Contribution of displacement, duration, and velocity on auditory motion direction perception in macaque monkeys

Abstract

Motion perception is a key aspect of sensory processing that enables successful interaction with the environment. While visual motion perception has been extensively studied, little is known about the determinants of auditory motion perception. Our study explores how the perception of auditory motion direction changes with manipulations of low-level stimulus parameters in nonhuman primates (NHPs). Macaque monkeys were trained to perform a 2-AFC task in which they judged the direction of noisy auditory motion stimuli. We systematically manipulated stimulus duration, velocity, and displacement to evaluate their respective influence on motion sensitivity. Displacement had the greatest impact, while the relative influence of duration versus velocity depended upon the duration of the stimulus. These findings suggest that auditory motion direction is most likely processed by a snapshot mechanism, in which stimulus velocity is inferred by sequential snapshots of auditory stimulus location, rather than by velocity-selective motion detectors similar to those found in the visual system. To our knowledge, this study is the first to characterize the influence of low-level stimulus parameters on auditory motion perception in awake, behaving NHPs, and forms the basis for future neurophysiological investigations.

Introduction

In typical listening scenarios, it is uncommon for sound location cues to stay fixed over time because the head, body, and external sound sources are frequently in motion. As a result, effective auditory scene analysis relies on the capacity to encode movement—a change in location over time. The resulting property of velocity is derived from the stimulus’ duration and displacement of motion. However, it is unclear how the stimulus factors of velocity, displacement, and duration are weighted during auditory motion perception. Sensitivity to these motion parameters must be understood in a psychophysically meaningful way in order to manage their covariation in the experimental design and the interpretation of the effective stimulus features underlying the perception of auditory motion.

While there are some examples of cortical and subcortical structures with demonstrated sensitivity to auditory motion^{1, 2, 3, 4, 5, 6–7}, the nature of the representations in these areas remains debated^8,9. Sound location is primarily determined by the difference in time (interaural time difference, ITD) and sound level (interaural level difference, ILD) reaching the two ears^10,11, as well as by monaural spectral cues caused by the pinna filtering the sound^12,13. Neurons in the superior olivary complex are particularly sensitive to the interaural spatial cues, which allow the auditory system to estimate the azimuthal location of a sound source^{14, 15–16}. However, how motion is derived from these spatial cues remains unresolved, with two primary theories proposed. The first, often called the snapshot theory, posits that auditory motion velocity is not directly represented but instead inferred by successively sampling sound location and calculating the change in position over time^{17, 18–19}. Since this theory depends on at least two “snapshots” of stimulus location taken over time, the displacement (i.e., change in position) and duration of a moving sound would be the only information needed in order to compute auditory motion²⁰. The second theory posits that the auditory system contains specialized motion detectors similar to those seen in the visual system^{21, 22, 23, 24–25}, with neurons demonstrating selectivity for auditory motion velocity²⁶. For such a mechanism to exist, listeners’ behavior would be sensitive to velocity without necessarily being sensitive to the sound’s displacement and duration. Testing between these theories is complicated by the challenges of designing an experiment in which these naturally covarying components of motion can be separated. This complication highlights the need to understand the relative contribution of motion characteristics in a psychophysically meaningful way.

Some previous psychophysical studies attempting to differentiate between these two theories have implemented velocity discrimination tasks, therefore biasing responses by directing subjects towards a particular auditory feature (i.e., velocity²⁷). Alternatively, a human psychophysics study using an oddball paradigm has suggested that displacement and duration are the primary cues for auditory motion perception, while velocity—unlike in vision^28,29—is only used when distance and duration cues are unreliable³⁰. Evidence regarding these two theories in behaving non-human primates, however, has yet to be gathered. This gap is surprising given that non-human primates have long served as an important model for understanding the neural mechanisms underlying spatial processing, offering critical insights into how sensory information is integrated to guide goal-directed behavior. Non-human primates are uniquely suited for such investigations due to their well-characterized neural circuits and sophisticated behavioral capabilities, which have been shown to closely parallel those of humans in many domains including visual motion processing. Additionally, our ability to conduct neurophysiological measurements of brain activity to investigate neural mechanisms underlying auditory motion perception makes them an ideal model for these studies.

