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First published online October 5, 2007
Journal of Experimental Biology 210, 3661-3676 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.003764
Phonotactic walking paths of field crickets in closed-loop conditions and their simulation using a stochastic model
Centre for Ecological Sciences, Indian Institute of Science, Bangalore 560012, India
* Author for correspondence (e-mail: rohini{at}ces.iisc.ernet.in)
Accepted 6 August 2007
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Summary |
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 TOP Summary Introduction(A) PHONOTAXIS EXPERIMENTSResults(B) SIMULATION OF WALKING...ResultsDiscussionReferences |
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Key words: walking phonotaxis, closed loop behaviour, multiple sound sources, simulation, field cricket, Plebeiogryllus
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Introduction |
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TOPSummaryIntroduction(A) PHONOTAXIS EXPERIMENTSResults(B) SIMULATION OF WALKING...ResultsDiscussionReferences |
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). Each species of cricket produces a calling song with a
unique combination of spectral and temporal features
(Otte, 1992). Females use
these acoustic mate attraction signals to distinguish between conspecific and
heterospecific males and also to discriminate between conspecific males
(Gerhardt and Huber, 2002).
Females also use these songs to localize males in order to mate with them, a
behaviour termed phonotaxis (Regen,
1913). Cricket phonotaxis has generated a great deal of research
in the areas of acoustic pattern recognition and sound localization
(Hedwig, 2006). Recent work
has shown that pattern recognition and localization function at different
temporal scales and are experimentally separable by virtue of their temporal
dynamics (Hedwig and Poulet,
2004; Hedwig and Poulet,
2005; Poulet and Hedwig,
2005).
Field cricket females are believed to solve the complex task of localizing
one of multiple calling males by converting it into a simpler problem using
their pressure gradient ears (Larsen et
al., 1989; Michelsen et al.,
1994), selective attention
(Pollack, 1988) and contrast
enhancement (Horseman and Huber,
1994a; Horseman and Huber,
1994b). The pressure gradient ear of crickets suppresses the
representation of sounds from the contralateral hemisphere
(Larsen et al., 1989;
Michelsen et al., 1994) and
the mechanism of selective attention allows the representation of only the
loudest song on each ear, if the songs are sufficiently separated in sound
pressure level (SPL) (Pollack,
1988; Römer and Krusch,
2000). If selective attention fails to separate songs on the same
side of the animal (i.e. they are similar in SPL), these songs
would be perceived as having inappropriate patterns. Songs with inappropriate
patterns are ignored or responded to poorly
(Hedwig and Poulet, 2005;
Stabel et al., 1989). Neural
circuitry in the prothoracic ganglion provides contrast enhancement by
decreasing the strength of the response on the softer side
(Horseman and Huber, 1994a;
Horseman and Huber, 1994b).
Thus the problem of localizing multiple sources is reduced to a simple choice
in turning to one of the two sides, with varying turn magnitude depending on
the difference in response (evoked by the SPL difference of songs)
between the two ears and the clarity and appropriateness of the temporal
pattern. Females are known to turn towards the side with the louder
SPL if the song pattern is unmasked and conspecific
(Pollack, 1988;
Schildberger, 1994;
Stabel et al., 1989).
There have been several kinds of studies on field cricket phonotaxis. Many
use closed-loop compensated walking phonotaxis paradigms in which crickets
exposed to sound stimuli can change their heading angle to face the sound
source but cannot approach any closer e.g. Kramer treadmill
(Schmitz, 1985;
Schmitz et al., 1982;
Weber et al., 1981). More
recently, an open-loop paradigm (optical trackball system) has been devised in
which the female cricket can change neither her heading angle nor her distance
with respect to the sound source (Hedwig
and Poulet, 2004). Both open-loop and compensated phonotaxis
paradigms are better suited to dissecting the neural mechanisms underlying
pattern recognition and sound localization than arena phonotaxis. Female
phonotaxis in the field, however, occurs under closed-loop conditions and
female locomotor behaviour has direct consequences on the subsequent stimuli
perceived. Open-loop and compensated walking paradigms are thus unlikely to be
sufficient to understand natural phonotactic walking behaviour. There have
been only a few previous studies quantifying the phonotactic trajectories of
crickets walking in arenas (Bailey and
Thompson, 1977; Murphey and
Zaretsky, 1972; Oldfield,
1980; Stout et al.,
1983; Stout and McGhee,
1988).
