J. exp. Biol. 107, 495-499 (1983)

Printed in Great Britain © The Company of Biologists Limited 1983

LABIAL EXTENSION IN THE DRAGONFLY LARVAANAXIMPERATOR

495

BY D. A. PARRYDepartment of Zoology, University of Cambridge, Downing Street,

Cambridge CB2 3EJ

{Received 23 February 1983-Accepted 29 April 1983)

The extension mechanism of the larval dragonfly's labium has been underdiscussion since Snodgrass (1954) drew attention to the absence of muscles at thehead/postmentum joint (p—h, Fig. 1A) and proposed that it was extended by bloodpressure, due to the abdominal muscles which also cause jet propulsion. Thisproposition is supported by evidence that the anus closes (Pritchard, 1965), and theabdominal muscles contract (Caillere, 1972; Olesen, 1972) during labial extension;and by reports of an increase in abdominal pressure of 5000 Pa (Olesen, 1979) and4000-12 000 Pa (Tanaka & Hisada, 1980). From high-speed film of Aeschnanigroflava, Tanaka & Hisada (1980) calculate a maximum torque of 40 ^N.m (neglec-ting water resistance) and state that this would require a joint pressure of 6000 Pa.They also claim that the labium extends normally when a pressure of 8000 Pa isapplied to a dead animal under water, thus indicating the relatively small effect ofwater resistance. However, these conclusions raise a number of questions. In derivingthe pressure of 6000 Pa, they appear to have used the torque/pressure characteristicof the postmentum/prementum joint (p-p, Fig. 1A). Had they used the p-h jointcharacteristic (their Fig. 6) a required pressure of 24 000 Pa would have been ob-tained. And the statement that 8000 Pa, applied to a head preparation under water,

Fig. 1. (A) Anax imperator. Head showing partially extended labium with angles 0 and (p, measuredwith reference to the animal's 'perch'. (B) Inertial forces and torques acting on a jointed rod OPQrotating about O and P. Gi and Gz are the centres of mass of OP and PQ.

Key words: Dragonfly larva, labial mechanism, hydraulic joint.

496 D. A. PARRY

produces normal extension, is not borne out by a comparison of their Figs 5 and 8̂which again only relates to the p—p joint. Confusion between the p—h and p-p jointfmay be due to the erroneous view that the torques at the two joints must, for mechani-cal reasons, be equal. Their data on labial movement is subject to large standard errorand no estimate is made of the error caused by the use of a simplified model, whichassumes that the mass of the prementum is concentrated at the end of the postmen-tum.

I have used fresh data, from Anax imperator (Leach), and a less approximatemodel, to recalculate the p-h joint torque and estimate the effect of water resistance;and have also briefly considered the p-p joint extensor mechanism. Second-yearlarvae were filmed at 500 frames s"1 and 15-20 °C while attacking living Calliphoragrubs (Fig. 2). From a number of trials, three successful sequences were obtainedinvolving two specimens of different size. From plots of the angles 0and <p (Figs 1Aand 3), angular velocities (&>) and accelerations (a) were calculated over 4-ms inter-vals.

Fig. IB shows the inertial forces and torques acting on the labium, treated as ajointed rod OPQ. By d'Alembert's Principle, the sum of the moments about O and thehydraulic torque at O (To) must be zero, and we have:

To = [hae + m\a\2ae] + [mrfiaeih - at cos <5) + mTl\a>(f{ai sin <5)] +[ha<p — mzma^x cos 6 — ai) — m-2flt(ti<£().\ sin d)]

where the terms in square brackets relate to the rotation of OP about O, PQ about Oand PQ about P, respectively. I express the labium's mechanical characteristics interms of the conveniently measured prementum length h (see Table 1) which largelyremoves the effect of specimen size. Substituting mean values:

T0//25 = [2-7ae] + [U-$ae + 9-2(<y02 sin 6- ag cos 6)] +

[9-004, - 9-2(oty2 sin 6 + or* cos 6)] N.m/ms.

If, instead, as assumed by Tanaka & Hisada (1980), the mass of PQ is concentratedat P, this expression reduces to: To*//2S = 14-5 agN.m/ms. Neglecting water

Time intervals: 2ms

Fig. 3. Change of 6 and <p with time (time intervals: 2ms) for three labial extensions: specimen 13,sequences 11/3 and 14/2; specimen IS, sequence 19/3. Arrows indicate moment of contact withprey. Each angle was measured four times from 18cm X 12cm prints, giving s.D. mostly < ± 1 °.

