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First published online October 18, 2006
Journal of Experimental Biology 209, 4295-4303 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02529
The role of target elevation in prey selection by tiger beetles (Carabidae: Cicindela spp.)
Department of Entomology, Cornell University, Ithaca, NY 14853, USA
* Author for correspondence at present address: Department of Biological Sciences, University of Cincinnati, Cincinnati, OH 45221-0006, USA (e-mail: john.layne{at}uc.edu)
Accepted 6 September 2006
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Key words: depth perception, insect vision, flat world, predatory behavior
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). Nevertheless, there are strong selection
pressures on animals to extract reliable information. Most animals use
distance information to slow down appropriately as they approach a goal.
Arboreal animals need to know the distance to the next perch when jumping
across gaps. Many visual predators would like to know the distance to
potential prey so that they can gauge a strike or at least determine whether
the pursuit may be energetically worthwhile. A variety of visual cues may be
used to determine or estimate distance to an object in the visual field
(Hershenson, 1999). Retinal
disparity during static binocular vision, ocular vergence, accommodative state
and dynamic peering can directly determine object distance within a certain
range, even if the image is composed of random dots
(Julesz, 1971). Even insects,
with their narrow heads and rigid eyes and lenses, have been demonstrated to
determine object distance through stereopsis
(Rossel, 1983) and through
motion parallax derived from peering
(Collett, 1978;
Sobel, 1990). Most other cues,
such as occlusion, perspective, gradients of motion, size and texture, etc.
are indirect and allow only relative distances of objects in the scene to be
determined. Nevertheless, there is some evidence that insects or other
arthropods can use gradients of motion
(Forster, 1979) or size
(Collett and Land, 1978) as
cues to estimate distance.
Another indirect cue that could lead to precise distance determination, if
some geometric constraints of the natural environment are met, is elevation of
objects in the visual field (Gibson,
1950; Day, 1972;
Sedgwick, 1983). Support for
this `elevation hypothesis' has been clearly demonstrated in humans
(McGurk and Jahoda, 1974;
Wallach and O'Leary, 1982;
Warren and Whang, 1987;
Philbeck and Loomis, 1997;
Ooi et al., 2001) and frogs
(Collett and Udin, 1988). It
has also been strongly implied in arthropods, such as fiddler crabs
(Hemmi and Zeil, 2003) and
backswimmer bugs (Schwind,
1978). These latter two, in particular, would be predicted to use
elevation as a distance cue, because the geometries of the natural habitats of
both fiddler crabs (intertidal sand/mud flats) and backswimmers (pond water
surface) are dominated by a flat substrate, which is required for accurate
determination of distance from elevation. Indeed, the visual systems of both
animals appear to be well-adapted for converting elevation to distance
(Schwind, 1980;
Schwind, 1983;
Zeil et al., 1986;
Zeil et al., 1989;
Zeil, 1990;
Land and Layne, 1995;
Zeil and Al-Mutairi,
1996).
The present study tests whether tiger beetles, Cicindela spp., use
elevation of potential prey in the visual field as a cue for their distance.
Tiger beetles are visual hunters and most species pursue their prey in open,
relatively flat habitats, such as sand bars, paths in woodlands, and barren
ground scrubland (Pearson,
1988; Kaulbars and Freitag,
1993). Moreover, the beetles' visual optics also exhibit some
adaptations to flat-world geometry, such as increased visual acuity around the
horizontal equator of the eye (Layne et
al., 2003). Thus, visually guided pursuit of prey by the beetles
might be expected to make use of elevation as a distance cue.
