An easy, cheap computerized method to assess two-dimensional trajectory parameters

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Belg. J. Zool., 142 (2) : 147-153 July 2012
An easy, cheap computerized method to assess
two-dimensional trajectory parameters
Marie-Claire Cammaerts1,*, Frederic Morel2,
Fabian Martino2 & Nadine Warzée2
1 Faculté des Sciences CP 160/12.
2 Faculté des Sciences Appliquées, Service LISA CP 165/57, Université Libre de Bruxelles, 50, Av. F. Roosevelt, B-1050
Bruxelles, Belgium.
* Corresponding author: mtricot@ulb.ac.be
KEY WORDS: angular speed, cemetaries, drugs,
linear speed, orientation.
Movement is essential for the survival of
mobile organisms. Its study can help to determine
taxonomic status (1), to isolate pheromones (2)
and to understand biological mechanisms (3).
It can also provide information on the health,
physiological state and motivation of animals.
However, it has rarely been rigorously quantied.
We devised a manual method in 1973 (4) and
computerized it in 1991 (5) but, despite its
continuing use (e.g. 6), this processing became
obsolete due to the evolution of computers. Plenty
of modern programs exist (7 and references
therein, 8, 9 and references therein) but require
expensive equipment, take a long time and
are generally appropriate for only one kind of
assessment. We developed a user-friendly, cheap
method that allows simultaneous assessment of
orientation, linear speed and angular speed of
any moving agent.
This software was tested on the ant Myrmica
rubra, in a colony being maintained in the
laboratory (Fig. 1A). Stimuli presented to the
foragers were pieces (1 cm2) of white paper
and isolated heads of congeners, which emit the
species’ alarm pheromone.
Ant trajectories were manually recorded, using
a water-proof marker pen, on a glass slide set
over the ants’ foraging area. They were then
traced onto transparent polyvinyl sheets, which
stuck to the screen of any PC (Fig. 1B). The
trajectories could then be analyzed using the
newly elaborated software installed on the PC:
Fig. 1. – Three steps in the computerized analysis of trajectories. A: ants are kept in the laboratory in articial
nests. Trajectories are recorded on a glass slide set above the ants’ tray and are then traced on a polyvinyl sheet.
B: this sheet is stuck to the screen of a PC. Each trajectory is entered using a mouse. C: the updated software
visualizes each trajectory and quanties its orientation, linear and angular speed.

148
1. The distance between two points on the screen,
initially assessed in pixels, is converted into a
metric unit using a dialog box, for both the X-
and Y-axes.
2. The successive points of the trajectory are
entered by clicking with the mouse, which
visualizes, in red, the trajectory on the screen
(Fig. 1C). The point towards which the moving
agent was expected to go is then located, in
green, on the screen (Fig. 1C).
3. The user then states that the trajectory entering
is nished and, after that, he/she enters, in a
window, the total time spent by the moving
agent to move along its trajectory.
4. Validating the last operation starts the
calculation, by the newly-elaborated software,
of the three following variables (Fig. 2). The
orientation (O) of the moving agent towards a
given point of the environment is the sum of the
angles, measured at each successive point of
the registered trajectory, made by the segment
‘point i of the trajectory – given point’ and
the segment ‘point i – point i + 1’ divided by
the number of measured angles. This variable
can be measured in angular degrees, for
instance. The linear speed (V) of the agent is
the length of its trajectory divided by the time
spent moving along this trajectory. It can be
measured in mm/s, for instance. The angular
speed (S) (i.e. the sinuosity) of the animal’s
trajectory is the sum of the angles, measured at
each successive point of the trajectory, made
by the segment ‘point i – point i – 1’ and the
segment ‘point i – point i + 1’, divided by the
length of the trajectory. This variable can be
measured in angular degrees/cm, for instance.
5. The required calculated values appear on
the screen of the PC, the entire operation
lasting 20-30 sec. The user can then ‘shut the
program’ or ‘begin again’, directly entering a
new trajectory.