In addition, most studies of phonotaxis have used single sources of calling
song (Oldfield, 1980;
Schmitz et al., 1982), or
multiple sources with only one source active at a given time
(Murphey and Zaretsky, 1972;
Schmitz et al., 1982). Some
studies have used multiple sound sources that produce the same stimuli
simultaneously (Hedwig and Poulet,
2005; Schmitz,
1985) or produce calling song with fixed timing relationships
between chirps (Hedwig and Poulet,
2005; Stout and McGhee,
1988; Weber et al.,
1981). Pollack and Hoy
(Pollack and Hoy, 1979;
Pollack and Hoy, 1981) used a
walking phonotaxis paradigm with two speakers to test female preference for
conspecific versus heterospecific song and to different components of
songs. To our knowledge, a detailed quantification of natural closed-loop
walking phonotactic behaviour with systematically varied natural conspecific
calling song SPL from multiple, simultaneously active, aphasic,
calling song sources has not so far been carried out.
An important approach to integrating and testing our current understanding
of field cricket phonotaxis, whether at the behavioural or neurobiological
level, has been the creation of quantitative models. The usefulness of models
in understanding animal behaviour has been extensively reviewed
(Webb, 2000). A strong
motivation for such studies is that dynamic quantitative models, whether
simulation-based or robotic, make explicit a hypothesis about the mechanisms
generating a particular behaviour and can be used to test sufficiency in
explaining the target behaviour. Many aspects of phonotaxis behaviour have
been recreated using a series of robotic models
(Horchler et al., 2004;
Reeve et al., 2005;
Webb, 1995;
Webb, 1998;
Webb and Scutt, 2000). A first
generation robot of the field cricket used the compensated walking phonotaxis
paradigm as its basis and, using neuro-mimetic circuitry, qualitatively
reproduced several behaviours displayed by crickets in the closed-loop walking
compensator paradigm (Webb and Scutt,
2000). Subsequent robots have been modified not only to better fit
known details of field cricket neurophysiology but also to incorporate a
walking mechanism and mechanosensory receptors, and they successfully localize
single sources of calling song (Horchler
et al., 2004; Reeve et al.,
2005). These second generation robots have not, however, been
tested using multiple sound sources, the natural acoustic conditions
encountered by field cricket females
(Mhatre and Balakrishnan,
2006). Also, since several sources of data were used, it has not
been possible to make direct and quantitative comparisons between the original
data of field cricket behaviour and the data obtained from the robotic
approach.
Ideally, it would be best to create a quantitative model of walking phonotaxis with multiple sound sources, using data from a single system. Such a model could then be demonstrated to quantitatively recapture the data used to create it. The behaviour produced by the model should then be tested in situations that were not included in the modeling effort, the outcomes of which are, however, known from behavioural experiments with real crickets.
Plebeiogryllus guttiventris females in the field are known to
encounter multiple simultaneously calling males whose calls vary in
SPL and are aphasic (Mhatre and
Balakrishnan, 2006). The task of sound localization under these
situations is expected to be more demanding than the situation studied in
conventional phonotaxis experiments. In this study, we first characterized
walking phonotactic paths of female field crickets in response to two
simultaneously active sound sources playing calling songs, which were
identical in quality but aphasic with respect to each other.
Data generated from the experimental phonotaxis trials and current
knowledge about the auditory physiology of crickets were then used in
combination to simulate walking phonotaxis using a stochastic model. We
attempted to recapture in the simulation important and quantifiable features
of the original phonotactic paths. We then quantitatively tested the
predictions of the simulation against phonotactic paths of females observed in
a separate outdoor phonotaxis experiment. We also qualitatively validated this
model by replicating two classical experiments in the simulation, i.e. the
removal of one ear of the cricket (Kohne
et al., 1991) and the reduction of directionality by disrupting
the pressure gradient ear (Schmitz,
1985).
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(A) PHONOTAXIS EXPERIMENTS |
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). A laboratory
culture of P. guttiventris was established in 2002 and is regularly
outbred with wild-caught individuals. The culture was maintained in large
plastic barrels with a 12 h:12 h light:dark cycle. The animals in the culture
were fed with Nutripet CatChow and Sandoz Calcium tablets. Water was provided
ad libitum. Adult virgin females were used for phonotaxis trials 3–4 weeks after the final moult. Each female was given an individual code number and a small pin was mounted on her thorax using a 1:1 mixture of beeswax and colophonium. After allowing the female time to get accustomed to the pin, it was used to place the female precisely during the start of the phonotaxis trials. Experiments were carried out in the laboratory between June–August 2004 and June–July 2005.
