Available online at www.sciencedirect.com
Hearing
Research
Hearing Research 238 (2008) 94–109
www.elsevier.com/locate/heares
Research paper
Can measures of sound localization acuity be related to the
precision of absolute location estimates?
Jordan M. Moore *, Daniel J. Tollin 1, Tom C.T. Yin
Department of Physiology, University of Wisconsin—Madison, Madison, WI 53706, USA
Received 26 August 2007; received in revised form 20 November 2007; accepted 20 November 2007
Available online 28 November 2007
Abstract
Studies of sound localization use relative or absolute psychoacoustic paradigms. Relative tasks assess acuity by determining the smallest angle separating two sources that subjects can discriminate, the minimum audible angle (MAA), whereas absolute tasks measure subjects’ abilities to indicate sound location. It is unclear whether or how measures from the two tasks are related, though the belief that the
MAA is specifically related to the precision of absolute localization is common. The present study aimed to investigate the basis of this
relationship by comparing the precision of absolute location estimates with a measure of spatial acuity computed from the same data.
Three cats were trained to indicate apparent sound source locations that varied in azimuth and elevation via orienting gaze shifts (combined eye and head movements). The precision of these absolute responses, as measured by their standard deviation, was compared with
acuity thresholds derived from receiver operating characteristic (ROC) analyses of the cumulative distributions. Surprisingly, the acuity
measures were occasionally very poor indicators of absolute localization precision. Incongruent results were attributed to errors in mean
accuracy, which are disregarded in analyses of traditional relative tasks. Discussion focuses on the potential for internal biases to affect
measures of localization acuity.
Ó 2007 Elsevier B.V. All rights reserved.
Keywords: Minimum audible angle (MAA); Auditory space map; Cat
1. Introduction
Behavioral studies of sound localization typically
employ one of two different psychophysical methods that
can be broadly defined as relative or absolute tasks. Relative tasks assess spatial acuity by determining the smallest
angle separating two sound sources, the minimum audible
angle (MAA), that subjects can reliably discriminate (e.g.,
Mills, 1958; Perrott and Saberi, 1990; Huang and May,
1996). Absolute tasks, on the other hand, measure subjects’
ability to actually indicate the location of a sound source
*
Corresponding author. Address: Department of Neurobiology and
Behavior, W345 Mudd Hall, Tower Road, Cornell University, Ithaca, NY
14853, USA. Tel.: +1 607 255 1352; fax: +1 607 254 1303.
E-mail addresses: jmm256@cornell.edu (J.M. Moore), Daniel.Tollin@
UCHSC.edu (D.J. Tollin), yin@physiology.wisc.edu (T.C.T. Yin).
1
Present address: Department of Physiology and Biophysics, University
of Colorado Health Sciences Center, Aurora, CO 80045, USA.
0378-5955/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.heares.2007.11.006
(e.g., Stevens and Newman, 1936; Perrott et al., 1987;
Populin and Yin, 1998; Tollin et al., 2005). Numerous
and extensive studies have used one or the other of these
two paradigms, and it is commonly assumed that they are
closely associated because manipulations of stimulus
parameters such as signal duration, spectral content, or spatial location have analogous effects on subject performance
in each (Perrott et al., 1987; Middlebrooks and Green, 1991;
Chandler and Grantham, 1992; Strybel and Fujimoto,
2000). Nevertheless, there have only been a few reports
directly aimed at elucidating whether and how the two task
types are related and whether or not the same neural mechanisms mediate performance in each (Hartmann and
Rakerd, 1989; Recanzone et al., 1998; May, 2000).
When discussing the relationship between absolute and
relative measures of sound localization, it is critical to distinguish between the concepts of localization accuracy and
precision (Heffner et al., 2005). Accuracy describes the
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
relation between an apparent location, be it a single behavioral response or the mean of a cumulative distribution,
and the actual target location. Precision refers to a subject’s
consistency over multiple trials and is indicated by the
width of a cumulative behavioral response distribution.
Unambiguous estimates of both accuracy and precision
can be obtained from absolute paradigms but only a single
measure of acuity, the MAA, is computed from relative
tasks. It has frequently been inferred (e.g., Perrott, 1984;
Perrott et al., 1987; Heffner and Heffner, 1992; Grantham
et al., 2003), and occasionally directly suggested (Hartmann and Rakerd, 1989; Makous and Middlebrooks,
1990; Recanzone et al., 1998), that the MAA is specifically
related to the precision of absolute sound localization estimates. In other words, the size of the MAA is singularly
dependent upon the resolution with which a subject’s auditory system computes directional cues, and therefore it
conveys the consistency with which that observer could
report the apparent location of sound sources in an absolute task. The theoretical framework for this relationship
is provided by signal detection theory (Green and Swets,
1966), and in particular the equation
jl lR j
d ¼ zðhit rateÞ zðfalse alarm rateÞ ¼ T
;
r
0
95
dict the commonly held notion that acuity and precision
measure the same capabilities.
On the other hand, it remains possible that absolute and
relative tasks do employ the same neural mechanisms but
the manner in which the behavioral data are compared
needs to be refined. We explored this idea, and our hypothesis can be stated in the following way: If the basis of localization acuity is indeed a just-noticeable change in the
perception of source location, as is tacitly assumed and
as suggested by the psychophysical experiments and modeling by Hartmann and Rakerd (1989) and Recanzone
et al. (1998), then fine acuity will correspond with precise
absolute localization, and vice versa, for a particular
source. In other words, absolute localization data can be
reasonably used as a proxy for the internal representation
of source location. To study this, we manipulated the duration and spectral content of acoustic stimuli and trained
cats to localize sources in an absolute task. We then used
the tools of signal detection theory to calculate a corresponding measure of acuity from the same data and
compared the results.
2. Materials and methods
ð1Þ
where hit rate specifies the proportion of trials in which a
change in target location was correctly identified and false
alarm rate is the fraction of Type I errors. Regarding the
latter portion of Eq. (1), lT and lR represent mean values
of random variables along an internal decision axis that
correspond to target and reference speakers, respectively,
and r signifies the standard deviation (SD) common to
both distributions. In this way, then, data from two-alternative forced-choice (2AFC) tasks are regularly converted
into a graphical depiction of how auditory systems represent external space.
Despite a general correspondence between absolute and
relative psychophysical measures (Makous and Middlebrooks, 1990; Recanzone et al., 1998), there are several
examples of severe departures between them. For example,
humans have repeatedly been measured to have MAAs
near 1° for both low- and high-frequency pure tone stimuli
(Mills, 1958; Perrott, 1969; Blauert, 1997), yet subjects who
are required to actually indicate the spatial location of such
stimuli often display large variability and poor accuracy in
their responses (Stevens and Newman, 1936; Middlebrooks, 1992). There is also evidence of a discrepancy from
animal studies. Cats with a lesion of the dorsal cochlear
nucleus, a peripheral auditory nucleus believed to be
important for the localization of sounds along the median-sagittal plane (Young et al., 1992), were significantly
hindered in their ability to localize sounds in elevation
and yet retained small, normal MAAs (May, 2000). Second, barn owls exhibit poorer acuity in a simulated echoic
versus anechoic environment but display comparable precision across the two conditions (Spitzer et al., 2003; Spitzer
and Takahashi, 2006). These observations seem to contra-
2.1. General
Three adult female cats were selected for this study
based on their willingness to perform similar tasks in previous experiments. Detailed descriptions of surgical procedures, experimental equipment, and search coil
calibration are given elsewhere (Populin and Yin, 1998;
Tollin et al., 2005). Briefly, a fine wire coil was surgically
implanted around the eyeball by which eye position could
be monitored with a resolution of 0.1° using the magnetic
search coil technique (Fuchs and Robinson, 1966). All surgical and experimental procedures were approved by the
University of Wisconsin Animal Care and Use Committee
and conformed to animal use guidelines of the National
Institutes of Health.
