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3510
Introduction
The use of traps for predation has evolved independently in
several groups of animals (e.g. spiders, wormlion larvae,
trichopteran larvae) (Alcock, 1972). This strategy reduces the
amount of energy expended in hunting and chasing prey, but
the construction of the trap is itself energy- and time-
consuming. Spiders are the main group of trap-building
animals, with over 10·000 species (Foelix, 1996). Despite
considerable variation of web architecture, and the stunning
beauty of some webs, very few studies have investigated the
costs and benefits of web architecture (Opell, 1998; Craig,
1987; Craig, 1989; Herberstein and Heiling, 1998). The most
recent comprehensive study, based on the large energy budget
of the Zygiella x-notata spider, showed that a small increase in
web size translates into a large increase in prey biomass, due
to an increase in the likelihood of catching large and heavy prey
(Venner and Casas, 2005). Thus, spiders clearly adapt their
traps as a function of costs and benefits. The geometric
complexity of spider webs, differences in material and
structural properties and the re-ingestion of webs by many
spiders make it difficult to study the optimality of construction
of these structures. The geometric simplicity of the antlion
(Myrmeleontidae) trap makes this model more accessible than
spiders’ webs for studies of the relationship between predation
and the structure of the trap – the object of this study.
Several antlion species live in sandy habitats and their larvae
dig funnel-shaped pits to catch small arthropods, primarily ants.
The pits are dug starting from a circular groove, the antlion
throwing sand with its mandibles. Afterwards, the antlion
gradually moves down in a spiral from the circumference
towards the centre, making the pit deeper and deeper
(Tuculescu et al., 1987; Youthed and Moran, 1969). At the end
of construction, the antlion is generally located at the trap
centre. It may move away from the centre over time (personal
observations). The antlion trap functions by conveying the prey
towards the base of the trap (Lucas, 1982). When the prey
arrives at the bottom of the pit, the antlion rapidly closes its
mandibles. If the prey is not bitten at the first attempt and tries
to climb up the walls of the trap, the antlion violently throws
sand over it to destabilise it and attempts to bite it (Napolitano,
1998).
The costs inherent in trap-based predation can be minimised
by choices concerning: (1) the location of the trap, (2) the
‘giving up time’, defined as the time for which the predator is
prepared to wait before changing location and (3) the structure
of the trap (Hansell, 2005). The location of the trap is
determined on the basis of a number of criteria, including prey
density (Griffiths, 1980; Sharf and Ovadia, 2006), soil granule
size distribution (Lucas, 1982), the density of other animals of
the same genus (Matsura and Takano, 1989) and disturbance
Assessing the architectural optimality of animal
constructions is in most cases extremely difficult, but is
feasible for antlion larvae, which dig simple pits in sand to
catch ants. Slope angle, conicity and the distance between
the head and the trap bottom, known as off-centring, were
measured using a precise scanning device. Complete attack
sequences in the same pits were then quantified, with
predation cost related to the number of behavioural items
before capture. Off-centring leads to a loss of architectural
efficiency that is compensated by complex attack
behaviour. Off-centring happened in half of the cases and
corresponded to post-construction movements. In the
absence of off-centring, the trap is perfectly conical and
the angle is significantly smaller than the crater angle, a
physical constant of sand that defines the steepest possible
slope. Antlions produce efficient traps, with slopes steep
enough to guide preys to their mouths without any attack,
and shallow enough to avoid the likelihood of avalanches
typical of crater angles. The reasons for the paucity of
simplest and most efficient traps such as theses in the
animal kingdom are discussed.
Supplementary material available online at
http://jeb.biologists.org/cgi/content/full/209/18/3510/DC1
Key words: animal construction, antlion pit, sit-and-wait predation,
physics of sand, psammophily.
Summary
The Journal of Experimental Biology 209, 3510-3515
Published by The Company of Biologists 2006
doi:10.1242/jeb.02401
Efficiency of antlion trap construction
Arnold Fertin* and Jérôme Casas
Université de Tours, IRBI UMR CNRS 6035, Parc Grandmont, 37200 Tours, France
*Author for correspondence (e-mail: arnold.fertin@etu.univ-tours.fr)
Accepted 21 June 2006
THE JOURNAL OF EXPERIMENTAL BIOLOGY
3511Antlion trap construction
(Gotelli, 1993). In some species, the giving up time is
determined as a function of the frequency of prey captured
(Heinrich and Heinrich, 1984; Matsura and Murao, 1994).
