J. Zoo!. Land. (1996) 240, 659 675

Pronounced heterochely in the ghost shrimp, Neotri’paea californiensis(Decapoda: Thalassinidea: Callianassidae): allometry,

inferred function and development

Lt\DA V. LABDtL n A. R. PAL\trR’*

Bani/teld .lfai’ine Station, Barnfield, BritiIz Colunthia J ‘OR IBO Canada andDepartment of Biological Sciences, L ‘nii’ersitt’ o/ .1 Iberra, Edmonton, Alberta T6G 2E9 Canada

(.4 ccep ted 8 November 1995)

(With plate and 6 figures in the text)

To understand their function and ontogeny better, we conducted a morphometric analysis ofclaw size and shape variation in the strikingly heterochelous. north-eastern Pacific ghost shrimp,\eotrypaea (formerly Callianassa) cali/irnien.sis. Master claws approached 25° o of total bodyweight in mature males, but rarely exceeded l0° in females. Minor claws were less than 3% ofbody weight in both sexes. The proportions of right and left master claws did not differsignificantly from 50: 50. Males exhibited a greater positive allometry than females in bothmaster and minor claw size, though master claws differed more than minor claus. Sexualdimorphism was also observed in master but not minor claw shape: compared to females.mature male master claws: a) ssere proportionally higher relative to their length: b) exhibited adeeper propodal notch and consequently a larger gape: c) developed a more slender and moredistally hooked dactyl: and dl exhibited more well-developed teeth abotit the periphery of theclaw gape.

The shape of the conspicuous gape in mature male master claws bore a close resemblance tothe cross-section of similar-sized master claws. The shape of this gape. and the presence of fineteeth about its periphery, strongly suggests that master claws function in a highly stereotypedform of grappling during agonistic encounters or perhaps during mating between similar-sizedconspecifics, In addition, a landmark morphometric analysis of relative growth suggested thatthe pronounced propodal notch develops via localized deformations near the base of the fixedfinger rather than sta a more generalized contraction of the ventral mantis region. Finally, apreliminary survey suggests that the distinctive propodal notch. sv hich may be diagnostic of thehypothesized grappling function, has evolved at least twice in the Callianassidae, once in theCallianassinae and once in the Callichirinae. Sexual selection may have significantly influencedthe evolution of these unusual master claws.

Introduction

Incidence and adaptive .cignficance ofprominent heterochely

Hypcrtrophied claws in crustaceans are used primarily for feeding and defence, and simplemechanical principles tell us the form they should take to maximize speed or strength (Warner,1977). Yet some claws are sufficientl unusual in form or magnitude of asymmetry that they musthave evolved f’or some other primary function, such as mating. sexual signalling, or intra-sexual

° Order of authorship alphabetical.‘uthor to whom correspondence should he addressed: Bamficld Marine Station. Bamfield. British C’olurnhia.

VOR I BR e-mail: rich.palmer ualberta.ca

659

1996 The Zoological Society of London

660 L. V. LABADIE AND A. R. PALMLR

combat. Hence, prominent claw asymmetries may reveal a great deal about the interplay betweensexual and natural selection. Furthermore, the sometimes peculiar shapes of these hypertrophiedclaws raise questions about how they arise developmentally.

Pronounced heterochely appears to hae evolved several times in clades of otherwisebilaterally symmetrical decapod crustaceans. It can reach rather surprising proportions inbrachyuran crabs (e.g. fiddler crabs, Ocypodidae) (Crane, 1975), lobsters (Astacidea) (Herrick.1895), and various shrimp, including snapping and river shrimp (Caridea: Alpheidae, Paleomonidae) (Williams, 1965). and mud or ghost shrimp (Thalassinidea: Callianassidae, Ctenochelidae)(Biffar, 1971; Manning & Felder, 1991). For most of these groups, the function of thehypertrophied master claw is reasonably well understood. Male fiddler crabs use their claws toattract females or to combat other males for territory or mates (Crane, 1975; Hyatt & Salmon,1978). Lobsters use them for crushing hard-shelled invertebrates (Elner & Campbell, 1981), or inintraspecific agonistic encounters (Douglis, 1946), while those in snapping shrimp may aid interritorial interactions (Nolan & Salmon, 1970). Curiously, even though the magnitude of clawasymmetry in many callianassid shrimp approaches that of the more widely studied fiddler crabs,snapping shrimp and lobsters, virtually nothing is known about how their hypertrophied andseemingly specialized master claws actually function. This lack of information is especiallypuzzling given the impressive variety of master-claw form within the family (Edmondson, 1944;Biffar, 1971; Manning & Felder, 1991).

Inferring function from Jrm

Claw function is most easily determined by direct field or laboratory observations. The paucityof such information for callianassid shrimp no doubt results from their retiring, almostexclusively subterranean habit (Pohl, 1946). Even though they will construct artificial burrowsin laboratory fossaria, observations in such a setting have yielded information mainly aboutfeeding (MacGinitie, 1934; Devine, 1966; Dworschak, l987a), respiratory (Torres, Gluch &Childress, 1977), or burrowing behaviour (Dworschak, 1983; Griffis & Chavez, 1988). Theimpressive master claws are thought to be used in aggressive interactions or mating (MacGinitie,1934; Felder & Lovett, 1989), but direct observations of such behaviours are either lacking(Devine, 1966) or a potential artefact of unnatural forced encounters outside of burrows(Rowden & Jones, 1994). Although relative growth has been examined in other species[Cailianassa kraussi (Forbes, 1977), Callichirus major (Rodrigues, 1985), Lepidophthalmuslouisianensis (Felder & Lovett, 1989), Callianassa subterranea (Rowden & Jones, 1994)], thesestudies used rclatively crude measures of claw size and shape, and hence shed little light on thedetails of master claw growth and use.

