positive allometry with carapacesize. Leg 5 possesses a slope less than legs 2 and 3, butequal to leg 4.

Moment arm

The mean extensor and £exor moment arms of thelobsters legs as a function of M-C £exion angle ¢t quitewell to second order curves (Figure 6, Table 2) withinthe physiological range of motion. The extensormoment arm is the smaller of the two in all legsexamined and peaks at M-C joint £exion anglesbetween approximately 758 and 1158 among the fourlegs (Table 3). The range through which the peakoccurred was de¢ned as the top 20th percentile of thedistribution of moment arms. During the extension ofthe leg there is an increase in extensor moment armfrom M-C £exion angles of 258^358 to the peak andthen subsequent decline through angles up to 1658. The£exor apodeme has a maximum moment arm exceedingthe extensor and peaks at a greater value of leg £exion

(i.e. in the range of 1158 to 1458 M-C £exion angle).During leg £exion from an extended limb, this momentarm e¡ectively begins at its maximum value and under-goes a decline as the leg is £exed. Thus within the rangeof movement of approximately 608 to 1408 for the lobsterboth extensor and £exor are initiating their movementsat the maximum moment arm and then declining downtheir respective curves as £exion/extension occurs.Reversal from extension to £exion corresponds tomoving from the declining extensor curve in Figure 6to the upper £exor curve and then following that curveas the leg is £exed. In all four legs of the lobster the twoapodeme moment arms are approximately equivalentin the range of 558^708; there exists a crossover pointin this range, and below this the £exor moment arm issmaller than the extensor.

The snow crab extensor apodeme moment arm di¡ersfrom the lobster in that the moment arm does not declinesigni¢cantly at low £exion angles (i.e. M-C £exion angles5558). It exhibits more of a plateau at these lower £exionangles, maintaining a relatively high moment arm value atlow M-C joint £exion angles (e.g. Figure 6). The extensorin this species reaches its maximum moment arm in thejoint £exion range of 558^858 (Table 3) and declines fromthere up to M-C £exion angles of 1608. This places themaximum extensor moment arm for this species at alower M-C £exion angle than for the lobster. The £exorapodeme moment arm displays a similar pattern to thelobster with an increasing moment arm with joint £exionangle up to a maximum where it plateaus. Peak £exormoment arm occurs in the joint £exion angle range of 958



Table 4. Summary of ordinary least squares (OLS) regressions of maximum moment arm on carapace size for lobster and snow crab.Statistical di¡erences between slopes (b) and slope elevations (Elev) for extensor vs £exor moment arms within each leg are alsopresented. Asterisks are as in Table 1. If slopes are not di¡erent, the common slope is presented.

Leg Apodeme Equation bOLS 95% CI r2 NComparison of slopes

Ho: bext¼b£ex

Comparison ofelevations

Ho: Elevext¼Elev£ex

Lobster2 Extensor Not signi¢cant

Flexor Y¼1.412*X72.255 0.802^2.022 0.442 13

3 Extensor Not signi¢cantFlexor Y¼1.016*X71.44 0.436^1.596 0.511 14

4 Extensor Y¼1.464*X72.589 0.143^2.785 0.292 13 bcommon¼1.255 Elev£exElevext***Flexor Y¼1.05*X71.485 0.374^1.726 0.471 13

5 Extensor Y¼2.406*X74.454 0.727^4.085 0.487 11 bext4b£ex*** Elev£ex4Elevext***Flexor Y¼0.922*X71.223 0.296^1.547 0.442 13

Snow crab2 Extensor Y¼2.042*X73.621** 1.433^2.65 0.85 11 bext4b£ex* Elev£ex4Elevext***

Flexor Y¼1.028*X71.374 0.323^1.733 0.497 11

2 Extensor Y¼1.487*X72.532 0.537^2.437 0.475 13 bcommon¼1.219 Elev£ex4Elevext***Flexor Y¼0.937*X71.242 0.575^1.298 0.725 13

