Neural images of pursuit targets in the photoreceptor arrays of male and female houseflies Musca domestica
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
Author for correspondence (e-mail:
s.laughlin{at}zoo.cam.ac.uk)
Accepted 11 July 2003
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Summary |
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Key words: photoreceptor, target, tracking, retina, coding, housefly
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Introduction |
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How great is the improvement? To answer this question we have abandoned
conventional stimuli, such as flashes and white noise. The conventional
stimuli are powerful and convenient because they define the performance of a
cell with standard measures (e.g. impulse response, frequency response, SNR),
which can be used to derive responses to more realistic stimuli, such as small
moving targets (Juusola and French,
1997). However, neuroethologists have long appreciated the value
of testing sensory systems with the stimuli that they have evolved to receive
(Camhi, 1985). Sensory systems can be so sensitive to natural patterns that
they are not properly characterised using conventional stimuli. For example,
white-noise stimuli would tell us little about the mechanisms for echolocation
in bats. Even in a simpler peripheral system, Rinberg and Davidowitz
(2000
) found that the
cockroach's cercae respond to white-noise air currents in a way that is
inconsistent with their responses to more natural air flow.
Natural stimuli are increasingly used in vision research
(Reinagel, 2001;
Simoncelli and Olshausen,
2001
) because visual mechanisms are adapted to their properties. A
`natural' approach to phototransduction is advisable because neurones in the
early stages of both vertebrate (Atick and
Redlich, 1992
) and invertebrate
(van Hateren, 1992
;
Laughlin, 1981
) vision are
tuned to the statistics of natural images. The processing of natural scene
sequences (the time series of intensity generated as a photoreceptor scans
across a natural scene) has been examined directly in fly photoreceptors
(van Hateren, 1997
) and the
results suggest that non-linearities improve coding
(van Hateren and Snippe,
2001
). This role was not apparent from earlier analyses using
conventional stimuli (Laughlin et al.,
1987
; Juusola et al.,
1994
).
In addition to scanning across natural scenes, flies track moving targets
which generate a different image
(Wehrhahn, 1979). Tethered
houseflies can pick out a moving spot against a moving background, suggesting
the existence of a sensory gate for moving targets somewhere in the fly's
brain (Srinivasan and Bernard,
1977
). We applied more natural stimuli of known behavioural
relevance, i.e. simulated moving targets, to male and female photoreceptors to
see how much selectivity for moving targets emerges during
phototransduction.
Although both male and female flies track moving targets
(Wehrhahn, 1979;
Wehrhahn et al., 1982
), these
stimuli are especially important for the male who must catch a female in a
brief and vigorous aerial chase prior to mating. Several observations, largely
of houseflies, indicate that the male eye is particularly adapted for the
pursuit task. During pursuit, the male housefly tries to keep the female's
image in a sex-specific frontal eye region, the `lovespot'. This region, of
roughly 300 facets, points forwards and upwards so that the female is viewed
at high contrast against the sky
(Wehrhahn, 1979
). Contrast is
further improved by peculiarities of lovespot R7 and R8 photoreceptors.
Instead of expressing distinct photopigments and feeding into a presumed
chromatic pathway, as in the female and other parts of the male eye, lovespot
R7 and R8 express the same pigment as R1-6 photoreceptors and, like R1-6, feed
into the achromatic (contrast) pathway
(Hardie, 1985
). The lovespot
has larger lenses, smaller inter-receptor angles and narrower point spread
functions than other eye regions (Land,
1997
; Land and Eckert,
1985
). These features provide the lovespot with high spatial
resolution. Frontal male photoreceptors have faster responses than other
photoreceptors in both the female eye
(Hornstein et al., 2000
) and
other parts of the male eye (Burton et al.,
2001
), providing better temporal resolution.
We recorded the electrical responses of photoreceptors to pursuit stimuli in both sexes of the housefly Musca domestica. Using published measurements of the positions and velocities of flies during the chase and our own physiological measurements of photoreceptor point spread functions, we were able to simulate, using a fixed, spatially uniform light source, the signals received by a photoreceptor as a target moves across its axis. The electrical responses to stimuli in the behavioural range of target distances and speeds define the neural images that one fly `sees' as it chases another. We compare the neural images in the male's lovespot with those formed in the corresponding frontal region of the female retina to show that male lovespot photoreceptors respond particularly strongly to pursuit stimuli, and to evaluate the optical and neural specialisations responsible. White-noise analysis does not adequately predict these responses, emphasising the value of using biologically appropriate stimuli, even at the level of phototransduction.