Stimuli
Phonotaxis trials were carried out at a temperature of 24±2°C. A
five-syllable chirp from a P. guttiventris song recorded at
24.6°C at a sampling rate of 44.1 kHz, with features appropriate for this
temperature (Mhatre and Balakrishnan,
2006), was selected to prepare the stimulus. This chirp was used
to synthesize two songs, each 40 s in length. The period for each chirp in
each song was randomly selected from the appropriate chirp period
distribution. The synthesized songs were found to be aphasic, similar to songs
produced by simultaneously singing P. guttiventris males
(Mhatre and Balakrishnan,
2006). While the songs did overlap considerably, 25% of the
syllables of each song were not overlapped by those of the other. In pilot
experiments, two sets of females were presented with songs of equal
SPL (at 61 dB and 66 dB, respectively). The positions of the
speakers were interchanged to break the association between song and
direction. Female orientation responses indicated no preference for either
song (
2 tests, 61 dB: P=0.34, N=18; 66 dB:
P=0.69, N=28). The songs were played out using the software
Goldwave Shareware Version 3.03 (1996 Chris Craig) via a Creative
SoundBlaster D/A card and two Philips BA109 loudspeakers (frequency range: 100
Hz–18 kHz).
Arena set-up
The two speakers were placed 60 cm apart on a sheet of high-density
acoustic foam with their faces parallel to each other. Sheets of high-density
foam were placed around the arena in order to suppress echoes. Females were
released midway between the two speakers with both speakers at 90° to the
female's midline.
The phonotactic responses in all trials were recorded using an infra-red
(IR) sensitive video camera (Sony DCR-TRV17E) with an IR source. The camera
was mounted so that the plane of the foam surface was exactly parallel to the
lens. The area of the arena that was recorded was limited to a rectangle of 30
cmx20 cm centered upon the female. While P. guttiventris
females in the field do encounter males at this low spatial separation, the
spread of choruses is usually higher
(Mhatre and Balakrishnan,
2006) and it would have been ideal to record longer paths. The
limitations of our recording equipment, however, forced us to use this high
magnification in order to accurately measure the heading angle and centre
point of the female in each frame. A 5 cmx5 cm grid was used to scale
the video during analysis.
Sound pressure level measurements
The sound pressure level (SPL) of each speaker was measured
before each set of trials using a Bruel and Kjaer microphone (Type 4133) and
Integrating Sound Level Meter (Type 2231) set at fast RMS with a 500 Hz high
pass filter. SPL measurements were made by placing the microphone
on the surface of the arena, at the release position of the female, facing
each active speaker, with the other muted. The sound field for each playback
SPL was also measured by recording the SPL at each grid
node in a 5 cmx5 cm grid and then interpolated to a 1 cmx1 cm
grid. This matrix is referred to as the SPL profile of a
speaker.
Experimental design
We tested the effect of relative SPL (i.e. difference in
SPL between the two speakers) and baseline SPL (the
SPL of the softer of the two speakers) on the phonotactic walking
paths of females. Females were tested at three baseline SPL values,
55 dB, 61 dB and 67 dB, and at four relative SPL values, starting
at each of these baselines: 0 dB, 3 dB, 6 dB and 9 dB, in a total of 12
stimulus conditions. Treatments will hereafter be described in the following
manner: `55 d3dB', where 55 dB is the baseline SPL and 3 dB is the
relative SPL.
Six sets of females were tested. Each female within a set was tested at a single baseline SPL paired with all relative SPL values. To account for possible effects of order of presentation, two sets of females were tested at each baseline SPL, the first with relative SPL values in ascending order and the other in descending order. To control for directional biases, the first set of females was presented with the louder speaker on the left for the relative SPL values d3dB and d9dB and on the right for d6dB and vice versa for the second set.
All phonotaxis trials were carried out in complete darkness between 18:30 h and 20:30 h, the normal activity period. The test trial with both speakers active was carried out first. If the female did not move within 3 min of release, the trial was aborted. If the female moved, her response was recorded until she left the arena or 5 min had elapsed since release. After the test trial the female was allowed at least 10 min of rest and then the control trial was carried out with only the baseline SPL speaker active. If the female turned towards the single active speaker within 5 min she was considered responsive. If she did not turn towards the single active speaker or turned away from it, the response to the test trial was discarded. Each female was presented with only one test trial followed by a control trial on a given night.
The female was then tested with the next treatment in the series on the next night. If a female failed to respond to a particular treatment on two subsequent nights, trials were discontinued. Data from females who completed the entire set of trials were used for analysis. Additional data from females who had completed the relative SPL d0dB trial at all baseline SPL values were also used.