M.-C. Cammaerts, F. Morel, F. Martino & N. Warzée
Fig. 2. – Mathematical reasoning underlying the quantication of the orientation (O), linear speed (V) and an-
gular speed (S) of a trajectory. The three variables are dened in the text.

149
Control mean difference
O M
L
74.6 124.2 101.9 119.3 105.0 114.0 86.8 106.1 57.3 101.1
70.4 113.8 98.3 118.1 91.5 109.7 89.9 101.6 44.5 97.2
99.8
93.5 6.5%
V M
L
11.0 7.0 8.0 8.0 12.5 10.0 11.5 9.0 10.0 10.0
11.6 6.8 10.3 6.0 10.8 10.6 9.5 10.1 9.3 10.3
9.6
8.5 12%
S M
L
137 156 183 63 138 138 155 253 119 214
138 149 182 62 153 149 166 225 113 201
162
154 5%
Test mean difference
O M
L
53.3 38.0 46.0 39.2 33.3 42.0 60.9 20.0 60.0 31.3
55.2 36.2 43.3 37.0 31.5 44.9 64.3 17.2 52.3 22.9
42.4
40.5 4.6%
V M
L
12.0 16.0 18.0 20.0 18.0 22.0 24.0 17.0 24.0 18.0
13.4 15.4 18.2 17.2 16.6 19.2 21.9 16.5 26.7 17.7
18.9
18.3 3%
S M
L
109 100 106 109 106 99 115 145 105 157
93 109 73 126 87 111 122 150 105 183
115.1
115.8 0.6%
Table 1
Comparison of the manual (M) and the computerized (L) method. Ten ant trajectories obtained in the presence
of a blank paper (control) and of an isolated congener’s head (test) were analyzed and the difference between the
two methods was evaluated. Differences are less than the experimental errors. O=orientation (angular degrees),
V=linear speed (mm/sec), S=angular speed (angular degrees/cm).
T. castaneum N V (mm / sec) S (angular degrees / cm)
Control
+ GSM on
+ GSM off
42
31
29
5.2 (4.6 - 5.8)
3.8 (3.2 - 4.4) P < 0.001
5.1 (4.7 - 6.2) NS
150 (120 - 183)
398 (343 - 469) P < 0.001
174 (145 - 220) NS
P. caudatum N V (mm / sec) S (angular degrees / mm)
Control
+ GSM on
+ GSM off
23
34
32
0.63 (0.57- 0.67)
0.50 (0.39 - 0.58) P < 0.001
0.66 (0.59 - 0.74) NS
179 (138 - 200)
465 (340 - 534) P < 0.001
172 (117 - 196) NS
Table 2
Assessment of the linear (V) and angular speed (S) of Tribolium castaneum and of Paramecium caudatum under
control and experimental conditions. T. castaneum was observed directly, like the ants, while P. caudatum was
observed under a stereomicroscope (Mag. = 23 X), this requiring a unit adaptation. N = number of individuals
observed; results of non-parametric χ2 tests between control and experiments: P= level of probability; NS = dif-
ference not signicant at P = 0.05. An activated GSM had an impact on the observed animals.
An easy method to assess two-dimensional trajectory parameters

150 M.-C. Cammaerts, F. Morel, F. Martino & N. Warzée
The manual and the computerized methods give
identical results (Table 1), but the computerized
one is 30 times faster and therefore allows
analysis of many more trajectories, and is more
precise, human errors being avoided.
The newly-computerized method was then used
to make ve assessments, and was thus tested.
1. Trajectories of the beetle Tribolium castaneum
were successfully analyzed under normal
conditions, near a switched-on mobile phone
(GSM) and near a switched-off GSM (Table
2). The new method is particularly applicable
to small moving animals. Note the effect of an
activated GSM on the insects’ movement.
2. Trajectories of the protozoan Paramecium
caudatum were analyzed under normal
conditions, near a switched-on GSM and
near a switched-off GSM (Table 2). A camera
lucida was applied to the stereomicroscope
under which P. caudatum were set. The new
method allows analysis of the movement of
any microscopic agent in this manner. Note,
once more, the effect of an electromagnetic
eld on living organisms.
