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J Exp
Biol.
(1971), 54. 443-452
With 6 text-figures
Printed in Great Britain
THE LOCOMOTION OF THE COCKROACH
PERIPLANETA AMERICANA
FRED DELCOMYN*
Department
of
Biology, University
of
Oregon
Received 8 September1970)
INTRODUCTION
Much attention
is
currently being directed toward
the
problem
of
control
and
co-ordination of leg movements during locomotion in insects (Wilson, 1965, 1966;
Runion Usherw ood, 1966, 1968; Pearson lies, 1970). Yet, a detailed, quanti-
tative description
of the leg
movements
of
insects during walking does
not
exist
for
the most common experimental animals. Wendler (1964) supplied suchadescription
for legmovementsin the stick insect, but this insect is little used in physiological
studies of locom otion. A description of locomotion in cockroaches
was
given by Hughes
(1952),
but itis in generalaqualitative one, and no longer provides the dep thofdetail
required by thephysiologist.
The present work w as undertaken
to
provide
a
firm foundation
of
behavioural data
on whichtobase hypotheses concerning the mechanismsofcontrol and co-ordination
of leg movements (Delcomyn, 1971).Themain finding has been that the gait used by
the cockroach, Periplaneta americana, the alternating tripod or alternating triangle
gait,
is
essentially the same over nearly the entire range
of
observed speeds
of
locomo-
tion. Only atvery lowspeedsisthere any significant deviation.
MATERIAL AND M E T H O D S
All animals used in this study were intact adult American cockroaches,
P.americana
L. Each subject was placedin anoblong Perspex boxforobservation. The bottomof
theboxwas lined with graph papertogivea reference grid formovements,and its
walls were coated with petroleum jelly to prevent the animal from escaping.The
cockroaches were photographed with a Hycam rotating-prism, high-speed motion
picture camera (Red Lake Labs, Santa Clara, California) at 200 or 500framesper
second as they moved freely along the lengthof thebox.Thecamera was arrangedso
that four to seven full stepsofeachlegcouldbecapturedon thefilm. Lighting was
provided by two Photoflood lights, one above each
end of
the box. These lights were
turned
off
periodically
for
brief periods during
the
photographic sessions
to
prevent
overheatingofthe animal.
The films were examined withthe aid of an analytical motion picture projector
(L-W Photo, Inc., Van Nuys, California). Analysis consisted
of
counting the num ber
of frames occupied by protraction and retraction (definitions below) during each
cycleofmovement, foreach leg.Theparametersof interest, protraction, retraction,
* Present address: Department of Zoology, University of Glasgow.
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444
FRED
DELCOMYN
cycle duration, protraction/retraction ratios, and relative phase positions were calcu-
lated from the frame data with the aid of a digital computer. G raphs of the p attern of
leg movements (e.g. Fig. 2) were drawn for each walking sequence and used as the
basis for editing the com puter output. Steps during which the animal abruptly changed
speed or direction were excluded, since the parameters under these conditions often
bore different relationships to frequency of leg movement than they did during steady
locomotion.
The terms used in describing the results are similar to those already established in
the literature (Hughes, 1952; Wilson, 1966), and are as follows:
Protraction:
the forward movement of a leg relative to the body and the ground.
Retraction:the backward movement ofaleg relative to the body. N o movement rela-
tive to the ground.
Lag:
the time from the beginning of protraction of one leg to the beginning of
protraction of another.
Phase:
the lag between two legs divided by the cycle duration of the leg which
moved first, i.e. the time relation between the movements of two legs.
RESULTS
Cockroaches do not generally run straight for long distances. However, the long
narrow structure of the running box and the petroleum jelly on the walls combined
to produce a large number of relatively straight runs through the field visible to the
camera. In add ition, the lighting was arranged so that the ends of the box were not as
well lit as the centre, which tended to increase the probability that the negatively
phototactic cockroach would continue through the well-lit centre rather than stop in
mid-run.