Antlions are also able to adapt the design of their trap (e.g. the
diameter/height ratio) in response to variations in prey
availability (Lomáscolo and Farji-Brener, 2001). The direct
impact of the geometric design of the trap on the efficacy of
predation at a given constant prey density remains unknown.
This animal-built structure is constrained by the physical
properties of the soil, in particular the crater angle, which is a
physical constant of the sand that defines the steepest possible
slope not leading to an avalanche (Brown and Richards, 1970).
This angle should be distinguished from the talus angle, which
is valid for a heap of sand. The crater angle is greater than the
talus angle because it involves arch and buttress phenomena
(Duran, 2000).
Attack behaviour (i.e. behaviour such as sand throwing and
bite attempts) when the prey attempts to escape involves an
energy cost for the antlion with respect to the situation in which
the prey is conveyed immediately to the base of the trap and
immobilised with the first bite. Cost of predation is minimal
when there is no attack behaviour. Trap slope modifies prey
movements: the weaker is the slope, the easier the locomotion
is (Botz et al., 2003). We can thus expect a decrease of
predation cost with trap angle (Fig.·1). The aims of this study
were to define the efficiency of trap geometry in terms of attack
behaviour.
Materials and methods
Three-dimensional analysis
We calculated the three-dimensional (3D) surface of the trap
by measuring all three dimensions with a scanner system
developed in the laboratory and inspired by the work of
Bourguet and Perona (Bourguet and Perona, 1998). This
system functions by projecting the shadow of a plane on the
surface of the trap (Fig.·2A) (see supplementary material for
the calculus details). A camera (Euromex VC3031) records the
deformation of the shadow. The data were extracted as pixel
co-ordinates in ImageJ (Abramoff et al., 2004) and were then
processed digitally in the R environment. The surface of the
trap was reconstructed by linear interpolation of the scattered
points on a grid (with each square on the grid being
0.5·mm⫻0.5·mm) (Akima, 1996) (Fig.·2B). Various geometric
parameters were calculated from this surface (Fig.·2C). The
centre of the trap was identified as the lowest point of the
surface, corresponding to the point at which all objects falling
into the trap should arrive. The height of the trap is the
difference in height between the centre and the mean height of
the points on the rim of the trap. The data were subjected to
least mean square adjustment on the conical surface given by
the equation:
(x – O
x
)
2
+ (y – O
y
)
2
– (z – O
z
)
2
tan
2
[(/2) – ␣] = 0·, (1)
The parameter ␣ is the mean angle with respect to the
horizontal of the walls of the trap. The estimated points
(O
x
,O
y
,O
z
) correspond to the summit of the inversed conical
surface. The diameter was determined from the adjusted
surface, at the mean height of the points of the rim of the trap.
The goodness-of-fit of the data was assessed by determining
the root mean square error (RMSE):
RMSE = 冑RSS/n·, (2)
where RSS is the squared sum of the residuals and n is the
number of points on the surface of the trap. RMSE gives a mean
difference in mm of the deviation from the adjusted conical
model. As an example, a RMSE of 0.4·mm corresponds to a
mean lack of conicity by about two grains of sand. The 3D co-
ordinates of the head of the antlion (corresponding to the
median point between the eyes) were calculated from the pixel
co-ordinates on the image and by projection on the surface. The
distance separating the head from the centre is referred to as
off-centring (Fig.·2C).
Behavioural experiments
Stage 2 and 3 larvae of Euroleon nostra Fourcroy
(Neuroptera, Myrmeleontidae) were collected at Tours
(47°21⬘16.36⬙N, 0°42⬘16.08⬙E, France) and raised in the
laboratory for six months with constant nutrition provided.
Larval stage was determined by measuring the width of the
cephalic capsule (Friheden, 1973). Lasius fuliginosus Latreille
(Hymenoptera, Formicidae) workers were used as prey in
observations of predation behaviour, as carcasses of this
species were frequently observed around traps in the field. The
antlions were provided with sand of known particle size
distribution (Fontainebleau sand SDS190027, particles of 100
to 300·m in size). The antlions were placed in square Perspex
boxes (11⫻11⫻6·cm) 16·h before the experiment. The traps
constructed were thus studied the first time they were used. The
boxes containing the animals were placed on a base mounted
on ball bearings so that they could be correctly positioned for
filming without disturbance. All experiments were carried out
at the same time of day (between 10.00 and 10.30·hours), in
Angle
Predation cost
0
α
WO
α
WO
Physical limit of sand
Maximal
efficiency
Loss of
efficiency
Fig.·1. Hypothetical relationship between predation cost and trap
angle. The shaded part of the graph corresponds to angles greater than
crater angle (␣
c
), which cannot be achieved because of the physical
properties of sand. ␣
WO
is the theoretical angle without off-centring.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
3512
conditions of controlled temperature (24.4±1.7°C) and
humidity (43.7±6.3%; mean ± standard deviation). We scanned
the pits dug by the antlions before introducing an ant into the
box, close to the trap. Predation sequences were filmed in their
entirety with the same camera used to record the scan. These
sequences were then analysed frame-by-frame (25·frames·s
–1
).