Here we present evidence that tiger beetles initiate pursuit of a target based on its estimated absolute size, which the beetles compute using elevation as the primary cue for target distance, which is in turn used to convert angular subtense to absolute size. Our evidence is twofold: first, results of behavioral experiments demonstrate that tiger beetles prefer targets of different angular size at different elevations. Second, these empirical data are accurately reproduced by a computer simulation `beetle' that selects prey based on estimating its absolute size from visual angular size and distance, the latter derived from elevation. Our methodology is unique among tests of the `elevation hypothesis' in that we present the same stimuli to the beetles at locations above and below the horizon. Previous studies of elevation as a distance cue only presented targets below the horizon, because according to the `elevation hypothesis' only these locations have a defined distance.
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Protocol
Beetles were tested from June to October; 
90% of the beetles were
Cicindela hirticollis (Say) (Carabidae), with the rest being either
C. repanda (Dejean) or C. rufiventris (Dejean). Beetles were
fed to satiation then starved for 3 or 4 days prior to their initial test and
between subsequent tests, and were tested between 10:00-17:00 h to correspond
with their natural period of activity. For each trial (stimulus combination),
11-26 beetles were chosen randomly from a population of 98 individuals, save
for those excluded from a particular trial due to the feeding/starvation
regimen. Individual beetles were tested only once with each stimulus
combination, and no beetle was tested with every combination. At the beginning
of a trial the beetle was acclimated to the arena for 5 min, during which time
it would invariably move to the edge of the arena and come to rest at a small
angle to the transparent wall. It was then presented with a single stimulus of
a given size, speed and elevation, whose perceived direction of approach
varied slightly due to the uncontrolled difference in angles at which the
beetles faced the wall. The beetle was allowed 3 min to strike at the moving
target (for slow-moving stimuli) or five passes of the stimulus across the
beetle's midline. Trials were scored on a binary system, strike vs no
response. A strike was scored when the beetle struck with its mouthparts
against the transparent arena wall in the direction of the stimulus. In almost
all cases of striking, the beetle followed the target around the arena wall,
striking repeatedly. The rare (<10%) occasions when the beetle followed,
but did not strike, were counted as no responses. Behavior across species did
not vary.
Statistical model
To determine which of the stimulus parameters (size, speed and elevation)
statistically influenced striking behavior, we fitted the results of the prey
selection experiments with a logistic general linear model (GLM;
1992, SAS Institute). All stimulus parameters and interactions between them,
plus a dummy variable (see below), were used in an all-subsets regression for
variable selection using SAS software. All assumptions of the regressions were
met. The resulting variables were used to model striking behavior in Matlab
(The Mathworks, Inc., Natick, MA, USA). The final statistical model of strike
probability, P, had the form
P=1/(1+e-L), where
L=ß0+ß1(size)+ß2(speed)+ß3(elevation)+ß4(size·z)+ß5(elevation·z)+ß6(size·elevation)+ß7(size·elevation·z)+error;
(N=150), where z is a factor for discriminating between
targets above and below the horizon: z=0 if the elevation of the
upper edge of the target >0, otherwise z=1.
Simulation model
The proportion (p) of beetles striking at prey stimuli was
simulated as the product of three stimulus-dependent factors (F)
according to the equation:
 | (1) |
These factors were computed under the following assumptions. (1) There is
an ideal absolute size (in cm) and speed (in cm s-1) of prey; such
targets elicit maximum striking behavior, and striking decreases as prey size
and/or speed deviates from the ideal. (2) Tiger beetles use flat-world
geometry to infer the absolute quantities from the angular quantities and
determine strike tendency by discerning to what degree an experimental
stimulus resembles the ideal (see Fig.
1). The simulation requires predetermined input of beetle height
above the ground, and absolute ideal prey size and speed. Because no target
may exactly match the ideal, and tiger beetles do pursue prey having a range
of sizes (Pearson and Mury,
1979), the simulation must also strike at targets that differ from
the ideal, and must have some rule for deciding strike tendency for these. We
have a good independent estimate of what the ideal prey size should be, but
there are no data available on the relationship between variation in prey size
and strike tendency for tiger beetles, i.e. how general is the search image.