In the present study, we aim to determine the degree to which motion velocity, displacement, and/or duration contribute towards perception of auditory motion direction. We trained two macaque monkeys to respond to the direction of a simulated motion stimulus presented at various signal-to-noise ratios, velocities, durations, and displacements, and compared the sensitivity to motion direction across conditions. This study represents the first concerted effort to understand the factors governing primate auditory motion perception for stimuli moving in the azimuthal plane. Our findings indicate that auditory motion direction perception is predominantly driven by displacement cues, with lesser contributions from duration and velocity.

Methods

Subjects

We selected rhesus macaques as our model species due to their well-characterized auditory system, which shares critical anatomical and functional similarities with humans³¹. Specifically, macaques possess large heads and a hearing range that includes low frequencies^32,33, enabling effective use of ITDs, which are a key spatial cue also used by humans³⁴. Unlike smaller mammals or animals with highly mobile pinnae like cats, macaques exhibit limited pinna movement, reducing variability in spectral cue availability^35,36.

This study contains data from two adult male rhesus macaques (Macaca mulatta) obtained from the California National Primate Research Center (Davis, CA). The ages of the macaques, referred to as Monkey “A” and Monkey “B,” were 8 and 6 years old, respectively, at the beginning of the study. Their weights were between 11–13 kg when the study began. The diet of these macaques included a standard feed (LabDiet Monkey Diet 5037 and 5050, Purina, St Louis, MO) with additional fresh produce and items for foraging. Various types of enrichment such as manipulative tools and sensory stimuli (auditory, visual, and olfactory) were provided on a rotating schedule. The macaques underwent fluid restriction and were given municipal water that was filtered. Weight was monitored 4 to 5 times a week, ensuring the weights remained within the veterinarian-approved reference range for healthy study conditions.

The animals were kept on a consistent 12-h light/dark cycle, with all experimental activities conducted between 8 AM and 6 PM during the light period. Despite efforts through behavioral assessments to find suitable social companions, the macaques were individually housed due to social incompatibility; however, they maintained visual, auditory, and olfactory contact with other macaques within the same room. This housing environment was part of an AAALAC-accredited facility and adhered to the Guide for the Care and Use of Laboratory Animals, the Public Health Service Policy on Humane Care and Use of Laboratory Animals, as well as the Animal Welfare Act and Regulations. The macaques also received regular health checks, including biannual physical examinations and tuberculosis screenings and adjustments to their reference weights as needed. All experimental protocols involving these animals were approved by the Animal Care and Use Committee at Vanderbilt University Medical Center (VUMC) and carried out in accordance with ARRIVE guidelines.

Surgical procedures

The preparation of monkeys for behavioral experiments adhered to established methods in nonhuman primate research^{37, 38, 39–40}. This behavioral study was conducted in head-restrained animals in part due to a larger effort to investigate the neural correlates of auditory motion perception in the same subjects. To minimize head movement, reduce variation in sound pressure level at the ear, and allow for future simultaneous behavior and neurophysiology experiments to be conducted, a headpost made of stainless steel was affixed to the monkeys’ skulls. This device helped stabilize head position across sessions, and minimize variations in sound pressure level at the ear. First, magnetic resonance imaging (MRI) was conducted in a Philips Intera Achieva 3T scanner, equipped with SENSE Flex-S surface coils positioned either above or below the animal’s head. The purpose of the resulting T1-weighted gradient-echo structural images was to determine the best placement location of the headpost while sparing the skull over potential sites for neurophysiological recordings. For surgical procedures, anesthesia was induced using ketamine and midazolam, followed by maintenance with isoflurane. While anesthetized, the headpost was anchored to the skull with 7 mm titanium screws (Gray Matter Research LLC, Bozeman, MT) and was secured further with bone cement (Heraeus Incorporated, Yardley, PA).

Throughout all surgical procedures, fluids and antibiotics were administered intra-procedurally, with pre- and post-operative analgesics provided under the supervision of veterinary staff. The monkeys were continuously monitored under veterinary oversight until the monkeys fully recovered from surgery.

Apparatus and stimuli

Monkeys were seated and head restrained in a primate chair that was designed and constructed in-house and secured to a fixed pedestal, located 55 cm from the screen and speakers that delivered visual and auditory stimuli. Stimulus generation, event timing, task control, and fluid reward delivery were done with MatLab (The MathWorks, Inc., Natick, MA) and OpenEx software (System 3, TDT Inc., Alachua, FL). Stimuli were presented using PsychToolbox version 3⁴¹.