3. Pieces of white paper (1 cm2) were deposited
for 8 days on ant cemeteries (Fig. 3A) and were
Fig. 3. – Three illustrated uses of the method. A: pieces of paper were deposited on ant cemeteries and then
presented to foragers. They were not attractive to the ants but decreased their angular speed. They thus may be
impregnated with trail pheromone deposited by ants leaving the cemeteries sites. B: isolated heads of three ant
species were presented to foragers of these species to see if such cross tests can help recognizing unknown spe-
cies. Here, the head of an individual of M. sabuleti (pointed by an arrow) is presented to workers of M. rubra,
which are not attracted by the non-specic stimulus. Cross tests and assessments using our method can thus help
discriminating between species. C: trajectories of ants moving near a small amount of ethanol or chloroform.
Ethanol increased the ants’ linear and angular speed while chloroform decreased their linear speed. Simple
ethological tests together with our software-based method can help detect minute amounts of drugs in samples.
then presented to foragers whose movement
was analyzed using the described method
(Table 3). The foragers were not attracted by
the papers but their angular speed considerably
increased. Ants transporting corpses move thus
randomly away from their nest and in a sinuous
increasingly slowing-down pattern as they
come nearer to a cemetery. They nally stop
there and drop the corpses. While returning
then to their nest, they deposit their trail
pheromone along a short distance (personal
observation), which explains the ethological
effect of cemetery sites on the ants. The new
computerized method thus provided, in a few
minutes, an explanation for the presence of ant
cemeteries, on given places, far from the nests.
4. Myrmica ants are attracted by their specic
alarm pheromone contained in the head of
workers (Table 4). Cross-tests using isolated
heads of known and unknown ants (f.i. newly
collected) (Fig. 3B) followed by analysis
of the numerous recorded ant trajectories
enable recognition of an unknown (f.i.
collected) species. Such a long process can
be efciently performed only by using this
rapid computerized method. Such taxonomic
recognition of closely related species can be

151
variable untreated paper paper deposited at cemeteries statistics
Orientation
Linear speed
Angular speed
N = 60 89.3 (66.6 – 105.3)
N = 60 12.8 (11.8 – 14.7)
N = 60 183 (147 – 211)
N = 30 91.1 (75.7 – 107.0)
N = 30 11.1 (9.2 – 14.8)
N = 30 223 (211 – 245)
NS
P < 0.05
P < 0.001
Table 3
Locomotion of Myrmica sabuleti foragers in front of their cemeteries. Blank pieces of paper or paper deposited
for 8 days at cemeteries were presented to foragers. The orientation towards the paper (angular degrees), the
linear speed (mm/sec) and the angular speed (angular degrees/cm) of 60 or 30 (= N) foragers were assessed
using our software. The distributions of the values obtained for each two stimuli were compared using the non-
parametric χ2 test. P = level of probability; NS = difference not signicant at P = 0.05.
Species whose head
was presented
Tested species
M. rubra M. ruginodis M. sabuleti
Myrmica rubra
O 44.7(42.5-52.0)
V 24.6(24.1-26.3)
S 77 (75-80)
O 105.5(86.2-119.8)
V 19.3(16.8-20.6)
S 91 (76-106)
O 81.4(69.5-96.7)
V 17.2(16.2-17.9)
S 130 (121-150)
Myrmica ruginodis
O 82.8(76.9-89.7)
V 19.6(18.9-20.8)
S 116 (111-148)
O 34.1(31.4-46.0)
V 29.8(27.6-32.8)
S 79 (63-91)
O 93.9(82.9-101.5)
V 22.5(20.2-24.9)
S 116 (110-127)
Myrmica sabuleti
O 107.2(95.7-118.2)
V 19.6(17.6-22.5)
S 160 (147-170)
O 93.6(74.8-118.2)
V 20.0(17.3-20.7)
S 121 (97- 134)
O 44.4(35.1-57.3)
V 22.8(19.3-24.1)
S 126 (106-143)
Table 4
Cross-tests between three Myrmica species, using isolated worker heads presented to foragers. The orientation
(O; angular degrees) towards the head, the linear speed (V; mm/sec) and the angular speed (S; angular degrees/
cm) of 10 foragers were assessed each time, using our software. Ants clearly oriented themselves only towards
isolated heads of their own species. Cross-tests, together with our computerized method, are thus helpful for
taxonomic purposes.
