|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online March 27, 2009
Journal of Experimental Biology 212, 1120-1130 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.020768
Visual control of flight speed in Drosophila melanogaster
1 Institute of Neuroinformatics, University of Zürich and ETH Zürich,
Switzerland
2 Institute of Robotics and Intelligent Systems, ETH Zürich,
Switzerland
3 Bioengineering, California Institute of Technology, MC 138-78, Pasadena, CA
91125, USA
* Author for correspondence (e-mail: steven{at}ini.ch)
Accepted 21 January 2009
 |
Summary |
|---|
 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Key words: Drosophila, flight control, behavior, vision
|
INTRODUCTION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
), provides insects with an external frame of reference
[allocentric cues (Wehner,
1992)], which plays a particularly important role in the control
of various aspects of flight, such as altitude and flight speed (for a review,
see Collett et al., 1993).
Therefore, the mechanisms underlying the processing of optic flow by the
visual system and the means by which it can generate appropriate motor control
signals for velocity and course control have been met with strong research
interest over the past several decades (for reviews, see
Egelhaaf and Kern, 2002;
Srinivasan and Zhang, 2004)
[for a recent paper on visual free-flight control in Drosophila, see
Mronz and Lehmann (Mronz and Lehmann,
2008)].
Rotational control
Classic studies of visual motion processing
(Hassenstein and Reichardt,
1956; Kunze, 1961;
Fermi and Reichardt, 1963;
Götz, 1964;
Eckert, 1973) applied a
black-box approach in which the visual processing mechanisms were inferred
from the turning responses measured from tethered walking or flying insects in
the presence of rotating gratings of varying temporal and spatial frequencies
(Fig. 1A). Because tethering
breaks the reafferent visual coupling normally experienced during free
movements, this preparation allows arbitrary visual stimuli to be presented to
an insect without the animal's behavioral response affecting the sensory input
in any way [open-loop condition (e.g.
Taylor et al., 2008)].
|
; Srinivasan et al.,
1999). This observation, first made by Hassenstein and Reichardt
in walking Chlorophanus beetles
(Hassenstein and Reichardt,
1956), has been repeatedly confirmed in tethered preparations
using walking [e.g. Drosophila
(Buchner, 1976)] and flying
[Apis (Kunze, 1961);
Drosophila (Götz,
1964)] insects. The spatio–temporal response properties are
consistent with the predictions of the influential `correlation-type' motion
detector model (Fig. 1B),
proposed by Reichardt (Reichardt,
1961) almost 50 years ago. According to this model, motion signals
are computed locally by elementary motion detectors (EMDs) from a
spatio–temporal correlation of intensity signals sensed in neighboring
visual channels (for reviews, see Buchner,
1984; Borst and Egelhaaf,
1989; Egelhaaf and Borst,
1993; Hausen,
1993; Borst and Haag,
2002). This view is consistent with a broad body of
electrophysiological evidence showing that inputs of correlation-type EMDs are
integrated by the well-characterized lobula plate tangential cells (LPTC),
whose outputs are believed to represent control signals for corrective
steering maneuvers (for reviews, see
Egelhaaf and Borst, 1993;
Borst and Haag, 2002).
Translational flight control
Visual behaviors have also been explored extensively in freely flying
insects (Collett et al., 1993;
Srinivasan and Zhang, 2004).
Most of the available data have been obtained from honeybees, which can be
easily trained to fly through experimental setups under well-controlled
conditions. In various experiments and behavioral contexts, honeybees have
been shown to maintain a consistent flight speed with respect to a perceived
pattern, irrespective of its spatial frequency and contrast
(Srinivasan et al., 1991;
Srinivasan et al., 1996;
Baird et al., 2005).
This phenomenon, often referred to as `pattern invariance' or `velocity
dependence', is not limited to honeybees. Similar evidence has emerged from
free-flight studies performed in other insects, including fruit flies. David
(David, 1982), for example,
induced Drosophila virilis to hover stationary in a wind tunnel by
manually adjusting the speed of a surrounding `barber's pole' pattern. He
showed that the flies hovered at a particular `preferred' pattern speed,
irrespective of whether the pattern consisted of broad (72 deg.) or narrow (40
deg.) stripes [see fig. 8 in David (David,
1982)]. Furthermore, he showed that the preferred flight speed was
invariant to substantial changes in headwind [see
fig. 3 in David
(David, 1982)], as is the case
in other insect species [e.g. Aedes
(Kennedy, 1939); Apis
(Barron and Srinivasan, 2006)].
The strict dependence on optic flow makes flight speed control a powerful
model behavior to characterize optic flow processing in the context of free
flight.
|
)]. Various suggestions have been put forth to explain
pattern-invariant behaviors based on the known mechanisms of motion
computation, including hypothetical correlation-based mechanisms
(Zanker et al., 1999), or
higher order motion processing circuits that extract a more accurate velocity
estimate from arrays of differently tuned correlators
(Srinivasan et al., 1999).
More recently, the sensory and behavioral ecology of visual flight control
have received increased attention. This more ethological approach suggests
that the known properties of motion-sensitive visual interneurons will make
more functional sense if the spatio–temporal properties of real visual
scenes are taken into account, including an insect's actual body motion during
flight maneuvers (O'Carroll et al.,
1996; Egelhaaf et al.,
1998; Egelhaaf et al.,
2002; Lindemann et al.,
2005; Straw et al.,
2008). The relevance of experiments performed using highly
controlled but partially unrealistic laboratory conditions deserves explicit
attention.
The apparent discrepancy in the motion processing mechanisms observed from
turning and flight speed responses may relate to the disparate conditions
under which the experiments were performed. First, turning responses were
measured in the presence of panoramic patterns of constant angular wavelength
whereas flight speed responses were measured using planar patterns (compare
Fig. 1A with
Fig. 1C; also see
Fig. 2B). From the vantage
point of the fly, the planar pattern is geometrically distorted such that the
angular wavelength (
) of the pattern is maximal at lateral positions
and decreases toward frontal and caudal positions
(Fig. 2B). Second, turning
responses were measured under tethered conditions, in which various sensory
feedback loops relevant for flight control are broken
(Taylor et al., 2008). The
interruption of feedback loops, in particular haltere feedback, is the likely
cause for significant behavioral artifacts observed in tethered flying fruit
flies (Fry et al., 2005).