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Materials and methods |
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Stimuli and recording
White-noise stimuli and pursuit stimuli were delivered by a blue-green
light-emitting diode (LED, max=505 nm; LEDtronics,
Torrance, CA, USA) via a fluid-filled light guide, subtending an
angle of 30° at the eye. Recordings were made at an effective photon flux
greater than 5x106 s-1, calculated by
extrapolating bump counts made under dark-adapted conditions for each
photoreceptor. A PC interfaced with an LED driver and an Axoclamp 2A amplifier
(Axon Instruments, Union City, CA, USA) controlled the stimuli and recorded
the responses. Sampling was usually at 1250 Hz, but was higher for the
briefest pursuit stimuli (see below). To avoid aliasing, responses were
low-pass-filtered by a 4-pole Butterworth filter with a cut-off frequency of
500 Hz prior to analogue-to-digital conversion.
For a given photoreceptor the stimulus programme was divided into three sections. The first and last consisted of white-noise stimulation, used to assess the stability of the response, to construct Wiener kernels and to form predictions for signal detection analysis (see below). Pursuit stimuli were presented in the middle section. Finally, the electrode was withdrawn from the cell and the electrode noise was recorded for off-line adjustment of photoreceptor noise estimates.
White-noise stimuli
Five Gaussian white-noise stimuli were presented, each 50 times. Each
stimulus was 1024 sample points long and was constructed in the frequency
domain to have a cut-off frequency of 400 Hz. White-noise stimuli had the same
time-averaged intensity as the adapting light and a contrast standard
deviation (S.D.) of 0.25 (S.D. of intensity divided by
the mean). Stimulus production was at 1250 Hz.
Pursuit stimuli
Pursuit stimuli were generated by modulating the output of the LED.
Although a moving target is a spatio-temporal stimulus, it can be simulated
using a uniform source because it is experienced by the single photoreceptor
as a signal in time only. Here we derive an expression (Equation 4) for this
signal from approximations of a target's shape and the actions of the fly's
optics.
For analytical simplicity, we model the target's image before filtering by
the fly's optics as a 2-D Gaussian function in angular coordinates. We also
consider a dark fly against the sky to have practically maximum contrast. With
respect to background light intensity, the relative intensity
X(,t) of the target as a function of angular position
and time t is then defined as:
![]() | (1) |
In nature, the target would then be filtered by the point-spread function
L() of the eye's optics, which approximates another Gaussian
function (Snyder, 1979
), thus:
![]() | (2) |
The optical image, I(,t), of the target on the
retina is then the convolution of the target with L(
):
![]() | (3) |
For simplicity, consider a photoreceptor whose optical axis is at the
origin [=(0,0)]. The target passes directly over the photoreceptor at
time t=0, with an angular speed of
. Performing the
convolution of Equation 3 and substituting
t for
||
x(t)||, the relative intensity
C(t) received by a photoreceptor as a function of time is:
![]() | (4) |
Note, for off-axis targets, an extra factor of
exp[-(4ln22)/(
x2+
2)]
is introduced into the second term of Equation 4, where
is
eccentricity.
Equation 4 defines the LED light signal delivered to the photoreceptor to
simulate the moving target for different target angular widths
x and angular speeds
. By inspection, we see
that a given stimulus has a duration (width at half maximum amplitude)
c of:
![]() | (5) |
![]() | (6) |
![]() | (7) |
For the acceptance angle, , angular sensitivity functions were
constructed from the responses of dark-adapted photoreceptors to flashes of
light delivered from a point source placed at different positions in the
photoreceptors' receptive fields (see
Burton et al., 2001
).
was measured as the half-width of the angular sensitivity
function. Mean values for
were 1.25° for males
(N=13) and 2.45° for females (N=18). These figures were
reduced by 20% to 1.00° and 1.96°, respectively, to take account of
changes in acuity that occur upon light adaptation
(Hardie, 1979
).
The number of sampling points and the sampling rate for generating and
recording a given pursuit stimulus were chosen to allow simple measurement of
response parameters such as amplitude and width. Sampling frequency was
usually 1250 Hz, but for brief stimuli (fast moving targets) this figure was
raised to maintain at least 16 samples (often 40) per stimulus duration,
c. The order in which chasing stimuli were presented was
completely randomised. At least 25 responses were recorded for each stimulus
for later averaging.
Analysis and presentation
Target detection
To assess the detectability of the photoreceptor's response to a low
contrast target, we form the signal-to-noise ratio,
d'=E[A]/, where E[A] is the expected
response amplitude and
is the standard deviation of photoreceptor
noise, both measured after suppressing the effects of noise with the
appropriate linear filter (Papoulis,
1991
, pp. 384-386). That is,
if h(t) is the filter and H(f) its Fourier transform, then
![]() | (8) |
![]() | (9) |
![]() | (10) |
In our analysis, (t) was generated
by convolving photoreceptor impulse responses with contrast signals of the
form of Equation 4. Both photoreceptor impulse responses and noise spectra
were calculated from white-noise analysis, as described by Burton et al.
(2001
). Briefly, the impulse
response is equal to the inverse Fourier transform of the photoreceptor
transfer function. We obtained the transfer function as the ratio of two
spectra, the spectrum of the average response to a white-noise stimulus and
the spectrum of the stimulus itself. Noise power was calculated as the power
spectrum of the residual responses to the white-noise stimulus (individual
responses minus the average response). It was then adjusted by subtracting the
electrode noise power spectrum. Both impulse response and noise power measures
were averaged across several white-noise stimuli.