Detailed morphometric analyses can yield strong inferences about the function of particularstructures, even where behavioural observations are impossible, as in extinct but well fossilizedorganisms (e.g. the toes and feathers in Archaeopteryx (Feduccia, 1993; Speakman & Thomson,1994). We report the results of a morphometric study of relative claw growth in Neotrypaea(previously Callianassa) caflforniensis Dana (1854). whose master claws are unusual even bycallianassid standards [relations within the Callianassidae have recently been revised, and wefollow Manning & Felder’s (1991) classification throughout]. These analyses lead to specificpredictions about how their master claws may function and about the developmental processesthat gie rise to such a peculiar shape. They alco set the stage for a more thorough understandingof the evolution of heterochely within the Thalassinidea.

HETIRO( HEI.Y IN GHOST SHRIMP 661

Materials and methods

Thu/a csinidean hEology and (‘ol/eclion

Mud or ghost shrimp lhalassinidea are a distinctise, georaphicalh widespread group that isheterogeneoti both eeo1ogica11 and morphologically. Fssi1s attributed to CaIIia,io.a 1 w’nsu law> areknown trom the Mesozoic Rathhun. 1926). Liing species range in size from Biffarius l’ilorniis. whichmature at 20mm (Manning & Felder, 1991). to Callichiru,s major and Acotrtpaea gigac, which can reach orexceed 150 mm hod length (PohI. 1946: Ilaig & Abbott. 1980>. Some feed on decasing plant material. whileothers are deposit- or suspension-feeders (Griffis & Suchanek. 1991>. hut their conspicuous master clawsappear to play on1 a mmor role in feeding (Dworschak, 1987a).

Ihalassinidean shrimp are almost exclusi\ely fossorial. The can reach high densities in habitats that rangefrom high intertidal mud fiats to the margins of the continental shelf(Dw orschak. 198Th). and their burrowingactis ities can has e a major impact on sediment d namics (Rowden. Jones & Morris. 1996). Burrow formappears to be related to mode of feeding (Suchanek, 1985; (riffis & Chaez, 1988), and ranges from simpleU-or Y-shaped tubes to networks of tunnels with multiple branches or chambers that can exceed depths of100cm jDw orsehak. 1983). Most burross appear to be inhabited by only I or sometimes 2 shrimp at a time.Among callianassid species. only one ( \‘eon’i’paea a/Inns) has been confirmed to live in pairs (Dworschak,1983). although MacGinitie (1934) has suggested that the burrows of N. eali/rnieizsd interconnect.

Neotrypaeu cali/ornic’nsi.s occurs along the west coast of North America from Alaska to lower California,and can reach great numbers on intertidal bottoms of mixed sand and mud in bays and estuaries (Haig &Abbott, 1980). Indis iduals of both sexes, ranging from 18 to 90mm total length, were collected from a singleintertidal population in a sandy beach on Fleming Island (48 53’ N, 125 08’W), in Barkley Sound on thewest coast ofVancouver Island. Canada. They were distinguished from a potential congener. N. giga.s. basedon diagnostic characteristics of the master claw (KozlotY. 1987). Samples were collected in August. 1994 byshoelling trenches in the substratum and capturing shrimp as they struggled to the surface of the collapsingsediment, Shrimp were transported to the laboratory alive and subsequently frozen. Sex was determined byexamining the pleopods. 2 pairs of which occur on the anterior abdominal segments of females but notmales. Wet-weights of intact individuals, as well as cephalothorax weight. abdomen weight. and weights ofthe master and minor chelipeds (all limb segments were included in cheliped weight) of disarticulatedshrimp, were determined using a Mettler balance (BB240) accurate to 0.1 mg. To ensure a standard measureof li’e weight. shrimp t’rozen prior to weighing were corrected for small weight losses due to freezing(approx. lO°o) by least-squares linear regression techniques.

lleasuren ten (.5

All body dimensions were measured along the dorsal midline of intact, straightened specimens whose preabdominal membranes had been folded inside the carapace: I) total body length (tip of rostrum to tip oftelson: 2) carapace length (tip of rostrum to posterior margin of carapace): 3 abdomen length (anteriormargin of the first to the posterior margin of the last abdominal segment: this excluded both the broadmembrane between the abdomen and carapace. and the telson): and 4) telson length (anterior to posteriormargin). These measurements were taken with Brown and Sharp digital callipers (Digit-Cal. Model No, 599-571-3) accurate to 0.01 mm. Trunk sections and claws were then preserved in 70° o ethanol.

