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First published online August 30, 2006
Journal of Experimental Biology 209, 3510-3515 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02401
Efficiency of antlion trap construction
Université de Tours, IRBI UMR CNRS 6035, Parc Grandmont, 37200 Tours, France
* Author for correspondence (e-mail: arnold.fertin{at}etu.univ-tours.fr)
Accepted 21 June 2006
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Summary |
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Key words: animal construction, antlion pit, sit-and-wait predation, physics of sand, psammophily
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of abbreviationsReferences |
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). 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 (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.
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Materials and methods |
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) 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 mmx0.5 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:
 | (1) |
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is the mean angle with respect to the horizontal of
the walls of the trap. The estimated points
(Ox,Oy,Oz) 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):
 | (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 µm in size). The antlions were placed in square
Perspex boxes (11x11x6 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 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 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,
RMSEc, 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
RMSEc as follows:
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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, 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).
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Results |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of abbreviationsReferences |
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wo and RMSEwo). A linear model accounting for
changes in 
angle as a function of off-centring
(R2=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 (R2=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,
RMSEwo=0.2478±0.0533 mm, is therefore not significantly
different from the RMSEc 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.
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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 (R2=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). 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
(R2=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).
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Discussion |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of abbreviationsReferences |
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). 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.
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List of abbreviations |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of abbreviationsReferences |
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c
c
anglec and trap angle
RMSE
wo
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Acknowledgments |
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Footnotes |
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of abbreviationsReferences |
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