Auditory stimuli were presented in the free field via two speakers (3W 8 Ω 5.08 × 7.62 cm loudspeaker, Allied Electronics, Inc) located 86.36 cm (78°) apart in the frontal field. Each speaker was calibrated with a ¼ inch microphone (378C01, PCB Piezotronics, Depew, NY) positioned at the location where the entry to the monkey’s ear canal would be during experiments. The speaker output was calibrated to ensure that frequency responses were within ± 3 dB up to 20 kHz. During experiments, auditory stimuli were presented at an average overall level of approximately 60 dB SPL, with mid-frequency components (e.g., 1–4 kHz) reaching levels of 65–70 dB SPL.

To simulate auditory motion with variable coherence, we adapted a stimulus design from a previous study¹⁷, using four broadband white noise components (N1–N4; see Fig. 1a). All noise signals were sampled at 48,828 Hz and band-limited from 0.005 to 24.4 kHz, with 10 ms onset and offset ramps. N1 and N2 were independent, uncorrelated white noise streams (inter-signal correlation = 0) presented from the left and right speakers, respectively, serving as spatially diffuse masking noise. N3 was a correlated white noise signal (inter-signal correlation = 1) presented simultaneously through both speakers at equal amplitude, producing a spatially ambiguous, centrally located percept. N4 was the motion signal with an amplitude envelope that shifted linearly from one speaker to the other over the duration of the trial, creating the percept of motion in azimuth. The direction of N4 alternated between leftward and rightward across trials, and motion displacement was centered at the midline.

Fig. 1 [Images not available. See PDF.]

Stimulus and behavioral task design. (a) Auditory stimulus design. Sounds were presented in the free field via two speakers located 34 inches apart in the frontal field (left speaker (green); right speaker (blue)). The auditory stimuli consisted of four different components: uncorrelated white noise streams presented through each speaker (100% amplitude; N1 and N2); a correlated white noise signal presented through both speakers (100% amplitude, inter-signal correlation = 1; N3); the apparent motion cue, in which the sound’s amplitude faded between the two speakers from 100 to 0% over the course of one trial (inter-signal-correlation = 0.5; N4) to create binaural motion cues at 11 different coherences. The ‘ + ’ symbols indicate summation of signals, and the ‘x’ symbols represent amplitude modulation of N4 by a linear envelope that controls how the noise fades across speakers. Motion coherence was defined as the proportion of N4 relative to the total stimulus energy, and was changed by increasing or decreasing the slope of the stimulus envelope coming from each speaker. (b) The two-alternative forced choice (2-AFC) task design. The subject fixated on a fixation point for 0.20 s then maintained fixation as the stimulus was presented. After stimulus presentation, the fixation point was extinguished and two target points appeared on either side of the screen. The subject was required to saccade to the target corresponding to the direction of the stimulus and fixate on that target for 0.15 s. Successful fixation on the correct target resulted in a fluid reward. A saccade to the incorrect target resulted in no reward. Both outcomes resulted in a 0.80 s inter-trial interval followed by the next trial. A failure to fixate on the fixation point or target for the necessary amount of time resulted in a 2.5 s time out. (c) Example psychometric functions. The slope of the dynamic range is a measure of the perceptual sensitivity to auditory motion direction.

Each stimulus consisted of a weighted combination of these components. The ‘+’ symbols in Fig. 1a indicate summation of signals, and the ‘x’ symbols represent amplitude modulation of N4 by a linear envelope that controls how the noise fades across speakers. Motion coherence was defined as the proportion of N4 relative to the total stimulus energy. At 0% coherence, the stimulus included only the non-directional background components (N1–N3), providing no coherent motion cue. At 100% coherence, the stimulus was composed entirely of N4, producing a fully directional motion percept. Intermediate coherence levels were created by mixing N4 with N1–N3 in varying ratios. The sign of the coherence value denoted motion direction: positive coherence values indicated rightward motion (i.e., N4 ramping from left to right speaker), and negative values indicated leftward motion (N4 ramping from right to left speaker). This sign convention allowed us to combine leftward and rightward motion trials in a single psychometric function, centered at 0% coherence, which reflects a directionally ambiguous stimulus. Each condition was presented at 11 log-spaced coherence levels, spanning from fully noise (0% motion) to fully signal (± 100% motion). The velocity, duration, and displacement (centered at midline) varied between conditions (Table 1). This stimulus design allowed precise control over the strength of the motion cue while embedding it within a consistent acoustic structure. It enabled us to measure motion direction sensitivity across a wide range of signal-to-noise conditions in a way that reflects the complexity of natural listening environments, where directional cues must often be extracted from noisy auditory scenes.