The simulation therefore uses an optimization algorithm to determine a total
of nine coefficients that are associated with strike tendency for non-ideal
targets. We are not so interested in finding out via optimization
what these coefficients really are in the biological system - these should be
acquired in formal prey-choice experiments - but rather in whether any such
coefficients exist that allow the simulation to closely match the performance
of real beetles. In addition to target size and elevation, we vary target
speed. The simulation treats target speed as it does target size, and
similarly finds coefficients for targets of non-ideal speed.
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Rationale
Choosing ideal prey absolute size and speed
The model was provided with the beetles' eye-height above the ground, and
ideal prey to which it would be most attracted (i.e. the means of the
pseudo-normal distributions in Fig.
1). From ground level observations of hunting C.
hirticollis we estimate eye height to be 8 mm. We imbued the model with
the same ideal prey size and speed templates exhibited by real beetles.
Pearson and Mury presented tiger beetles of seven species, having mean body
lengths ranging from 6-20 mm, with live prey of a range of sizes
(Pearson and Mury, 1979). They
found that median prey length (PL) eaten was related to beetle
mandible length (ML) by the relation
PL=7.69·ML-7.91 [r2=0.92; units
are mm; computed from table 1
in Pearson and Mury (Pearson and Mury,
1979)]. While their precise method of measuring of mandible length
was difficult ascertain, those authors further showed that mandible length is
related to body length (BL) as ML=0.202BL+0.027 (in
mm; note: Pearson and Mury estimated this ML/BL relationship
using 17 species). The mean BL (± s.d.) of our C.
hirticollis was 13.07±0.66 mm. This corresponds to a mean
ML of 2.67 mm, which in turn corresponds to an ideal PL of
12.6 mm. That C. hirticollis tend to prefer 12.6 mm prey is
corroborated by the behavioral results of the present study. We transformed
our experimental target sizes into their perceived absolute values using
flat-world geometry and the empirical results showed that targets eliciting
the highest strike proportion were 12.3 mm, which is very close to the 12.6 mm
prey preferred by similar sized beetles in the Pearson and Mury study. Over
all stimulus permutations our beetles tended to prefer slower-moving stimuli.
Thus we chose an absolute speed of 3 cm s-1, the slowest absolute
speed to which any of our target angular speeds translated (using rearranged
Eqn 3). This is a reasonable speed for a prey item, and significantly less
than the speeds achieved by hunting beetles
(Gilbert, 1997).
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How angular dimensions of ideal prey vary with elevation
The elevation hypothesis states that the visual angular size and speed of
an ideal prey item vary as a function of stimulus elevation and three
constants:
 | (2) |
 | (3) |
where H=the height of the beetle's eye above the substrate in cm, L=ideal prey size in cm, S=ideal prey speed in cm s-1, and E=elevation in the visual field in degrees.
A problem arises with this formulation when stimulus elevation approaches
the horizon (E=0°): both 
' and 
' reach
zero directly at the horizon, which creates the paradoxical situation in which
the hypothetical ideal prey has zero size and speed. Furthermore,
' is smaller than the beetle's optical resolution limit in a
narrow region above and below the horizon. To avoid this in the simulation,
the ideal angular size was given a lower limit equal to the beetle's visual
resolution, namely:
 | (4) |
where 
is the interommatidial angle. Interommatidial angles
have been mapped over the entire eye of C. hirticollis and aligned
with the visual surround (Layne et al.,
2003). For this model we used a vertical section through the front
of the eye where the highest resolution is directed at the horizon. For
similar reasons, ideal angular speed in this small region was computed as a
function of the interommatidial angle (now equal to ideal prey size in this
small region) and absolute speed of the ideal prey:
 | (5) |
Defining the strike factors F
The `simulation beetle' assigned a strike proportion of unity to those
stimuli that were of ideal angular size 'E and angular
speed 'E for their particular elevation (the subscript
emphasizes that both ' and ' vary with elevation).