Video analysis
Video recordings of the trials were digitized using the ATI All-in-Wonder
128 Pro Video capture card (Sunnyvale, CA, USA). They were converted to image
stacks with 5 frames s–1 saved as separate serialized bitmap
files using Ulead Video Studio (Version 5.0, 2000, Ulead systems Inc., Taipei,
Taiwan) and Adobe Premiere Pro (Adobe Systems Inc., San Jose, CA, USA). The
position of the female expressed in Cartesian co-ordinates and her heading
angle in each frame was measured from the bitmap file using a background
subtraction technique implemented in the software ImageJ 1.32j (Wayne Rasband,
NIH, USA). These data were then used to reconstruct the path of the
female.
Analysis of walking phonotaxis
Path vectors
Path vectors were calculated using standard formulae
(Batschelet, 1981). The path
vectors were mirrored when necessary and then pooled by stimulus condition.
The mean path vector and angular deviation for each condition
(Batschelet, 1981) were
calculated. Females presented with two songs of the same quality at the same
SPL are expected not to make a choice and to have a mean path
vector direction of 0°. Similarly females are expected to turn 90°
towards the louder speaker in all other trials. Path vectors were tested using
a V-test (Batschelet,
1981) with 0° as the expectation at d0dB and 90° as the
expectation at all other relative SPL values (
level=0.05).
Path vectors, which were not significantly directed towards their hypothetical
direction, were tested with a Rayleigh test for a uniform distribution
(Batschelet, 1981) (
level=0.05).
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Baseline and relative SPL perceived at pauses
We inferred the baseline and relative SPL of song perceived by
females at each pause using the following three steps.
(i) Attenuation generated by distance and peripheral auditory directionality
For each ear of the female, the SPL of both songs at the
female's position was inferred using the SPL profiles of both
speakers and the attenuation expected to be generated by the directionality of
the cricket ear and the angle subtended by the speaker to the female's
midline. The peripheral auditory directionality (PAD) curve of the Gryllus
bimaculatus ear (Michelsen et al.,
1994) was used. The PAD curve of Gryllus campestris,
which is closer in size to P. guttiventris, has also been reported
(Larsen et al., 1989). In
order to be parsimonious, however, we used the G. bimaculatus
measurements, as the directionality generated by its pressure gradient ear is
lower (15 dB at contralateral position) than that of the G.
campestris ear (nearly 30 dB at the contralateral position)
(Larsen et al., 1989;
Michelsen et al., 1994).
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). Assuming no excess attenuation, the calling song would be
100 dB SPL at about 0.5 cm from a calling male. At such short
distances, directional cues from song are probably not important and the
response of auditory neurons might saturate with few maladaptive effects.
Similarly if the SPL of a song at either ear was found to be below
40 dB, the behavioural threshold for P. guttiventris females
(Mhatre and Balakrishnan,
2006), it was set as being below phonotactic threshold. This
provides a dynamic range of nearly 60 dB, within the range observed in the
tympanal nerve of Teleogryllus oceanicus
(Imaizumi and Pollack,
2001).
(iii) Selective attention and masking
After subtracting all sources of attenuation from the SPL of
calling song, we determined which of the speakers was loudest at each ear of
the female. Using the principle of selective attention
(Pollack, 1986;
Pollack, 1988), if the two
songs at each ear were at least 3 dB apart in SPL, we considered
the stimulus to be unmasked. At the end of this exercise, the SPL
and masking status of song at each ear of the female was available and the
baseline and relative SPL could be calculated for the female's
position during each pause.
Angle changes
During pauses, females usually stood still and the heading angle stayed
relatively constant. The change in heading angle occurred gradually during
walking bouts, forming curved paths. To estimate total angle change between
pauses, the average heading angle of the female at each pause and the change
in the average heading angle between consecutive pauses was calculated.
The first angle change was defined as the angle change in longitudinal body
axis made during the first walking bout. Mean first angle changes and the
deviation of this angle change were calculated using standard formulae
(Batschelet, 1981).
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We then further subdivided the data on the basis of different baseline and relative SPL values to test the relationship between stimulus angle and angle change. Pauses were binned on the basis of baseline SPL at 5 dB intervals, starting from 40 dB SPL. Each set of pauses in a particular baseline SPL bin was then further subdivided using relative SPL bins of 3 dB bin width starting from d1dB. Pauses with relative SPL d0dB to d1dB at all baseline SPL values were treated separately. Regressions of angle change against stimulus angle were calculated and the slopes of these regressions were then plotted in a 3D surface against the centre of each baseline and relative SPL bin.