Journal of Experimental Biology, Vol. 107 Fig. 2A

'•I

Fig. 2. /bio* imperator. Labial extension filmed at 500 pictures per second (2 ms between frames).The beginning of the extension has been omitted. Scale bar = 5 mm.

D. A. PARRY (Facing p. 496)

Journal of Experimental Biology, Vol. 107 Fig. 2B

D.A.PARRY (Facing p. 497}

r ST K

Tab

le 1

. Mec

hani

cal

char

acte

nstic

s of

labium

of A

nax

impe

rato

r m

Abs

olut

e va

lues

V

alue

s in

ter

ms

of p

rem

entu

m l

engt

h 12

P X 2

+Sp

ecim

en 1

3 ts

peci

men

15

Spec

imen

13

Spec

imen

15

Mea

n 'S

o Po

stm

entu

m

s.

Mas

s m

l 13

.5 m

g 3.

5 m

g 16

.781

; kg

m-'

16.2

0 12 k

g m

-' 16

.49

12 kg

m-'

Len

gth

ll

6.4

mm

4.

2 m

m

0.69

1~

0.7

01

~

0.69

l2

f Cen

tre

of m

ass a1

3.

3 m

m

2.1

mm

0.

35 h

0.

35 12

0.

35 12

it

f Rad

ius

of g

yrat

ion

kI

1.8

mm

1.

2mm

0.

1912

0.

2012

0.

20h

M.I

. 1

1 =

klh

l 43

-74

X l

o-"

kg m

2 5.

04 x

lo-

" kg

m2

0.63

1; kg

m-'

0.65

125 k

g m

-' 0.6

41:

kg m

-' %

Prem

entu

m

%

Mas

s m

z 20

.4 m

g 5.

2 m

g 25

.361

; kg

m-'

24.0

7 12

3 kg

m-'

24.7

212

kg m

-' L

engt

h 12

9.3

mm

6.

0 m

m

-

-

-

$

f Cen

tre

of m

ass

a2

5.0

mm

3.

2mm

0.

5412

0.

53 h

0.

5412

%

Rad

ius of

gyr

atio

n k2

2.

4 m

m

1.7m

m

0-26

12

0.28

l2

0.27

12

M.I

. IZ

=k

22

m2

11

7.50

X 1

0-12

kgm

2 15

.03

X 1

0-~

~k

grn

~

1.69

Iz5 k

g m

-' 1.

93 12

5 kg

m-'

1.81

12kg

m-'

b Q + M

ass

: 77

7 m

g; l

engt

h: 3

9mm

. t M

ass:

259

mg;

len

gth:

25

mm

. f

Det

erm

ined

gra

phic

ally

fro

m a

pho

togr

aphi

c ou

tlin

e of

the

dor

sal

surf

ace.

E T 2

'-I R

498 D. A. PARRY

resistance, maximum values for T0/I25, and the corresponding torques To , for thethree sequences analysed, were:

Specimen Sequence T0//25 To To* Pressure(N.m/m5) (/zN.m) (/iN.m) (Pa)

13(/2 = 9-3mm) 11/3 108000 7-5 10-7 410014/2 132000 9-2 7-2 5000

15(/2 = 6-0mm) 19/3 168000 1-3 1-8 2600677 000 - 40-0 23 900]

Tanaka & Hisada (1980, Fig. 6) obtain a torque/pressure ratio equivalent to 0*0023h3 N.m/Pa for the p-h joint of A. nigroflava. Now torque/pressure « AV/A0 whereV and 6 are joint volume and angle (Parry & Brown, 1959) and as the anatomy of thejoints in this species and in A. imperator are similar, I have applied the same ratio tothe latter, giving the pressures shown above. These pressures are well within themaximum values recorded. The much greater torque and corresponding pressure inA. nigroflava is mainly due to its much more massive prementum (»i2 = 60-4/23

kgm~3 c.f. 24-7/23kgm~3 in A. imperator). Note that concentrating the mass of theprementum at the end of the postmentum may over- or underestimate the maximumtorque depending on the exact configuration of the extending labium.