Thus, for stimuli corresponding to ideal prey,
Fsize=Fspeed=1. Stimuli that differed
from these ideals should produce a reduced strike proportion, but how reduced
should the response be? The answer has to do with the generality of a tiger
beetle's prey search image. We assumed strike proportion to be inversely
proportional to the deviation of a stimulus from the ideal. Strike proportion
was assumed to fall away from unity following a normal probability
distribution centered on the ideal (Fig.
1). We allowed for the possibility that there may be an asymmetry
in strike proportion on either side of the ideal. For instance, there may be a
larger drop in strike proportion if the stimulus is smaller than the ideal
size (rather than larger), or faster than the ideal speed (rather than
slower). Thus, the size factor has the form of a lopsided, pseudo-normal
distribution:
 | (6) |
where is the experimental stimulus size, 'E
and 
are the ideal mean and standard deviation of the
normal distribution, respectively, and 
is a constant
(see Fig. 1). The speed factor
is likewise computed as
Fspeed=f(|'E,
,). The constant
allows for an asymmetry in the effect of stimuli deviating to one side of the
ideal or the other; =1 when
>>'E (stimulus is larger than ideal),
otherwise 
1, and =1 when
'E (stimulus is slower than ideal), otherwise
1. This means that the width of the response
curve for stimuli larger than ideal will be determined solely by
, and the width of the response curve for stimuli
smaller than ideal will be determined by a multiplier on
, namely, . <1
produces a narrower normal distribution, and a greater reduction in striking
for stimuli smaller or faster than ideal, while >1 produces a
smaller reduction in striking for stimuli smaller or faster than ideal.
We have formulated the above ideal size and speed in a way that reflects at
the horizon, i.e. they produce identical strike proportions as a function of
elevation above the horizon and below. There is a good reason, however, to
believe that this is not biologically realistic. For an observer that uses
flat-world spatial geometry to produce perceptual visual size constancy, a
target seen above the horizon should be interpreted either as an object larger
than the observer itself or as airborne object; in either case such targets
are likely to be unattractive as potential prey. Our empirical results showed
this plainly. We therefore come to the third factor in the model,
Felevation. Based on previous studies on the effect of
elevation on prey selection and predator evasion (e.g.
Schwind, 1980;
Land and Layne, 1995;
Gilbert, 1997;
Layne et al., 1997;
Layne, 1998), we hypothesized
that, regardless of angular size and distance, targets at low elevations
produce a higher strike proportion than those at high elevations. Thus, the
elevation factor is Felevation=1-RE,
where RE is the reduction from unity in strike proportion
for a given elevation; 0
RE1 (see
Fig. 1).
Setting generalization and elevation initial states
As discussed, model strike tendency depends on the width of the
pseudo-normal distributions that define the reduction in strike proportion for
the deviation of a given stimulus size and speed from the ideal, and on
RE, which sets the reduction in strike tendency at high
elevations (see Fig. 1). The
widths of the pseudo-normal distributions are determined by what we will call
the prey generalization parameters: ,
, and
. Unlike the absolute ideals, we have no pre-existing
knowledge of what values these parameters should have. Instead, the model
arrived at values via a simplex optimization algorithm [Matlab's
fminsearch function; the algorithm is described elsewhere
(Lagarias et al., 1998)]. The
optimization function was seeded with arbitrary prey generalization parameter
values. By adjusting the latter, the simulation algorithm sought to minimize
the absolute difference between the model strike proportions and those
measured empirically, summed over all 150 combinations of sizes, speeds and
elevations tested. That is, it minimizes the term:
 | (7) |
where MD is what we call the model deficit.
Due to trapping by local minima, optimization algorithms may produce
different results with different initial seed values. Thus, we ran the
optimization 500 times, seeded with values drawn from uniform random
distributions having the following ranges: , 10-100
(cm); , 100-25 000 (cm s-1);
RE, 0-1; and
, 0-2. After 500 test runs the model showed a strong
tendency towards a minimum MD for a certain optimized parameter
combination; the combination that produced the smallest MD was chosen
as the best model.