The cockroaches did not appear to be excessively disturbed by the lights, for after
10-15
m m m
the box some moved about quite slowly. In addition, they tended to carry
their bodies well off the floor of the box. Dragging the body is a mode of behaviour
characteristic of cockroaches in poor condition. The range of speeds observed was
about 2-80 cm/s (at a maximum temperature of
29
0
C ). The maximum speed observed
here is similar to that reported by others (Hughes, 1965).
In the present study the animals' rates of forward progression were measured
directly from the films in cm/s, and also estimated by measuring the frequency of leg
movement in Hertz (Hz). The latter measure has the dual advantage of allowing
cycle-by-cycle plotting of parameters, and of freeing the experimenter from the
necessity of measuring d irectly th e animal's rate of progression, a measurem ent which
is not possible under some experimental conditions. For these reasons, frequency of
leg movement was substituted for rate of forward progression as the independent
parameter in this study. The nearly linear relationship between average frequency of
leg movement and rate of forward progression (Fig. 1), shows that the substitution
is a straightforward one.
The movement of an animal's legs during locomotion can be visualised with the
aid of diagrams of stepping patterns, such as those shown in Figs. 2 and 3. These
diagrams illustrate typical sequences of leg movements at stepping frequencies from
1-5 t o 23 Hz, and show qualitatively the behaviour of both th e individual step
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The locomotion of the cockroach 445
parameters, protraction and retraction, and the inter-leg timing parameter, phase.
The behaviour of each of these parameters as a function of the frequency of leg move-
ments is described in detail in the following sections.
90
r
70
S. 50
< 30
10
10 20
Average frequency of leg movement Hz)
30
Fig. 1. The average speed of locomotion as a function of the average frequency of leg move-
ment. Each point represents a single continuous run. All data are for intact, unrestrained
animals.
Individual leg movem ents
The durations of both protraction and retraction decrease as the cockroach moves
at progressively higher speeds, but they do so at different rates. This may be seen in
the diagrams of stepping patterns (Figs. 2 and 3), and in Fig. 4. Retraction is nearly
three times longer than protraction at the lowest frequency of leg movement, but it
falls more rapidly than protraction as frequency of leg movement increases, until at
the highest observed stepping frequencies it is often shorter than the latter.
This differential rate of decrease is also reflected in the protraction/retraction
p/r)
ratio (Fig. 5), which increases linearly with increases in frequency of leg movement.
The relationship betweenp/r and frequency is nearly the same for each of the legs.
The parameters of the regression lines and other statistics for the data for each leg are
shown in Table 1. There is no significant difference between the slopes of any of the
distributions, i.e. the rate at which p/r increases as stepping frequency increases is
essentially the same for each of the legs.
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446
FRED DELCOMYN
However, the mean
p/r
ratios of each of the legs do not show such uniform ity, those
of the middle legs (R.2 and L2) being lower than those
of
the remaining four legs
(Table1).This difference betweenthemeanpjrof R 2 and L2and each of the remaining
R3
R2
R
L 3 -
L2f-
L1
m - - - -
- -
i-
m
-
1-
L
mi m
1 H
- - - -
1 H
Ms
B
L 3
-
m
m m m m
L2- - - - - - - - - - - - i
0-2s
Fig. 2. Stepping patterns
of
rapidly moving intact animals. Th e co nventions established by
Wilson (1966) have been followed. Th e legs on the r ight (R) and left (L) sides of the body are
numbered from front torear. Each row represents the movementsofthe indicated leg, the
solid bars representing protraction, dotted lines retraction. The diagram reads from leftto
right. N otice the simultaneous movements of the tw o sets of three legs, R3 , R i , L2 and L3 ,
L i , R2, each of which form a triangle. A . Frequen cy of leg movement about 22 H z. B. F re-
quency of leg movement about 9 Hz.
Table 1.
Correlation
and
regression parameters of
the
p / r ratio distributionfor each
leg
Leg
R i
R 2
R 3
L i
L 2
L 3
n
66
64
6 2
58
65
63
r
0-6922
0-8113
07031
07239
c-7457
0-7901
bs.e.
0-026510-0035
0-0358 + 0-0033
00344 00045
00308 0-0039
0-0279 0-003 1
00336 0-0033
y int.