Calibrated drawings were made at magnifications from 60 310 x using a ca/nero lueicla attached to a WildM’S microscope. Claws from different sexes and sizes of shrimp were drawn in random order, to avoidunconscious bias. Prior to drawing. claws were placed on a bed of spherical beads and positioned so that thedactyl was 50 to 5° open. and the maximum projected area of the prepus was as close as possibleperpendicular to the stewing angle, Landmarks were identitied while the claw and drawing were stillsuperimposed, and were latci digitized using a Suminagraphics digitizing tablet (20 dots per mm resolution)and the digitizing program \lac’sleasurell (ser. 2.33. as ailable from ‘.R.P.. Landmarks were selected to

L. V. 1. \BADIF A\L) A. R. PALMER

Fin. I Master clas of a mature male .\eornpoen u1i/or,ziemij (total both length 89mm) illustrating the landmarks

digitized on all claws. Most landmarks identified biologically well-defined (developmentally homologous) points,

including hinge points (#1, 4, #6), intersections between the dactylar membrane and the propus margins (#3, #5), the

tips of the propus and dactyl (#2. #17). the base of the propodal notch (#22). and the insertion points of seseral readily

identifiable tufts of setae (=24 #28). Some ssere taken using others as a guide: landmark =7 is the midpoint betsseen

landmarks #1 and 6, landmarks 48 through #11 and #14 through #16 nere defined by the intersection ith the manus

margin of lines drawn perpendicular to the midline of the manus (#3 #7) at 25° o intersals, landmarks #12. #13, #18. and

#19 were defined by the intersection with the manus or dactyl margin of lines drawn perpendicular to the midpoint of the

lines connecting 2 =11. #2 #3. #3 #17. and #4 =17. respectively.

Class dimensions vere computed as Euclidean distances between pairs of landmarks: propus length (#1. #2). manus

length (#3. #7), manus height (#9, l5). total dactyl length (#4. y17), dactl lever length (43, 4). mid-dactyl length (#4.

#27: to avoid complications with curvature of the dactyl tip). mid-dactyl height (#18, #19), gape length (#2, #22). Angles

were computed using three landmarks (the middle landmark ss as the vertex): propodal notch angle (#2, #22, #3). dactyl

tip angle (l 7. =27. #28). Mechanical advantage vsas computed as dactl lever length total dactyl length.

sample claw features as uniformly as possible, and cla dimensions used in subsequent analyses were

computed from these landmarks (Fig. 1).

StalLs deal analyses

To estimate the combined error of drawing and digitizing, at least 10 master and minor claws of various sizes

were drass n and digittzed a second time. The average errors (S.D. of repeat measurements) vs crc approximately

(1.11 and 0.15mm (generally < 2° s for all but the smallest dimensions) forvariousdirnensions ofminorN 12)

and master claws (N .. 10). respectively. These values overestimate the measurement error of the remaining

analyses because duplicate drawings were made of early. less reliable drawings All subsequent analyses were

conducted ssith lEe measurements from the more reliable duplicate drawings.

Allometric coefficients ssere computed as reduced major axis IRMA) regression coefficients from log1-

transformed data. RMA slopes ssere calculated from ordinary least-squares linear regression slopes IOLSI

by dividing the OLS slope by the correlation coefficient (LaBarbera. 1989). Allometric coefficients ere

IlL FERO( 1-lEt ‘ Lx (311081 SHRIMP

Incidi mi of ight and kit rnaiirr los tO Motrypaea caliJorniensi.i and is dptndri na v or inaturiti llatui 1IV 00’ 05 sony d t a, at a t to ha/i ngth f bU ‘nih. 4 / -

t It alan. fl 0 ii t r is ted 1)1 tontouiitt So? a & Rhif. /981 Ihe a’ for ost railsj/ bias ias her ss’n ohstrved nai i.sp itd 24 ICI:t 24/i a

Side at maxter ilass

Sex \1aturit Right Left T ttii P

MaleImmature 9 — 16Mature 8 4 12 08”fotal l’ II 28

FemaleIminature 6 9\‘Iaiure 5 3 IIFond ii 9 2u

Grand total 28 2(1 48

Male Female 0.01 0.92immature vs. Mature 1.19 0,22Oserall Side Bias 1 02 0.31

compared between sexes and class ti pes ss ith i-tests using standard errors of the OLS slopes. Where oneor both OLS slopes were not significant statistically. hosseser. saud P values could not be computed(McArdlc. 1988). Statistical anal\ses ssere conducted with Stats iess 11 iser. 1.03 Abacus Concepts). andlandmark-morphometric analyses were conducted ss oh Morphometrika (ser. 2.00. .1. Walker).

Results

lie terochely liequencies

Males were more common in our samples than females. but we obser ed no significant difference inthe frequencies of right or left master claws, either between the sexes, or betw ceo immature and matureindividuals (Table I). In addition, although master claws occurred more commonly on the right sideoserail. this desiation from an expected frequency of 50: 50 was not significant statistically.

ieasures of ovet all hod5 size

Even though the claws in ‘S’eotripaea alzforniensic were sexually dimorphic (sec below), wedetected few differences between the sexes in measures of oserall body size. Both carapace lengthand abdomen length increased isometricailx with body length iregresslons I 4.Appendix).Although males exhibited a weak negatixe allometr for abdomen length (regression 3). thiswould not be significant statisticallx frdiossing a sequential Bonferroni adjLlstment for multipletests (N 4: Rice. 1989). Lixe weight exhibited a highly significant positive aliometry relative tobody length for males hut not females, and the sexes dilThred significantly from each other(regressions 5. 6. Appendix) Howexer, these differences were due entirely to the contribution ofthe claws, since trunk weight (lixe weight minus eheliped weight) saried isometrically with bodylength for both sexes (regressions 9. 10).