Wiener kernels
Higher order predictions of the responses to moving targets were calculated
by convolving the target stimuli with both the photoreceptor's impulse
response and its second order Wiener kernel
(Marmarelis and Marmarelis,
1978). Second-order Wiener kernels were derived according to the
correlation method described by Marmarelis and Marmarelis
(1978
).
Responses to chasing stimuli
The angular width x and angular speed
of the
target at the eye may be manipulated to provide absolute distances and flight
speeds. If the absolute distance of the target is s and the true
width of an animal (or the half-width of a Gaussian function representing the
animal) is b, then:
![]() | (11) |
![]() | (12) |
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Results |
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The chasing fly is directed by a few simple target cues: the target's
angular position, angular width and angular speed (or equivalents, see
Materials and methods; Land and Collett,
1974; Wagner,
1986b
; Wehrhahn and Hausen,
1980
; Wehrhahn et al.,
1982
). From the perspective of a single photoreceptor, however,
which does not have explicit access to place information, the male's view of
the female is described only by her angular width
x and
her angular speed
(Fig.
1A). These parameters are determined by the female's absolute
size, distance and relative flight speed, and the male's turning rate. We
define likely combinations of
x and
by
examining published reports of target distance s, flight speed
u and angular speed
, and by applying two geometric
relationships (Fig. 1B; see
Materials and methods). First, for small targets, angular width,
x, is inversely proportional to distance s,
independent of the target's angular speed
(Fig. 1B, broken lines).
Second, for a given flight speed, u, angular speed
is
inversely proportional to distance s
(Fig. 1B, solid lines). We
consider two stages of pursuit, the detection of a target and the subsequent
chase.
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Detection
When a male detects a target, he is either stationary or cruising in a
steady forward flight, punctuated by fast `saccadic' turns >1000 deg.
s-1 (Schilstra and van Hateren,
1999; Wagner,
1986a
). Because saccades occupy a small proportion of the flight,
the target's angular speed is usually determined by its flight speed
u, relative to the male. Musca domestica usually flies at
20-60 cm s-1, but reaches 100 cm s-1 in brief bursts
(Wagner, 1986a
). Thus when a
female is detected she is between the 10 cm s-1 and 100 cm
s-1 lines on Fig.
1B. Because the visual space viewed by the lovespot forms a cone,
whose volume increases with distance from the animal, a previously unseen
target is likely to be distant and will lie below the 10 cm dashed line in
Fig. 1B. The optical point
spread function reduces the visibility of distant targets by increasing their
apparent width and lowering their contrast
(Fig. 1C). The male's lovespot
has better optics than the female eye. Consequently, target contrast will
reach detection threshold at greater distances for males. We set our smallest
target width to 0.3°, corresponding to a distance of 76 cm. This distance
is well beyond the 20-25 cm at which males orient to other flies
(Wagner, 1986b
) and is
associated with an optical image contrast of less than 10% in both sexes.
Chasing
Chasing is performed at distances of 1-10 cm
(Wagner, 1986b), represented
in the upper part of Fig. 1B,
so we set our largest target width
x to 30° (a
female at <1 cm). At chasing distances the target's optical image has a
high contrast (>0.84 in the male's lovespot) and reaches high angular
speeds, due to movements by both the target and the chaser. The distribution
of angular speeds has not been published but velocity scattergrams show that
speeds of 102-103 deg. s-1 are common. Higher
speeds occur during the male's saccadic turns
(Wagner, 1986b
), so we set an
upper limit of 10 000 deg. s-1. Our lower limit of 3 deg.
s-1 is as close as we can practically approach zero in recordings
of limited duration.
We simulate a set of targets that cover the behaviourally relevant range of
angular widths and speeds as follows. We take a hypothetical target of given
angular width and a peak contrast -1.0 against a uniform bright background and
blur it with the photoreceptor optical point spread function. A straight track
through the centre of this blurred image defines the time-varying contrast
signal received by the photoreceptor as the target moves directly across its
optical axis (Fig. 1D, see
Materials and methods), scaled by angular speed: the faster the target, the
shorter the signal duration. This signal is delivered to the photoreceptor by
a stationary LED positioned over the optical axis, and the response is
recorded. Although the stimulus is spatially uniform, the photoreceptor's
response is equivalent to the response to a moving target because
photoreceptors show no significant lateral interactions
(Smakman and Stavenga,
1987).
Photoreceptor response overview
For the male lovespot photoreceptor
(Fig. 2, blue lines),
detectable responses first occur around a target size of 0.3° and angular
speeds <100 deg. s-1 (see below). Response amplitude increases
with angular width and the largest responses are in the chasing range
(3-30° targets; angular speeds 100-1000 deg. s-1). These
chasing responses are biphasic and reach amplitudes (18 mV in this
photoreceptor) that are much larger than the response to white noise
(Fig. 2, top left trace,
above). At higher angular speeds, the responses decrease, the off-transient
may remain and the ascending phase can exhibit a notch. Remarkably, the male
photoreceptor responds to 3.0° targets (equivalent to a female at 7.6 cm)
at the `saccadic' velocities of 3000 and 10 000 deg. s-1. At the
lower speeds, 3-30 deg. s-1, the response amplitude falls slightly,
off-transients tend to disappear and the response becomes more symmetrical.