Table 1. Table of task conditions organized into sets according to the motion parameter that remains constant in each set.

Motion parameter	Constant duration conditions						Constant velocity conditions						Constant displacement conditions
Duration (s)	0.834						0.133	0.367	0.601	0.834	1.10	1.30	0.133	0.367	0.601	0.834	1.10	1.30
Displacement (°)	8	22	36	50	66	78	8	22	36	50	66	78	22
Velocity (°/s)	9.59	26.38	43	59.95	76.74	93.5	59.95						165.4	59.95	36.61	26.38	20	16.9

Visual task components (fixation point and targets) were presented on a 1280 × 1024 cathode ray tube (CRT) monitor screen (HP p1230 22″) located in the frontal field 55 cm from the monkey’s head at eye level and centered horizontally between the two speakers. The monitor had a refresh rate of 75.025 Hz, and the screen subtended 40.56° × 30.98° of visual angle.

Eye position was monitored and recorded continuously at 120 Hz using an eye tracker (Applied Science Laboratories Eye-Trac 6). Eye position was calibrated daily prior to each monkey beginning the task. A Minolta Chroma Meter CS-100 was used to verify the luminance of the visual stimuli.

Behavioral training and task design

Prior to being trained on the task used in the present study, both monkeys mastered the same task using visual motion rather than auditory motion stimuli. Monkeys were then trained to perform the task (detailed below) using the aforementioned auditory motion stimuli over the course of approximately one year, completing at least 160 training sessions (one session per day) consisting of 200–2000 trials (median = 1300 trials for Monkey A, 1450 trials for Monkey B) per session. Over the course of this training period, multiple versions of the auditory stimuli were used but the task structure remained the same. Monkeys were considered to have mastered the task once they completed at least 1300 trials with 80% or greater accuracy across all trials (i.e., across trials with different stimulus coherences) in 8 out of 10 consecutive sessions. This criterion reflected stable engagement and performance, with day-to-day variability in percent correct remaining below 5%, indicating asymptotic behavioral performance.

The sequence of each trial is depicted in Fig. 1B. At the beginning of each trial, a 0.4° diameter white fixation point (111 cd/m²) appeared on a black background (0.7 cd/m²). The monkey had one second to initiate fixation on the fixation point within an 8° diameter circular window and maintain it for 0.2 s. If fixation was maintained, then the auditory stimulus (simulated leftward or rightward motion) was presented for the duration specified by the condition. If fixation was maintained during stimulus presentation, the fixation point was extinguished at the end of the stimulus duration and a white, 0.4° diameter target point appeared on the left and right sides of the screen. Once the targets appeared, the monkey had 1.5 s to initiate and maintain fixation for 0.15 s on the target corresponding to the direction of motion of the stimulus. If the monkey responded correctly, a fluid reward (water or juice) was dispensed from a spout. The subsequent trial began after a 0.8 s inter-trial interval. If the monkey failed to initiate fixation within the waiting period or broke fixation early once initiated at any point during the trial, they were given a 2.5 s time out with a black, blank screen. Trials for each coherence were ordered randomly across the session. At least 300 trials for each coherence were collected per condition per monkey across several sessions.

Analyses

For each condition (i.e. each unique combination of stimulus velocity, duration, and displacement; Table 1) for each monkey, the probability of rightward response across coherences for leftward (negative coherences) and rightward (positive coherences) trials were plotted then fit to a modified cumulative gaussian that takes into account lapse rate. The slope of the dynamic range of this function was then calculated and taken to represent behavioral sensitivity to auditory motion direction. The slope of the dynamic range of the psychometric function was calculated as the change in response probability between the 10% and 90% saturation points, adjusted for lapse rates. These points were computed from the fitted cumulative Gaussian parameters, and the slope was taken as the difference in predicted response probabilities divided by the difference in coherence values at these points. This approach provides a robust measure of motion sensitivity across the dynamic region of the function, rather than at a single coherence value. Mean slopes and standard deviations were calculated using a Monte Carlo resampling procedure (also known as Repeated Random Subsampling Cross-Validation), where in each iteration, a random 10% of the data was removed, the slope was calculated on the remaining 90%, and this process was repeated for 1000 permutations.