Third, turning responses have been characterized from their open-loop transfer
properties (see above) whereas speed responses have been characterized from
the stable-state flight conditions reached under different experimental
conditions. While the latter approach can provide insights into the visual
mechanisms at play when the insect flies at its preferred flight speed, e.g.
from the observed invariance to pattern spatial frequency and contrast, it is
unsuited to explore how flight speed is actually controlled from varying optic
flow conditions. For this, transient responses need to be measured in the
presence of experimentally defined optic flow stimuli that vary over a large
spatio–temporal parameter range.
|
|
). To do so, we equipped a wind tunnel with a real-time 3-D
path tracking system, i.e. Trackit 3D (Biobserve GmbH, Bonn, Germany) (see
also Fry et al., 2004) and an
image rendering system, i.e. the VisionEgg (v. 1.0;
www.visonegg.org)
(Straw et al., 2006). By
experimentally de-coupling the retinal slip from the fly's flight speed, we
were able to measure the open-loop transfer function over a broad range of
spatio–temporal frequencies (Fig.
1F). Automation from software control allowed us to collect a
large data set of visual responses (n=12,711 trials) to a broad range
of visual stimulus parameters. Our results show that visual control of flight speed in fruit flies depends on linear pattern velocity (V=TF/SF) over a broad range of spatio–temporal frequencies (for definitions of V, TF and SF, see Coordinate system in Materials and methods). Furthermore, visual responses are largely invariant to spatial frequency composition, image contrast and wind speed. Our results suggest the presence of a sophisticated motion-processing pathway that is able to robustly extract V as a control signal for flight speed control.
|
MATERIALS AND METHODS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
TrackFly experimental setup
Experiments were performed using TrackFly; a wind tunnel equipped with
virtual reality display technology, described in more detail elsewhere
(Fry et al., 2008). In the
present study, we provide an overview of the system components that are
principally relevant for the understanding of the concepts and methodology
applied in the present study.
Wind tunnel
The behavioral tests were performed in a commercial, open-circuit,
closed-throat wind tunnel (Engineering Laboratory Design, Inc., Lake City, MN,
USA). The wind tunnel provided a laminar airflow in a working section made of
clear acrylic, 1.55 m in length and 
0.305 m in width and height. Standard
tests were performed using a wind speed of 0.29 m s–1. To
motivate the flies to fly upwind, we vaporized an attractant odor (`Kressi'
herb vinegar, diluted to 5% water solution) using an ultrasonic humidifier
(Boneco, Plaston AG, Widnau, Switzerland) at a rate of 
7.2 mg
s–1 from four nozzles positioned in front of the air intake
end of the wind tunnel. This procedure provided a homogenous dispersal of the
odor, thus preventing a plume structure or a concentration gradient that the
flies could have used as additional cues.
Real-time position tracking
Flies were tracked from above using Trackit 3D
(Fry et al., 2004), equipped
with two infrared-sensitive video cameras. Homogeneous back lighting was
provided from a custom-built lamp emitting in the long wavelength spectrum
(>700 nm). Fruit flies are comparatively insensitive to long wavelengths
(Heisenberg and Buchner, 1977;
Stark and Johnson, 1980) and,
consistently, we did not notice any effects resulting from the light shining
from below. The three-dimensional (3-D) position of single flies was
transferred with short delay to a client computer at a rate of 50 Hz using a
TCP/IP (Transmission Control Protocol/Internet Protocol) network
interface.
Image rendering and display
On the client computer, visual stimuli were rendered using custom
programmed software based on the VisionEgg open-source image rendering library
(Straw and O'Carroll, 2003;
Straw et al., 2006). The
images were displayed at a refresh rate of 60 Hz on a flicker-free LCD (liquid
crystal display) projector (Sony, VPL-ES1, Tokyo, Japan). The image was split
and projected via mirrors onto tracing paper screens (1.0 mx0.3
m) attached to the sidewalls of the wind tunnel
(Fig. 2A). Various calibrations
and control measurements were performed to ensure that the patterns defined in
the software were displayed faithfully onto the wind tunnel screens. The
average latency of TrackFly between measuring the fly's position and
displaying the position-dependent stimulus was 0.038 s.
Coordinate system
Throughout the text, capitalized and non-capitalized symbols are used to
denote linear and angular metrics, respectively. We define the spatial
frequency [SF (unit: m–1)] of the displayed sine
grating, with reference to the sidewalls of the wind tunnel, as the number of
cycles per unit length of the visual display
(Fig. 2). Accordingly, linear
pattern wavelength ()is given by 
=1/SF (unit: m).
+X denotes upwind direction. The temporal frequency (TF) of
the pattern is defined as the number of cycles passing a given point of the
display per unit time (unit: s–1) positive upwind. In the
present experiments, TF and SF were varied
systematically.
Due to perspective distortion of the pattern as viewed by the fly, the
angular spatial frequency (sf) and angular velocity (v) are
not constant across the visual field but instead vary with azimuth.
Alternatively, we could have stimulated the flies with a single sf by
rendering a cylindrical projection of the pattern centered on the fly
(Fry et al., 2008). Such
experiments are indeed useful to test specific hypotheses about optic flow
processing (N.R. and S.N.F., in preparation); however, this was not the aim of
the present study. To instead explore how the fly controls its flight speed
with respect to realistic optic flow conditions, we displayed planar patterns;
these appear largest and fastest in the lateral field of view, just like any
object a fly passes by under natural free-flight conditions (e.g.
David, 1982;
Srinivasan et al., 1996).
Measurement procedure
Process automation
The detailed measurement of a response surface over a broad
TF–SF parameter space required a large number of
trials. We automated the measurement procedure by implementing the `optomotor
clamp' procedure inspired by David's
(David, 1982) earlier
approach. For this, we manipulated the perceived visual flight speed of the
flies by varying the horizontal speed of a sine grating pattern
(SF=6.66 m–1), depending on the fly's position in
the wind tunnel. If the fly was too far upwind, we simulated fast, forward
flight by increasing the downwind pattern speed, in response to which the fly
reduced flight speed and drifted downwind. Likewise, if the fly was too far
downwind, we simulated slow, forward flight by decreasing the downwind pattern
speed, in response to which the fly increased flight speed and moved upwind.
In consequence, the fly was kept hovering near the middle of the wind tunnel
(X=0), where the pattern was moving at the flies' preferred speed. A
test was performed as soon as a fly was measured to hover stably near the
center of the wind tunnel.