When large targets are viewed at the lowest speed the response terminates
prematurely, asymmetry increases and off-`transients' reappear. Generally, the
most powerful responses run from bottom left to top right in
Fig. 2 in the zone commonly
occupied by pursuit targets.
|
The equivalent female responses are smaller and show weaker transients
(Fig. 2, red lines), especially
for small and fast targets. These sex differences reflect the lower optical
contrast experienced by the female photoreceptor
(Fig. 1C) and the sexual
dimorphism in the frequency response of phototransduction
(Hornstein et al., 2000). In
the following sections we analyse seven male and seven female photoreceptors
to quantify the sex differences in performance under both detection and
chasing regimes and to separate the contributions made by optics and
phototransduction to response amplitude and duration.
Detection thresholds
The S.D. of voltage noise (corrected for electrode noise) in
male and female photoreceptors was 0.205 mV (N=7) and 0.161 mV
(N=7) respectively. The photoreceptors' responses to target stimuli
approach these values at target widths of around 0.3° for the male and
0.7° for the female. To quantify the response reliability in this
`detection' regime, we performed a conventional `ideal observer' analysis of
the small-target responses of both sexes
(Green and Swets, 1966). In
this analysis, we imagine a random set of trials in which the fly is presented
either with the target or with nothing, with equal probability. On each trial,
the photoreceptor response is optimally filtered to amplify the target, if
present, and to suppress intracellular and photon noise. The observer then
decides whether the target was presented on that trial based on the amplitude,
A, of the filtered response. The performance of an ideal observer at
this task is related to a signal-to-noise ratio,
d'=E[A]/
, where E[A] is the
expected filtered response amplitude and
is the S.D. of the
filtered noise. The optimal decision rule is to identify the target as present
whenever A/
>d'/2. The greater
d', the more frequently the observer will be correct.
The expected signal E[A] may be calculated using mean target
responses. However, the means we obtained were still highly corrupted by
photoreceptor and electrode noise. Instead, we formed predictions of these
responses from impulse responses obtained by white-noise analysis. As we show
later, this is a valid procedure in the detection regime as the photoreceptor
responds linearly to low-contrast stimuli. was also obtained from
white-noise analysis (see Materials and methods). In
Fig. 3 we plot
d' for all target speeds and for small targets in both sexes.
Comparing these values to the 5% error level, we see that the male response to
0.3° targets provides satisfactory amplitudes at target speeds of up to
300 deg. s-1. The female performs nearly as well at the same speeds
when the target width is 0.7°. A fly is 0.3° across at a distance of
76 cm. At this distance, an angular speed of 300 deg. s-1
corresponds to an absolute speed of 4.0 m s-1, well beyond the
normal flight speed of a conspecific. We conclude that, despite choosing
stimuli that comfortably include the behavioural range of distances, the male
photoreceptor is still providing detectable signals at distances beyond that
range.
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Response amplitude and contrast amplification
Although responses can be biphasic (Fig.
2), for uniformity with previous studies we define response
amplitude V as the maximum hyperpolarisation from the
background membrane potential. Following previous studies
(Juusola and French, 1997
;
Srinivasan and Bernard, 1975
),
we plot
V against target angular speed
(Fig. 4A,B). The male response
is larger and, unlike the female, peaks in the chasing range 100-1000 deg.
s-1. The peak shifts to higher speeds for larger (nearer)
targets.
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To place the data in their behavioural context, we replot V
against the target speed u in cm s-1, according to the
target distance s (Fig.
5A,B). In both sexes the response amplitude falls as the target
moves further away and subtends a smaller angle because optical blur reduces
contrast (Fig. 1C). At any
given target distance and speed, the male response is much larger than the
female and the male photoreceptor is adapted to respond to other houseflies by
responding most vigorously to targets travelling at normal Musca
flight speeds of 20-60 cm s-1.
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Further analysis separates the contributions made by optics and
phototransduction to improving the male response. The lovespot's narrower
point spread function increases the peak contrast C and
reduces the duration at half peak contrast
c of the optical
signals produced by moving targets (Fig.
1C,D). We normalise for contrast by taking the ratio,
V/
C, and take account of differences in
stimulus duration by plotting this ratio against
c. With these
adjustments, male photoreceptors are still consistently more responsive than
female photoreceptors (Fig.
6A,B), indicating that male photoreceptors have a higher gain.
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The sex-specific differences in photoreceptor gain can be determined at
stimulus durations that are brief enough to generate impulse responses. For
c <7 ms, the contrast amplification
V/
C is proportional to stimulus duration
(Fig. 6A,B), consequently
V is proportional to stimulus energy (the product of duration
and contrast). The slope of this relationship (
V divided by
stimulus energy) defines a gain that is over four times greater in the male
photoreceptor (3200±450 mV s-1, N=7) than in the
female (720±295 mV s-1, N=7).