Statistical tests on features of phonotactic paths
All statistical analyses dealing with linear variables were carried out
using Statistica (1999, Statsoft Inc., USA) software. The influence of
stimulus conditions on different features of phonotactic paths, i.e.
sinuosity, pause number, mean pause duration, mean walking bout duration and
length, within a path, were tested using separate two-way repeated-measures
ANOVAs with the baseline and relative SPL values as the independent
variables and the specific feature as the dependant variable. If the variable
in question was non-normally distributed, it was Box–Cox transformed
using the statistical toolbox in Matlab (Version 6.5, The Mathworks Inc.,
Natick, MA, USA), then tested for normality using the Kolmogorov–Smirnov
test (pause durations: P=0.20; walking bout duration:
P=0.20; walking bout length: P=0.20) before being used for
the ANOVA. Only data from females who had completed all trials were used for
this analysis.
The displacements between all frames of a walking bout were summed to
calculate walking bout length. Sinuosity was calculated using the following
formula (Bovet and Benhamou,
1988) where a higher value indicates a more sinuous path, the
minimum possible value being zero:
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=standard deviation of angle changes
between frames, and P=mean displacement between frames.
Walking behaviour transition
We found that much of the angular change made by a female was achieved in
the initial part of the path, over small distances. In the latter part,
females walked further with lower changes in heading angle. Data from 151 of
205 paths (73.65%) showed this pattern and were used to find the transition
point at which females switched from one type of walking behaviour to
another.
To find the transition, a plot of cumulative absolute angle change against distance walked was smoothed using a moving average method with a span of three points. It was then fitted with two lines, the first to all points between the first and the nth pause, the second from the n+1th pause to the last. Multiple such pairs of lines were fitted by varying n from the second to the penultimate pause. The R2 value was calculated for each line. The average R2 value for each pair of lines was calculated and the pause n at which this average value was the highest was designated as the transition.
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Path vectors
The path vectors were uniformly distributed at the relative SPL
d0dB (Fig. 2A), suggesting no
marked preference for either of the speakers in the d0dB condition. The path
vectors were significantly directed towards the louder speaker, i.e. 90°
in five out of nine cases at the other relative SPL values
(Fig. 2). The clearest
preference for the louder speaker was seen at the relative SPL d6dB
(Fig. 2). The angular deviation
of the path vectors was high, indicating high inter-individual variability in
female response.
First angle change
The first angle changes made by females at all baseline SPL
values at d0dB were clustered around 0°
(Fig. 3A), suggesting no
preference for either speaker. At all other relative SPL values,
they veered towards the louder speaker. The clearest preference for the louder
speaker was seen at the relative SPL d6dB, and there was a
subsequent dip in the mean first angle change at all baseline SPL
values at the relative SPL d9dB
(Fig. 3A). The angular
deviations around the mean were high in all treatments, suggesting a highly
variable response across individuals. The similarities between the patterns
seen in path vectors and first angle changes suggested that the initial
decisions, i.e. first angle changes made by females, might influence the
direction of entire paths. The direction of a female's path was found to be
significantly correlated with the first angle change she made
(Fig. 3B,
R2=0.32, P<0.01, N=205), suggesting
that this was indeed the case.
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Pauses
The number of pauses made by females during phonotaxis varied significantly
only between the different baseline SPL conditions
(Fig. 5A, baseline
SPL: P<0.01, relative SPL: P=0.68,
interaction effect: P=0.22). More pauses were observed at baseline
SPL 55 dB than at 61 dB and 67 dB. The number of pauses was not
significantly different between 61 dB and 67 dB baseline SPL values
(Tukey's HSD test, 55 dB and 61dB: P<0.01; 55 dB and 67 dB:
P=0.04; 61 dB and 67 dB: P=0.60). The duration of the pauses
was also affected only by baseline SPL
(Fig. 5B, baseline
SPL: P=0.03, relative SPL: P=0.47,
interaction effect: P=0.09). Pauses at baseline SPL 55 dB
were significantly longer than those at 67 dB; however, no difference was
observed in other combinations (Tukey's HSD test, 55 dB and 67 dB:
P<0.03; 55 dB and 61 dB: P=0.16; 61 dB and 67 dB:
P=0.67).
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Walking bouts
Average walking bout durations did not vary with either baseline or
relative SPL and showed no interaction effect (baseline
SPL: P=0.66; relative SPL: P=0.57;
interaction effect: P=0.24). The average walking bout length was
similarly unaffected by stimulus conditions (baseline SPL:
P=0.14; relative SPL: P=0.74; interaction effect:
P=0.29).