During experimental sessions, cats were placed in the
center of a dark, sound-attenuated chamber (2.2 2.5 2.5 m). An array of 15 loudspeakers (RadioShack model
40-1310B; Fort Worth, TX) that was positioned on two
arcs, one along each of the horizontal (spanning ±45°)
and vertical (±23°) meridians, was placed 0.62 m from
the cat’s head. In addition, 2.0-mm-diameter red (kmax =
635 nm) light-emitting diodes (LEDs) were mounted in
the center of each speaker. A black, translucent cloth hid
the speakers from view but allowed sound and illuminated
LEDs to be easily detected. Due to the physical size of each
speaker, the smallest attainable LED-speaker separation
with this configuration (9°) substantially exceeded previously reported MAAs of cats (5°). Therefore, two additional LEDs were suspended midway between speaker
locations (0°, 0°) and (9°, 0°) in azimuth and between
(0°, 0°) and (0°, 9°) in elevation to achieve smaller effective
LED-speaker separations of 4.5°. One of the cats (cat21)
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J.M. Moore et al. / Hearing Research 238 (2008) 94–109
performed trials in a different chamber with speakers
spaced by 10° rather than 9° and without targets varying
in elevation. Several cats, including cat21, performed training sessions in both chambers and the behaviors of each
were similar across locales.
2.2. Acoustic stimuli and psychophysical procedures
Acoustic stimuli were broadband noises (BBN) (1.5–
25 kHz) of three durations (15, 164, and 1000 ms) and
highpass and lowpass noises (HPN and LPN; cut-off frequency = 5 kHz with 1000 dB/octave filter slopes) of
164 ms duration. These durations were chosen to vary the
presence of dynamic cues and the spectral contents chosen
to vary the presence of concurrent versus isolated binaural
cues (interaural time- and level-differences) and of particular frequency ranges needed for localizing sources in elevation. Sound level was roved by ±6 dB in 2 dB steps on a
trial-by-trial basis to minimize the potential use of level differences between speakers as an identification cue. A Microvax-2 computer (Digital Equipment Co., Maynard, MA)
controlled all equipment used for stimulus generation and
data collection.
Cats were trained using operant conditioning to make
gaze shifts (combined eye and head movements) to acoustic
targets. On a given trial, the cat was first required to visually fixate an LED located at (0°, 0°), (4.5/5°, 0°), or
(0°, 4.5°). Its eye position was required to enter and remain
within a 9°-wide square virtual acceptance window centered about the target for 750–1250 ms (time period determined randomly). If the cat’s gaze position exited the
acceptance window at any time after entering it, the trial
ended prematurely and no reward was given. But if the
cat satisfied this criterion, the LED was turned off and an
acoustic stimulus was immediately presented from any
one of the 15 speakers, and the cat was required to make
an orienting gaze shift to the apparent source location
within 1000 ms of the sound onset. Once its eye position
entered another 9°-wide square virtual acceptance window
around the second target location, the cat was again
required to remain looking within that window for 750–
1250 ms (time period determined randomly) in order to
receive a food reward. A small (2 ml) portion of food
paste, consisting of ground cat food and water, was given
following each successful trial. The feeding tube was driven
by a peristaltic pump and the spout was kept directly in
front of the cat’s mouth by a lightweight (40 g) aluminum
headset connected to the head post. A variable inter-trial
interval (6 s) followed successful trials, and this time
was doubled after missed trials as a punishment.
2.3. Data analysis
The variable of interest in these experiments was final
gaze position, which we treated as an indication of the cats’
internal estimate of speaker location. The beginning and
end of a gaze shift were defined using a velocity criterion
(Populin and Yin, 1998). Mean gaze velocity was first computed during steady LED-fixation from 100 ms prior to
30 ms after the onset of the acoustic stimulus, and gaze
onset and offset were defined as the instances when gaze
velocity exceeded and returned within, respectively, two
SDs of that mean velocity. Corrective saccades, defined
as additional gaze shifts made within 200 ms of a return
to fixation, were included in the analysis provided they
did not occur after the food reward. Horizontal and vertical components of gaze shifts were computed separately.
Examples of eye traces from a single session are given in
Fig. 1. The data show the horizontal component of cat18’s
responses to 15 ms noise stimuli with the LED located at
(4.5°, 0°) and the speaker (arrow) at (0°, 0°). The bracket
surrounding the arrow indicates the acceptance window
for a food reward, and the vertical line at 0 ms indicates
the time when the LED was extinguished and the sound
was turned on. The cats most often made short latency,
rapid responses toward the acoustic stimulus, but they
occasionally did not shift their gaze position at all. It was
impossible to know the causes for such non-responses,
but there are two main possibilities. First, the cats ignored
the target altogether and so did not respond due to laziness
or inattention. Second, the cats determined that the sound
source location was consonant with where they were
already looking. In the first case, if the cats simply ignored
a certain proportion of trials [consistent with a ‘lapse-rate’
in human psychophysical experiments (Wichmann and
Hill, 2001)] then the proportion of non-responses would
be approximately equal across all trials. Our experimental
data are largely contrary to this, however. We plotted the
non-response fractions to each stimulus type in each direction separately, and in most (78%) cases the propensity to
Fig. 1. Examples of gaze shifts to acoustic targets. The traces show the
horizontal component of gaze shifts made by cat18 to 15 ms duration
BBN stimuli for 4 trials from a single training session. The initial fixation
LED was positioned at (4.5°, 0°) and the auditory stimulus was delivered
from (0°, 0°), indicated by the arrow on the right. At time 0 ms, the LED
was turned off and the auditory stimulus turned on. The bracket indicates
the size of the acceptance window for a food reward. The cats typically
made overt responses toward the sound sources but occasionally, as in the
one example here, they did not shift their gaze at all. The dependent
variable in these experiments was the eye position at the end of the gaze
shift.
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
make a gaze shift was highly dependent on the LEDspeaker separation. This trend is apparent in Fig. 2, which
shows average non-response fractions (+1 SD) across cats
and stimuli as a function of angular LED-speaker separation. Some of the LED-speaker separations were plotted
slightly offset from their actual value for clarity. This regularly observed increase in non-responses for small LEDspeaker separations would be expected if the auditory
source location was not perceived as different from where
the eyes were initially directed. To be conservative, all trials
in which the cats satisfied the initial LED fixation requirements (i.e., an auditory stimulus was presented) were analyzed, regardless of whether the reward contingencies to the
speaker were met or even whether the cats made an overt
gaze shift. Clearly, some of these trials are likely to be those
in which the cats did indeed ignore the stimulus, but we
have no way of determining that. As a result, the cats’ true
localization abilities are at least as good as those reported
here because this analysis procedure increased their
response variance.
2.3.1. Accuracy and precision
We analyzed the performance of the cats by measuring
the final response azimuth and elevation for each trial to
the five stimuli previously mentioned. Final gaze positions
to each target (LED-speaker separations in azimuth &
upward elevation of 4.5°, 9°, 13.5°, 18°; and in downward
elevation of 0°, 4.5°, 14°, 18.5°, 23°) were pooled from
Fig. 2. Average non-response fractions (+1 SD) across cats and stimuli as
a function of LED-speaker separation in each of the four directions. Some
LED-speaker separations were plotted slightly offset from their actual
value for clarity. Non-responses were included in the analyses because the
likelihood of a cat making an overt response was highly dependent upon
LED-speaker separation, and this pattern was consistent with the
assumption that the cat was looking where it perceived the sound source
to be located.
97
many experimental sessions and localization accuracy
(mean unsigned and signed errors) and precision (response
distribution SD) were calculated. Only measures along the
same plane in which the speaker differed from the initial
LED are discussed: horizontal errors and SDs are used
for sources displaced in azimuth and vertical errors and
SDs are used for those varying in elevation.