The recording of the sequence continued until the death of the
prey. Capture time was measured by counting the number of
frames between the moment at which the prey arrived at the
bottom of the trap and the moment at which the fatal bite was
delivered. This final bite was followed by a specific pattern of
behaviour, in which the ant was shaken and then buried in the
sand. The cost of prey capture was quantified by counting the
number of attempts to bite the prey or to throw sand over the
prey for each predation sequence. Each attack behaviour entails
a cost in terms of time and energy. To summarize, an
experiment followed this sequence: we first put an antlion in a
box of sand with known granular properties, it was allowed to
dig a trap and 3D modelling of the trap was undertaken; we
then put an ant in the box and analysed the attack behaviour
and trap geometry.
Measurement of crater angle
The measurement and definition of the drained angle of
repose can be achieved by three types of analysis, each of
which provides a slightly different angle: conical heap, two-
dimensional slope and crater angle (Brown and Richards,
1970). By analogy with the funnel-shaped trap of the antlion,
we chose to measure crater angle. This angle was measured on
A. Fertin and J. Casas
30 artificial cones obtained by filling a circular box (8·cm in
diameter, 2·cm high), in which a 1.19·mm hole had been made
in the base, with the same sand as was used in the experiments
described above. A crater is formed when the sand escapes
via the hole. The angle of the slope of this crater is the crater
angle. These cones were scanned and their surfaces were
reconstructed and adjusted, based on conical area, as described
above. Thus, for each artificial cone, we obtained a
measurement of crater angle and a measurement of deviation
from the model cone. The mean angle obtained, ␣
c
,
corresponds to the value of the drained angle of repose by a
crater. The mean RMSE value obtained, RMSE
c
, corresponds
to the smallest deviation from the model cone, taking into
account the precision of the apparatus and the size of the grains
forming the surface. The values of crater angle and RMSE
measured on the traps dug by the antlions were compared with
␣
c
and RMSE
c
as follows:
⌬
angle
= ␣
c
– ␣ and ⌬
RMSE
= RMSE – RMSE
c
.
Statistical analysis
We assessed the correlations between various geometric,
behavioural and predation variables, by calculating Pearson’s
correlation coefficients and carrying out Student’s t-tests. We
used linear models for the correlation between certain variables
for which the significance of the correlation was tested by
means of F-tests. The narrow range of angles measured allows
us to apply a linear model without transformation (Batschelet,
Fig.·2. Reconstruction and 3D
measurements of an antlion trap.
(A) Diagram of the set-up. The
light source projects a shadow of
the edge of the plane on the scene.
The edge of the plane and the
shadow are projected onto the
normalised image plane of the
camera, and the resulting image is
used to reconstruct the three-
dimensional scene in the camera’s
reference frame O(X,Y,Z). (B)
Reconstruction of the trap surface.
(C) Geometric variables measured
on the surface of the trap (green
line) and on the conical surface
(black line). The figured off-
centred position is exaggerated for
the purpose of illustration.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
3513Antlion trap construction
1981). The significance of differences of variables between
larval stage 2 and 3 was tested by means of Wilcoxon tests.
The significance of the parameters generated by these models
was assessed by means of Student’s t-tests. All means and
estimates are given with their 95% confidence interval (mean
± 95% confidence interval).
Results
Trap architecture
The values of RMSE are weak, from 0.18·mm to 0.71·mm,
indicating that traps are never far from a perfect conical model.
Out of 24 antlions, seven had an off-centring of less than 1·mm,
and 15 had an off-centring less than 2·mm. Thus, off-centring
is generally minimal, of the order of the size of its head.
Diameter, height, angle, RMSE and off-centring measured on
stage 2 larvae were not distinct from those measured on stage
3 larvae (respectively: W=40, P=0.720; W=54, P=0.3311;
W=84, P=0.494; W=43, P=0.1056; W=42, P=0.0933; N=24).