A transition between two motor patterns was observed in several paths, with tighter turns in the initial parts of the path, followed by low angle change with straighter paths in later parts (Fig. 7A). An attempt to find stimulus conditions that co-occurred consistently with this transition failed. The distance at which these transitions occurred was also different in different paths (Fig. 7B). However, the angular and translational velocities of females were different before and after the transition (before transition: P<<0.01, N=918; after transition: P<<0.01, N=752; Fig. 8).
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Internal validation of the simulation
To test whether the models of female phonotaxis specified in these
simulations captured the major features of the actual paths, we used several
different measures of female paths: mean path vector direction, angular
deviation and sinuosity. These measures were found to be uncorrelated with
each other in real paths and hence represent independent measures of the
success of the simulation (mean direction vs angular deviation of
heading angles: P=0.51, N=12; mean heading angle vs
sinuosity: P=0.51, N=12; angular deviation of heading angles
vs sinuosity: P=0.57, N=12).
Twenty runs of fifteen paths each were carried out at all treatment conditions and the above measures were calculated for each run in order to capture the variation. The mean ± s.d. for each of these measures was calculated. We then determined whether the values measured from the real paths fell within the range described by the mean ± 2 s.d., i.e. 96% of the values of paths derived from the simulation.
We also examined whether the first angle change was correlated with the path vector of the paths produced by the simulation. For this analysis, 16 paths were run at each stimulus condition, eight with the louder speaker on the left and eight on the right.
External validation of the simulation
Phonotaxis in the field
Outdoor phonotaxis was carried out between January and February 2005, at
peak activity time. The temperatures ranged from 18°C to 22°C. The
stimuli used for the experiment were synthesized in a manner similar to the
stimuli used for the indoor experiment with a chirp from a song recorded at
21°C. The temporal pattern features used were appropriate to this
temperature.
Two Creative speakers (frequency range 100 Hz to 15 kHz) were placed 62 cm apart with their faces parallel to each other. The female was released in the centre with both speakers at 90° to her midline. The entire phonotactic path of the female was recorded using the same apparatus as the indoor experiment, except with a larger field of view. One of the speakers broadcast the song at 76 dB SPL at source (i.e. 10 cm from the speaker) and the other at 70 dB SPL. Each female was first tested with only the softer speaker active in order to control for motivation, and only females who reached the speaker were further tested. The female was allowed a rest of at least 10 min and then tested with both speakers active. A total of 40 females were tested. Each female was tested only once. In order to control for positional effects, sets of 20 each were tested in two physically separate locations in the field, with the orientations of the setups rotated 180° with respect to each other.
The paths were digitized as before at 5 frames s–1. The acquired paths were scaled using the distance between speakers. We measured only the centroid of the female's position, as it was not possible to measure female heading angle reliably. The path was measured until the background subtraction algorithm could not discern the female. In some cases the measured path ended before the female reached the speaker; however, this could be observed in the video and was separately noted. The angle of each displacement between frames with respect to the speakers was calculated and these angles were used to estimate the path vector as described before.
Simulations were run, mimicking the experiment. A 2 test
was carried out to test whether the frequency of females reaching the two
speakers in the simulation was similar to the real data. To measure the number
of females that reached a speaker in the simulation, any path that came within
2 cm of the speaker was considered to have reached it. When comparing path
vectors between the simulation and real data, only the directions of the path
vectors were used to calculate mean direction and angular deviation.
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). The excess attenuation at the position of
the female was randomly selected from a normal distribution whose mean
± s.d. were derived depending on distance from the source [from data
published elsewhere (Mhatre and
Balakrishnan, 2006)]. The step involving angle change was also altered. For the outdoor phonotaxis, we did not use the 3-D surface that describes the intercept of the regression of stimulus angle against the subsequent angle change. The intercept describes biases in angle change, which were probably an artifact of the indoor phonotaxis set-up and were ignored for the field experiment. In the outdoor experiment, two set-ups rotated by 180° were used to control for any biases due to non-auditory cues. In the indoor setup, we did not change the physical orientation of the setup and this could have resulted in biases due to non-auditory cues.
One-eared phonotaxis
We tested the simulation with auditory input removed from one ear at a
time. The simulation was run to produce five paths at a larger spatial scale
than the previous simulation, with the speakers broadcasting at 76 and 70 dB
SPL at 10 cm from the speaker using ideal transmission. The louder
speaker was on the side of the intact ear. The auditory input from the
`deafened' ear of the virtual female was set just under threshold
SPL at all pauses. Since the female will perceive a high relative
SPL at all times, the stimulus angle was always set at +90°
when the left ear was intact and –90° when the right ear was
intact.