Male photoreceptors maintain a higher gain when stimulus duration
increases. For a stimulus of near maximum contrast
(x=30°; s=0.76 cm), and near optimum
duration (
c
30 ms), the male's contrast amplification
(
V/
C=21.6±3.4 mV, N=7), is
over three times that of the female
(
V/
C=6.31±2.00 mV, N=7)
(Fig. 6A,B). Even at the
longest stimulus duration,
c
3 s, where the female response
is largest (Fig. 6A,B), the
male is still more sensitive
(
V/
C=16.2±1.7 mV, N=7;
cf.11.4±2.4 mV, N=7, in the female). When the stimulus
duration
c is >7 ms, male photoreceptors amplify
high-contrast targets more than low-contrast targets
(Fig. 6A), but females only
show this non-linearity at the longest stimulus durations,
c>100 ms (Fig.
6B). Consequently only male photoreceptors preferentially boost
close-quarter pursuit stimuli, which are of short duration and high contrast,
above more distant stimuli.
Male photoreceptor gain is highest when the stimulus duration is between
10-30 ms (Fig. 6A). It is this
simple time dependency that tunes the male photoreceptor to a female's flight
speed, independent of distance (see Fig.
5A). Because the angular speed and angular width
x of a female moving at fixed velocity both fall
linearly with viewing distance, a given flight speed always roughly
corresponds with a particular stimulus duration (approximately the ratio
x/
). Thus, by having cells respond maximally to
a particular stimulus duration, a robust preference for the flight speed of a
prospective mate is generated without recourse to complicated neural
circuitry.
The effects of optical blur and motion blur on spatial
localisation
Motion blur, the loss of spatial resolution for moving images, results from
the finite duration of the neural response, and combines with optical blur to
determine the width of a target's neural image. The angular width of the
neural image v (in the direction of motion) is the
product
v, where
is angular target speed and
v is the duration of the photoreceptor voltage response to
this moving target at half maximum amplitude. Models of motion blur in insects
have made clear predictions (Juusola and
French, 1997
; Srinivasan and
Bernard, 1975
). At low image speeds optical blur dominates so that
the width of the neural image
v approximately equals
the width of the target after optical blurring
c. At
high image speeds, the photoreceptor response duration
v is
limited by its impulse response, motion blur dominates and the angular width
of the neural image
v increases linearly with target
speed.
These two regimes are evident (Fig.
4C,D) for both sexes but at low speeds our data depart from
previous models. Surprisingly, the neural width drops below the optical width
and, in the extreme, is narrower than the target itself (i.e.
v<
x, as indicated by the
broken lines). This sharpening must be neural, as opposed to optical. Some of
this neural sharpening can be attributed to the band-pass nature of the
photoreceptor response, which produces transients
(Fig. 2).However, in a linear
system the neural image should asymptote to the optical width
c when the target speed approaches zero. The fact that
it does not in Fig. 4C,D suggests that the photoreceptor is not a simple linear filter. Instead,
additional dynamic mechanisms must be operating to shorten responses to longer
stimuli and maintain a low blur factor for even very slow moving targets.
Because the neural image of a large target can tolerate more blur than that
of a small target, we define a blur factor as the ratio of the
angular widths of the neural image and the target,
v/
x. Plots of blur factor
against target speed u (Fig.
5C,D) for the three closest targets (s=0.76, 1.5 and 3.3
cm, equivalent to angular widths of 30°, 15° and 7°) are almost
identical, with blur factors <1 up to a speed of
50 cm s-1
in the male, compared with
15 cm s-1 in the female. The precise
figures for a 30° (s=0.76 cm) target, derived by linear
interpolation of measured points on log-log axes, are 49.5±3.3 cm
s-1 (N=7) and 14.4±8.1 cm s-1
(N=7). Note that for the male the blur factor is <1 over much of
the normal range of flight speeds. Males are also more effective at sharpening
small targets. For a target width of 1.5° (s=15 cm), the male's
blur factor is <1 for speeds up to 27.3±5.4 cm s-1
(N=7) (Fig. 5C), but
the female's is never <1, and reaches 2 at 40 cm s-1
(Fig. 5D).
The female photoreceptor performs worse than the male because it has poorer
optics and slower and less transient electrical response. We take account of
optical differences by defining a second blur factor as the ratio of the
durations of photoreceptor response and stimulus waveform,
v/
c. This factor is plotted against stimulus
duration
c in Fig.
6C,D. The male clearly shortens the duration of its response more
than the female for long duration stimuli, corresponding with slow moving
targets. Furthermore, this difference increases for higher contrast stimuli.
Therefore, as with response amplitude, blur factor exhibits a non-linear
dependency on contrast that is stronger in the male.
In both sexes motion blur dominates at target speeds greater than 50 cm
s-1 (Fig. 5C,D)
where neural image width increases in proportion to both target speed and
impulse response duration (Juusola and
French, 1997; Srinivasan and
Bernard, 1975
). Fitting lines to the short duration (fast target)
regime of Fig. 6C,D gives
impulse response durations (width at half maximum height) of 4.90±0.33
ms (N=7) in males and 9.54±1.79 ms (N=7) in females.