2.3.2. Estimated acuity threshold
The same datasets were used as estimates of the cats’
underlying representations of auditory space. Using the
relationships described in Eq. (1) and signal detection theory (Green and Swets, 1966), the data were used to calculate estimated acuity thresholds for each stimulus type and
in each planar direction. Fig. 3 illustrates this procedure for
cat17’s responses to 15 ms stimuli displaced along left azimuth. In Fig. 3a and b, the arrows beneath the abscissa
indicate speaker positions relative to the fixation LED.
First, the behavioral response distribution corresponding
to the smallest LED-speaker separation, termed the ‘Proximal’ speaker (black arrow), was plotted on an axis representing relative space. The Proximal speakers for each
direction were those with the smallest LED-speaker separations: ±4.5° or ±5° for targets varying in azimuth, 4.5° for
upward elevation, or 0° for downward elevation (for an
explanation of downward elevation, see Results: Acuity).
Next, the response histograms to each of the remaining
‘Distal’ speakers (gray arrows) in a given direction were
plotted, one at a time, alongside the corresponding Proximal distribution for that direction.
We then posed the hypothetical question, ‘‘Which
speaker is the sound source?” (Fig. 3a). To ascertain how
a cat with the estimated auditory space map would perform
in such a 2AFC task, a hypothetical decision criterion was
swept along the abscissa in 100 equally spaced increments.
This process was repeated for each combination of Proximal and Distal distributions in a particular direction. For
every position of the decision criterion, the proportions
of each distribution on the ‘‘Distal” side (i.e., the side corresponding to the direction of a ‘correct’ gaze shift) of that
criterion were determined. This portion of the Distal distribution would correspond to the hit rate while that of the
Proximal distribution would equal the false alarm rate in
a 2AFC task. The 100 different pairs of hit rates and false
alarm rates were then used to generate a receiver operating
characteristic (ROC) curve (inset), the area under which is
equal to performance level (i.e., percent correct) in a 2AFC
task (Green and Swets, 1966). The same analysis was performed on the behavioral response histograms shown in
Fig. 3b, the only difference being the larger LED-speaker
separation for the Distal target. The areas under the
ROC curves generated by this procedure were subsequently
plotted as a function of speaker separation and fit with a
logistic function, as is done with data from relative localization tasks (Fig. 3c). The estimated acuity threshold was
defined as the angle producing an ROC area of 0.76, the
value that corresponds to a d 0 = 1.0. According to Eq. (1),
98
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
Fig. 3. Example of the procedure for calculating estimated acuity thresholds, using data from cat17 to 15 ms BBN along left azimuth. (a) Cumulative
behavioral response histograms were used as an estimate of the cat’s internal representation of acoustic space. The speaker from the smallest LED-speaker
separation in a given direction (in this case, left azimuth) was labeled Proximal (black arrow) and the speakers from each of the other LED-speaker
separations in that direction were termed Distal targets (gray arrow). Behavioral response distributions to each Distal location were plotted, one at a time,
with the response histogram to the Proximal location on an axis representing relative space. Next, we posed the hypothetical question: ‘‘Which speaker is
the sound source?” where one side of a decision criterion corresponded to an answer of ‘‘Distal” and the other to ‘‘Proximal.” The decision criterion was
swept along the abscissa in 100 equally spaced increments and the proportions of each histogram on the ‘‘Distal” side of the response criterion were
calculated at each point. If these distributions are indicative of the cat’s internal representation of space, then this proportion of the Distal distribution
would correspond to the hit rate and that of the Proximal distribution to the false alarm rate if the cat was engaged in a 2AFC task. These measures were
used to plot a receiver operating characteristic (ROC) curve (inset), the integral of which is equal to performance level (i.e. percent correct) in a 2AFC task.
(b) As in (a), except with a larger separation between Proximal and Distal speakers. (c) Example of a psychometric function used to calculate estimated
acuity thresholds. The ROC areas were plotted as a function of Distal–Proximal speaker separation, as is typically done in analyses of discrimination
tasks, and fit with a logistic function.
then, the estimated acuity thresholds should be equal to 1
SD of the absolute mean location estimates.
3. Results
Well-trained cats typically attempted 80–90% of about
500 trials in daily sessions that took 2–3 h. Only a small
(10%) proportion of the total trials per day corresponded
to this particular experiment, however, therefore data were
pooled across multiple sessions. On average, the mean
behavioral data for each stimulus and target combination
were derived from the following: cat17, 75 (range: 32–
109) trials from 32 (12–54) sessions; cat18, 62 (26–95) trials
from 30 (12–60) sessions; cat21, 55 (33–71) trials from 13
(9–16) sessions. Given the large number of trials required
for the many different experimental manipulations, not
all cats completed all experiments. Insufficient data were
collected for cat18’s responses to 1000 ms BBN stimuli with
LED-speaker separations of (±4.5°, 0°) and (0°, ±4.5°). As
a result, azimuthal acuity was calculated using distributions
to 9°, 13.5°, and 18° targets and compared to SDs from
responses to the (±9°, 0°) targets. There was not enough
data to do the same in elevation, however. Additionally,
only data to targets varying in azimuth were collected from
cat21 because it was tested in a chamber without speakers
displaced in elevation.
3.1. Accuracy and precision
The absolute localization means and ±1 SD bars of
cat18’s responses to 164 ms BBN are shown in Fig. 4,
which are representative of those collected from all three
cats to most of the different stimuli used. Targets are indicated by empty symbols and corresponding mean estimates
by filled symbols of the same shape. Trials beginning with
the fixation LEDs located at (4.5°, 0°) and (0°, 4.5°) were
superimposed with those beginning from (0°, 0°), therefore
the abscissa and ordinate indicate LED-speaker separations and not absolute position. The LED location relative
to each speaker is denoted with an ‘‘X” at the origin.
Responses to targets in each of the four directions were
analyzed separately because there were frequently discrepancies between them, even between the left and right sides.
For example, cat18 was very accurate to the left but consistently underestimated the actual LED-speaker separations
to the right, sometimes by nearly 50% (Fig. 4). Such biases,
when they existed, were present regardless of whether or
not non-responses were included in the analysis and therefore were not artifacts of potentially different non-response
fractions between the two sides.
Localization performance of the cats is given in Table 1,
including two distinct measures of localization accuracy.
Unsigned errors are the mean absolute differences between
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
Fig. 4. Summarized absolute localization data from cat18 to 164 ms BBN
stimuli. Empty symbols represent actual target locations, filled symbols
are corresponding mean location estimates with ±1 SD bars. Data from
trials beginning at different initial LED locations were superimposed,
therefore the axes represent LED-speaker separations [from the ‘‘X”
plotted at (0°, 0°)] and not absolute speaker locations in the chamber.
behavioral responses and target locations and signify the
average error magnitude irrespective of direction. Mean
signed errors, on the other hand, are sensitive to the direction of errors and estimate the cats’ average perceived
source locations; negative errors indicate an underestimation of LED-speaker separation whereas positive errors
denote an overestimation. Finally, localization precision
is specified by response distribution SDs.
The data listed in Table 1 are restricted to the two smallest LED-speaker separations in each direction for two
main reasons. First, a principal goal of this study was to
compute a measure of acuity from absolute localization
data. The responses to these targets had the greatest impact
on the values of acuity thresholds and were therefore most
relevant to use in comparisons between the two measures.
Secondly, the SDs of estimates close to the point of initial
fixation were least impacted by the inclusion of nonresponses. Although non-response fractions generally
decreased as a function of LED-speaker separation
(Fig. 2), there still existed cases in which they were sufficiently high at eccentric locations (which we would have
assumed to be easily discriminable separations) to increase
the SDs by a substantial amount. For example, the nonresponse fractions to (18°, 0°) and (18°, 0°) in Fig. 4 were
0.12 and 0.08, respectively, and the SDs to these targets
were 6.8° and 4.4° when non-responses were included but
each were just 2.9° when excluded. Comparatively, cat18
had non-response fractions of 0.05 and 0.13 to the
(4.5°, 0°) and (4.5°, 0°) targets and these only increased
the SDs by 0.3° and 0.1°, respectively.