Phonotaxis with reduced directionality
The PAD curve of Gryllus bimaculatus
(Michelsen et al., 1994) used
in the simulation was modified for the purpose of this `experiment'. We
maintained the shape of the curve but reduced the dB difference caused by the
change in angle of sound incidence. The PAD curve was scaled for maximum
directional differences ranging from 1 to 30 dB SPL. The
relationship between the stimulus angle and angle change was also reduced when
multiplying the slope of the regression by this ratio. These modified ears
were then used to simulate 15 paths over 20 runs at the treatment conditions
61d3dB and 61d6dB, louder speaker at left. We calculated the range of the mean
heading angles and angular deviations at each of these directionality values
and compared them with those obtained with the `normal' ear.
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External validation of the simulation
Phonotaxis in the field
The mean direction of the paths observed in the field was 9.73°
(towards the louder speaker) and the angular deviation was 39.84°
(Fig. 12A). The simulated
paths had a similar mean direction of 11.18° and an angular deviation of
41.80° (Fig. 12B).
Thirty-one of forty females in the real experiment reached the louder speaker
and three reached the softer speaker. Six females walked out of the arena
without reaching an active speaker (Fig.
12A). The simulation produced a similar result: 29 females reached
the louder speaker, two reached the softer speaker and nine females walked out
of the arena (Fig. 12B,
2 test: P=0.44).
One eared phonotaxis
The paths produced by the deafened `virtual' female crickets
(Fig. 13) had several features
similar to those of real deafened crickets
(Kohne et al., 1991). The
paths showed large meanders with loops on the side of the intact ear
suggesting poor localization abilities. There was a large spread of path
heading angles and the length of the mean path vector was quite small (right
deaf: 0.22; left deaf: 0.13). The angular deviation was also large (right
deaf: 71°; left deaf: 75°). However, virtual females in the simulation
did not continue making tight circles due to the shift in walking behaviour,
which straightens out the later part of the paths.
Phonotaxis with reduced directionality
In the simulation, at both stimulus conditions, reducing the directionality
of the ear below 10 dB caused females to localize poorly, as indicated by the
lower mean direction (Fig.
14A,B). The variation of heading angles around the mean also
increased with reduced directionality of the ear
(Fig. 14C,D).
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). Females made very few abrupt turns and the later parts of
their paths, which comprise the directed approach towards one of the speakers,
are better described as meanders rather than zig-zags.
The form did, however, vary within each path. Turns were sharper in the
initial part and straightened out in the later part of the path, with a
relatively clear transition between the two kinds of motor patterns. A
stimulus condition that consistently co-occurred with this transition was not
possible to find and the transition might occur when a certain amount of
`searching' behaviour has been completed. Previous phonotaxis experiments,
particularly those in compensated walking paradigms found relatively uniform
angular and translational velocities during walking bouts in the presence of
song (Schmitz et al., 1982),
suggesting that this may be a feature of closed-loop walking phonotaxis.
We expected other features of walking phonotaxis besides sinuosity to be
affected by stimulus conditions. It has been speculated that the decisions to
turn towards louder stimuli are made largely during pauses
(Bailey and Thomson, 1977;
Murphey and Zaretsky, 1972;
Weber et al., 1981). The
threshold of the omega neuron 1 is increased during walking, lowering
sensitivity to sound, particularly at the lower SPL values
(Schildberger et al., 1988).
Hence, at lower baseline and relative SPL values, the differences
between the two sources will be obscured by neuronal noise. We expected that
on average more and longer pauses would be made at lower baseline
SPL values in order to increase the integration window and the
signal-to-noise ratio. This was seen to be the case at the lowest baseline
SPL (55 dB). A larger number of pauses or longer average pause
durations during a phonotactic path did not, however, increase the accuracy of
orientation of the path towards the speaker or decrease path sinuosity.
Similarly, walking bout lengths and durations were not affected by stimulus
SPL. This suggests that behaviour within the walking bouts is
largely independent of stimulus intensity. These features of the phonotactic
paths may be influenced to a greater degree by other considerations such as
motivational factors, energetic costs or predation pressure
(Hedrick and Dill, 1993).
Angle change and path vectors
The orientation of female paths was affected by stimulus condition. First
angle changes made by females were biased towards the louder speaker.
Similarly, the mean direction of the path vectors also suggested orientation
towards the louder speaker. Both these measures of female responses, however,
showed high inter-individual variability.