4 Extensor Y¼2.024*X73.617 0.88973.16 0.604 11Flexor Not signi¢cant

5 Extensor Y¼2.495*X74.574 0.404^4.587 0.355 12 bcommon¼1.773 Elev£ex4Elevext***Flexor Y¼1.146*X71.728 0.508^1.784 0.578 12

ext, extensor; £ex, £exor.

to 1558. Moment arms of each joint angle are plotted withjoint angle during a snow crab stepping cycle in Figure 6.The £exor apodeme moment arm acts in phase with thejoint angle, reaching minima during joint £exion andmaxima during extension. In contrast, the extensorapodeme moment arm acts out of phase with joint angle,reaching minima during maximum joint extension andmaxima during joint £exion. So within the legs of thisspecies the extensor moment arm is maximal at one endof the M-C joint £exion angle spectrum (i.e. 5*858)and the £exor is maximal at the opposite end (i.e.4*958). A crossover point, where the two moment armstake on similar values, occurs at a joint £exion angle ofapproximatelly 458^758.

The calculated maximum moment arm as a function ofcarapace length or width formed signi¢cant regressionsfor all but three of the species/leg/apodeme combinations(Table 4). For the 13 signi¢cant regressions, all but one(snow crab, leg 2, extensor) were found to scale isometri-cally with body (¼carapace) size. It is important toemphasize that tests of isometry were conducted on theOLS slopes rather than RMA due to the generally low

coe⁄cients of determination (r2 of 0.3^0.7) which wouldgreatly in£ate RMA estimates and produce meaninglessresults. Nevertheless, the hazards inherent in using anincorrect model (OLS in place of RMA) in these andfollowing slope tests must be recognized.

Within each leg a comparison of the allometric slopes ofthe extensor and the £exor moment arm were either equalor showed the extensor moment arm increasing at a rategreater than the £exor (Table 4). Leg 2 of the crab andleg 5 of the lobster showed that the extensor slope isgreater than the £exor slope, the other legs which showedsigni¢cant relationships had equal allometric slopes for thetwo apodemes.This suggests that with increasing body sizeleg 2 of the crab and leg 5 of the lobster may take on rela-tively greater extensor functions than £exor; that is, theability to extend the leg to generate forces against theenvironment may become more important in the largeranimals in these legs. In order to assess di¡erences in sizeof the maximum moment arm between the extensor andthe £exor apodeme, the elevations of the regression lineswere compared. For both species, all legs for which theextensor and £exor moment arms could be compared (i.e.had signi¢cant relationships for both extensor and £exor)showed the size of the £exor moment arm to be consider-ably (1.6 to 2.0 times) larger than the extensor (e.g. Figure7). This implies that despite a greater slope value for theextensor moment arm over the £exor in some of the legs,the £exor consistently generates considerably largermaximum moment arms than the extensor; all else beingequal, this in turn results in greater torque generation bythe £exor complex.

DISCUSSION

The M-C £exion angle reported here for forwardwalking by the lobster (Homarus americanus) are less thanthose reported in previous studies. MacMillan (1975)found for leg 4 in the American lobster a joint angle of*1108�54.08 (SD) in forward walking. Ayers & Davis(1977) found £exion angles to range between 908^1108 inthis same leg, while Ayers & Clarac (1978) report similarangles (958^1228) during forward walking in the rocklobster (Jasus lalandii). The angles reported here for leg 4(91.48�13.88 [SD]) are in the low range of these latter tworeported studies. MacMillan’s (1975) small standarddeviation is due to his reporting for one animal only; hisestimate is based on approximately 20 steps by this singleanimal. In contrast, this study with six di¡erent sizedanimals moving at di¡erent Fr, results in a larger (andperhaps more physiologically realistic) standard deviationof values about the mean M-C £exion angle. The di¡eren-tial in Fr between the lobster walking sequences limitsdirect comparison as dynamic similarity may not beachieved. However, the inadvertent use of a range of Frsuggests that the M-C joint angles of legs 3, 4 and 5 of thelobster are held quite constant over a range of speeds, evenwhen dynamic similarity is not strictly met. This may beinterpreted as the M-C joint angle remains constantdespite variation in stepping patterns, at least over smallchanges in belt velocity relative to body size. The £exionangles for legs 3 and 5 found in this study are believed tobe the ¢rst reported measurements for these legs.