99
3.1.1. Azimuth
All three cats accurately localized each of the five stimuli
along the azimuth. While there was considerable variability, mean unsigned errors were 3° or smaller and signed
errors 2° or smaller in the majority (30/58 and 42/58,
respectively) of cases. Changes in stimulus duration did
not systematically affect two cats’ accuracy or precision,
but several statistically significant differences were present
nonetheless. Cat17 had larger unsigned errors to 164 ms
than to 15 or 1000 ms to (9°, 0°) and (±4.5°, 0°) (Dunn’s
post-hoc analysis following Kruskal–Wallis rank tests, all
p < 0.05), as did cat18 to (9°, 0°) (both p < 0.05). Cat17 also
had a larger SD to 164 ms compared to 15 or 1000 ms stimuli from the (4.5°, 0°) target but had better precision to
15 ms stimuli to (4.5°, 0°) than to longer durations
(Levene’s test, all p < 0.05). Cat18 exhibited few differences
in precision across durations and only a difference between
15 ms and 1000 ms stimuli to (9°, 0°) reached statistical significance (p < 0.05). In contrast, cat21’s localization performance did vary as a function of signal duration. Its
unsigned error to 15 ms to (10°, 0°) was larger than those
to 164 and 1000 ms (both p < 0.05), while its errors to
15 ms and 164 ms to (10°, 0°) were both larger than that
to 1000 ms (both p < 0.05). Cat21 was also more precise
to longer stimuli. Significant differences existed between
all SDs to (10°, 0°) and between that to 1000 ms and
the two shorter stimuli to (10°, 0°) (all p < 0.05), while the
SDs to 15 ms were significantly larger than those to 164
and 1000 ms for the (±5°, 0°) targets (all p < 0.05).
There were minimal differences between all three cats’
localization abilities for BBN, HPN and LPN along azimuth. Cat17’s unsigned error to 164 ms BBN to (9°, 0°)
was larger those to HPN or LPN (Dunn’s post-hoc analysis, both p < 0.05). Cat18 displayed equivalent accuracy
across stimuli to the left but was notably worse to LPN
from the right (all p < 0.05). Lastly, cat21 displayed larger
unsigned errors to BBN than to LPN for three targets,
(±5°, 0°) and (10°, 0°) (all p < 0.05). Regarding precision,
cat17’s SD to LPN from (9°, 0°) was smaller than those
to BBN or HPN, and its SD to BBN from (4.5°, 0°) was larger than those to HPN and LPN (Levene’s test, all
p < 0.05). Once again cat18 showed remarkable consistency
and its only significant difference in precision was that
between BBN and both HPN and LPN from (9°, 0°)
(both p < 0.05). Finally, cat21’s SDs to BBN were smaller
than those to HPN and LPN from both targets on the left,
as was its SD to BBN than LPN from (5°, 0°) (all p < 0.05).
3.1.2. Elevation
Cat17’s and cat18’s performances in elevation were largely similar to those along the azimuth in that they only
exhibited differences in some cases. Cat17 had a larger
unsigned error to 15 ms than to 164 or 1000 ms for the
(0°, 9°) target and a smaller error to 1000 ms than to
shorter stimuli for (0°, 4.5°) (Dunn’s post-hoc comparisons,
all p < 0.05). Similarly, cat18’s error to 1000 ms was smaller than those to 15 and 164 ms from (0°, 9°) (both
100
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
Table 1
Response errors and SDs (in degrees) from all cats to targets with the two smallest LED-speaker separations in each direction
LED-speaker separation
(X°, Y°)
BBN (15 ms)
BBN (164 ms)
Unsigned
error
Signed
error
SD
Unsigned
error
Signed
error
SD
Unsigned
error
Signed
error
SD
cat17
(9, 0)
(4.5, 0)
(4.5, 0)
(9, 0)
(0, 9)
(0, 4.5)
(0, 4.5)
(0, 14)
3.4
2.7
3.2
3.9
4.8
4.2
4.9
4.0
0.2
1.6
2.0
2.2
0.9
2.0
2.3
3.2
4.5
3.0
3.1
4.3
4.4
4.4
5.1
3.5
4.6
4.6
4.7
4.0
2.9
3.5
4.3
4.6
2.1
0.1
0.4
3.0
1.0
1.9
0.3
3.9
5.1
5.5
5.4
4.2
4.0
3.8
5.2
3.7
3.3
2.6
3.3
3.5
3.2
1.9
4.1
4.2
0.1
0.2
1.3
1.0
0.9
0.2
2.2
0.8
4.3
3.2
4.1
4.4
4.2
2.5
4.4
6.0
cat18
(9, 0)
(4.5, 0)
(4.5, 0)
(9, 0)
(0, 9)
(0, 4.5)
(0, 4.5)
(0, 14)
2.1
2.2
2.6
2.8
4.9
2.3
3.1
3.0
0.7
0.8
2.5
2.3
4.9
1.3
2.1
0.7
3.2
2.6
2.0
2.7
3.3
2.6
3.1
4.2
2.5
2.3
3.1
3.8
3.5
2.7
2.9
3.4
0.6
1.2
2.8
3.8
3.4
2.6
1.3
1.8
3.2
2.4
2.2
2.5
2.3
1.9
3.7
5.0
2.5
–
–
2.8
2.2
–
–
3.7
1.6
–
–
2.8
0.0
–
–
1.8
3.8
–
–
2.3
2.1
–
–
2.8
cat21
(10, 0)
(5, 0)
(5, 0)
(10, 0)
4.1
3.2
2.3
3.6
1.4
1.5
0.7
1.5
5.4
4.0
3.1
4.4
2.0
2.2
1.3
2.5
0.5
1.2
0.4
0.5
2.5
2.5
1.6
3.1
2.0
2.8
1.5
1.7
1.7
1.6
1.0
0.0
1.6
3.0
1.5
2.2
HPN (164 ms)
BBN (1000 ms)
LPN (164 ms)
Unsigned error
Signed error
SD
Unsigned error
Signed error
SD
cat17
(9, 0)
(4.5, 0)
(4.5, 0)
(9, 0)
(0, 9)
(0, 4.5)
(0, 4.5)
(0, 14)
3.3
4.4
3.6
3.8
3.6
3.2
4.5
3.9
2.1
0.8
1.4
0.7
1.9
2.1
1.5
2.3
3.6
4.9
4.0
4.7
4.2
3.2
5.0
4.7
2.8
3.7
3.0
4.5
4.3
4.2
5.0
6.6
2.0
0.3
0.6
3.5
3.5
2.7
0.7
0.2
2.7
4.5
3.3
4.2
4.2
4.7
6.2
8.3
cat18
(9, 0)
(4.5, 0)
(4.5, 0)
(9, 0)
(0, 9)
(0, 4.5)
(0, 4.5)
(0, 14)
1.7
2.4
3.3
3.5
4.3
3.2
3.0
2.4
0.4
2.2
3.0
3.3
4.1
2.5
1.9
0.6
2.1
1.9
2.2
2.5
2.8
2.8
3.3
3.0
1.9
2.1
4.3
5.7
4.2
3.0
4.2
9.3
0.4
1.4
4.2
5.5
4.1
2.7
4.2
9.3
2.3
2.2
2.3
2.7
2.5
2.5
1.9
4.1
cat21
(10, 0)
(5, 0)
(5, 0)
(10, 0)
3.0
2.9
1.7
2.5
0.4
0.1
0.1
1.1
4.0
4.1
2.3
3.0
4.0
3.8
2.2
3.2
0.1
3.1
0.0
1.6
5.0
3.5
3.1
3.5
Signed errors were computed such that negative values indicate an underestimation of actual LED-speaker separation and positive values signify an
overestimation (see Results); unsigned errors are the mean absolute errors. Values indicate the gaze component corresponding to the plane of LEDspeaker displacement: horizontal errors and SDs are for targets varying in azimuth and vertical errors and SDs are for those varying in elevation.