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The General Linear Model (Table
1) demonstrated significant effects on the probability of striking
related to stimulus size, speed, elevation, and the interactions between size
and z, and elevation and z. In the simulation model, the
final optimized prey generalization parameters are
=82.55, =15817,
R-20=0.06, R-10=0.28,
R0=0.35, R110=0.48,
R20=0.64, =0.31,
=0.03 (d.f.=7,142). The Least Absolute Deviation
(LAD) of the simulation from the empirical data (LAD=MD/N)
is 0.0570, meaning for any given stimulus permutation, the model differs from
real beetles by just under 6%. This simulation performed nearly as well as the
GLM (LAD=0.055), a fact borne out in the results of a regression
model that tests whether the GLM or the simulation was a better
predictor of the empirical data. Both had a significant effect
(P<0.001), with the simulation having a slightly lower coefficient
(0.41 compared with 0.62; F=239, d.f.=2, 147).
The values of , ,
and need explanation.
Results from the 500 test runs (data not shown) revealed that
and can have a wide range
of values, as long as their product is about 25, and
is much higher. This means that variation in perceived size of targets that
are larger than ideal has little impact on striking, while targets smaller
than ideal cause a clear drop-off in striking with decreasing size. Such
asymmetric drop-offs are consistent with the beetles' biology as generalist
predators that may take prey several times larger than themselves, e.g.
caterpillars (C.G., unpublished), but spatial resolution of the visual system
and prey handling abilities of the mandibles may ultimately limit responses to
tiny objects. A similar relationship emerged for and
, the generalization parameters that control the
striking of targets of non-ideal speed. They can have an enormous range of
values with little impact on the fit of the model, as long as their product is
about 475. Thus, variation in the speed of slower-than ideal targets matters
little, while striking clearly decreases as targets move faster than the
ideal. Such asymmetric drop-offs are consistent with the beetles' biology as
visual predators that also scavenge on stationary objects, but dynamics of the
visual system may ultimately reduce the response to fast moving objects.
To illustrate the effect of size and elevation and their interactions with z, we show strike proportion related to size, grouped by elevation and also strike proportion related to elevation, grouped by size, both data sets are averaged across all speeds (Fig. 2A,B). The effect of speed is shown grouped by size and averaged over elevation (Fig. 2C); its effect is similar when grouped by elevation. In addition, to clearly see the effect on striking of varying target size, speed and elevation without averaging over any significant variables, we sliced the four dimensional stimulus space of the simulation along the three stimulus axes, in the planes corresponding to the exact stimulus values tested (Fig. 3). The simulation captures major trends that readily yield to mechanistic explanation, although there are also small-scale variations in the response that are more difficult to decipher.
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There is a clear increase in overall response to stimuli moving closer to the horizon (0° elevation) or just below, with the response drop-off above 0° being sharper than below. Indeed, elevation·z was the most important single statistical factor in explaining strike tendency (Table 1). This means there is a strong difference in the effect of elevation above and below the horizon. An increase in stimulus elevation from -20° to 0° increased strike probability by 30% on average, while further raising the stimulus from 0° to 20° decreased strike probability by 44%. Elevation alone is a significant factor, because of a trend towards higher strike proportions at low elevations. It had much less explanatory power overall, however, because striking was maximal at middle elevations (-10°, 0°), with minima above and below. The fact that elevation·z explains the most variance shows that elevation, as a generic notion, is the most important factor in determining the beetle's strike probability.