Figure 7. Maximum moment arm as a function of (A) cara-pace length for lobster leg 4 and (B) carapace width for snowcrab leg 3 (B). ., Extensor; <, £exor

For both the lobster and the snow crab (Chionoecetes opilio)the meropodite forms a constant proportion of the total leglength. As this leg segment is the longest of all segments, thisis indicative that all four walking legs are constructed verysimilarly, the smaller are simply scaled down versions of thelarger. There does appear to be a decrease in meropoditelength, and thus overall leg length, with respect to carapacesize moving posteriorally along the body. For both animalsthe longer anterior-most legs allow a raising up of theanterior part of the body while using the last two or threeleg pairs to maintain balance. This behaviour may beobserved during agonistic interactions by lobster andclimbing activities of the snow crab. Such behaviourwould also elevate the animals’ sensory organs�the eyesand antennae�and defensive chelae. One of the moststriking features of the two animals is the di¡erence inmeropodite length relative to body size, the snow crab hasmeropodites approximately twice as long as the lobster perunit carapace dimension. This di¡erence results in a smallcrab having considerable stride length relative to thelobster (see also below), but may also have implicationsfor torque production about the M-C joint as the distancefrom the body mass to the fulcrum becomes considerable.It is conceivable that due to torque limitations of this joint,long meropodites relative to body mass may only bepossible for compact body/lightweight crabs such asChionoecetes and Macrocheira (Japanese spider crab).

The scaling of the meropodite length with carapace sizeis isometric, or nearly so, in the lobster and with positiveallometry in the snow crab. The only other crustaceans forwhich the growth of walking legs relative to body size hasbeen examined are two species of ghost crab. Burrows &Hoyle (1973) found that total leg length increases propor-tionally with carapace width (with a slope of approxi-mately 1.0; see ¢gure 7A in their paper) in Ocypode

ceratophthalma, while Blickhan et al. (1993) report a nega-tively allometric relationship (slope¼0.279�0.006;isometry¼0.33) between the meropodite length of thesecond walking leg and body mass for O. quadrata.

Through the majority of the physiological range ofmotion for all legs of both species the £exor possesses thelarger moment arm compared with the extensor apodeme,implying that, all else being equal, the £exor generatesgreater torque about this joint than the extensor. For mostof the legs of these two crustaceans the £exor apodeme hasa larger surface area than the extensor apodeme (seeMitchell & DeMont, 2003), representing a greater musclecross sectional area acting, further suggesting that forcesand torques generated by the £exor muscle^apodemecomplex are greater than the extensor. This, in turn,implies that the £exing motion of the leg generatesgreater torque than extension and so may be signi¢cantin locomotion. That is, the lateral walking animal may be‘pulling’ with its leading legs as much or more than‘pushing’ with its trailing legs. This is in contrast to othercrab species. Burrows & Hoyle (1973) and Blickhan & Full(1987) suggest that the main power for locomotion inOcypode is provided by the trailing legs pushing o¡ of thesubstrate. However, Hafemann & Hubbard (1969) reportthat the muscle mass associated with the £exor apodemewas over twice that associated with the extensor inPachygrapsus transversus, implying greater force generationby the £exors for this species.

The £exor moment arm is maximal when the leg isextended and declines during leg £exion, to the point thatboth the £exor and extensor are of equal length (thoughthe £exor may still be generating greater torque due to itsgreater muscle area) around 45o to 758 M-C £exion angle.Therefore, the greatest torque generation by the £exor iswhen the leg is fully or near-fully extended. By similarreasoning, the extensors are maximal at relatively lowM-C £exion angles. Based on this, it would appear reason-able that the laterally walking crab should extend itsleading legs to a greater extent (to take advantage of thelarger £exor moment arm) than the trailing legs, andalso only £ex its trailing legs to a minimum of 558,below this the moment arm length does not increase.During lateral walking by the snow crab legs 2 and 3show similar M-C joint angle excursion for bothleading and trailing legs. In contrast, leg 4 indicatessome asymmetry between the leading and trailing sideswith greater degree of £exion (i.e. smaller £exion angle)and extension on the leading side. This is unlike thedi¡erence in the angle of excursion shown by Carcinus