BBN, broadband noise; HPN, highpass noise; LPN, lowpass noise; SD, standard deviation.
p < 0.05). Cat17 displayed finer precision to 1000 ms than
to 15 or 164 ms from (0°, 4.5°), but this cat had poorer precision to 1000 ms than to shorter stimuli from (0°, 14°)
(all p < 0.05). The precision of cat18 was largely consistent
across durations, with the only significant differences being
between its SD to 1000 ms and those to 15 and 164 ms from
(0°, 9°) (both p < 0.05).
Changing spectral content had slightly more substantial
effects on the cats’ localization capabilities in elevation.
Cat17 had an unsigned error to LPN that was significantly
larger than that to BBN from (0°, 9°), and its error to LPN
from (0°, 14°) was larger than those to both BBN and
HPN (Dunn’s post-hoc comparisons, all p < 0.05). Cat18
displayed equivalent accuracy to different stimuli in
upward elevation but had larger errors to LPN than both
BBN and HPN to each downward target (all p < 0.05).
The precision of cat17 was comparable across stimuli to
most targets except (0°, 14°), for which it had significantly
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
larger SDs to LPN than to BBN or HPN (both p < 0.05).
Cat18, on the other hand, had finer precision to LPN from
(0°, 4.5°) than to BBN or HPN (both p < 0.05).
3.2. Acuity
Behavioral data obtained from the absolute localization
task were used to obtain estimates of their acuity. In the
majority (37/48) of cases the cats’ estimated acuity threshold was finer than the smallest LED-speaker separation
attainable with this array (4.5° or 5°), therefore the thresholds were inferred from a logarithmic function that was fit
to the data when plotted as a function of speaker separation (e.g., Fig. 3c). The angle producing an ROC area of
0.76, and a d 0 = 1.0, was defined as the estimated acuity
threshold. Thresholds for each stimulus and direction are
listed in Table 2 under the columns labeled ‘Target’.
The thresholds reported here were calculated from
behavioral distributions that were slightly offset from the
origin. Data were also collected to an auditory target that
was in the same location as the initial fixation LED, but
these responses were ultimately excluded from the analysis
when possible. This was done because the SDs of these estimates were always significantly smaller (Levene’s test, all
p < 0.05) than those to targets displaced from the initial
LED, even those separated by just 4.5° or 5°. Rather than
indicating finer precision at (0°, 0°), this likely reflected the
cats’ enhanced abilities to fixate the visual LED compared
to the subsequent auditory target. We were constrained to
use these distributions to compute the MAA in downward
elevation, however; otherwise, the smallest Proximal-Distal
separation close to horizontal plane would have been 9.5°,
which would have provided an even poorer estimate of the
cats’ acuity threshold.
3.2.1. Azimuth
Changing stimulus duration had inconsistent effects on
the original acuity measures (‘Target’ column) of cat17
101
and cat18, both of which also showed irregular differences
between their left and right sides. The thresholds of cat17
to the left were largely similar (4°) while that to 164 ms
on the right (6.5°) was notably larger than those to 15 or
1000 ms (4.4°). Cat18 had a much smaller threshold to
1000 ms (1.4°) than to shorter stimuli (4.4°) on the left,
but this tendency was reversed on the right where its smallest threshold was to 15 ms bursts. Cat21’s estimated thresholds were more similar between sides and were also slightly
larger to 15 ms (4.7°) than to the longer durations
(4.1°). Varying spectral content did not cause systematic
differences between the estimated acuity thresholds of any
of the cats. Cat17 had quite variable threshold estimates
to its right, and cat21 had a much smaller threshold to
LPN (1.6°) than to BBN or HPN (4.2°) on its left but a
larger threshold (5.1° compared to 4.3°) on its right.
3.2.2. Elevation
Stimulus duration affected the cats’ acuity measures in
elevation. Both cat17 and cat18 had much larger estimated
thresholds to 15 ms BBN (7.7°) than to longer stimuli
(3.9°) in upward elevation. Cat17 had relatively consistent acuity measures in downward elevation, but cat18
had poorer acuity to 15 ms (7.0°) than to 164 ms (5.2°).
The cats’ acuity estimates were also affected by altering
stimulus spectral content. Cat17 had a slightly larger estimated threshold to LPN (4.9°) than to BBN or HPN
(3.9°) in upward elevation but was consistent in downward elevation. Conversely, cat18’s measures were stable
in upward elevation but its acuity to LPN (11.5°) was much
worse than to BBN or HPN (5.0°) in downward
elevation.
3.3. Comparison between precision and acuity
To assess the relationship between localization acuity
and precision, estimated acuity thresholds were compared
to SDs of mean location estimates to the (±4.5/5°, 0°)
Table 2
Spatial acuity measures (in degrees) of each cat to all stimuli in each direction
BBN (15 ms)
BBN (164 ms)
BBN (1000 ms)
HPN (164 ms)
LPN (164 ms)
Target
Target
Response
Target
Response
Target
Response
Target
Response
cat17
Left
Right
Up
Down
3.9
4.3
6.7
4.6
5.6
4.1
4.0
5.0
4.0
6.5
3.7
4.3
5.9
1.4
4.4
5.7
4.3
4.5
4.4
4.6
4.5
4.2
3.4
3.6
3.8
4.2
4.0
4.6
6.1
4.8
4.2
4.1
3.9
5.0
4.9
4.8
Response
5.7
2.0
4.2
4.7
cat18
Left
Right
Up
Down
4.3
2.8
8.6
7.0
2.9
3.8
2.8
1.5
4.5
4.3
3.7
5.2
2.6
3.1
2.8
2.2
1.4
4.1
–
–
2.3
2.3
–
–
4.0
3.8
4.3
4.7
2.5
3.7
2.9
1.7
4.3
4.1
4.2
11.5
3.4
3.0
2.9
3.3
cat21
Left
Right
4.8
4.6
4.8
3.8
4.0
4.2
4.2
3.9
4.1
4.0
3.8
2.9
4.4
4.3
4.0
3.3
1.6
5.1
5.2
3.5
Those listed in ‘Target’ columns were calculated by using the Proximal–Distal speaker separation as the independent variable in the psychometric
functions, whereas those in ‘Response’ columns were computed using the separation of Proximal and Distal behavioral means.
BBN, broadband noise; HPN, highpass noise; LPN, lowpass noise.
102
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
and (0°, ±4.5°) targets. There were some qualitative consistencies between the two measures, such as cat21’s improved
precision and acuity to signals of longer durations. More
notably, however, there were substantial departures from
quantitative identity between the two. While some of the
corresponding thresholds and SDs were nearly equal, a
sizeable proportion of them were divergent by 50% or
more. Fig. 5 shows a correlation between the measures
for all stimuli in all directions, where a perfect agreement
would lie on the dashed line with slope = 1.0. These data,
however, suggest no relationship between our estimates
of acuity threshold and precision with r = 0.02
(p = 0.90) and a slope = 0.03. This lack of a correlation
was surprising because, according to signal detection theory, they should have been equal.