Although male photoreceptors have faster responses than female photoreceptors,
they also suffer less optical blurring. Because motion blur starts to dominate
when the impulse response duration exceeds the duration of the optical signal,
these factors tend to cancel out. This observation explains why the motion
blur regime begins at roughly the same speed, u, in both sexes
(Fig. 5C,D).
In summary, the blur factors in males are consistently lower than in females for any target size and speed because the male photoreceptors have better optics and faster, more band-pass responses.
What does the neural image of a moving target look like?
We reconstruct the neural images of targets that males and females `see'
during pursuit from recordings of responses to simulated targets. We
incorporate the sex-specific differences in photoreceptor sampling densities
(Land, 1997;
Land and Eckert, 1985
),
optical point spread functions and electrical responses. With the data
recorded so far (responses to targets that pass through the centre of a
photoreceptor's field of view) we can only reconstruct the neural image along
a single row of photoreceptors, aligned with the target's trajectory. To
reconstruct the two-dimensional neural image formed in the photoreceptor array
we must measure the responses of photoreceptors in adjacent rows, which view
the target obliquely. Accordingly, we simulated the intensity signals received
by male and female photoreceptors as targets moved at different eccentricities
(see Materials and methods) and applied these stimuli to male and female
photoreceptors. For a given target, 22 eccentricities were considered and the
responses of photoreceptors were averaged across 30 (male) or 40 (female)
presentations. For reasons of space, we present the reconstructed neural image
of just one target, with angular width 3.44° and angular speed 180 deg.
s-1 (Fig. 7). This
is typical of targets encountered during pursuit and gives a stimulus duration
of 20 ms, the optimum duration for a male fly
(Fig. 6A,C).
|
Fig. 7 presents different images of the target at a single instant. Contours in Fig. 7A-C show the Gaussian light intensity distributions of the target before (Fig. 7A) and after blurring by male (Fig. 7B) and female (Fig. 7C) optics. Vertical lines indicate the width at half maximum amplitude in each case. The contours in Fig. 7D,E show the photoreceptor voltage responses for males and females, plotted continuously over all retinal positions without regard for the photoreceptor sampling lattice. Fig. 7F,G present these neural images, sampled discretely by the male and female photoreceptor arrays.
These reconstructions demonstrate just how much better the male's optics
and photoresponses are than the female's at increasing the amplitude of the
target's neural image and reducing its width. After optical blurring, the
target contrast C is 0.92 in the male but 0.755 in the female,
a difference of 22% (Figs 1C,
7B,C). Target width is
increased by 4% in the male from
x=3.44° to
c=3.58° (Fig.
7B) but by 15% in the female to
c=3.96°
(Fig. 7C). These discrepancies
are even larger in the final neural images owing to the larger amplitude of
the male's photoreceptor response, its more nonlinear contrast gain and more
band-pass dynamics. The peak neural response is 24.5 mV in the male and only
11.9 mV in the female, now a difference of 106%
(Fig. 7D,E). In the male, the
widths of the retinal representation parallel and perpendicular to the
direction of motion are 2.77° and 3.23°, respectively. In females
these widths are 3.62° and 3.56°. A more rapid, more biphasic male
response (compare the depolarising responses behind the target in
Fig. 7D,E) also reduces spatial
lag. In contour plots (Fig.
7D,E) the peak of the male response lags 1.4° behind the true
position of the target, equivalent to a delay of 7.8 ms. In the female the lag
is 1.5°, equivalent to a delay of 8.3 ms. Finally we note that the male's
improved spatial resolution is roughly matched by the higher sampling density
of his retina (Fig. 7F,G).
Kernels derived from white-noise analysis do not predict pursuit
responses
Here we demonstrate the importance of using behaviourally appropriate
stimuli by showing that white-noise analysis fails to describe the neural
image of near, moving targets. Photoreceptor responses to white-noise
stimulation are usually linear (French,
1980; Juusola et al.,
1994
). Accordingly, Juusola and French
(1997
) used linear system
kernels derived by white-noise methods to predict the responses of fly
photoreceptors to moving points of light. Because pursuit stimuli and
responses differ considerably from white noise in waveform and amplitude
(Fig. 2), we compared recorded
pursuit responses with the predictions of white-noise analysis.
First- and second-order Wiener kernels, constructed from responses to
Gaussian white noise (see Materials and methods), were used to predict the
average responses of individual photoreceptors, both to a further white-noise
stimulus and to representative pursuit stimuli. We confirmed that fly
photoreceptors behave remarkably linearly in response to white noise
(French, 1980;
Juusola et al., 1994
). The
mean squared error between the linear (first order) prediction and the average
response to white noise was typically 5%. This figure was only marginally
improved when the second-order kernel was introduced (not shown).