Angle was negatively correlated with RMSE (r=–0.7248,
t=–4.9350, P<0.001, N=24). Angle was also negatively
correlated with off-centring (r=–0.6481, t=–3.9917, P<0.001,
N=24). RMSE was positively correlated with off-centring
(r=0.7833, t=5.9112, P<0.001, N=24). Thus, the two geometric
parameters, trap angle and RMSE, vary similarly with off-
centring. As off-centring was observed in all cases, we also
investigated the values of trap angle and RMSE in the absence
of off-centring (␣
wo
and RMSE
wo
). A linear model accounting
for changes in ⌬
angle
as a function of off-centring (R
2
=0.42,
F=15.93, P<0.001, N=24) predicted that, in the absence of
off-centring, ⌬
angle
would be significantly different from
zero (intercept: ⌬
angle
=4.5279±1.2674°, t=7.409, P<0.001)
(Fig.·3A). The theoretical angle ␣
wo
(37.0594±1.2674°) is
therefore significantly smaller than the crater angle ␣
c
(41.6085±0.2366°; N=30). The study of the distribution of
angles measured on antlion constructions showed that the mode
was located in the confidence interval of ␣
wo
(Fig.·4). Only one
trap had an angle greater than the upper limit of this confidence
interval. Similarly, linear regression (R
2
=0.6136, F=34.94,
P<0.001, N=24) was used to predict ⌬
RMSE
in the absence of
off-centring (Fig.·3B). The predicted ⌬
RMSE
in the absence of
off-centring did not differ significantly from zero (intercept:
⌬
RMSE
=0.0359±0.0533mm, t=1.396, P=0.177). The theoretical
RMSE, RMSE
wo
=0.2478±0.0533·mm, is therefore not
significantly different from the RMSE
c
of 0.2098±0.0130·mm
(N=30). In the absence of off-centring, the antlion is therefore
able to construct a perfectly conical trap with a slope shallower
than the maximal slope permitted by the physics of sand.
Impact of trap geometry on predation cost
All ants were captured during the experiments, ensuring a
finite capture time. Out of 24 antlions, seven displayed no
attack behaviour to catch their prey, and five used attack
behaviours consisting of only one sand throwing or bite
attempt. We did not observe avalanches triggered by ant
struggle. Capture time was positively correlated with the
number of times sand was thrown (r=0.9292, t=11.79,
P<0.001, N=24), and with the number of attempts to bite the
prey (r=0.7349, t=5.0824, P<0.001, N=24). Capture time was
a linear function of the number of times sand was thrown and
the number of attempts to bite the prey (R
2
=0.9329, F=145.9,
P<0.001, N=24). Capture time was therefore considered to
represent the cost of predation, as it is known that the number
of times sand is thrown has a strong effect on predation cost
(correlation between capture time and number of times sand
thrown: r=0.9292, t=11.7899, P<0.001, N=24; correlation
between capture time and number of biting attempts:
r=0.7348753, t=5.0824, P<0.001, N=24). We then focused
primarily on correlations between capture time and geometric
variables. There was no difference in capture time between
stage 2 larvae and stage 3 larvae (W=38.5, P=0.05651, N=24).
Once the prey had fallen into the trap, the capture cost was
totally independent of the size of the trap. Indeed, capture cost
was not correlated with trap diameter (r=0.1846, t=0.8812,
P=0.3878, N=24) or trap height (r=–0.0616, t=–0.2894,
P=0.7750, N=24). Capture time was negatively correlated with
angle (r=–0.5545, t=3.1254, P<0.001, N=24) and positively
correlated with RMSE (r=0.6793, t=4.3416, P<0.001, N=24).
0 2 4 6 8
0 2 4 6 8
Δ
angle
(deg.)
A
Off-centring (mm)
Δ
RMSE
(mm)
B
0
0.1
0.2
0.3
0.4
0.5
12
10
8
6
4
2
Fig.·3. Changes in ⌬
angle
(A) and ⌬
RMSE
(B) as a function of off-
centring. The straight line corresponds to the linear model fitted on
the data. The open circles are data points and the closed circles are the
predicted values of ⌬
angle
and ⌬
RMSE
in the absence of off-centring,
making it possible to obtain RMSE
wo
and ␣
wo
: RMSE
wo
=
⌬
RMSE
(0)+RMSE
c
and ␣
wo
=␣
c
–⌬
angle
(0).
THE JOURNAL OF EXPERIMENTAL BIOLOGY
3514
Capture time was also correlated with off-centring (r=0.8992,
t=13.3903, P<0.001, N=24), and this relationship was
expressed in terms of a linear model (R
2
=0.8085, F=92.9,
P<0.001, N=24) (Fig.·5). The intercept of this regression line
was not significantly different from zero (intercept=
–0.5154±0.3571s, t=–1.443, P=0.163, N=24). Thus, a capture
time of zero can be obtained only if there is no off-centring (i.e.
the trap must be perfectly conical).