The inertial effect of the surrounding water can be estimated by calculating theadditional torque due to the mass of water accelerated by the transverse componentsof labial movement. We can take its effective mass (mw) to be \JISHQ where 5 and / arethe width and length of the labial segment, and p is the density of water (Lighthill,1975, p. 74); and assume that its centre of mass and radius of gyration coincide withthat of the corresponding labial segment. We find that mw//23 = 26-l and 121-1kgm~3 for the postmentum and prementum respectively, and:

To(w)//25 - [4-3afl] + [(58-2 cos 6 - 45-3)(a0 cos <5 - coe1 sin 6)} +

[04,(44-1 -45-3 cos 6] N.m/m5.

Maximum values of T0//25 and To(w)/'2S do not coincide and their combined values,in the three sequences analysed, do not exceed twice the value of T0/I25 alone. Thusthe required pressure still lies within the maximum values reported.

Proceeding as above, I have calculated the maximum torques at the p-p joint andfind that, if it were to operate hydraulically, the required pressure would be similarto that at the p—h joint — the more favourable torque/pressure relation (Tanaka &Hisada, 1980, Fig. 6) being offset by the greater inertial water resistance. But thismethod of extension cannot be assumed without taking into account the pressuregradient in the postmentum, due to blood flowing into the p-p joint. By Pousieulle'sequation,

nr*

where v = joint volume (=0-008/23, determined by cannulating the head with abubble-containing capillary); t = time for joint to open (= 20ms); / = postmentum

Labial extension in the dragonfly larva Anax imperator 499

length (= 0-69/2); r = equivalent radius of postmentum (= 0-OSlzfwhere/= equiva-knt radius/external radius); and r\ = blood viscosity (taken as 0-0017Pas1 - Frew,1929). This gives a pressure drop of 30//4Pa. Now the postmentum contains twopairs of muscles and a large trachea, so/is unlikely to be more than 1/3-1 /4, givinga pressure drop of the same order of magnitude as the p—h joint pressure. So we mayconclude that the p-p joint is unlikely to operate by blood pressure despite its favour-able configuration (for which the need to fold back on itself offers an alternativeexplanation). This is in accordance with the presence of extensor (and flexor) musclesat this joint.

Tanaka & Hisada (1980) attach importance to a click mechanism at the p—p jointolAeschna nigrvflava - viz. paired knobs on the postmentum that slide along groovesin the prementum 'as if the engaged position is the real pivot of the p—p joint' (whichwould be inconsistent with a firm joint articulation). In Anax imperator no suchstructure has been found and the joint may be observed to rotate smoothly about itsarticulation.

The high-speed film was taken by Mr Gordon Runnals, and specimens were collec-ted with the help of Drs Janet and Norman Moore. I am also most grateful to ProfessorCharles Gurney and Dr K. E. Machin for their advice on the mechanical analysis, andto Dr Machin for his comments on the manuscript.

R E F E R E N C E S

CAILLEKE, L. (1972). Dynamics of the strike mAgrion (syn. Calopteryx) splendens Harris 1782 larvae (Odonata:Calopterygidae). Odonatologica 1, 11—19.

FREW, J. G. H. (1929). Studies in the metabolism of insect metamorphosis. J. exp. Biol. 6, 205-218.LIGHTHILL, J. (1975). Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics.

Philadelphia.OLESEN, J. (1972). The hydraulic mechanisms of labial extension and jet propulsion in dragonfly nymphs. J.

comp. Pkysiol. 81, 53-55.OLESEN, J. (1979). Prey capture in dragonfly nymphs (Odonata, Insecta): labial protraction by means of a

multipurpose pump. Vidensk. Mtddr dansk naturh. Foren. 141, 81-96.PARRY, D. A. & BROWN, R. H. J. (1959). The hydraulic mechanism of the spider leg. J. exp. Biol. 36, 423-433.PRITCHARD, G. (1965). Prey capture by dragonfly larvae. Can.J. Zool. 43, 271-289.SNODGRASS, R. E. (1954). The dragonfly larva. Smithson. misc. Collns 123 (2), 1-38.TANAKA, Y. & HISADA, M. (1980). The hydraulic mechanism of the predatory strike in dragonfly larvae. J .

exp. Biol. 88, 1-19.