The decrease in response at high SPL values has been interpreted
as search behaviour shown by females as they approach a calling male
(Hedwig and Poulet, 2005;
Schmitz, 1985;
Schmitz et al., 1982). We did
not, however, observe the characteristic tight and repeated loops seen during
search behaviour even at the highest baseline and relative SPL
values. An alternative explanation for this phenomenon might be the saturation
of receptors, as observed by Givois and Pollack
(Givois and Pollack, 2000). The
comparison between the two sides to determine the louder side is made on the
basis of the response strength, which saturates sooner at higher
SPL values (Pollack,
2003). Hence, a poorly directed response is expected when the
calling song is presented at high SPL values
(Givois and Pollack, 2000;
Pollack, 2003).
The behaviour of females when presented with calling songs with no
difference in SPL was different from that previously reported in
some paradigms. Bushcricket males responding to female clicks of equal
intensity stimuli, presented from two sides of their midline, track a central
path in a compensated walking paradigm
(von Helversen et al., 2001).
Females tracking equally loud calls, in our experiment, rarely walked down the
centre of the arena. One of the speakers was chosen and tracked throughout the
path. This is similar to the observations made by von Helversen et al. when
they recreated the previous experiment under natural walking conditions
(von Helversen et al.,
2001).
Can the stimulus angle influence female decisions in multi-source conditions?
The relative SPL inferred to be perceived by females during
pauses in our analysis would be what females computed over long integration
times. This relative SPL did not correlate with the heading angle
changes subsequently made by females. We found, however, that stimulus angle
was correlated with these heading angle changes. Our current understanding of
cricket auditory physiology suggests that females scale their turns to the
direction of the stimulus (Pollack and
Plourde, 1982). They infer the direction of a stimulus using the
perceived relative SPL after the cricket ear has generated the
requisite directionality (Boyan,
1979; Boyd and Lewis,
1983; Larsen et al.,
1989; Michelsen et al.,
1994), at least in the presence of a single source. Hence, the
absence of a correlation between angle change and relative SPL is
not easily reconciled with a correlation between angle change and stimulus
angle.
The processing and perception of a single song in the auditory system of a field cricket, however, is expected to differ from that of multiple songs. If the female simultaneously receives a perfectly synchronous second song, the relative SPL perceived by her will now depend on the relative SPL values of the two sources and their positions with respect to the female. A female should no longer have the ability to determine the stimulus angle of either source based on relative SPL alone.
If the two songs are alternating or aphasic, however, some syllables of
each of the songs will be unobscured by the other song. Earlier experiments
(Hedwig and Poulet, 2004)
indicate that females are able to estimate the actual stimulus angle over
short periods of the order of single syllable durations, suggesting short
integration times. Thus, the stimulus angle has the potential to influence the
female's turns.
Initial responses might influence long-term behaviour
The direction of the path of the female was correlated with her initial
turning decision, at least at the spatial scales of our experiment. In a
closed-loop paradigm, a behavioural decision made by the female changes the
stimulus perceived by the female. A turn towards a source will reinforce the
representation of that source at the expense of others which might bias her
path in that direction. Due to the stochastic nature of the turning angle
decision, an initial turn will occasionally be in the direction of the softer
source. An initial erroneous decision has the potential to propagate
throughout the entire path. Maintenance of initial stochasticity through error
propagation might explain the higher angular deviations seen under closed loop
conditions compared to those observed in compensated walking and open-loop
paradigms (Hedwig and Poulet,
2005; Schmitz,
1985; Schmitz et al.,
1982).
Simulated phonotaxis
The simulation was sufficient to explain multiple independent features of
the real phonotactic paths. It produced paths with a range of possible values
of mean direction, angular deviation and sinuosity, within which the observed
values lay. It also captured another feature of the real paths, the influence
of first angle change on the heading angle of the path vector. The model is
principally based on the `turn towards the side which is more
stimulated' rule (Schildberger,
1994). In the same review, Schildberger suggests an alternative
`turn towards the side increasingly stimulated' algorithm that
incorporates history, which he believed might better explain some features of
phonotactic behaviour (Schildberger,
1994). We found, however, that the first rule is sufficient to
explain the observed behaviour. Historical effects were also not apparent in
the phonotactic behaviour of females in open-loop paradigms
(Hedwig and Poulet, 2004;
Hedwig and Poulet, 2005).
We unsuccessfully attempted several other approaches to recreate paths that were qualitatively and quantitatively si
made by females presented with calling
songs at different baseline and relative SPL values. A positive
value indicates a turn towards the louder speaker. Error bars indicate the
angular deviation around the mean. (B) The first angle change 
and the angle change 