664 L. V. I BADIL ND \. R. PA.LMER

Although carapace length has often been used by others (Forbes, 1977: Felder & Lovett. 1989:Roden & Jones. 1994), we used total body length to describe overall size in subsequent anahses forthree reasons: I) it aried isometrically relative to carapace length. abdomen length. telson length

(data not shown). cephalothorax weight with claws removed. and abdomen weight (regressions1 10. Appendix). hence it provided as unbiased a measure of’size’ for subsequent analyses as any ofthese other traits: 2) it \ielded a more precise prediction of live weight than did cephalothoraxlength (r- = 0.992 vs. 0.989: data not shon: and 3) it is an easier measure of ‘size’ to visualize thanmeasures of eight or partial both length when presenting and interpreting results.

Variation in claw ,sie

Allometry in claw weight differed markedly between clax types and between sexes (Fig. 2a;regressions 11 14, Appendix). Relative to body length, master claws were more positivelyallornetric than minor claws for both sexes (P < 0.001 for both males and females). males weremore positively allometric than females for both claw types (F < 0.001 for both master and minorclaws), and all but female minor claws exhibited statistically significant positive allometry relativeto body length. When expressed as a proportion of the body weight. however, only the master clawsexhibited significant positive allometry (regressions 1 5 18. Appendix). As a consequence of theirstriking positive allometry. the master claw could contribute up to 25°o of total body weight inlarge males (Fig. 2a). Master claw weights of males and females began to diverge most noticeably at50 60mm body length (carapace length of 12 14mm), and above this size female master clawsgrow nearly isometrically with body length (i.e. the slope of the ratio is nearly zero).

Manus height of the master claws exhibited highly significant positive allometry relative tobody length for both sexes (regressions 23. 25, Appendix), but minor claws did not differ fromisometry (regressions 24, 26). Manus length, on the other hand, exhibited positive allometry onlyin males and a weak negative allometry in females (regressions 27 30). Only for male masterclaws, however, would this allometry be significant statistically following a sequential Bonferroniadjustment for multiple tests (N = 4).

Variation in claw shape

Claw shape also differed dramatically between claw types and between sexes. Master claws grewhigher relative to their length than minor claws, and among mature shrimp, male master claws grewup to 30% higher than female master claws (Fig. 2b). As for claw weight, the difference between thesexes became most apparent at total body lengths greater than 60 mm. Dactyl shape in master clawsexhibited a somewhat complex pattern of variation (Fig. 3a). Mid-dactyl height exhibited significantpositive allometry relative to mid-dactyl length for both sexes (regressions 35 and 37, Appendix), butthis allometry disappeared in males above 7mm mid-dactyl length (regression 36). Hence, dactyls of

master claws became proportionally higher in both sexes up to a total body length of 60mm, but theallometry disappeared in males above this size, yielding more slender dactyls than v ould have beenexpected given their earlier pattern of growth. Finally, mechanical advantage increased withincreasing size for master and minor claws, and was nearly 50% higher for master claws (Fig. 3h),but it did not differ between the sexes for either claw type (regressions 38 41).

Angles were more appropriate to quantify the acuteness of the propodal notch and the curvatureof the dactyl tip. Both the angle formed b the propodal notch, and the angle formed at the tip ofthe dactyl became more acute with increasing size for all claus (Figs 4a. b). hut these increases were

HETEROCHEL’t IN GROSS SHRIMP

ci)0.

0)

0

(b)

1.6

a:0)

1.40)

ci)

ci)1.2-I:0)a)

-C

1.0Cci)

0.8

100

Total body length (mm)

Fin. 2. Variation in relative cheliped weight (a) (weight of all limb segments total body weight including chehpeds) andmanus shape (h) (height lengthI of master and minor claws as a function of total body length in Neotrvpaea cahfornienszs,Lines Lorrespond to least-squares linear regressions (see Appendix. regression i 5 22 for statistics). Note that the apparentlack of a difference between the slopes for minor claws in (a), esen though the allometric coefficients clearly differ(regression 12 and 14). results in part from comparing claw weight against total weight. nhich includes the claws, and inpart from plotting the cheliped wt. body t. ratio against body length as opposed to log(hody length).

only significant for master claws (regressions 42 49, Appendix). In addition, only the propodalnotch angle differed heteen the sexes. Curiously, gape length (tip of fixed finger to base ofpropodal notch) varied isometricall\ with manus height in the master claws of both males andfemales (regressions 50 and 52). even though manus height exhibited a substantial positieallometr relatie to bod length (regressions 23 and 25). These three traits rexealed the mostabout potential cla function.

(a>

0.25

0.

c Female master

• Male master 1.•

EJ

0.05

40 60 80

L. v. LAB \DIF AD A. R. PAt MFR

(a>

50

40

a)- 30>,C.)

-o2.0

1.0

4

F i S. variation in mid-dcctyl he ght as a f nction of mid dactyl length at master claws (a) and mechanical ads antageas a function of total body length of master and minor class (b) in \ on spm a alJorn ns s F ines correspond to leastsquares line ir regic sions or d dashed lines indic te separate rcgres ions for malLs smaller or larger than mm mid-dactyllength (5cc Fig. l for dimens ons mea ired and ppendix. rgre sian 35 41 for statistics). Fcs females had dactyls thislarge oi largcr becausc fcma L5 hose relatisel smaller master classs oserall.