maenas (as reported in Evoy & Ayers, 1982) in whichthere was a 308 increase in excursion angle fromleading to trailing sides. For the snow crab leg 2 onlyshowed an 118 increase in excursion, leg 3, 68, and leg 4a value, 278, closer to that reported for C. maenas. Thesole study reporting angles of M-C joint £exion duringlateral walking in H. americanus (Ayers & Davis, 1977)include £exion angles of 608 to 1308 by the leading legs,and 858 to 1308 by the trailing legs. A study on therelated species Palinurus vulgaris reports £exion angles of668 to 1308 for the leading legs and 748 to 1378 for thetrailing legs (Ayers & Clarac, 1978).

During forward walking the lobster M-C joint angle oflegs 3 and 5 (*508^558) results in approximately equalextensor and £exor moment arms, while leg 4 joint angle(*908) occurs at the peak extensor moment arm. Thisimplies that legs 3 and 5 are maintained at angles inwhich the £exor and extensor moment arms are approxi-mately equal; possibly this is so in order to maximizetorque in either a pushing or pulling direction. Leg 4meanwhile, appears to maximize the extensor momentarm. Leg 4 may be used largely for support, and it doesthis by pushing outward against the substrate. Due to thecentre of gravity being located near legs 4 and 5(MacMillan, 1975; Nauen & Shadwick, 1999) the lesserangles of legs 3 and 5 may be providing vertical supportfor the body mass, while leg 4, at closer to 908, mayprovide much of the propulsive and directional control.Legs 4 and 5 are considered to be the primary legs forlocomotion in many lobster and lobster-like crustaceans(Lockhead, 1960; Chasserat & Clarac, 1983, Clarac &Chasserat, 1983, Klarner & Barnes, 1986). The equality ofthe lobster mean power and return strokes implies thatduring the return phase of the step cycle the M-C joint isonly extended slightly, enough to clear the substrate butnot lifted excessively high of the bottom. That the meanjoint £exion angle during the moving belt is equal to thatduring stable bed walking suggests that despite the ‘arti¢-cial’ environment of the moving substrate, the animal iswalking in a normal manner. This provides furthersupport that treadmill walking is representative of freewalking.



In summary, the growth of lobster legs appears to beisometric, the three posterior legs appear to performdi¡erent functions based on M-C joint angle, and thetorque generation potential is maximized for both £exionand extension in legs 3 and 5, and extension for leg 4. Thesnow crab shows positively allometric growth of leg lengthwith carapace size, and the leading and trailing legs are,for the most part, kinematically similar. Kinematics andrelative moment arm sizes of the £exor and extensorapodemes suggest that the crab and lobster may exertmore of a pulling force by the leading legs than pushingby the trailing legs in lateral walking. This is di¡erentfrom other crab species, and may represent a previouslyunreported mechanism of crustacean locomotion. Forceplate studies of these laterally walking animals arerequired to con¢rm these hypotheses.

We would like to acknowledge the assistance and support ofMikio Moriyasu and Marc Lanteigne of the Department ofFisheries and Oceans, Moncton, New Brunswick for providingexperimental animals, support, and reviewing early drafts ofthis manuscript.We also thank JimWilliams of St Francis XavierUniversity, Antigonish, Nova Scotia for early review of themanuscript. Anne Louise MacDonald of the Animal CareFacility at St Francis Xavier University cared for the live animalsprior to and after experimentation and Werner Schnepfconstructed the treadmill for our use, for which we thank them.Funding for this work was provided by a Natural Sciences andEngineering Research Council of Canada grant to M.E.DeMont. We also thank two anonymous referees for valuablecomments to improve the manuscript.

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Submitted 21 October 2002. Accepted 8 October 2003.



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