When predicting responses to pursuit stimuli (Fig. 8), the first-order (linear) kernel works well at the lowest response amplitudes (distant targets), as demonstrated in Fig. 8A where real and predicted responses overlap. However, with increased stimulus contrast and photoreceptor response amplitude (Fig. 8B), the first-order prediction (dotted line) captures only 75% of the peak-to-peak response amplitude of the real response (solid line), and the second-order kernel is required to produce a reasonable approximation (broken line). With longer duration pursuit stimuli even the second-order kernel becomes inadequate. The recorded response to a 15° target moving at 300 deg. s-1 is almost 30% larger than predicted from the second-order model (Fig. 8C, c.f. solid and broken lines). The same width target moving at 10 deg. s-1 elicits a response that is not only 70% larger than predicted but is also biphasic (Fig. 8D). Similar differences are observed in the responses to a 3° target moving at 1000 deg. s-1 (Fig. 8E) or 10 deg. s-1 (Fig. 8F). While the second-order kernel predicts the same amplitude response in both cases, the recorded response is substantially larger for the longer stimulus.
|
Thus, although the photoreceptor behaves remarkably linearly to white-noise stimuli, white-noise analysis does not predict the responses to many of the moving targets that male flies track during pursuit.
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Discussion |
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Previous studies have examined the resolution of the insect eye for moving
objects using point stimuli (Juusola and
French, 1997; Srinivasan and
Bernard, 1975
). In both cases, the responses of photoreceptors to
these stimuli are made from impulse responses obtained using conventional
analytical stimuli (flashes or Gaussian white noise). Our study differs from
this work because we have recorded photoreceptor responses directly to pursuit
stimuli. Our direct approach demonstrates specializations that are not
predicted from responses to conventional analytical stimuli. We find the male
photoreceptor has a distinct optimum target speed (Figs
4,
5), a feature more reminiscent
of previous predictions of interneurone responses (large monopolar cells) than
of photoreceptor responses (Juusola and
French, 1997
). A nonlinear dependence of response on contrast
boosts responses to near targets, particularly in the male
(Fig. 6). The spatial
resolution of moving targets is higher than expected, particularly at lower
speeds where the blur factor is less than 1 in both sexes
(Fig. 5). This reduction
contradicts the prediction from impulse responses
(Juusola and French, 1997
)
that response width asymptotes to the optical width of the target at low
angular speeds.
We suggest that Gaussian white-noise (GWN) analysis fails to predict pursuit responses because pursuit stimuli cover a larger range of contrasts than GWN can adequately test. GWN is concentrated near its mean. Consequently, GWN predictions of responses to high-contrast stimuli are largely based upon extrapolation, a notoriously unreliable procedure. This problem is especially acute for longer stimuli (Fig. 8) because these have particularly powerful low-frequency components. Such stimuli are not prominent features of GWN, which by definition spreads power equally across all frequencies.
We have also, unlike previous work, considered target distance and angular
width. An assumption that targets can be modelled as point sources is invalid
for much of the chase. Because near objects are large, they can be moving at
very high angular speeds before significant blurring occurs or response
amplitude falls. Thus, like Juusola and French
(1997), we find that the
response to small (point) or distant targets starts to deteriorate at 200 deg.
s-1, but for near targets the male photoreceptor's optimum response
is at approximately 1000 deg. s-1
(Fig. 4). Generally, when we
convert angular speeds (
) to absolute flight speeds (u)
(Fig. 5), male responses easily
follow a female at natural speeds (60 cm s-1). This observation has
implications for understanding the neural mechanisms of tracking:
photoreceptors rarely compromise target tracking during pursuit.
Target detection
In an ideal observer task we found that the male photoreceptor generates a
detectable response to a cruising fly at a distance of at least 76 cm
(Fig. 3). The female performs
similarly at slightly less than half this distance (33 cm). The difference
primarily reflects superior male optics. The distance at which the optical
image exceeds a given contrast is inversely proportional to photoreceptor
acceptance angle (Equations 7,11; see Materials and methods) and the lovespot
acceptance angle is half the female value. Optics therefore play a crucial
role in determining target detectability.
What is surprising, however, is how far behavioural measurements fall short
of these photoreceptor limits. The male housefly gives chase when the leading
fly is only 20 cm directly ahead, although there is evidence for orientation
at 25 cm(Wagner, 1986b). What
could be the reasons for this discrepancy? One is simply that behavioural
measurements have been taken indoors where, with lower light levels, the
signal-to-noise ratio (d') is much less than we were
able to obtain with an LED. It is also likely that the assumptions of the
`ideal observer' model are inappropriate. In the model we assume that the
stimulus-present and stimulus-absent trials are equally probable, that
identification of either condition carries equal pay-off, and that the fly
knows both what the stimulus will be (for optimal filtering purposes) and when
in a trial that stimulus can occur. The natural situation may encourage more
cautious decision-making than these assumptions generally allow. For example,
pay-offs are not equal. A `positive' choice always incurs the energetic cost
of chasing, but may not result in a successful mating if the target is
misidentified or other males have intercepted the target first (see
Collett and Land, 1978
;
Thornhill, 1980
). These
factors might raise the decision threshold despite the reproductive forfeit of
a false negative decision.