Master claws also diffeted between the sLxes in other ways (Plate I). In addition to beingsignificantly larger oserall. the propodal notch in males wa. deeper and less acute at its base andexhibited more welhdeeloped teeth alone its dorsal marein thus mature males exhibited a largergape hen cla sserc ci med unic vU Iric t cth scrc ao mora well dcxcloped along the innermargins of the dactyl and ixd fincr f maics,

o Female

• Male •

S

2

-

4

Middactyl length (mm>

0)

C011

-Da)

a)C)Clao

-CC)a)

Total body length (mm)

HETFROCHELY I\ GhOST SHRIMP

Fic;, 4 Variation in propodal notch angle (a) and dactI tip angle (b) as a function of total body length in Veoirtpacu(ali!ornknsis. I ines correspond to least-squares linear regressions (see Fig. 1 for dimensions measured and Appendix,regression 42 49 for statistics).

Discussion

Heterochelt and clan tuncrion

Master claws of thalassinidean shrimp exhibit an impressive variet\ of sizes and shapes(e.g. see Edmondson, 1934; Biffar, 1971; Manning & Felder. 1991). Unlike upogehiid shrimp,where males and females are effectively homochelous (MacGinitie. 1934; Ngoc-Ho, 1977). mostcallianassid and ctenochelid shrimp are conspicuously heterochelous (Manning & Felder, 1991).The proportion of right master claws in Neorrtjata cali!ol7nensrs ‘o.as approximately 0.5

(a) 0 Female minor

• [ • Male minorFemale master

• Male master

(b)

C)a)

a,C)Ca,

C-)0C

a,

0000

160

C)a)

140C)Ca,C

5. 120C-)a,U

100

20 40 60 80Total body length (mm)

100

668 I. LAB \DIE ANI) A. R. P&LMI R

(Table I). as also obser\ed in most fiddler crabs (Crane. 1975). American lobsters

(Herrick. 1895). and snapping shrimp (Darh\. 1934). The se\ual dimorphism ohsered ina/iloriiwnai.s males exhibited more well—dex eloped claws than females is also v ide-

spread among sexualix-dimorphic hrach uran crabs (Vcrmeij. I 9Th. Thus. aithuugh it hascertainl evolved independently. ihe prominent heteroehel ohserxed in A. aJi/rnienais sharesmuch in common with other markedl heterochelous decapods.

The master cla in mature male .Veorripttca CUIIIUO1U11si% (Plate I) is unustlal e encallianassid standards. Although some callianassid species ha e comparable-sized ela s. onl\

Trypaea (1us.’ra/ien.sLs exhibits a deeper propodal notch ( 13i[far, 1971: Manning & I elder. 1991 i.

The peculiar shape of this hypertrophied master claw implies that male A V a/ifornknsis must useit in some form of highly stereotyped encounter hose outcome has a large impact on fitness.

Several lines of evidence suggest that Neotrvpaea ali!orniensis master c1as are used tograpple with the master claws of similar-sized conspecifics during agonistic interactions or duringmating. First. most thalassinidean shrimp are particle feeders and, although they may aid ithburrowing, the claws appear to play only a minor role in feeding (Dorschak. 1987h), Second.the propodal notch makes little sense inechanica1l for a claw that would be used primarily forapplying forces along the middle or distal portions of the fingers. as when biting or nipping. Thisnotch, which becomes markedly deeper with increasing size (Fig. 4a). would localize such forces

Pr S TF I. \Iasier cIass trom maiure male a: s5.5 mm mial both length arii iemale h .s9n rem ii bnris length

\ r”’n paea (a/i fti/Ift 0 ‘a. Stale bar i lii mm.

HFTFROCHELY IN GHOST SHRI\IP 669

at its base and thus increase the likelihood that the fixed finger ould break oil under load.Damaged master claws are, in fact, more common in Lt’pidophthalnius iouisianensi.s during thebreeding season (Felder & Lovett. 1989). Third. the shape of the gape in mature males is quitesimilar to that of the cross-section of the manus. both at the middle and base (Fig. 5). This woulda1lo one individual to grasp another’s master claw very precisel). Fourth, the length of this gapeincreases isometrically with manus height for both males and females (regressions 50 and 52,Appendix), even though manus height exhibits a marked positive allometr relative to manuslength (Fig. 2b, regressions 23 and 25). As a consequence. the gape would be too large to graspeffectie1y the much smaller minor claws or een the master claws of much smaller individuals.Fifth, the sharply curved tip to the dactyl. which becomes quite hooked in mature animals(Fig. 4b, Plate 1). seems much better suited to grappling than to biting or nipping. Sixth, thenumerous fine, regularly shaped teeth that line the gape (Plate I) ould appear to providemultiple points of contact for a firmer grip, and bear no resemblance to the coarser molariform orsharper cutting teeth of predatory crabs (Brown. Cassuto & L.oos, 1979). or to the specializedsolitary teeth of male fiddler crabs whose master claws are used for fighting (Crane. 1975).Finally, the mechanical advantage of master claws (0.l8—0.22. Fig. 3b)is closer to that of’fast’claws of other decapods (Warner & Jones. 1976: Brown eta!.. 1979: Elner & Campbell. 1981). butit is substantially less than that observed in durophagous crabs (0.30—0.55; Vermeij. 1977). Thus,in spite of their large size, these claws do not appear to have been selected for increased strength.

Although the circumstantial evidence seems strong, direct behavioural observations will berequired to confirm the inference that the peculiar form of Neotnpaea calijbrniensis master clawshas evolved for a specialized form of grappling between similar-sized conspecifics.