For each monkey, slopes across conditions were then fit with all possible unique linear regression models that could be created with slope as the dependent variable and velocity, duration, and/or displacement (and their two- and three-way interactions) as the independent variables. This was also done for each of the 1000 different data sets created in the aforementioned permutation testing, each with one slope per unique condition. The adjusted R² values for each model was calculated by modifying the R² values to account for the number of predictors and the sample size. This adjustment involved subtracting the proportion of unexplained variance, scaled by the ratio of the total sample size minus one to the sample size minus the number of predictors minus one. This scaling penalized the mean R² value for models with a higher number of predictors, ensuring that the metric reflects the model’s true explanatory power rather than the mere inclusion of additional variables. Adjusted R² values for each model were then averaged across the 1000 permutations for each monkey, and 95% confidence intervals were calculated. An additional set of linear regression models and mean adjusted R² values was also created in the same manner, but with slopes from conditions with durations below 0.367 s excluded from the data set.

Results

Psychophysical performance

First, we analyzed psychometric performance for each monkey on the motion direction task to compare their performance across conditions with the same duration, displacement, and velocity as exemplified in Fig. 1C. These functions plot the proportion of rightward responses as a function of stimulus coherence, with random motion (coherence 0) at the x-axis center and fully coherent motion (coherence − 1 and 1) at either extreme. Since performance improved with increased stimulus coherence (higher proportion rightward response on rightward trials, lower proportion rightward response on leftward trials), comparing the slopes of these psychometric functions across conditions allowed us to assess the monkeys’ sensitivity to auditory motion. Figures 2, 3, and 4 show these psychometric functions for both monkeys under three sets of conditions, respectively: those with the same duration but different velocities and displacements, those with the same velocity but different displacements and durations, and those with the same displacement but different durations and velocities. Figure 5 summarizes these results by plotting the slopes of each psychometric function for the various conditions and combinations.

Fig. 2 [Images not available. See PDF.]

Psychometric functions indicating motion direction discrimination performance across the constant duration condition set. (a) Psychometric functions for Monkey ‘A’ for a constant stimulus duration of 0.834 s. Symbols with different colors indicate the different combinations of displacement and velocities, with colors corresponding to the table below. The colored curves represent the modified cumulative gaussian fits to the psychometric functions. Positive (negative) coherences indicate rightward (leftward) motion stimuli. (b) Psychometric functions for Monkey ‘B’. Format is similar to (a).

Fig. 3 [Images not available. See PDF.]

Psychometric functions indicating motion direction discrimination performance across the constant velocity condition set. (a) Psychometric functions for Monkey ‘A’ for a constant velocity of 59.95°/s. Symbols with different colors indicate the different combinations of durations and displacements, with colors corresponding to the table below. The colored curves represent the modified cumulative gaussian fits to the psychometric functions. Positive (negative) coherences indicate rightward (leftward) motion stimuli. (b) Psychometric functions for Monkey ‘B’. Format is similar to (a).

Fig. 4 [Images not available. See PDF.]

Psychometric functions indicating motion direction discrimination performance across the constant displacement condition set. (a) Psychometric functions for Monkey ‘A’ for a constant displacement of 22°. The colored curves represent the modified cumulative gaussian fits to the psychometric functions. Positive (negative) coherences indicate rightward (leftward) motion stimuli. (b) Psychometric functions for Monkey ‘B’. Format is similar to (a).

Fig. 5 [Images not available. See PDF.]

Motion direction sensitivity summaries. (a) Mean auditory motion direction sensitivity is shown as a function of displacement with a duration of 0.834 s (varying velocity), circles and solid lines; and with a velocity of 59.95°/s (varying duration), triangles and dotted lines. Red and black symbols and lines represent data from monkey ‘A’ and ‘B’, respectively. Error bars show the standard deviation of the mean slopes. (b) Mean auditory motion direction sensitivity is shown as a function of velocity with a displacement of 22° (varying duration), diamonds and dashed lines; with a duration of 0.834 s (varying displacement), circles and solid lines. Format is similar to (a). (c) Mean auditory motion direction sensitivity as a function of duration with a displacement of 22° (varying velocity), diamonds and dashed lines; with a velocity of 59.95°/s (varying displacement), triangles and dotted lines). Format is similar to (a).