`One-parameter open-loop' testing paradigm
Individual flies were stimulated for 1 s with a moving sine grating,
defined by TF and SF. To hold TF constant with
respect to the fly (open-loop condition), the pattern phase was continually
adjusted according to the fly's current position along the wind tunnel. Thus,
only one parameter, the TF of the horizontal optic flow stimulus, was
controlled in open-loop, i.e. decoupled from the fly's resulting behavioral
response. All other sensory feedback, such as mechanosensory feedback from the
halteres or antennae, remained under natural closed-loop conditions. This
measurement paradigm is accurately termed `one-parameter open-loop' condition
but for simplicity we will use the term `open-loop condition' throughout the
paper. The fly's 3-D positions were logged, together with the stimulus
conditions, to a data file for later analysis.
The testing protocol consisted of four test conditions and a control condition (TF=–2 Hz, SF=10 m–1), which were repeated sequentially until sufficient data were acquired for each pattern condition. We used the control condition to detect any significant differences in response strength that might have resulted from inter-individual differences or uncontrolled experimental conditions; however, this never occurred and the variability of the responses was consistently low (Fig. 4C). We therefore pooled the data and treated them as independent. Our approach was further justified by the large number of trials performed (e.g. n=12,711 for Fig. 3). Although the exact number of flies tested is unknown, we estimated it to be in the order of N=1000, based on our observation that a single fly contributed about 10 trials on average.
Tests with a photographic image
We also tested the flies' responses to a moving photographic image
containing a naturalistic mixture of spatial frequencies. The image is one of
a set in which each image evoked similar responses of LPTCs in the hoverfly
[image D in Straw et al. (Straw et al.,
2008); see Movie 1 in supplementary material]. In this case, the
pattern velocity was controlled in open-loop as to maintain a constant
V = TF/SF with respect to the fly.
Data analysis
The flies responded to open-loop regressive (back-to-front) motion stimuli
with a constant forward acceleration (Fig.
2C) that depended on stimulus conditions. A constant acceleration
is consistent with a constant net forward thrust, suggesting that the
aerodynamic effects of varying air speed on the wings and the body are
compensated. This view is consistent with the previously mentioned invariance
of flies to wind speed (see Introduction).
We extracted the acceleration from the raw X-position data as a
measure of response strength by fitting a second-order polynomial
(Fig. 2C) of the form:
 | (1) |
 | (2) |
Response surface in TF–SF parameter space
Because the spatio–temporal properties of a moving sine grating are
uniquely described by its TF and SF, the measured responses
are appropriately represented in a two-dimensional parameter space using
TF and SF as Cartesian coordinates
(Fig. 3). We interpolated the
accelerations measured from 435 different pattern conditions
(n=12,711 trials) using Matlab's (The MathWorks Inc., Natick, MA,
USA) griddata function (linear method). The accelerations are represented in
color code, with `hot' and `cold' colors representing up- and downwind
accelerations, respectively (Fig.
3; see Fig. 2B for
sign conventions).
|
RESULTS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
25 m–1, we observe a
response inversion, which is consistent with spatial aliasing at the spatial
resolution limit of the fly's eye. The response structure of downwind
accelerations (lower left of Fig.
3) is similar, albeit less clear and shifted toward lower
SFs.
Superficially, the measured speed response tuning is reminiscent of that
computed from a basic correlation-type motion detector (compare upper half of
Fig. 3 with
Fig. 1B) for rotating patterns.
First, the measured speed responses show a response plateau in a limited range
of TF and SF similar to the response maximum predicted by
the correlator model due to its spatio–temporal band-pass filter
properties (Fig. 1B). Second,
the speed responses diminish above SF25 m–1 and
reverse direction (note blue color code indicating backward accelerations for
SF around 30–55 m–1), as predicted by the
correlation model.
It would be premature, however, to postulate a basic correlation-type
motion detection process from these observations, which are well explained by
constraints of the visuomotor system rather than a common process of motion
computation. The measured response plateau, on the one hand, results from a
locomotor limit in flight speed attainable in the wind tunnel, as described in
detail below. The response attenuation and inversion, on the other hand, is
explained with spatial aliasing and a reduction of the contrast above the
Nyquist spatial frequency or twice the inter-ommatidial angle
[2
=9.6 deg., see fig.
3 in Götz (Götz,
1965)]. The maximal value of angular wavelength
(max) perceived in the fly's lateral field of view (in
deg.) is calculated from:
 | (3) |
max15.2
deg. Because decreases toward frontal and caudal azimuths,
will be close to or below the spatial resolution limit of the eye in most
parts of the visual field. Although not directly comparable due to the
different geometries of the experimental setups, it appears likely that the
response inversion observed in our experiments results from spatial
aliasing.
In conclusion, the conspicuous similarities between the measured response surface and the tuning properties of a basic correlation detector circuit reflect physiological constraints of the visuomotor system rather than a common motion processing mechanism.
A further constraint explains the previously mentioned differences in
upwind- and downwind-directed speed responses (positive and negative
accelerations in Fig. 3,
respectively). When accelerating upwind, the flies kept their body orientation
closely aligned with the wind tunnel long axis, as confirmed with high-speed
recordings made from the side through a slit in one of the display screens
(see Movie 1 in supplementary material). There must be limits, however, to the
degree with which the flies compensate increasing tailwinds with deceleration,
as this would eventually lead to the somewhat paradoxical situation of flies
flying backward with respect to the surrounding air. Indeed, the flies
tolerated only little front-to-back retinal slip before they reversed their
body orientation, as revealed by high-speed video analysis (data not shown).
Likewise, Kennedy (Kennedy,
1939) identified a threshold for front-to-back pattern motion,
above which mosquitoes reversed their flight direction and flew downwind.
Because the retinal stimulation changed along with the fly's turning
responses, the data are difficult to interpret and were therefore excluded
from further analysis.
Visual encoding properties of the speed response
To gain insight into the strategy of visual control of flight speed, we
focused our analysis on forward-directed acceleration responses in a reduced
parameter range that is most likely to be relevant for flight speed control
(Fig. 4A). Because previous
research has shown that preferred flight speed depends on pattern velocity
(see Introduction), it is meaningful to evaluate the response surface in view
of identical pattern velocities represented by the different combinations of
TF and SF. The linear velocity V of a sine grating
corresponds to the ratio of its TF and SF
(V=TF/SF). Therefore, all sine gratings that move
at a particular V fall onto a diagonal line through the origin with
slope V=TF/SF. For example, the 0.5 m
s–1 pattern iso-velocity line connects all TF and
SF coordinates for which V=TF/SF=0.5 m
s–1, such as (6,12) and (2,4).