One potential cause for these inequalities lies within the
method for calculating acuity thresholds. The value of each
threshold is contingent upon the response distributions to
at least two speakers [Proximal and Distal(s)], whereas
the reported SDs are only from responses to Proximal
speaker. In nearly half of the conditions (23/48), the variances of the Proximal and neighboring Distal behavioral
histograms were significantly different (Levene’s, test,
p < 0.05). Although equal variances are not required by
ROC analyses, these differences certainly contributed to
the lack of relationship in Fig. 5 to some extent. This issue
could potentially be addressed by changing the method for
calculating the acuity threshold. Specifically, the extent to
which Proximal and Distal distributions overlap can be
indicated by the standard separation, D, which also
Fig. 5. Correlation between estimated acuity thresholds and SDs for all
cats to all stimuli in all directions (r = 0.02; p = 0.90). Data from cat17
are black, from cat18 are gray, and from cat21 are open symbols. The
estimated acuity thresholds were calculated using Distal–Proximal source
separation as the independent variable in the psychometric functions.
accounts for unequal variances (Sakitt, 1973). Unlike d 0
[Eq. (1)], however, this measure bears no direct relation
to ROC curve areas or performance in a 2AFC task, therefore it was not used here. Nevertheless, it was doubtful that
the large discrepancies seen in Fig. 5 were caused entirely
by unequal variances.
According to classical signal detection theory, there are
two ways to improve acuity: decrease the variability of
internal estimates [denominator, Eq. (1)] or increase the
rate of change along the decision axis with respect to
changes in external space [numerator, Eq. (1)]. The analysis
above suggests that acuity need not correspond with internal estimate variability, therefore the slope of the internal
representation of space versus actual source location is
likely to be a major factor in its determination. Given this,
a likely explanation for the incongruities between the measures of acuity and precision can be found when errors in
mean accuracy are taken into account. For example,
cat18’s downward responses to all stimulus types produced
estimated acuity thresholds and SDs that were especially
dissimilar. Examination of the absolute localization data
highlights seemingly slight yet consistent errors in mean
accuracy: the cat looked 1–2° below the (0°, 0°) target
and 1–2° above the (0°, 4.5°) target. As a result, the separations between Proximal and Distal mean estimates were
also typically 1–2° rather than 4.5°. Such errors are not
accounted for in psychometric functions that use actual
source separation as the independent variable, as was done
here (e.g., Fig. 3c) and as is done in the analyses of traditional relative localization tasks. Yet, these errors in mean
accuracy appeared to be the cause of the disproportionately large thresholds because they significantly affected
the amount of overlap between the Proximal and Distal
distributions.
Three examples of the extent to which errors in mean
accuracy affected the values of estimated acuity thresholds
are illustrated by the psychometric functions in Fig. 6. The
typical method for analyzing data from relative tasks, in
which the abscissa indicates physical speaker separations,
is denoted by the black traces. If measures of acuity calculated by this procedure (including the MAA) are to be
interpreted as an estimate of the auditory system’s resolution, one must either assume that the accuracy of the cat’s
internal space map is perfect or that internal biases are constant in both magnitude and direction across targets. The
gray traces in Fig. 6 plot ROC area as a function of mean
behavioral estimate separation. In Fig. 6a, which shows
cat17’s responses to HPN from targets varying in downward elevation, the separation between mean estimates of
the (0°, 0°) and (0°, 4.5°) speakers was close to the actual
separation. This was in spite of the cat’s 1.5° mean error
to the (0°, 4.5°) target (Table 1), an average-sized error
for this cat, because it also localized the (0°, 0°) target to
be 1.1° above its actual position. As a result, the behavioral
mean separation (4.1°) was similar to the actual source separation (4.5°) and the two threshold estimates were in close
agreement. The discrepancy between behavioral mean and
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
103
Fig. 6. Psychometric functions showing the effect of errors in mean accuracy on the calculation of estimated acuity thresholds. The black traces use Distal–
Proximal speaker separation as the independent variable while the gray traces use Distal–Proximal behavioral mean separation. The SDs of the response
histograms to the Proximal target are listed for comparison. (a) Separations between mean estimates that are similar to actual source separations produce
nearly equivalent acuity measures, both of which compare reasonably well with distribution SD. (b) Mean estimate separations that diverge from speaker
separations, even if slight, can produce sizeable differences in estimated acuity thresholds. (c) Large biases can lead to large acuity measures despite small
distribution SDs.
source separation is slightly larger in Fig. 6b, which plots
cat21’s ROC areas to LPN along right azimuth. This cat
had reasonably good accuracy; its mean estimate of the
(5°, 0°) target was perfect and that of the (10°, 0°) speaker
had a signed error of only 1.6°. Nevertheless, the acuity
threshold was 33% smaller when calculated with the separations between behavioral means instead of targets.
Finally, the calculation of cat18’s threshold to 15 ms
BBN in upward elevation is shown in Fig. 6c. Here, the
cat had substantial errors in accuracy that grew progressively larger to more eccentrically placed targets. The
impact of these errors is obvious, and only the acuity
threshold calculated using behavioral mean separation provides a reliable indication of behavioral precision. The estimated acuity thresholds calculated using mean response
localization for each cat and each condition are shown in
Table 2 under the columns labeled ‘Response’. These measures (mean threshold of 3.6°) were usually, but not always,
smaller than those computed from speaker separation
(mean threshold of 4.5°).
It is clear from Fig. 6 that the accuracy of source location estimates significantly affected the size of acuity
thresholds. However, errors in accuracy per se did not necessarily cause discrepancies between the estimates of acuity
and measures of precision. Rather, the thresholds were
only dissimilar from corresponding SDs when the angular
separation between means diverged from that of the actual
speakers or, in other words, when the signed errors to adjacent targets varied in direction and/or magnitude. The nature of these errors is important because even seemingly
small errors of one or two degrees can be large relative to
the size of distribution SDs, and these can significantly
impact the value of acuity thresholds. Using mean response
separation rather than source separation as the independent variable in the psychometric functions produced both
a vastly improved correlation (r = 0.46, p = 0.001) between
thresholds and SDs and a regression line slope (0.46) closer
to the diagonal (Fig. 7). The remaining scatter was likely
the result of two sources. First, there were differences
between the variances of Proximal and Distal histograms,
as discussed above. Second, the logistic curves were usually
based on one or two consequential data points and these
inexact estimates of the function slope contributed noise
to the correlation.
4. Discussion
4.1. Comparisons with other studies and species
Both relative and absolute paradigms are frequently
used in the field of sound localization and each can offer
advantages depending on the aim of a particular experiment. Absolute tasks unequivocally require subjects to
localize sounds and permit the measurement of both accuracy and precision. This task type is also more ethologically
appropriate for many of the commonly used model systems
because it makes use of a natural orienting response
(Sparks, 2005; Tollin et al., 2005). On the other hand, relative paradigms assess the ability of subjects to detect a
change in stimulus location by requiring them to discriminate between two successive sounds. These produce behavioral data that are both free of motor errors and that can be
easily correlated with physiological activity. Given the
prevalence of these two tasks and their distinct benefits, it
104
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
Fig. 7. Correlation between estimated acuity thresholds and SDs
(r = 0.46; p = 0.001). Colors are as in Fig. 5. The estimated acuity
thresholds were calculated using the separation of behavioral mean
estimates as the independent variable in psychometric functions.
is important to uncover any possible relationships linking
the data they generate.