Size taken alone, like elevation, is less important than other factors, and in fact is not significant: a tenfold increase in stimulus size (2° to 20°) increases strike probability by only 30% on average. However, there is a strong difference in the effect of size above and below the horizon. The interaction size·z is clearly seen in Fig. 2A,B and Fig. 3B,C, where below the horizon there is a clear tendency to strike larger targets, but not above. Furthermore, there is an interaction between size and elevation below, but not above, the horizon, as indicated by the interaction size·elevation·z. At -20°, -10° and 0° there is a tendency for the most favorable stimuli to shift from large to small as elevation increases. This is precisely the pattern we would expect if the elevation hypothesis were in effect.
The influence of speed is generally the same for all sizes and elevations, and on both sides of the horizon (Fig. 2C, Fig. 3B). There is an obvious decrease in response with increasing speeds, though the quantitative effect is subtle: increasing speed by a factor of 6 (80 to 480 deg. s-1) decreased strike probability by only 21%. Note again in Fig. 3B the clear shift from striking at large sub-horizontal stimuli to striking at small stimuli near the horizon.
The data slices at the tested stimulus speeds (Fig. 3C) most clearly show the strong interaction between size and elevation in eliciting strikes. Each panel shows the same pattern: there is a high-response band extending from 0° elevation for small sizes, to -10 or -20° elevation for large sizes. Note the lack of any strong between-panel trend, indicating the modest effect of variation in speed over the ranges of values used.
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Do simulations demonstrate sufficiency?
The degree to which accurate simulation of empirical data may be considered
evidence that the components of the model describe those of the physical
system is a specific form of a longstanding critique of science in general,
namely, the underdetermination inherent in scientific experimentation
(Duhem, 1951;
Quine, 1951). The argument,
simply put, is that any conclusion drawn from the results of an experiment is
but one of many logically possible conclusions and therefore all conclusions
are, at the very least, weakened. The debate over this issue is ongoing, but
many philosophers of science now accept the moderate and pragmatic position
that even if there are numerous logically possible reasons for the outcome of
an experiment, it does not follow that all options have the same rational
merit (cf. Curd and Cover,
1998). Applied to simulation, this means that it falls upon the
creator of the model to professionally and responsibly argue its merit
(Schmidt, 1987;
Laudan, 1990;
Law and Kelton, 1991;
Kleindorfer, 1993;
Kleindorfer et al., 1998;
Robinson, 1999), particularly
with respect to alternatives. Several simple alternative hypotheses to our
model are that there is a direct relationship between striking and either
target size, the number of ommatidia subtended by targets, or the number of
ommatidia stimulated by the leading edge of the moving targets. These are
quickly dismissed by the fact that the most favorable target at different
elevations had a different angular size
(Fig. 3), while all of these
alternative hypotheses predict that the largest target would be favored. A
better alternative is that favored targets stimulate a certain number of
ommatidia (e.g. Zeil et al.,
1986; Schwind,
1978; Schwind,
1980; Schwind,
1983; Zeil and Al-Mutairi,
1996). This could account for the fact that preferred target size
decreases near the horizon, since optical axis density is highest in this area
(Layne et al., 2003). In fact,
this hypothesis is basically equivalent to the elevation hypothesis, if
vertical resolution varies with elevation in the same way that angular size
does for objects at different distances on the ground
(Zeil et al., 1986). However,
this relationship does not hold for vertical resolution in our species.
Furthermore, there is no peak in strike proportion for any particular number
of subtended ommatidia; targets eliciting the five highest strike proportions
subtended from 9 to 161 ommatidia (overall range: 1-210). Similarly, the
number of ommatidia stimulated per second by leading edge of targets also
shows no peak in strike proportion; targets eliciting the five highest strike
proportions stimulated from 276 to 3240 ommatidia per second (overall range:
20-5040).
To what degree does our model test the `elevation hypothesis'?