Pattern iso-velocity lines for –0.1V1 m
s–1 are shown as labeled white lines superimposed over the
response surface shown in Fig.
4A. Whereas the Cartesian TF–SF coordinate
system describes the patterns from their temporal and spatial frequency
composition, the superimposed polar coordinate system describes the patterns
in terms of their velocity, with the angular coordinate
=tan(V). The radial coordinate
describes
whether a moving sine grating is composed of high or low spatio–temporal
frequencies. As shown below, the measured response characteristics are
suitably evaluated with respect to their velocity characteristics (i.e. the
polar coordinates), rather than their spatio–temporal tuning properties
(the Cartesian coordinates).
Set-point transfer properties
We first evaluate the measured response surface in view of the previous
finding that the `preferred' flight speed of free-flying insects is invariant
to the spatial pattern properties (see Introduction). In control terms, the
`preferred' flight speed represents the controller's set point, which defines
the stable equilibrium under normal closed-loop conditions. In an open-loop
input–output function, the set point is identified from a zero crossing
of a response function, with a positive slope indicating a stable equilibrium
point (Strogatz, 1994). If
consistent with previous free-flight data, we would expect our response
surface to reveal a zero response contour line (the zero-crossing) that is
flanked by a positive response gradient (required for closed-loop stability)
and follows a pattern iso-velocity line (required for pattern invariance).
As shown in the lower part of Fig.
4A, the zero response contour line (shown bold and marked with a
black arrow) indeed runs roughly diagonally, corresponding to a pattern
velocity of approximately –0.15 m s–1 (i.e.
front-to-back). This preferred pattern velocity is similar to the preferred
flight speed of D. melanogaster measured in free flight
(Tammero and Dickinson, 2002).
Our data show that the preferred pattern velocity of D. melanogaster
spans a roughly 8-fold range of SF (between about 2–16
m–1), consistent with previous findings in honeybees
(Baird et al., 2005).
The findings based on the zero response iso-line measured under open-loop conditions are consistent with previous data measured under closed-loop flight conditions, validating our experimental approach for a functional analysis of free-flight control.
Pattern velocity as a control signal for corrective speed maneuvers
The particular shape of the response surface reveals the
spatio–temporal pattern properties relevant for speed control and how
corrective speed maneuvers depend on them. Over a broad range of the response
surface shown in Fig. 4A, the
response iso-lines are roughly aligned with the diagonally oriented pattern
iso-velocity lines, suggesting a close correspondence between the response
strength and pattern velocity, rather than a response tuning to a particular
combination of TF and SF.
To quantify the dependence of response strength on the open-loop pattern velocity, or retinal slip speed (Vslip), we evaluated the response surface along four radial paths in the two-dimensional TF–SF parameter space (red, green, dark blue and light blue arcs in Fig. 4A, with r values of 4, 8, 12 and 16, respectively). The responses, sampled over a broad TF–SF parameter space, show a similar dependence on Vslip and are statistically indistinguishable from one another. The responses increase with Vslip and saturate at around 3 m s–2 for Vslip>0.6 m s–1 (Fig. 4B). The variance of the mean responses (likewise linearly interpolated) is shown with error bars for the 48 measurement conditions. The standard deviation is roughly constant at about ±0.5 m s–2 and increases to about twice this value at high retinal slip speeds.
Averaging the responses measured for radii between 8 and 16 (i.e. along the pattern iso-velocity lines between the red and light blue arcs in Fig. 4A) reveals a linear-dependence (R2=0.985) of response strength for Vslip<0.6 m s–1, above which the responses saturate at around 3 m s–2 (black line in Fig. 4C). Within the linear range, therefore, the flies' accelerations depend directly on the linear pattern velocity V=TF/SF as the relevant visual control parameter for flight speed.
Linearity in response provides constant reaction time
The linearity of the response function within the dynamic range is a
remarkable characteristic of the visual control of flight speed, the
functional relevance of which, however, remains unknown. In control theory
terms, the measured slope of 3.73±0.11 s–1 corresponds
to the open-loop gain (GOL) of a purely proportional
control system. The zero crossing of the acceleration at –0.17 m
s–1 preferred flight speed corresponds to the controller's
set point velocity (Vset). The linear regression of the
measured acceleration (Acc) is:
 | (4) |
 | (5) |
 | (6) |
T relates only to the period of constant acceleration and does not include a constant response time lag of approximately 0.10 s (see Fig. 2C, analysis not shown). We therefore estimate the total time required by the fly to correct a visual perturbation to lie slightly above 0.37 s. A more detailed analysis of the control properties will be presented elsewhere (N.R. and S.N.F., in preparation).
Speed responses are robust for SF composition and image contrast
Previous research has explored the possibility that pattern invariance
could arise in a correlation-based motion-processing pathway from the
processing of images with a broad spatial frequency spectrum, as is found in
natural visual environments of flies (see Introduction). Indeed, stimulation
with a broad SF spectrum is expected to result in more meaningful
responses if non-linearities in the visual system operated on various spatial
frequency components. To test this possibility, we measured flight speed
responses in the presence of a moving photographic image that was used in a
previous electrophysiological study to reflect the broad spatial frequency
spectrum of a fly's natural habitat (Straw
et al., 2008). We controlled the image velocity in open-loop and
measured the resulting acceleration responses as before. Whereas the previous
experiments used a single TF–SF combination for
individual trials, the image presentation experiments tested the responses to
a simultaneous presentation of TF–SF combinations,
corresponding to numerous points along the respective iso-velocity line in the
TF–SF parameter space.
The responses to the photographic image were indistinguishable from the averaged responses measured using sine gratings (compare green and black traces in Fig. 4C). We therefore conclude that the computation of pattern velocity by the fly's visual system is largely invariant for spatial frequency content of the planar patterns. Single SFs and a broadband photographic image both lead to robust flight velocity control.
Additionally, although image contrast differed considerably between the
sine grating (Michelson contrast: C=0.5) and the photographic image [see image
C in Straw et al. (Straw et al.,
2008); see also for a discussion of contrast metrics for natural
images], this did not lead to a significant difference in response strength,
suggesting that speed responses are largely contrast invariant, consistent
with recent findings in honeybees in a similar behavioral context
(Baird et al., 2005). A
biologically plausible explanation for contrast invariance could lie in
contrast saturation in the early visual system
(Dror et al., 2001), although
other mechanisms are known to be responsible for contrast insensitivity
observed in the tangential cells of other fly species
(Straw et al., 2008).