Here, cats were engaged in an absolute task and the
accuracy and precision of their gaze shifts to various auditory targets were measured. While motor errors almost cer-
tainly affected final gaze positions to some extent, we
nevertheless treated these data as an indication of the cats’
perceptual abilities because of their robust performance,
remarkable accuracy and precision [the cats’ localization
of visual stimuli was extremely accurate and precise, thus
indicating negligible motor errors in their ability to indicate
locations via gaze shifts (Tollin et al., 2005)], and predictable responses to illusory stimuli (Tollin and Yin,
2003a,b). Acuity thresholds were then estimated from the
same data. Clearly, an independent measurement of the
cats’ MAAs using a traditional relative localization task
would have been ideal, but we were unable to perform such
experiments for various reasons. It is therefore of interest
to compare the present data with results from studies which
did engage cats in a discrimination task. Fig. 8a shows the
MAAs of individual cats from previous studies and the
acuity threshold estimates to 164 ms BBN along azimuth
(average between left and right) from this study. Mean
MAAs across subjects were 5.9° (Casseday and Neff,
1975), 3.4° (Martin and Webster, 1987), 6.0° (Heffner and
Heffner, 1988), 4.1° (Huang and May, 1996), and the estimated thresholds from this study were 4.6° (Target) and
3.5° (Response). The localization abilities of cats appear
to vary considerably, both within and across studies, but
the acuity threshold estimates from this analysis are at least
ostensibly consistent with those from traditional relative
tasks. It is important to note that there is no a priori reason
why this should have been the case; the cats very well
could have produced highly variable absolute localization
data which would have produced large acuity threshold
Fig. 8. (a) Comparison of the estimated acuity thresholds (gray) to 164 ms BBN (average of left and right azimuth) with MAAs (black) measured in cats
using traditional relative paradigms. Estimated acuity thresholds labeled as ‘Target’ were calculated using speaker separation as the independent variable
in psychometric functions while those labeled as ‘Response’ were computed using mean behavioral location estimates. Symbols represent the measures for
individual cats from each study. Abbreviations are CN ‘75: Casseday and Neff (1975); MW ‘87: Martin and Webster (1987); HH ‘88: Heffner and Heffner
(1988); HM ‘96: Huang and May (1996). (b) Comparisons of MAAs (diamonds), SDs (squares), and mean signed errors (circles; negative values indicate
an underestimation of actual target separation) to BBN between cats (black symbols), barn owls (gray), and humans (open). Data points and bars
represent means ±1 SD, respectively. Cat MAAs are averaged from the four sources listed in (a), cat SDs and errors from this study; owl MAAs are from
Spitzer et al. (2003), SDs and errors are from Knudsen et al. (1979); all human data are from Recanzone et al. (1998).
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
estimates in our analysis. The finding that the cats actually
localized sound sources with a high degree of accuracy and
precision and that, in the context of decision theory, they
yielded acuity estimates similar to actual MAAs lend credence to our approach and hypothesis.
In Fig. 8b, localization measures of cats are compared to
those of barn owls and humans, two common subjects in
the study of sound localization. Data points indicate mean
values across subjects with ±1 SD error bars, and negative
signed errors signify an underestimation of actual target
separation. The cat MAA listed is the average from the
four studies cited in Fig. 8a, and SDs and errors are from
the three cats in this study to 164 ms BBN to (9°, 0°) or
(10°, 0°). Owl MAAs (n = 3) were computed using a
pupillary dilation response to 25 ms or 100 ms BBN (single
source data; Spitzer et al., 2003), while the SDs and errors
(n = 2) were measured from head orienting responses to
75 ms BBN along left azimuth (Knudsen et al., 1979). All
human data (MAAs, n = 3; errors and SDs, n = 4) are
reported in Recanzone et al. (1998), who used 200 ms
BBN in lever-pressing and head-orienting responses as relative and absolute tasks, respectively. The localization acuity, precision, and accuracy of cats compare reasonably
well with those of owls and humans, both of which are
reputed to be superior at sound localization (Knudsen,
1981).
4.2. Relating behavioral measures to neural mechanisms
The MAA is a measure of sound localization acuity and
is generally believed to signify the resolution with which
auditory systems represent space (Bala et al., 2003, 2007).
As might be expected, this interpretation requires one to
make several assumptions about the neural processes
underlying the behavior (Hartmann and Rakerd, 1989;
Shinn-Cunningham et al., 1998). First, mechanistic models
of sound localization postulate that the perception of an
auditory stimulus generates an internal random variable
along a decision axis. Because such computations are
inherently noisy, each external position can be thought to
be represented by a Gaussian probability density function
of potential location estimates. Second, the positions of
the distribution means along the decision axis are assumed
to vary monotonically (though not necessarily linearly)
with respect to the actual target locations. As a result, adjacent points in space are represented by adjacent and overlapping probability density functions. Third, the variances
of proximate probability density functions are assumed to
be equal and thus a single MAA is reported despite its
dependence on a subject’s estimation of two speaker locations. Finally, an important but often implicit assumption
is that biases are either negligible or constant in magnitude
and direction across target locations. This last point
implies that the separations between means along the decision axis accurately represent those between the actual
sources, and its validity is critical for the interpretation of
the MAA as a measure of auditory system resolution. If
105
all conditions are satisfied, as they are usually assumed to
be, then a subject’s ability to discriminate between two targets is solely dependent upon the separation of two internal
distribution means in terms of their SD [indicated by the
index d 0 , Eq. (1)].
Strictly speaking, the units of decision axes are
unknown, potentially complex and cannot be simply converted to spatial units. However, the size of an MAA primarily depends on the encoding of directional cues,
therefore the decision axes ought to represent external
space in some way. This is similar to the assumption made
here that a cat’s performance in an absolute task depends
on its ability to encode directional cues and it too indicates
the cat’s internal representation of acoustic space. At the
neural level, one such internal representation that seems
to be involved in this decision-making process is an auditory space map in the midbrain. In the barn owl, external
space is represented by topographical neuronal populations
that exhibit firing patterns largely consistent with the
assumptions listed above (Knudsen and Konishi, 1978).
Moreover, the widths of cumulative neural response histograms closely correspond to the size of the MAA (Bala
et al., 2003, 2007). An auditory space map also appears
to exist in the superior colliculus of mammals, and though
its physiological properties are less well understood it too
appears to be consistent with many of the assumptions
mentioned above (Palmer and King, 1982; Middlebrooks
and Knudsen, 1984; Populin et al., 2004). Future work
investigating this area’s function will help to identify the
specific factors influencing decision variable computation
and whether or not the same mechanisms mediate behavior
in absolute and relative tasks.
The analyses performed here suggest that errors in accuracy can affect measures of acuity. One concern is that a
subject’s accuracy cannot be determined from a true measure of acuity (e.g., MAA from a discrimination task),
and any errors detected in an absolute task may be specific
to that task. For one, absolute paradigms often introduce
the caveat of motor errors. The cats in the present study
localized sounds via gaze shifts, which requires coordination between the neural representation of auditory space
and the motor systems controlling eye and head movements (Tollin et al., 2005). Localization errors may therefore result from any of several causes, including intrinsic
properties of the auditory system (Rayleigh, 1907; Stevens
and Newman, 1936; Yin, 2002), ambiguity in the encoding
of spatial cues (Wallach, 1939; Oldfield and Parker, 1984),
a mismatch between the auditory and visual systems
(Knudsen and Knudsen, 1985; Zwiers et al., 2003) and/or
limitations of the oculomotor system. While it is possible
that biases in absolute location estimates largely result
from motor effects, it seems at least equally plausible that
the computation and representation of acoustic spatial cues
are inherently imperfect. Space maps must integrate many
sources of information and their accuracy is highly dependent on the visual system (Knudsen and Knudsen, 1985;
King and Parsons, 1999; Zwiers et al., 2003). The develop-
106
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
ment of the mammalian space map is currently poorly
understood compared to that of the owl, but it conceivably
develops in a similar fashion given that the auditory and
visual systems converge in the superior colliculus to form
overlapping topographic maps (Gordon, 1973; Palmer
and King, 1982; Wise and Irvine, 1983; Middlebrooks
and Knudsen, 1984). These spatial representations must
coincide despite the fact that they are derived from entirely
different sets of information (i.e. interaural and spectral
cues vs. two-dimensional retinal cell arrays) and also must
account for changes in head, eye, or pinna positions (Jay
and Sparks, 1984; Populin et al., 2004). Therefore, despite
the difficulty in separating motor from perceptual errors in
absolute localization data, it seems reasonable to expect
internal representations of acoustic space to contain biases
and for these to affect performance in both absolute and
relative tasks.