Figure 2 shows the psychometric functions for the two monkeys under conditions with the same duration (0.834 s) stimulus. This duration was chosen because it fell in the middle of the range of durations included in our condition set, and allowed for the displacements in the constant duration and constant velocity condition sets to be the same. Note the similarity in the general shape of the psychometric curves for the two monkeys. When duration was held constant at 0.834 s, psychometric function slopes increased with increases in velocity and displacement for both monkeys. Thus, monkeys were more sensitive to auditory motion direction at higher displacements and velocities. To determine whether this effect is predominantly driven by displacement versus velocity and thus to elucidate the contribution of duration, two additional sets of experiments were conducted.

In the second set of experiments, velocity was held constant at 59.95°/s (Fig. 3). This velocity was chosen because it fell in the middle of the range of velocities possible in our experimental setup. It also allowed for the stimulus displacements to match those in the constant duration set of conditions, and the durations to match those in the constant displacement set of conditions. Again, note the similarities in the psychometric curves between the two animals. When velocity was held constant, the slope of the psychometric functions increased with increases in auditory motion duration and displacement. Note that the slopes for both monkeys were lowest (i.e., shallowest) for the 8°, 0.133 s condition. To round out the analyses, a final set of experiments was needed to elucidate whether displacement or duration is responsible for this reduced sensitivity to auditory motion direction.

In the third set of experiments, displacement was held constant at 22°, while velocity and duration varied in each condition. This displacement was chosen because it fell in the middle of the range of displacements possible in our experimental setup, and allowed for the stimulus durations in these conditions to match those in the constant velocity set of conditions. In the psychometric functions generated in these experiments, there was little increase in slope with increasing duration for durations longer than 0.367 s (Figs. 4; 5c). This suggests that sensitivity to auditory motion direction was most influenced by stimulus duration under our set of velocities and displacements—at least for stimuli less than 0.367 s in duration. Therefore, the minimum time needed for temporal integration of auditory motion cues likely lies somewhere between 0.133 and 0.367 s. At this point, the subjects had likely accumulated enough sensory evidence to make a decision regarding the direction of the auditory motion stimulus, so the additional evidence did little to improve sensitivity. Further support for this idea is detailed below.

Figure 5 summarizes the results of the psychometric functions shown in Figs. 2, 3 and 4. Figure 5 shows the changes in sensitivity (mean slope of the psychometric function calculated using a Monte Carlo resampling procedure with 1000 permutations) as a function of one of the parameters for changes in the other two parameters. Thus, in Fig. 5a, the mean slopes from the constant duration (varying velocity, solid lines) and constant velocity (varying duration, dotted lines) condition sets were plotted against displacement. Overall, increasing displacement resulted in increased mean slopes in both sets of conditions. This same general pattern can be seen for both monkeys (red–Monkey A, black–Monkey B). In Fig. 5b, the mean slopes from the constant displacement (dashed lines) and constant duration (solid lines) condition sets were plotted against velocity. In the constant displacement conditions, higher velocities had lower durations, while in the constant duration conditions, higher velocities had higher displacements. As velocity increases, both monkeys show an overall increase in auditory motion direction sensitivity in the constant duration (varying displacement) condition set, peaking at a slope of 1.75 (standard deviation = 0.021) for Monkey A and 2.36 (standard deviation = 0.047) for Monkey B, while for the constant displacement (varying duration) condition set, mean slopes peak at 1.29 for Monkey A (standard deviation = 0.061) and 1.23 for Monkey B (standard deviation = 0.026). Again, the overall pattern is similar in both monkeys.

The overall differences in how sensitivity changes with velocity between the constant duration (varying displacement) and constant displacement (varying duration) sets for both monkeys suggests a greater impact of changing displacement than changing duration on auditory motion sensitivity. This begs the question of whether the increase in mean slope with increasing displacement in the constant velocity (varying duration) condition set seen in Fig. 5a is being driven by the changes in displacement rather than changes in duration. To test this, we plotted the constant displacement (varying velocity, dashed lines) and constant velocity (varying displacement, dotted lines) condition sets against duration in Fig. 5c. Both monkeys performed similarly for both condition sets for durations of 0.133 and 0.367 s. For durations above 0.367 s, results for each condition set begin to deviate. For the constant velocity (varying displacement) condition set, both monkeys show a progressive increase in mean slope with increasing duration, peaking at a mean slope of 1.86 (standard deviation = 0.029) for Monkey A and 2.36 (standard deviation = 0.051) for Monkey B; however, for the constant displacement (varying velocity) condition set, overall sensitivity to auditory motion seems to plateau, peaking at 1.29 (standard deviation = 0.061) for Monkey A and standard deviation = 0.026) for Monkey B.