An easy method to assess two-dimensional trajectory parameters

152
extended to any animals that have specic
pheromonal secretions. It can be used as an
aid to morphological or genetic determination.
This technique should be applied, for instance,
to related bumblebee species (10), virgin
females responding only to the pheromonal
secretion of conspecic males.
5. Myrmica ants react to ethanol by increasing
their linear and angular speed (Fig. 3C), and
do so down to 0.0001 µl of ethanol, which
corresponds to an aqueous solution of 0.001%
(Table 5). These ants also react to chloroform,
but by decreasing their linear speed (Fig.
3C), this occurring down to a presentation
of 0.00001 µl of chloroform, e.g. an aqueous
solution of 0.0001%. For revealing these
kinetic reactions, many trajectories must be
analyzed, and this can be done, in a short time,
only by using this rapid, simple method. So,
using this method, Myrmica ants can be used
to detect small amount of any given drugs in
collected material.
M.-C. Cammaerts, F. Morel, F. Martino & N. Warzée
Concentration Quantity O V S
Pure water 66.3(61.2-71.7) 14.5(13.7-15.7) 142(133-153)
Ethanol
0.001
0.01
0.1
1
10
0.0001
0.001
0.01
0.1
1
80.9(70.3-108.8)
78.8(68.3-89.3)
81.1(61.7-105.8)
101.3(69.5-109.7)
77.9(67.3-91.8)
18.0(15.6-21.2) *
20.5(18.1-22.1) **
21.3(16.7-23.2) **
24.6(21.6-26.9) **
25.4(22.3-28.3) **
167(154-194) *
194(181-203) **
221(213-232) **
216(197-241) **
218(204-228) **
Chloroform
0.0001
0.001
0.01
0.1
0.00001
0.0001
0.001
0.01
77.3(60.7-93.2)
97.4(87.9-111.2)
88.5(80.4-102.0)
85.1(65.2-99.2)
12.8(12.2-14.2)
9.7(7.3-11.9) **
8.8(8.1-9.2) **
8.1(6.8-9.8) **
190(173-224) **
212(161-239) **
279(266-291) **
275(223-297) **
Table 5
Response of Myrmica sabuleti workers to ethanol and chloroform. 10 µl of differently-concentrated solutions
of these substances were presented to foragers and the locomotion of 10 of them was assessed using the here
related software. The concentration (%) is given in the rst column; the quantity (µl) presented, in the second
one. O = orientation towards the stimulus, angular degrees; V = linear speed, mm/sec; S = angular speed, angu-
lar degrees/cm. χ² tests between results for ‘pure water’ and ‘substances’: P = level of probability, * = P < 0.05
or 0.02, ** = P < 0.001, otherwise = result non signicant at P = 0.05.
In conclusion, Roduit (11) wrote: ‘no universal
solution exists for the analysis of trajectories’.
This is true when the solution requires highly
technical equipment, sophisticated software and
many conditions for being used. On the contrary,
a simple method ‒ requiring cheap material,
easy-to-use software and having no conditions
for being used ‒ may be universal or, at least,
used in a rst step to check if it may be promising
to use more onerous methods. The user-friendly
system we have here related is such a simple
method. It requires no program license and can
be used by many persons at the same time. It is
thus competitive with other more sophisticated
methods. The software, labeled OVS, will be
available on the website of the journal as soon as
the present paper is published.
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Received: July 19th, 2012
Accepted: July 31st, 2012
Branch editor: Schön Isa
An easy method to assess two-dimensional trajectory parameters