One commonly observed bias in cats as well as owls
and humans (Knudsen et al., 1979; Perrott et al., 1987;
Hartmann et al., 1998) is a ‘central bias’, meaning that subjects consistently underestimate the angular separation
between a point of initial fixation and a displaced sound
source. These biases usually increase in magnitude to more
eccentric targets and are present regardless of whether or
not non-responses are included in the datasets. Again,
these could arise purely from motor errors; alternatively,
they could at least partially come about because the auditory space map itself is compressed. The latter scenario
could result from limitations in the encoding of binaural
cues, for example, because symmetrical ears are most sensitive to interaural differences in the frontal hemifield (Sandel et al., 1955; Middlebrooks et al., 1989). Adding to this,
the extent of these underestimations can vary between adjacent targets and these deviations can be large relative to
distribution variance. If such behavioral imperfections are
indicative of the underlying space maps, then a central bias
and slight inconsistencies in error magnitude could significantly impact measures of acuity. The implications of this
Fig. 9. Illustration of two variables that can affect ROC areas. Arrows represent target locations. (a) If the separation between mean location estimates
coincides with that between the actual targets, then changes in the area under an ROC curve (i.e. performance in a 2AFC task) are solely dependent upon
the width of the two overlapping distributions. This scenario is indicative of the way measures of acuity are commonly interpreted. (b) Changes in the area
under an ROC curve can also result from imperfect mean location estimates that are inconsistent across targets. Errors that lead to increased distribution
overlap (short-dashed line) will decrease the area under an ROC curve and inflate measures of acuity; errors that overestimate target separation (longdashed line) have the opposite effect.
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
point are illustrated by Fig. 9. The amount of overlap
between two adjacent probability density functions,
whether they describe behavioral responses, the receptive
fields of neurons, or some undefined unit along a decision
axis, can be changed in two different ways. First, if the separation between distribution means is equal to that
between targets (as is assumed in traditional relative studies), then any change in acuity necessarily reflects a change
in distribution variance. This is the case illustrated in
Fig. 9a, where discrimination performance is proportional
to the area under the corresponding ROC curves. On the
other hand, performance can also be influenced by inconsistent errors across targets [Fig. 9b]. In this scenario, location-encoding errors causing a smaller mean separation
(short-dashed line) than the actual target separation (solid
line) will decrease the area under a corresponding ROC
curve and could inflate the MAA. Imperfections causing
a larger separation (long-dashed line) will have the opposite effect. The MAA, then, can only be interpreted as a
pure measure of spatial resolution by making a priori
assumptions about the accuracy of internal location estimates. While biases were apparently negligible in the two
integrative experiments done to date (Bala et al., 2003,
2007), the potential for errors in accuracy to affect measures of acuity should be greater when the stimuli are difficult to localize or the animal’s abilities have been
compromised. Indeed, disparities between MAAs and
SDs have been observed in exactly these cases (see below).
Finally, even if it is assumed that absolute and relative
tasks employ an auditory space map in a similar way, they
still place distinct demands on a subject that may differentially affect the properties of the space map. A trial in an
absolute task usually involves the presentation of a single
stimulus from one of many possible locations whereas that
in a relative paradigm is characterized by successive stimuli
emitted from two closely spaced speakers. The manner in
which subjects approach these tasks can affect performance
measures, as can factors unique to a particular paradigm.
For example, the length of interval between lead and lag
signals in a discrimination experiment affect acuity (Perrott
and Pacheco, 1989; Strybel and Fujimoto, 2000), but such
a stimulus feature is absent from absolute tasks. Secondly,
if internal biases change over time then the short inter-stimulus delay of relative tasks may minimize the effect of variable biases on acuity measurements. Or, if biases shift as a
result of a previous stimulus location then the close proximity of successive sources might minimize the potential
for inconsistent biases. Unfortunately, it is impossible to
test these hypotheses because measures of accuracy cannot
be extracted from relative localization data.
It might even be suggested that the two paradigms are
fundamentally different and results obtained from them
simply cannot be reconciled, similar to the way frequency
or intensity discrimination and identification tasks are
viewed (Durlach and Braida, 1969). However, this is not
how MAA experiments are typically interpreted because
animals have direct access to another map of external space
107
via the visual system. In fact, the size of the MAA is related
to the width of the visual field across species (Heffner and
Heffner, 1992) and it changes as a result of damage to
the visual system (King and Parsons, 1999). This is in contrast to the perception of frequency or intensity, for which
subjects have no external referents. To conclude, there are
many ways in which relative and absolute tasks differ and
at some level they likely employ distinct neural processes.
Despite this, performance in each primarily depends on
the subject’s ability to encode directional cues and it
remains possible that they utilize many of the same neural
mechanisms to do so in both task types.
4.3. Comparing psychophysical measures of acuity and
precision
As discussed earlier, the MAA is usually compared to
SDs of absolute location estimates because of the relationships outlined in Eq. (1) (Hartmann and Rakerd, 1989;
Makous and Middlebrooks, 1990; Recanzone et al.,
1998). Such comparisons could theoretically be valid if
the assumptions typical to analyses of 2AFC tasks are satisfied, if data collected from absolute tasks accurately represent a subject’s perceptual abilities, and that any effects
arising from the disparities between tasks are inconsequential. If each of the above are true, then the frequent agreement between MAAs and SDs is to be expected but the
discrepancies between them to lateral positions (Perrott
et al., 1987), to illusory or otherwise difficult-to-localize
stimuli (Wightman and Kistler, 1993; Spitzer and Takahashi, 2006), or following lesions of specific auditory nuclei
(May, 2000) are not. Furthermore, even in the cases where
the two measures appear to be similar, the MAA ought to
indicate the smallest possible SD attainable in an absolute
task (e.g., Van Trees, 1968). Generally speaking, however,
this scenario has not been realized in studies of cats
and owls. Both of these animals have been measured to
have smaller absolute localization SDs than MAAs (e.g.,
Table 1 and Fig. 8; Knudsen et al., 1979; Bala et al.,
2003; Spitzer et al., 2003; Tollin et al., 2005). While these
inconsistencies could result from differences between tasks
and/or because subjects employ distinct neural mechanisms
to perform them, an alternative explanation that has not
yet been explored is that they are caused by inconsistent
biases of internal space maps. If the space maps of cats
and owls are in fact compressed towards the midline, then
their reported MAAs are likely inflated and underestimate
the true resolution of their auditory systems. Our analysis
suggests that accuracy and precision estimates from absolute localization paradigms, interpreted in the context of
detection theory, offer a potentially more accurate estimate
of sound source resolution. Future integrative work will
need to address whether internal representations of space
are sufficiently accurate to justify the assumption of negligible biases.
In summary, the present study computed acuity
threshold estimates from absolute localization data in
108
J.M. Moore et al. / Hearing Research 238 (2008) 94–109
two different ways. When calculated with the methods
used to analyze traditional relative tasks, the estimated
thresholds were occasionally very disparate from absolute
distribution SDs despite the fact that they arose from the
same data. This occurred because response biases were
large but were disregarded in the calculations, as is customarily done in the analyses of discrimination tasks.
Our results suggest that biases can potentially have a
large impact on measures of acuity, and a proper analysis and interpretation of these measures with respect to
the neural mechanisms of sound localization ought to
account for this. This view contrasts with traditional
interpretations of acuity measures, such as the MAA,
which assume biases are negligible or constant and that
thresholds only indicate the variability of perceived
source locations.
Acknowledgements
We would like to thank Jane Sekulski and Ravi Kochhar for help with computer programming and John Hudson for assistance with animal training. This work was
supported by NIH grants DC-00116 and DC-02840 and
NRSA award DC-00376.
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