Response saturation
As shown above, accelerations reached a plateau of about 3 m
s–2 at pattern speeds above 0.6 m s–1. The
underlying cause of the response saturation is relevant to the understanding
of the underlying control mechanisms. We consider two likely explanations for
the saturation. First, saturation could occur in the visual pathways, limiting
the encoding of pattern speeds to a particular value. Second, the saturation
could result from locomotor limits, either due to an upper limit in
acceleration of 3 ms–2 or in the maximum air speed attainable
by the fly due to increasing drag acting on the wings and body [for drag
effects on the wing, see also Hesselberg and Lehmann
(Hesselberg and Lehmann,
2007)].
To distinguish between these two possibilities, we compared the
accelerations reached under standard wind conditions (–0.290 m
s–1) with those measured in the presence of an increased
headwind (–0.73 m s–1)
(Fig. 4D). Increasing the
headwind caused a significant reduction of the acceleration from 2.67 to 1.32
m s–2 (Fig.
4D), indicating that the response saturation did not result from a
limit of pattern velocities extracted by the visual system but instead
depended on the air speed. Apparently, the flies reached an upper limit of air
speeds at which they were able or willing to fly. When flying below their
maximum air speed, the flies' acceleration was invariant to the wind speeds
tested (data not shown), in accordance with results published for various
insect species [e.g. Aedes (Kennedy,
1939); Aphis (Kennedy and
Thomas, 1974); D. virilis
(David, 1982); Apis
(Barron and Srinivasan,
2006)].
|
DISCUSSION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
While our method allowed us to characterize an important free-flight reflex in a two-dimensional spatio–temporal parameter space, the one-parameter open-loop condition was experimentally induced, raising the question of whether our measurements were subject to artefacts, resulting from the highly artificial experimental conditions.
A first question relates to other sensory modalities, such as
mechanosensory feedback from the halteres and antennae and olfactory cues,
which remained in closed-loop and might have provided conflicting cues. The
experimentally induced disparity between the visual and other sensory inputs
is in fact by no means unnatural and mimics a control scenario faced by a fly
flying upwind quite closely. Whether flying against a constant wind or in
still air, a fly adjusts its air speed so as to maintain a constant
`preferred' retinal pattern slip speed [see
fig. 3 in David
(David, 1982)] (see also
Introduction). This situation is similar to our pre-test condition, in which
the fly was induced to hover near the middle of the wind tunnel, where the
visual pattern motion matched the fly's preferred retinal slip speed. In a
natural environment, a gust of wind from the front could easily cause the fly
to momentarily slow down or even be carried backward, in which case the fly
would perceive regressive (back-to-front) retinal slip. At this moment, the
retinal slip depends largely on the strength of the wind gust and not the
fly's behavior; a situation closely corresponding to the open-loop condition
we implemented using TrackFly.
While mechanosensory input is likely to provide information about the fly's
air speed [e.g. from the antennae
(Gewecke, 1967;
Taylor and Krapp, 2008)],
there is no mechanism besides vision known to provide the fly with a reference
for its ground speed. In this context, it is interesting to consider the role
of the halteres, which sense the Coriolis forces associated with angular body
velocity but probably not the much weaker forces resulting from linear
accelerations (Pringle, 1948;
Nalbach, 1993;
Nalbach and Hengstenberg,
1994). The halteres are therefore part of an inner control loop
mediating changes in body pitch, as required for flight speed control
(David, 1978;
Dickson et al., 2008), but are
unlikely to affect the outer control loop, which appears to be driven by
pattern velocity alone (Fig.
5). Our one-parameter open-loop paradigm therefore selectively
provided experimental access to the outer, visually mediated control loop,
while other sensory modalities remained under realistic closed-loop
conditions, as required for realistic free-flight control.
|
=38 ms (see Materials and methods), which is in the order of the fastest
visual behaviors documented in free-flying flies [e.g. 30 ms in chasing
Fannia (Land and Collett,
1974)]. The difference between the intended and the actual
stimulation was previously calculated for the present testing paradigm,
assuming a constant =38 ms and that the flies responded with a constant
acceleration (Fig. 2B). After
20 ms, the actual slip speed reached a constant level that was reduced by 7.6%
compared with the desired slip speed [see fig. 6 in Fry et al.
(Fry et al., 2008)].
Correcting our results for the measured inaccuracy of the stimulation, the
GOL is reduced from 3.73 to 3.45 s–1 and
the duration of the acceleration response is correspondingly increased from
270 to 290 ms. Otherwise our conclusions should not be affected by this
systematic error.
Together with a rough estimate of 100 ms response delay from Fig. 2C, the total time it takes for a fly to correct for a perturbation of flight speed is in the order of 400 ms, which is surprisingly long compared with the much faster responses of Fannia. This discrepancy is likely to reflect varying response dynamics of reflexes adapted to different behavioral tasks, as well as species- or scale-dependent differences in flight mechanics.
Control of corrective speed maneuvers
A proportional control law governs flight speed control
The zero acceleration iso-line in Fig.
4A identifies pattern properties that do not cause corrective
speed responses and therefore correspond to the stable-state condition of the
speed controller. We found that the zero-response iso-line corresponded to a
particular pattern velocity (V=TF/SF), consistent
with the previous finding that many insects maintain a `preferred' retinal
slip speed at steady state under normal closed-loop conditions (see
Introduction; Fig. 1D).
The ability to test flies in open-loop allowed us to furthermore explore how flies responded to visual perturbations of this steady-state flight speed, which under natural flight conditions would likely arise from wind gusts or air turbulence. We found that the speed responses depended linearly on the difference between the preferred pattern speed Vpref and the actual retinal pattern slip speed Vslip over a broad range of spatio–temporal frequencies.
Based on our open-loop response characterization, the fly's visual responses can be functionally interpreted to result from a feedback controller, whose process variable is Vslip and whose control output is flight speed (Fig. 5). By experimentally de-coupling the retinal slip from the fly's flight speed (symbolized by the open switch in the feedback loop in Fig. 5), we were able to measure the open-loop transfer function over a broad range of spatio–temporal frequencies, represented by the data shown in Fig. 3 and Fig. 4A. Under closed-loop conditions (closed feedback loop in Fig. 5), the fly would quickly reach a flight velocity at which the optic flow is perceived at the preferred slip speed.