Below the horizon the model accurately tests the hypothesis that tiger
beetles vary their prey size preferences in a manner consistent with using
elevation as a distance cue, and subsequently using this to convert angular to
absolute size. This is a reasonable hypothesis, since despite the beetles'
small size, their eyes are theoretically capable of providing this information
over a useful range. The lower extent of the frontal visual field is at least
-65°, so near objects seen in front, including our target stimuli, are
visible at close range. As for longer distances, for an 8 mm-tall beetle with
a minimum vertical interommatidial angle of 1.05° in the front of the eye
(Layne et al., 2003), the
farthest intersection of an ommatidial optical axis with the substrate is 8
mm/tan(1.05°)=436 mm. In reality the useful range is probably not this far
due to, e.g. inconsistencies in substrate topography, but certainly covers
normal prey-striking range. Gilbert found the mean distance at which walking
fruit flies elicited tiger beetle attacks was 79.4±9.1 mm (mean
± s.d., N=16), with a range of 47.8-125.8 mm
(Gilbert, 1997). This was done
in a 300 mm arena, so very large distances were not available. In a less
controlled experiment, Swiecimski tested the salience of various prey items in
a larger space and found foraging distances of 176.1±67.9 mm (mean
± s.d., N=19) with a range of 65-250 mm
(Swiecimski, 1957).
There are, however, two ways in which the elevation hypothesis is not strictly embodied by our model. First, near the horizon the model uses the beetles' minimum visual resolution as the ideal size, rather than the strict mathematical definition of objects at this elevation, which is infinitely small. Our observations show that targets in this area do elicit striking, and the model is designed to accommodate this observation.
Second, and more importantly, the model allows for striking at supra-horizontal stimuli. This represents a major deviation from the elevation hypothesis, especially if it is applied to small predators, because such targets should not have a computable size, and if anything should be considered threats. Experience with tiger beetles in the laboratory, however, shows that after several days they cease to attempt to flee from approaching humans, and will eventually even accept prey offered from above with forceps. None of the beetles in this study attempted escape from the targets. This is very different from their behavior in the field, where their vigilance makes them very difficult to approach, and the best way to do so is, in fact, to crouch low to the ground so as to occlude their dorsal visual hemifield as little as possible. Thus, they quickly become adapted to lab conditions. We do not know whether this changed their responses to the experimental targets.
A key point here is that in the very few tests of the elevation hypothesis,
both sub- and supra-horizontal stimuli have never been used, so it is not
known how even animals that compute distance from declination below the
horizon might react to targets above it. The only other animals having clear
visual adaptations for living in a flat world that have been tested with
supra-horizontal stimuli, semiterrestrial crabs, apparently make no judgment
of distance to objects at high elevations
(Zeil et al., 1989;
Land and Layne, 1995;
Layne et al., 1997;
Layne, 1998;
Hemmi, 2005a;
Hemmi, 2005b), and instead
treat such objects categorically as threats. Humans can use declination below
the horizon as a distance cue (Ooi et al.,
2001). In the human case the perceived increase in distance with
increasing elevation below the horizon does not continue above the horizon. In
fact, as demonstrated by the well-known moon illusion
(Hershenson, 1989), the
situation is reversed: the moon appears to grow closer as it rises in the sky.
This leads, then, to the inevitable perception that the moon must grow smaller
as it rises, since its angular subtense remains constant
(Kaufman and Kaufman, 2000).
Thus, in humans, as in our model, the perceptual phenomenon does apply above
the horizon, as a sort of mirror image of what happens below. Interestingly,
the most preferred targets for the five tested elevations from -20° to
+20° have sizes of 20°, 16°, 4°, 4° and 12°, i.e. they
seem to reverse near the horizon This is a little misleading, because the
preference levels are much lower above the horizon, but the pattern is
qualitatively similar to what humans perceive.
In the end, the model contains deviations from the strict form of the elevation hypothesis because tiger beetles do not use a strict form. They appear, however, to use it to some degree for estimating distance, likely in combination with other cues, as is certainly the case for humans and frogs.
'
'
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Acknowledgments |
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Footnotes |
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Present address: Mount Sinai Medical School, 1 Gustave L. Levy Place, New
York, NY 10029, USA 
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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