Claw growth and allometrv

The master claws in male Neotrvpaea caliJrnie,,sis. which can approach 25° o of total bodyweight (Fig. 2a). are nearly as large as those observed in fiddler crabs (Uca. which can reach40% of body weight (Neville. 1976). The prominent sexual dimorphism in the claws ofcallianassid shrimp has prompted several studies of the relationship between claw allometryand sexual maturity (reviewed in Felder & Lovett. 1989). As observed in Lepidophthalmuslouisianensis (Felder & Lovett, 1989). the master claws of immature N. californiensis of both sexesexhibit a substantial positive allometry up to 45 50mm total body length (Fig. 2a). Above thissize, which presumably represents the onset of sexual maturity, the positive allometry continuesin males, but virtually disappears in females (Fig. 2a). The change with increasing size in theallornetric coefficients of dactyl shape in male N. caljforniensis (Fig. 3a) also suggests a prepubertal and post-pubertal form, at least in males. Unlike previously studied callianassid shrimp,however, N. californiensis also exhibited sexual dimorphism in the allometry of minor claw size,including claw weight (regressions 12, 14 Appendix), and manus and propus lengths (regressions28. 30, 32. 34). Although no sexual dimorphism was observed in minor claw shape (regressions20. 22. 39, 41. 43. 45. 47. 49. 51. 53). the presence of some sexual size dimorphism in minor clawssuggests their growth is not completely independent of the factors that influence master claw size.

A landmark-morphometric analysis also yielded some insights into ho claw shape differencesarise developmentally in .Veotripaea cahformensis. The prominent propodal notch could develop inone of two ways: a) via a uniform contraction along the entire length of the manus in the region ofthe notch: or b> via a localized differentiation of cuticle and loss of tissue only in the immediate‘icinitv of the notch. These two hypotheses can be distinguished by comparing the change in relative

670 L. V. IABADJF AND A. R. PAIMER

d

Fio. 5. (a) Outline of the gape in a mature male (85.5 mm total body length) master claw, compared to cross-sections

from three regions of the same claw (b d. marked by dashed lines) of Neotnpoeo cali/ormensi,v. In each cross-section. the

Outer surface is to the right. All drawings are to the same scale and from the same individual. Scale bar iS 10mm.

position of distinctive patches of setae on the manus surface (in particular landmarks #25 and #26.Fig. 1) using the analytical tools of landmark-morphometrics (Bookstein. 1992). This analysisprovides strong evidence that the notch develops via the second mechanism (Fig. 6). Hence, substantial changes in claw shape appear to be achieved by very localized developmental mechanisms.

Sexual cliinorphisni and sexual selection

Although little is known about how they actually function, the notable sexual dimorphism inNeotrtpaea cal/forniensis master claws implies a more important role in males than females. First.master claws are disproportionately heavier (Fig. 2a). and higher relative to their length (Fig. 2b).in mature males compared to females. Second. in mature males the dactyl is distinctly moreslender in the middle (Fig. 3a. Plate I). and the propodal notch angle and dactyl-tip angle are bothmore pronounced (Figs. 4a. b). As a consequence. the gape is substantially larger and closer inoutline to a cross-section of the manus in males than in females (Plate 1). Male master claws thusappear to be better suited for grappling.

Callianassid shrimp may thus represent another example of the widespread associationbetween prominent sexual dimorphism in claws and male male competition for females inother crustaceans (Warner. 1977). Indeed, in forced Iaborator\ encounters, thalassinideanshrimp exhibit considerable aggression when they cannot escape from each other into burross(Tunherg. 1986: Rowden & Jones, 1994). However, for obvious reasons, behavioural observations

b C

9iC

HFTEROCHELY IN GHOST SHRINII 6 I

of isolated individuals in laboratory fossaria (MacGinitie. 1934: PohI, 1936: Torres ci 0/.. 1977:Dworschak, 1987a) have yielded no information about mating behaviour or intrahurrowagonistic interactions (Felder & Lovett, 1989).

Implications for Thalassinidean claw evolution

Thalassinidean shrimp exhibit a remarkable variety of claw form, ranging from barelysuhchelate and effectively hornochelous in some upogebiid species. through conspicuously

Fic 6. Changes in propus -.hape with increasing sue in master ciass s of male \ eolrrpaeu ( u/iiornien’i’: (a) chusvs ofsmall shrimp tmean total both length 33 2 mm. S.D .3.58. N — 5 mapped on to those of medium-sized Shrimp meantotal body length — 48.8. S.D. 3.16. N 5k )b)claws of medium-sized shrimp mapped on to those ot large shrimp (meantotal body length 851. S.D. 3.07. N 5). Dots correspond to landmarks used in the analysis (see Fig. I for landmarklocations). Gridlines represent total deformations (both uniform and non-uniform Components) from the thin-plate splineanalysis of Bookstein (1992). based on the mean landmark configuration of the the indiiduals in each size class.

(a) Small -> Medium

(b) Medium -> Large

L. V. EABADIF ANt) A. R. PAlMER

h pertrophied and heteroehelous forms in numerous ctenochelid and callianassid clades(Stevens. 1928: Biffar. 1971: Manning & Felder. 1991’). Since their claws are rarely used forfeeding. except among species that collect seagrass to decompose in their burros (Dworschak,l987b). some other factors must be driing claw evolution ithin the dade. As we have arguedabove, numerous lines of evidence suggest that the claws of Neotripaea saulorniensi.s are used forsustained grappling with similar-sized conspecifics. One of the most striking features ofN. cah/omnu’nsis claws is the pronounced propodal notch (Plate I). which ma\ be diagnostic oftheir use for grappling.