0456
0 1 9 9
0-386
O-344
0-301
0 3 3 0
Mean
Plr
0-825
0-713
0889
0788
0-704
o-8n
(,no.ofob servations;r, correlation coefficient; 6s.E., regression coefficient (slope)its standard
error;
y
int., ordinate intercept
of
regression line. Each m ean
pjr
corresponds to
a
frequency of leg
movementof about 14-5 Hz (except R i , 139).)
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The locomotion of the cockroach
legs is significant statistically to at least the 97-5 % level of confidence in each case.
The re is no significant difference between the mean ratios of legs R.2 and L 2 , nor
between those of any of the remaining four legs. Graphically, therefore, the regression
lines for R2 and L2 are depressed vertically compared to those from the remaining
legs (Fig. 5). Since all the slopes are the same, the p/rratio at any given frequency of
leg movement is lower for legs L 2 and R2 than for legs R i , L i , R3 or L 3 . This
means that the middle legs are off the ground for shorter periods at any given speed
R3 -1
R2 -
R1
L3
L2
L1
0-2Ss
0-5s
Fig. 3. Stepping patterns of slowly moving intact animals. Conventions are as in Fig. 2.
A. The alternating movements of the two triangles of legs are still maintained at this low
frequency of leg movem ent (4 Hz ). Protraction duratio ns have now become significantly
shorter than retraction, resulting in periods during which all six legs are on the ground at
once.
B. The alternating triangle pattern has begun to break down at this frequency of leg
movement (1-5 Hz), and might be termed 'uncoupled' alternating triangle.
of locomotion than are any of the four other legs. Although there is, in fact, a great
deal of variation in thepjr ratio at any speed, thus necessitating the statistical treatm ent,
this phenomenon may be seen quite clearly in the R2 steps in Figs. 2B and
3
A.
Timing of leg movements
Except at the very lowest speeds of locomotion (stepping frequencies less than about
3 Hz),
Periplaneta
always uses the alternating tripod gait. This may be seen qualita-
tively in the stepping patterns shown in F igs. 2 and 3. Clearly, the leg movements are
rarely synchronous; that is, the three legs comprising one tripod do not usually beg in
protraction at exactly the same instant. Nevertheless, the overall consistency of the
stepping pattern is also clear.
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448
FRED DELCOMYN
This consistency isreflected in thedistributions ofphase values. Exc ept at the ex-
treme low end
of
the range
of
walking speeds, there
is n o
significant change
in
phase
as afunction of the frequency ofleg mo ve me nt Fig . 6). Statistical tests su pp or t this
statement Table
2),
since
in no
case
is
there
a
significant correlation between phase
and frequency
of
leg mo vem ent when phase values corresponding
to
frequencies less
than 5 Hz are omitted. Th is is not surprising, of course, since phase is simply a
600
520
440
360
280
U 200
120
40
s
o
fP
Ofl,
8 J
6 10 14 18 22
Frequency
of leg
movement
(Hz)
26
Fig. 4. T he du ration of the two comp onents of each step , protraction filled circles) and retra c-
tion open circles), as a function of the frequen cy of leg movem ent of leg L 3) . W hile both
components occupy less time at higher frequencies of leg movement than at lower ones, the
rate of change is different for the two.
leasure of the timing relationships between th e
legs,
which in tu rn determine the gait
mployed during walking. The fact that the average phase of L1 on L3 and of R1 on
13 is0 954 indicates that each of the front legs generally begins protraction slightly
arlier than the corresponding rear legs, rather than at exactly the same time, as
rould be demanded for a rigid alternating triangle gait. At very low walking speeds,
t stepping frequencies of about 3-4 Hz, the protraction of each front and middle leg
egins earlier than usual relative to the ipsilateral rear legs, as shown in Fig.
B,
so
le corresponding phase values are reduced Fig. 6A). Th is change in phase at low
talking speeds occurs only in ipsilateral legs. The phases of contralateral leg pairs,
lat
is,
legs in a single body segment, do not show any reduction at low walking speeds.
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The
locomotion
ofthe
cockroach
449
T a b le
2.