Whereas free-flight experiments performed under steady-state closed-loop
conditions can reveal what is being controlled, the measured open-loop
transfer properties provide functional insight into how this control is
achieved. A quantitative model and simulations of open- and closed-loop
conditions will be presented elsewhere (N.R. and S.N.F., in preparation).
Recently, a PID (proportional-integral-derivative) control scheme was implied
to underlie visual control of flight altitude in honeybees
(Franceschini et al., 2007)
(see also Taylor et al.,
2008). Commonly used in engineering applications, PID controllers
also use a control signal's derivative and integral to control the output. We
found no evidence that this is the case for speed control, which depends
directly on the retinal slip speed, thus representing a simpler proportional
controller.
Simple control rules are based on sophisticated sensorimotor control pathways
Our control scheme is represented without reference to the physiology and
biophysics of flight, which in a control model are typically represented as
the plant dynamics. The physiological mechanisms underlying visuomotor flight
speed control are presumably highly complex and remain little understood.
First, the extraction of pattern velocity over a broad range of TF
and SF requires sophisticated neural processing that is not easily
explained with our current understanding of the fly's visual system. Second,
the control of flight speed depends on subtle motor control and additional
internal control loops. To modulate the flight speed, a fly needs to adjust
its pitch angle (David, 1978)
from exceedingly subtle changes in wing kinematics
(Fry et al., 2003;
Fry et al., 2005). Pitch
control itself depends on proprioceptive mechanosensory feedback from the
halteres (Pringle, 1948;
Nalbach, 1993;
Nalbach and Hengstenberg,
1994). An additional control loop to compensate for varying air
speeds may also exist, as acceleration responses below locomotor limits are
invariant to air speed (data not shown) [see also
fig. 3 in David
(David, 1982)].
Due to the immense complexity of the underlying control mechanisms, any attempt to isolate specific components of the controller would seem highly speculative and misleading. We have therefore restricted our analysis to the high-level control strategy without assumptions or inferences about the underlying sensorimotor control mechanisms.
Despite the high complexity of the involved sensorimotor mechanisms, visual
control of flight speed nevertheless obeys a surprisingly simple control rule.
An embedding of complex non-linear mechanisms into a comparatively simple
high-level control strategy may not be uncommon in biological systems
(Gewecke and Heinzel, 1980;
Sherman and Dickinson, 2004)
(see also Taylor et al.,
2008). Whereas the adaptive advantage of such simple control
strategies remains unknown, they evidently benefit insects, whose evolutionary
success is largely due to their superior flight capabilities
(Dudley, 2000).
Visual processing of optic flow
There is current debate over the degree to which rotational and
translational flight control is mediated by a common neural substrate (see
Introduction). Our open-loop speed response measurements provide a baseline
against which current and future models of motion-processing pathways can be
evaluated. Our results show that the motion-processing pathway pertaining to
speed control computes the linear velocity of planar patterns of arbitrary
spatial frequency content. Importantly, we have shown that a behavioral
characterization of the speed response can be meaningfully performed using
sine grating stimuli, which allows a response characterization in the
two-dimensional TF–SF parameter space. It would
therefore be informative to compare our results with electrophysiological data
and modeling results that are obtained with planar sine grating stimuli that
are systematically varied in TF–SF parameter space.
Such comparisons may be possible due to recent advances in
electrophysiological techniques, which have allowed recording from LPTC in
Drosophila (Joesch et al.,
2008).
Furthermore, the measurement of the transient response properties to a step
change in sensory input will allow a more detailed evaluation of the
underlying motion computations. It is essential to assess whether transient or
steady-state response properties of the motion-processing pathways dominate at
the behaviorally relevant time scales
(Borst and Bahde, 1986). Recent
electrophysiological studies in flies have explored transient response
properties of motion pathways in playback experiments that used realistic
optic flow stimuli reconstructed from free-flight behavior (e.g.
Kern et al., 2005;
Karmeier et al., 2006). The
finding that the steady-state physiology of a visual interneuron does not
predict its response to more dynamic stimuli emphasizes the importance of
re-examining behavioral responses under transient conditions, as performed in
our present study.
Outlook
Future studies combining advanced genetic techniques with detailed
behavioral analyses promise advances in our understanding of the neural
substrate for motion processing in different behavioral contexts. For example,
identified motion processing neurons can be genetically targeted
(Joesch et al., 2008), which
will allow them to be manipulated to explore their involvement and possible
role from the behavioral effects (Duffy,
2002). In a recent study, a forward genetic approach was applied
in walking Drosophila and selective effects of large field optic flow
were identified on walking speed and turning responses. Based on these
results, it has been proposed that visual pathways subserving the control of
translation and rotation may separate at the earliest stage of visual
processing (Katsov and Clandinin,
2008). It will be highly informative to combine advanced genetic
techniques with detailed flight control analyses in a meaningful functional
context to explore the physiological basis of speed control. In particular,
genetic modification of the known visual pathways may provide evidence for the
involvement and role of the known pathways in the context of visual control of
flight speed.
Finally, our results are of direct relevance for biomimetic robotic implementations, such as autonomous flying micro-robots. We showed that visual speed control is based on a remarkably simple control strategy, however, requires a sophisticated vision sensor to robustly signal the linear pattern speed. Our work suggests that the fly's speed control strategy could be meaningfully transferred into the context of autonomous micro air vehicles, while substituting the complex biological control mechanisms with functionally equivalent engineering solutions.
LIST OF ABBREVIATIONS
|
Footnotes |
|---|
We wish to thank Martin Bichsel for technical support with Trackit 3D, David O'Carroll for providing a naturalistic image used in previous studies, Jérôme Frei, Marie-Christine Fluet, Nils Perret and Martin Ehrensperger for preliminary experiments using TrackFly. We thank Richard Hahnloser, Martin Zápotocky and Petr Marsalek for valuable comments and suggestions, as well as two anonymous reviewers for their useful comments. Financial support was provided by the Human Frontiers Science Program, the University of Zürich, the Swiss Federal Institute of Technology (TH-11/05-3), the Volkswagen Foundation, the National Science Foundation (FIBR 0623527)) and the Air Force Office of Scientific Research (FA9550-06-1-0079 to M.H.D.).
|
References |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Baird, E., Srinivasan, M. V., Zhang, S. and Cowling, A.