A preliminary survey of the taxonomic distribution of propodal notches (Edmondson, 1944;Biffar, 1971; Manning & Felder, 1991) suggests they have evolved independently at least twicewithin the Callianassidae, First, propodal notches are weakly developed (Callianopsinae) orabsent (Ctenochelinae) in the closely-related family, Ctenochelidae. Second, within the Callianassidae itself, their development varies quite considerably among subfamilies. Propodal notchesare at best weakly developed in the Eucalliinae and appear to be lacking in the Cheraminae.Within the Callianassinae. other species of both Neotrypaea and Trypaea exhibit comparable ormore pronounced propodal notches, yet such notches are either weak or non-existent in othercallianassinc genera (Bif/arius, Callianassa). Similarly, within the Callichirinae propodal notchesrange from non-existent (Glypturus, some species of Callichirus), or weakly developed(Corallianassa. Neocallichirus) through to modest (Lepidophthalrnus, some species of Callichirus).

The development of modest propodal notches within both the Callianassinae and theCallichirinae. each of which also includes taxa that lack such notches, and the lack of suchnotches in other callianassid subfamilies and in the related Ctcnochelidae, all suggest thatpropodal notches have evolved at least twice, once within the Callianassinae and again in theCallichirinae. If such notches are diagnostic of a stereotyped intraspecific behaviour, then thisbehaviour too has presumably evolved twice. Needless to say. a formal comparative analysisbased on a more rigorous phylogeny will be required to confirm this hypothesis.

We thank Graeme Taylor for helping to collect the shrimp, the director and staff of the Bamfield MarineStation for their ongoing good-natured support. and L.ois Hammond, Tim Rawlings. and two reviewers forcomments on the MS. This research was funded by NSERC operating grant A7245 to ARP.

REFERENCES

Biffar. T. A. (1971). The genus Callianassa(Crustacea. Decapoda. Thalassinidca) in south Florida. with keys to western

Atlantic species. BullS/ar. Sd. 21: 637 715.Bookstein. F. L. (1992). .llorjshometrae too/s tar landmark data. Geometri and hiologr. New York: Cambridge University

Press.Brown. S .. Cassulo. S. R. & Loos. R. W. (1979). Biomechanics of chelipeds in some decapod crustaceans. J. Zoo!.

iLond. 188: 143 159.Crane. J. (1975). Fiddler rabs of the iorld. Oerpodidae: Genus (‘ca. Princeton: Princeton Universits Press.Darbs . H. (1 934). The mechanism of ass mmetrs in the Aiphetdae. Carnegie Inst. 11 ashingtosi. Papeis front the Tortu gas

Lab. 28: 349 361.Des inc. C. F.. ) 966). Ecologs of Ca/liana,ssa it/ho/i Milne—Fdssards 575 Crustacea. Thalassinidea). Trans. R. Sue. ‘s .Z.

ZOO!. 8: 93 110.Douglis. M. B. (1946). Some evidences of a dominance-suhordinanee relationship among lobsters. Jisanarus amerieanu.s.

That. Rev. 96: 553.Dworschak. P. C. (953). The hiologs of Upogshia pusilla (Petagna) Decapoda. Ehalassinideal 1. The burrows. War.

Ecol. Pubbi In Zoo!. ‘apoli I . 4: 19 43.

HEll RtICHEI.’t l\ UHOST SHR(\IP 673

1)ssors.h ik, P C (198 ) I ceding hchas sour f.. ogs /ia posit/s and (a//moos i rsrrhs no (Crustaeea. Decapoda.1 ha assinidc is In I go so Ps S91 vu, B Sm/Qua 51 (Suppl. 1): 421 429.

Dw rs..hak. P. C (198’hj Fh h’ol gy of C . ii pus Ia Petagna) (Decapoda. ihalassinidea) 11. Enstronments andis nation F/a I J4,/sf/ is Zn,! ‘sapo ‘ I 8: 33’ 8.

Fdniondson. F - H. 944,. C alli.in.,ssid a of’ :he C antral PaciSic. U as. Pap. Boson P. Bishop ‘i/us. 18: 35 61Finer, R X\ . & (‘:tnsp’Ji. A 1 . F orac. r’unctisrs and sechani..at ads antage in the cheije of the American lobster

H.anas-’,’ ui. ii .00 F)ecap oo’ Crrist.sej s. .J. /1. Loin;. 193: 269 256.1 ‘cduacia. A. 9’) . Es idenm n’n class aeonatr\ indi,ting so horeal habits of lv, hanq’ii rs a. .S C It ‘nlsingron DC

259: “)i5 9.FAder. D F. & Losen D. L. 1989). Relatii c grossth and sc\ual maturation in the cstuarine ghost shrimp Calliana.c.sa

lou sian, sins Schmitt, l9. J C rust. Blot. 9: 40 53

I ‘orhcs 5. 1 (l97) Breeding and growtt ol thc burro ing pran n C alliaisassa krauss Stebbing (C rustacea: Decapoda:I hala-,sinidea) Zoo/ 4 fr 12: 149 161.