Correlation and
regression
parameters ofthe phase distribution of
leg
pairs.
r ri)
Mean
Leg pair >5 Hzonly) r )
b
s.E. int. phase
R2,R
3
R i , R
3
L3.R3
R i,
R2
L2,Rz
L i ,
R I
L2 , L
3
L i , L
3
L i , L
2
0.1172
53)
0-2586
47)
-0-1293 53)
0-2207 52)
0-1045 52)
O-222I 56)
O-O3O8
50)
- 0 0 8 8 4
48)
- 0 - 1 6 3 8 54)
O-II28
62)
O-4953 55)
- 0 0 6 6 8 62)
0-3446 64)
0-0141
64)
- 0 1 8 2 8 6 6 )
0-2862
61)
0-1467
57)
- 0 - 0 5 4 3 63)
(Symbols
as
0-00079 0-00090
0-00500 + 0-00121
0-00042 + 00 008 1
0-00294 + 0-00101
0-00010 + 0-00091
000148+000099
0-00212 + 0-00092
0-00142 + 0-00129
0-00036 + 0-00102
in Table1.)
0-471
0882
0499
0425
0-508
0520
0-469
O-934
0-464
0-482
954
O-493
0 4 6 7
0510
0-500
0-499
O-954
-
459
1-8
r
1-2
0-8
0-4
1-8
r
1-4
1-2
0-8
0-4
15
2 3
Frequencyofleg movement Hz)
15 21
Fig. 5.Thep/r ratio of legs R3 (A) and R 2 (B) as a function of the frequency of leg movement,
with best-fit regression lines shown. There
is no
significant difference between
the
slopes
of
the distributions, butthere isbetween thevertical displacements, indicating that R 2 (and
L 2 , not shown) protractions
are
generally shorter at
any
given speed oflocomotion than
those
of
the remaining legs.See also Table 1 andtext.
Th is finding suggests the possibility that the m echanism(s) responsible for th e phasing
of leg movements may
be
different
for
contralateral leg pairs tha n
for
ipsilateral legs.
Descriptionofthe behaviourofanother parameterofthe timingofleg movements,
lag,
isimplicitinthe descriptionofphase given above. Phaseissimply lag dividedby
cycle duration. Since phaseisconstant over nearly
the
entire range oflocomotor
speeds, lag must bear a constant relationship to cycle duration, which issimplya
reciprocal function offrequency ofleg m ovement.
DIS C US S ION
While early work on insect locomotion had been concerned primarily withthe
correct description oflegmovement (e.g.Carlet, 1879;Morgan, 1886;Demoor,
1890),
current attention has turned
to
investigations
of
mechanisms by which patte rns
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FRED DELCOMYN
1-2
1 0
0-8
0-6
0-4
n.1
i.
I
o
__
A
oo
o
.
_ l
e
o
O
I
o
o
I
o
oo
c
a
o
I I I
12 15 18 21 24 27
0-7 r
0-5
0-3
0-7
0-5
0-3 U
I
L
I I I
I
0 3 6 9 12 15 18 21 24 27
Frequency of leg movement Hz)
Fig . 6. Pha se as a function of th e frequency of leg mov eme nt during walking. A. Op en circles,
phase of L i on L 3 ; filled circles, phase of L 2 on L 3 . Th ere is an apparent tendency for the
phase to fall at leg movements below about 3 Hz, reflecting the breakdown of the alternating
triangle gait below this speed. B. Open circles, phase of L i on R i ; filled c ircles, phase of
L3 on R3. There is no fall in phase at low speeds with these contralateral leg pairs. (The
horizontal lines in the graphs are i-o and 0-5 reference lines only.)
of leg movem ents might be generated (e.g. Hughes,
1957;
Wilson, 1965, 1966; Pearson
& lies, 1970; Delcomyn, 1971). The present work is especially relevant to some of
these . Pearson & lies (1970) have shown tha t alternating bursts of flexor and extensor
motoneurone activity can be obtained in partially de-afferented preparations of
Periplaneta,
suggesting that the production of these bursts may be under the control
of
a
central programm e generator. T heir results show an increase in both extensor and
flexor burst durations as the burst period increases (i.e. as the frequency at which the
bursts occur decreases), although the latte r relationship is a weak
one.