Still another reason for discrepancy might be that the fly is accustomed to operating in a more cluttered environment where image distractors are the dominant noise source. Although males try to chase targets against the sky, initial detection may be against a complex background, inevitably making the detection task more difficult. We have argued that male photoreceptor responses are adjusted to respond preferentially to moving targets. How they perform in `image noise' is a matter of some interest. We suggest that the nonlinear contrast gain of male photoreceptors may be an adaptation for amplifying the higher contrast targets against lower contrast clutter.
Pursuit responses
Once detected, a target fly is vigorously chased at distances associated
with angular widths of 3-30°. For 80% of the chase the male keeps the
target in the lovespot with an angular speed in the range 100-1000 deg.
s-1 (Wagner,
1986b). The lovespot photoreceptor is maximally responsive over
this range of target angles and speeds
(Fig. 4A) and its image of a
target is always sharper than its female counterpart
(Fig. 4C,D). Naturally,
fast-moving episodes are very brief and, therefore, they may be of limited
importance for flight control, but there is no doubt that during such
episodes, lovespot photoreceptors register target position.
We have identified and assessed the factors that improve the responses of lovespot photoreceptors to `chased' targets: optics, photoreceptor gain and photoreceptor response dynamics. Lovespot lenses, with their narrow acceptance angles, deliver shorter, higher contrast stimuli than female optics. However, at chasing distances, where targets fill the acceptance angles of both sexes, superior male optics provide much less of an advantage than they do in the detection regime. Consequently, it is mostly the lovespot photoreceptor that elevates performance during chasing.
At most speeds and for all contrasts, the gain of a lovespot photoreceptor
is 3-4 times the female value. Consequently the male responses to pursuit
stimuli are surprisingly large, reaching 25 mV in some animals. The way in
which these large male responses to moving targets are achieved is not clear,
but we can suggest some possibilities. First and foremost, the faster response
of the lovespot photoreceptor increases bandwidth
(Hornstein et al., 2000) and
hence the amplitude of responses to the rapidly changing pursuit stimuli. This
effect may then be amplified by self-shunting. As the light-gated channels
close due to the presence of a dark target, the resistance of the membrane
increases and the membrane voltage becomes more sensitive to further channel
closure. Such a mechanism could explain why contrast gain increases with
stimulus contrast.
This type of non-linear contrast gain function is thought to contribute to
the ability of the human visual system to deblur moving images
(Hammett et al., 1998). Neural
deblurring is a prominent feature of the male photoreceptor's response where
the pronounced transient, symptomatic of high-pass filtering in
phototransduction (Hornstein et al.,
2000
), reduces the spread of the response to a moving target in
the direction of motion (Fig.
6). Interestingly, high-pass filtering is also thought to
contribute to deblurring in the human visual system
(Pääkkönen and Morgan,
2001
).
Amplification depends as much on the duration of the stimulus (over two
orders of magnitude) as either its contrast or the final voltage predicted
from white-noise kernels (compare Fig. 8E
with F). This observation suggests that the male response could be
boosted by time-dependent mechanisms, such as voltage-sensitive ion channels.
In drone bee retina tetrodotoxin-sensitive Na+ channels amplify the
responses to the small brief decrements in intensity produced by over-flying
queen bees (Coles and Schneider Picard,
1989) and operate best in the behavioural response range (Vallett
and Coles, 1993). Voltage-gated Ca2+ channels at the
photoreceptor's synaptic terminal could play a similar role in fly
(Weckström et al.,
1992
).
Adapting retinal photoreceptors and neurones to behavioural
stimuli
It is well established that photoreceptor arrays can be tuned to specific
behavioural tasks (Lythgoe,
1979; Wehner,
1987
). For several animals, these tasks include the detection of
mates or prey. Photoreceptor spectral sensitivity and spatial and temporal
properties may each be adapted for this purpose
(Attwell et al., 1984
;
Cronin et al., 2000
;
Vallet and Coles, 1993
;
Zeil et al., 1986
). Using a
behaviourally relevant set of stimuli, we have shown that photoreceptor
responses in the male housefly Musca domestica, but not the female,
are well suited to the target speeds normally experienced during the pursuit
of conspecifics, a behaviour exhibited by males prior to mating. This finding
is perhaps a rudimentary example of the principle of matched filtering
(Wehner, 1987
). Might other
early visual neurones also show special pursuit responses?
A natural place to explore this issue further is in the fly's postsynaptic
large monopolar cells (LMCs). Although LMCs transmit information as graded
potentials, the LMCs, L1 and L3, will elicit `off'-spikes when photoreceptors
hyperpolarise deeply and quickly in sequence
(Hardie and Weckström,
1990; Uusitalo et al.,
1995
). Thus, the single off-spike could mark fast, high-contrast
targets. In this regard, it is interesting that one of the spiking LMCs, L3,
is larger in the lovespot than anywhere else in the male or female eye
(Braitenberg, 1972
). We suggest
that L3 may prove to be a filter for moving targets, activated by large
photoreceptor responses.
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List of Symbols |
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General |
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Stimulus construction |
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Target and stimulus parameters |
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Target detection |
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Acknowledgments |
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Footnotes |
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