Ciriffis R. B. & Chass.i F. L. 5 1 98u) Effects of sediment type on burros of C allianas.s’a aiifomnCnsis Dana and C. gigasDana. I Esp I/as. Bit. I., sit. 117: 779 251.

CinCh5. R. B. & Suchanek. T H. { 19911. A model of burross architecture and trophic niodes n thalassinidean shrimpDecapssda: I haiassinidea S liar. F ,q p,.,,,. 8.rr. 79: Fl 163.

H.sig. J. & Abbott. D. P.S 1980s. \lacura and Anomura. Ehe ghost shrimps, hermit crabs and allies. In Interridil inrerrehmate.c ofC’alits,’nia: 5’°’ 593. Morris, R. H Abbott, D. P. & Haderlie. F. C. (Fds). Stanford: Stanford L’nisersity Press.

Flernick, F-. .1. 1695). The American lobster: A study of its habits and deselopment. Fish. Bull. U.S. 15: 1 252.Hyatt, Ci ‘Ps. & Salmon. M (1978) Combat in the fiddler crabs Usa pugilaror and C. pui.’nas: A quantitati\c descniptise

analysis Behavior 68: 182 211Kozloff. F. N. (198). lAos ins ins, rihsatt s of’th Pat i/se ‘sorihisv sr. Seattle: Unisersity of Washington Press.1.aBarhera, M. I . (1989) Analsaing body size as a factot in ecology and esolution. 4nnu. Rev. FbI. Stir. 20: 97 117.MacCjinitie. C. F 1934). The natural histors of Cattianas,su eu/ifnm/en si.s Dana Am. 1/id/Au). 15: 166 177.Manning. R. B. & F-eider. D. F. (l99i t. Resision of the American Csillianassidae Crustacea: Decapoda: Thalassinideat

Boos . Biol us/i. 104: “64 “92McArdlc. B. H. l98X. The structural relationship: Regressions in hiolog Can. J. Zool. 66: 2329 2339.Neville. A C . 1 9”6 S. liCniul (1’’Hinis rot’ I ondon: Arnold.Ngoc—Ho, N. I 9”7. The lars al development of 1 posff’/’ui daririni (Cruslacea. Thalassinidea) reared in the laboratory.

with a redescription of the adult. ./ toot. Loud. 181: 439 464.Nolan, B. A. & Salmon M. (1970). The behavior arid ecology of snapping shrimp. Forina Funet. 2:289 335.PohI, M. E. (1946). Ecological observations on (altianassa lisa/or Say at Beaufort, North Carolina. Ecolugi’ 27: 71 80.Rathhun, M. 7. (1926). The fossil stalk-eyed Crustacea of the Pacific slope ofNorth America. C .S. Nail. Mu,c. Bull. 138: 1 155.Rice. W R. (1989). Analyzing tables of statistical tests. 1/rn/ui/on 43: 223 225.Rodnigues. S. d .\ (1965). Sohre o creseimento re/otis o de Cullichiri,s inn/or tSar - 1818) (Crustacea. Decapoda.

Thalassinidea). Bol. /,sss/. 9: 195 211Rosvden. A. A. & Jones. \1. II. 1994)..\ contribution to the biology of the hurross ing mud shrimp. Cal/iuna.s.su

so’uerronea( Decapoda’. Thsilassinidea). .1. lIar. Blot. 4.ics,,’. U.K. 74: 62a 635.Rnsden, A. A.. Joties. M. B & Morris. A. IS. (1996). Sedtment turnover estimates for the mud shrimp C a/liana.s,s’u suhteri’unei,

(Montagu) (1 halassinidea) and its influence upon sediment resuspension in the North Sea. Cont. S/u/I Res. (In press)Sokal, R. R. & RohlI. I - J. (1481). Biomstmv. 2nd edn. San Francisco: W.H. Freeman & Co.Speakman, J. R. & Thomson. S C. (1994). Flight capabilities of 4mshaeoptirvx. Nature Lond. 370: 513.Stevens. B. A. (1928). Callianassidae from the nest coast of North America. PuhI. Pug tSound liAr. Biol. Sm 6: 315 369.Suchsinek, F. H. 5 1986). ‘1 halassinid shrimp hurrons: Ecological significance of species-specific architecture. 5th mt.

( .,s’a/ Rn’) C ongr. Tah,ri : 25)5 2 10.‘l’nrres. J. J.. (iluch. D. L. & Childress I. ) l9”'i. Actisity and phrsiological significance of the pleopods in the

respiration of C’a’/iun,,s in a/i/omni, ,isis 5 Dana) (Crustucca: Thalassinidea 5. Blot. Bull. It 00115 Hole . 152: 134 146.Tunherg. B. (19865. Studies on the popul,iti’n ccsilog’s oft smehia Is/tauruS I.eachs iCrustacea. Thalassinidea). E,iuarine

asra/ S/ic/i S5 i. 22: “5)

k’ermeij, Ci. J S I 9Th Patterns in crab class size: I he geogiaphr of crushing. Si 5!. tool. 26: 138 151.\,Sainer Ci. F’ t197’). lAs I olng- I siaN. London’ P sul LIck ltd.1k amer. C. F. & Jones. A. R (I 9Th). Leverage and muscle type in crab chelae (C rustacea. Brachyura). J. /ssol. Lond.

180: (‘8SI illianss A B lOeSj. Marine decapod nmustaccans A ilte Carolinas. Fish. Butt. 1 .5. 65: I 296.

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