Th eir findings
fit reasonably well with the behavioural observation that
as
leg-cycle time increases, the
duration of both protraction and retraction increase. (In the leg they examined, R3,
flexion causes protraction, extension retraction.) T he weak relationship between flexor
burst duration and burst period would be accounted for if few or none of the flexor
muscles were active during the entire period of protraction (cf. the lobster swimmeret
system, Davis, 1968), so that the duration of a burst of activity in any one flexor
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Thelocomotion of thecockroach
451
muscle would not accurately reflect the duration of protraction. In this case, the re-
lationship between flexor activity and burst period would not necessarily be similar
to that between protraction and leg-cycle time, and their results would be fully com-
patible with the behavioural data.
The data reported above are also relevant to Wilson's (1966) model of insect
Wilson pointed out that with three conditions fulfilled, an insect's gait would be
a direct function of its speed of locomotion, over the whole range of speeds. These
conditions were that as speed of walking increased: (1) protraction remained con-
stant, (2) lag between ipsilateral legs remained constant, resulting in increasing phase
between them, and (3) phase between contralateral leg pairs in each body segment
remained constant at 0-5. Conditions 1 and 2 clearly do not hold for
Periplaneta,
so
that the gait of this insect does not change over most walking speeds. Wilson has
suggested (personal communication) that Periplanetamight be considered a 'fast
wa lker', that is, an insect in which gait is affected by speed of walking only at very
low speeds, and stays constant at higher speeds. While the data are not complete for
low-speed walking, they do suggest a change of gait as the animal slows down, and thus
support this notion.
Wilson based his model primarily on the work of Wendler (1964, 1966) on the
stick insect,
arausius
morosus, and Hughes (1952, 1957) on the cockroach, Blatta
orientalis.
The locomotion of
arausius
differs from that of
Periplaneta
in several
respects. As in
Periplaneta
the
pjr
ratio increases and retraction decreases with in-
creasing speed of walking, but protraction is constant. The phase of leg pairs within
a single body segment (e.g. L2 and R2) is independent of speed, as in the cockroach,
but phases of ipsilateral leg pairs drift, increasing as speed of walking increases. Thus,
in this insect gait is a function of the speed of locomotion, over the whole range of
walking speeds.
The results of Hughes (1952) on
Blatta
have been interpreted similarly (Wilson,
1966;Wendler, 1966). However, examination of his results suggests thatBlatta walks
more like
Periplaneta
than
Carausius.
Hughes sta tes: ' Cockroaches use very nearly
the same rhythm
(R1,
L 2 , R 3 , etc.) at all speeds from
1
to 15 cm/s [about 1-8
H z ] . . . '
(p.
279), and:
The same basic rhythm of leg movements is found at all speeds of
cockroach movement, although at the very slowest ones different rhythms may be
observed. But these grade insensibly into the normal rhythm with an increase in
speed . . . (p .280).The basic rhyth m is the alternating triangle gait (cf. Fig.3 Aabove),
as shown in some of the graphs of leg movements appearing in his papers (Hughes,
1952,
1957). None of the phase values which can be calculated from his data are su b-
stantially different from those forPeriplanetashown in Figs. 4 and 5 above. Thu s, in
Blatta,gait is independent of the speed of walking at medium and fast speeds, and is
a continuous function of speed during very slow locomotion.
Mechanisms of locomotion in stick insects and cockroaches need not be as different
as the above descriptions of their patterns of locomotion might suggest. In
Periplaneta
the data suggest that at stepping frequencies below 3 -4 Hz , gait is a direct function of
velocity. The data of Hughes (1952, 1957) suggest that non-alternating tripod gaits
inBlattaalso appear only below this stepping frequency (equivalent to about 5 -7 cm /s,
see Fig. 1).
arausius
is a mu ch more slowly moving animal, and while the alternating
triangle gait is used only at the highest walking speeds, the speed at which it appears
29 EXB 54
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