(2005). Visual control of flight speed in honeybees.
J. Exp. Biol. 208,3895
-3905.
Barron, A. and Srinivasan, M. V. (2006). Visual
regulation of ground speed and headwind compensation in freely flying honey
bees (Apis mellifera L.). J. Exp. Biol.
209,978
-984.
Borst, A. and Bahde, S. (1986). What kind of movement detector is triggering the landing response of the housefly? Biol. Cybern. 55,59 -69.[CrossRef]
Borst, A. and Egelhaaf, M. (1989). Principles of visual motion detection. Trends Neurosci. 12,297 -306.[CrossRef][Medline]
Borst, A. and Haag, J. (2002). Neural networks in the cockpit of the fly. J. Comp. Physiol. A 188,419 -437.[CrossRef][Medline]
Buchner, E. (1976). Elementary movement detectors in an insect visual system. Biol. Cybern. 24, 85-101.[Medline]
Buchner, E. (1984). Behavioral analysis of spatial vision in insects. In Photoreception and Vision in Invertebrates (ed. M. A. Ali), pp.561 -621. New York: Plenum Press.
Collett, T., Nalbach, H. O. and Wagner, H. (1993). Visual stabilization in arthropods. Rev. Oculomot. Res. 5,239 -263.[Medline]
David, C. T. (1978). The relationship between body angle and flight speed in free-flying Drosophila. Physiol. Entomol. 3,191 -195.[CrossRef]
David, C. T. (1982). Compensation for height in the control of groundspeed by Drosophila in a new, `barber's pole' wind tunnel. J. Comp. Physiol. A 147,485 -493.[CrossRef]
Dickson, W. B., Straw, A. D. and Dickinson, M. H. (2008). Integrative model of Drosophila flight. AIAA Stud. J. 46,2150 -2164.[CrossRef]
Dror, R. O., O'Carroll, D. C. and Laughlin, S. B. (2001). Accuracy of velocity estimation by Reichardt correlators. J. Opt. Soc. Am. 18,241 -252.[CrossRef]
Dudley, R. (2000). The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton, NJ: Princeton University Press.
Duffy, J. B. (2002). GAL4 system in Drosophila: a fly geneticist's Swiss army knife. Genesis 34,1 -15.[CrossRef][Medline]
Eckert, H. (1973). Optomotorische Untersuchungen am visuellen System der Stubenfliege Musca domestica L. Biol. Cybern. 14,1 .
Egelhaaf, M. and Borst, A. (1993). Movement detection in arthropods. In Visual Motion and its Role in the Stabilization of Gaze (ed. J. Wallman and F. A. Miles), pp.53 -77. Amsterdam: Elsevier.
Egelhaaf, M. and Kern, R. (2002). Vision in flying insects. Curr. Opin. Neurobiol. 12,699 -706.[CrossRef][Medline]
Egelhaaf, M., Kern, R. and Warzecha, A.-K. (1998). Sensory ecology and neural coding in arthropods. Z. Naturforsch. C 53,582 -592.
Egelhaaf, M., Kern, R., Krapp, H. G., Kretzberg, J., Kurtz, R. and Warzecha, A. K. (2002). Neural encoding of behaviourally relevant visual–motion information in the fly. Trends Neurosci. 25,96 -102.[CrossRef][Medline]
Fermi, G. and Reichardt, W. (1963). Optomotorische reaktionen der fliege Musca domestica.Kybernetik 2,15 -28.[Medline]
Franceschini, N., Ruffier, F. and Serres, J. (2007). A bio-inspired flying robot sheds light on insect piloting abilities. Curr. Biol. 17,329 -335.[CrossRef][Medline]
Fry, S. N., Bichsel, M., Müller, P. and Robert, D. (2000). Tracking of flying insects using pan-tilt cameras. J. Neurosci. Methods 101, 59-67.[CrossRef][Medline]
Fry, S. N., Sayaman, R. and Dickinson, M. H.
(2003). The aerodynamics of free-flight maneuvers in
Drosophila. Science 300,495
-498.
Fry, S. N., Müller, P., Baumann, H. J., Straw, A. D., Bichsel, M. and Robert, D. (2004). Context-dependent stimulus presentation to freely moving animals in 3D. J. Neurosci. Methods 135,149 -157.[CrossRef][Medline]
Fry, S. N., Sayaman, R. and Dickinson, M. H.
(2005). The aerodynamics of hovering flight in Drosophila.J. Exp. Biol. 208,2303
-2318.
Fry, S. N., Rohrseitz, N., Straw, A. D. and Dickinson, M. H. (2008). TrackFly: virtual reality for a behavioral system analysis in free-flying fruit flies. J. Neurosci. Methods 171,110 -117.[CrossRef][Medline]
Gewecke, M. (1967). Die Wirkung von Luftströmung auf die Antennen und das Flugverhalten der blauen Schmeissfliege (Calliphora erythrocephala). J. Comp. Physiol. A. 54,121 -164.
Gewecke, M. and Heinzel, H. G. (1980). Aerodynamic and mechanical properties of the antennae as air-current sense organs in Locusta migratoria.1. Static characteristics. J. Comp. Physiol. A 139,357 -366.[CrossRef]
Gibson, J. J. (1958). Visually controlled locomotion and visual orientation in animals. Br. J. Psychol. 49,182 -194. Reprinted in Ecol. Psychol. 10, 161-176 (1998).[Medline]
Götz, K. G. (1964). Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila. Kybernetik 2, 77-92.[CrossRef][Medline]
Götz, K. G. (1965). Die optischen Übertragungseigenschaften der Komplexaugen von Drosophila.Kybernetik 2,215 -221.[CrossRef][Medline]
Hassenstein, B. and Reichardt, W. (1956). Systemtheoretische Analyse der Zeit-, Reihenfolgen- und Vorzeichenauswertung bei der Bewegungsperzeption des Rüsselkafers Chlorophanus. Z. Naturforsch. 11b,513 -524.
Hausen, K. (1993). Decoding of retinal image flow in insects. Rev. Oculomot. Res. 5, 203-235.[Medline]
Heisenberg, M. and Buchner, E. (1977). The rôle of retinula cell types in visual behavior of Drosophila melanogaster. J. Comp. Physiol. A 117,127 -162.[CrossRef]
Hesselberg, T. and Lehmann, F.-O. (2007).