Discussion
Off-centring is the distance between the head and the lowest
point of the trap. This off-centring is the result of post-
construction actions: after constructing its trap, the animal
moves, triggering one or several avalanches of various sizes.
Off-centring therefore leads to a deviation from the perfect
cone shape and a decrease in trap angle as a result of the
A. Fertin and J. Casas
avalanches. Greater off-centring is associated with more
frequent and/or larger avalanches, leading to a simultaneous
decrease in angle and increase in RMSE. The loss of conicity
indicates deviations from a perfect conical surface due to dips
and humps in the trap surface. A loss of smoothness of the trap
surface may make it easier for the prey to climb back up the
trap. Similarly, the angle of the slope may affect the
displacement of the prey (Botz et al., 2003). This would explain
why off-centring affects capture cost: the prey arrives at a point
out of reach of the mandibles of the antlion and can move about
more easily within the trap. Off-centring therefore seems to be
the key factor determining predation cost. Thus, off-centring
leads to a loss of architectural efficiency that is compensated
for by attack behaviour.
We can now revisit our hypothetical model of costs and
benefits of the pit construction on the basis of our results
(Fig.·1). In the absence of off-centring, the trap is perfectly
conical and the angle (␣
wo
) is significantly smaller than that
defined by the physics of sand (␣
c
). Thus, before off-centring,
the antlion constructs a trap that is perfectly conical but has an
angle smaller than the crater angle. The angle ␣
wo
therefore
corresponds to the shallowest slope allowing prey to be
captured as efficiently as possible. The antlion gains no
advantage in terms of efficiency from building a trap with an
angle greater than ␣
wo
. Any perturbation leading to avalanches
leads to higher maintenance cost. Thus the slope angle targeted
by the antlion can be somewhat shallower than the crater angle.
As described in the Introduction, the animal constructs its trap
by defining an initial diameter and then digging down in a spiral
to the bottom of the funnel (Tuculescu et al., 1987; Youthed
and Moran, 1969). The creation of perfect traps requires that
the antlion begins with an initial perfect circle, digs itself down
with a spiral movement, and stops before reaching the crater
angle. We do not know the stimuli used for making this
decision, but the production of avalanches and/or the forces
acting on the numerous mechanosensors on the body may be
used.
Pits are the simplest possible type of trap, and their rarity
remains puzzling (Hansell, 2005). This foraging strategy is not
new. These insects changed habitat before the fragmentation
of Gondwana, moving from the trees to sand (i.e. from
arboreal life style to psammophily) and pit construction was
the key to the emergence of a small but successful group
within the Myrmeleontidae, the Myrmeleontini (Mansell,
1996; Mansell, 1999). Other groups that developed later,
including the Palparini, did not adopt this strategy, but have
also been successful. Pit construction does not require specific
morphological adaptations. Wormlion larvae (Diptera,
Vermileonidae, Vermileo), which have no legs or strong
mandibles, also construct pits in sand (Wheeler, 1930). Thus,
insect larvae of all morphologies are potentially able
to build such traps. Finally, the type of prey and the
microhabitat requirements are not necessarily unusual or
restrictive in any way. It therefore remains a mystery why such
simple traps have so rarely been adopted by the animal
kingdom.
An
g
le (de
g
.)
14
12
10
8
6
4
2
0
Frequency
28 30 32 34 36 38 40 42
α
c
α
wo
Fig.·4. Distribution of the angles achieved in antlion constructions.
The number of classes is given by Yule’s formula (k=5.53). The bars
with solid lines correspond to ␣
wo
and ␣
c
, and the dotted lines indicate
the 95% confidence intervals for these angles.
02468
Off-centrin
g
(mm)
8
6
4
2
0
Capture time (s)
Fig.·5. Linear changes over time in capture as a function of off-
centring.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
3515Antlion trap construction
List of abbreviations
␣ angle with respect to the horizontal of the trap
RMSE root mean square error
␣
c
drained angle of repose by a crater
RMSE
c
root mean square error by a crater at ␣
c
⌬
angle
difference between ␣
c
and trap angle
⌬
RMSE
difference between trap RMSE and RMSE
c
␣
wo
theoretical angle without off-centring
RMSE
wo
theoretical RMSE without off-centring
We would like to thank three anonymous reviewers for their
instructive comments on the first version of this manuscript, as
well as Olivier Dangles and Sylvain Pincebourde. This work is
part of the PhD thesis of A.F. financed by the Ministry of
Higher Education and Research.
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