Turning behaviour depends on frictional damping in the fruit fly Drosophila.
J. Exp. Biol. 210,4319
-4334.
Joesch, M., Plett, J., Borst, A. and Reiff, D. F. (2008). Response properties of motion-sensitive visual interneurons in the lobula plate of Drosophila melanogaster. Curr. Biol. 18,368 -374.[CrossRef][Medline]
Karmeier, K., van Hateren, J. H., Kern, R. and Egelhaaf, M.
(2006). Encoding of naturalistic optic flow by a population of
blowfly motion-sensitive neurons. J. Neurophysiol.
96,1602
-1614.
Katsov, A. Y. and Clandinin, T. R. (2008). Motion processing streams in Drosophila are behaviorally specialized. Neuron 59,322 -335.[CrossRef][Medline]
Kennedy, J. S. (1939). The visual responses of flying mosquitoes. Proc. Zool. Soc. Lond. A Gen. Exp. 109,221 -242.
Kennedy, J. S. and Thomas, A. A. G. (1974). Behavior of some low-flying aphids in wind. Ann. Appl. Biol. 76,143 -159.[CrossRef]
Kern, R., van Hateren, J. H., Michaelis, C., Lindemann, J. P. and Egelhaaf, M. (2005). Function of a fly motion-sensitive neuron matches eye movements during free flight. PLoS Biol. 3,e171 .[CrossRef][Medline]
Kunze, P. (1961). Untersuchung des Bewegungssehens fixiert fliegender Bienen. Z. Vgl. Physiol. 44,656 -684.[CrossRef]
Land, M. F. and Collett, T. S. (1974). Chasing behaviour of houseflies (Fannia canicularis). J. Comp. Physiol. A 89,331 -357.[CrossRef]
Lindemann, J. P., Kern, R., van Hateren, J. H., Ritter, H. and
Egelhaaf, M. (2005). On the computations analyzing natural
optic flow: quantitative model analysis of the blowfly motion vision pathway.
J. Neurosci. 25,6435
-6448.
Mronz, M. and Lehmann, F.-O. (2008). The
free-flight response of Drosophila to motion of the visual environment.
J. Exp. Biol. 211,2026
-2045.
Nalbach, G. (1993). The halteres of the blowfly Calliphora: I. Kinematics and dynamics. J. Comp. Physiol. A 173,293 -300.[CrossRef]
Nalbach, G. and Hengstenberg, R. (1994). The halteres of the blowfly Calliphora: II. Three-dimensional organization of compensatory reactions to real and simulated rotations. J. Comp. Physiol. A 175,695 -708.
O'Carroll, D. C., Bidwell, N. J., Laughlin, S. B. and Warrant, E. J. (1996). Insect motion detectors matched to visual ecology. Nature 382,63 -66.[CrossRef]
Pringle, J. W. S. (1948). The gyroscopic mechanism of the halteres of Diptera. Philos. R. Soc. Lond. B Biol. Sci. 233,347 -384.[CrossRef]
Reichardt, W. (1961). Autocorrelation, a principle for relative movement discrimination by the central nervous system. In Sensory Communication (ed. W. A. Rosenblith), pp.303 -317. New York: MIT Press.
Sherman, A. and Dickinson, M. H. (2004).
Summation of visual and mechanosensory feedback in Drosophila flight
control. J. Exp. Biol.
207,133
-142.
Srinivasan, M. V. and Zhang, S. (2004). Visual motor computations in insects. Annu. Rev. Neurosci. 27,679 -696.[CrossRef][Medline]
Srinivasan, M. V., Lehrer, M., Kirchner, W. H. and Zhang, S. W. (1991). Range perception through apparent image speed in freely flying honeybees. Vis. Neurosci. 6, 519-535.[Medline]
Srinivasan, M. V., Zhang, S., Lehrer, M. and Collett, T. S. (1996). Honeybee navigation en route to the goal: visual flight control and odometry. J. Exp. Biol. 199,237 -244.[Abstract]
Srinivasan, M. V., Poteser, M. and Kral, K. (1999). Motion detection in insect orientation and navigation. Vis. Res. 39,2749 -2766.[CrossRef][Medline]
Stark, W. S. and Johnson, M. (1980). Microspectrophotometry of Drosophila visual pigments: determinations of conversion efficiency in R1-6 receptors. J. Comp. Physiol. A 140,275 -286.[CrossRef]
Straw, A. D. and O'Carroll, D. C. (2003). Motion blur applied to eliminate artifacts in apparent motion displays. J. Vis. 3,782 .
Straw, A. D., Warrant, E. J. and O'Carroll, D. C.
(2006). A `bright zone' in male hoverfly (Eristalis
tenax) eyes and associated faster motion detection and increased contrast
sensitivity. J. Exp. Biol.
209,4339
-4354.
Straw, A. D., Rainsford, T. and O'Carroll, D. C. (2008). Contrast sensitivity of insect motion detectors to natural images. J. Vis. 8, 1-9.[Medline]
Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Cambridge: Perseus Books.
Tammero, L. F. and Dickinson, M. H. (2002). The
influence of visual landscape on the free flight behavior of the fruit fly
Drosophila melanogaster. J. Exp. Biol.
205,327
-343.
Taylor, G. K. and Krapp, H. G. (2008). Sensory systems and flight stability: what do insects measure and why? Adv. Insect Physiol. 34,231 -316.
Taylor, G. K., Bacic, M., Bomphrey, R. J., Carruthers, A. C.,
Gillies, J., Walker, S. M. and Thomas, A. L. R. (2008). New
experimental approaches to the biology of flight control systems.
J. Exp. Biol. 211,258
-266.
Wehner, R. (1992). Arthropods. In Animal Homing (ed. F. Papi), pp.45 -144. New York: Chapman & Hall.
Zanker, J. M., Srinivasan, M. V. and Egelhaaf, M. (1999). Speed tuning in elementary motion detectors of the correlation type. Biol. Cybern. 80,109 -116.[CrossRef][Medline]
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
0, the flies were stimulated in open-loop
(TF=4 s–1; SF=12.5 m–1;
stimulus condition is marked with an asterisk in
0.6 m s–1;
SF<25 m–1) in presence of low (left: –0.29
m s–1; N=941) and high (right: –0.73 m
s–1; N=45) wind speeds. The measured accelerations
reveal a significant dependence on the wind speed, suggesting an
air-speed-dependent response saturation (Wilcoxon test,
P<0.001).