Modeling

Although it is not possible to fully disentangle the effects of duration, displacement, and velocity due to their inherent collinearity, the design of our condition set allowed us to assess the relative contribution of each motion attribute and their combinations to behavioral outcomes. To achieve this, we generated all possible unique linear regression models using slope as the dependent variable, with velocity, duration, and/or displacement (along with their two- and three-way interactions) as independent variables. We then compared the mean adjusted R² values of each model—calculated using Monte Carlo resampling with 1000 permutations—to determine which motion parameters or combinations best explained the data while accounting for model complexity. A higher mean adjusted R² indicated a better model fit.

Figure 6a and b display the mean adjusted R² values for models run on all conditions for each monkey separately, with models detailed in Table 2. While some differences were observed between the two animals, the overall pattern of results was highly similar. The model that included only velocity as a predictor (Model 1) did not significantly explain variance in slope (Monkey A: n = 15, coefficient estimate = 0.001, standard error = 0.003, t = 0.150, p = 0.884; Monkey B: n = 15, coefficient estimate = 0.002, standard error = 0.005, t = 0.455, p = 0.657). Models that included only duration (Model 2) or both duration and velocity (Model 4) as main effects had significantly lower mean adjusted R² values than all other models, except Model 1 (Mann–Whitney U tests with Bonferroni correction, n = 1000, α = 0.0029; Monkey A: p < 1.0e−150; Monkey B: p < 1.0e−300).

Fig. 6 [Images not available. See PDF.]

Modeling motion sensitivity. Figures show mean adjusted R² values of all unique linear regression models that could be to model perceptual sensitivity as a function of velocity, duration, and/or displacement (and their two- and three-way interactions) for monkey ‘A’ (circles) and monkey ‘B’ (triangles). Error bars represent 95% confidence intervals across 1000 permutations of Monte Carlo resampling. Model formulas corresponding to the model numbers on the x-axis are provided in Table 2. Red markers indicate mean adjusted R² values for models without interaction terms included in the independent variables, blue markers indicate mean adjusted R² values for models that have a two-way interaction as at least one of its independent variable(s), and green markers indicate mean adjusted R² values for models that have a three-way interaction term as its independent variable. (a) Mean adjusted R² values of the linear regression models run on slopes from all conditions for Monkey ‘A’. (b) Mean adjusted R² values of the linear regression models run on slopes from all conditions for Monkey ‘B’. (c) Mean adjusted R² values of the linear regression models run on slopes from conditions with durations > 0.367 s for Monkey ‘A’. (d) Mean adjusted R² values of the linear regression models run on slopes from conditions with durations > 0.367 s for Monkey ‘B’.

Table 2. Table of regression model formulas and their model numbers that correspond to the x-axis labels in Fig. 6.

Regression model number	Regression model formula
1	slope ~ 1 + velocity
2	slope ~ 1 + duration
3	slope ~ 1 + displacement
4	slope ~ 1 + velocity + duration
5	slope ~ 1 + velocity + displacement
6	slope ~ 1 + duration + displacement
7	slope ~ 1 + velocity + duration + displacement
8	slope ~ 1 + velocity*displacement
9	slope ~ 1 + velocity*duration
10	slope ~ 1 + duration*displacement
11	slope ~ 1 + displacement + velocity*duration
12	slope ~ 1 + duration + velocity*displacement
13	slope ~ 1 + velocity + duration*displacement
14	slope ~ 1 + velocity*duration + velocity*displacement
15	slope ~ 1 + velocity*duration + duration*displacement
16	slope ~ 1 + velocity*displacement + duration*displacement
17	slope ~ 1 + velocity*duration + velocity*displacement + duration*displacement
18	slope ~ 1 + velocity*duration*displacement

However, Model 4 (which included both duration and velocity) had a significantly higher mean adjusted R² than Model 2 (which included only duration), indicating that velocity provided additional explanatory power when combined with duration (Mann–Whitney U test with Bonferroni correction, n = 1000, α = 0.0029; Monkey A: p = 3.313e−192; Monkey B: p = 1.067e−317). All subsequent models shown in Fig. 6a and b (except for Model 9: slope ~ 1 + velocity * duration) included displacement as an independent variable, either on its own or as part of a two- or three-way interaction term. These models produced significantly higher mean adjusted R² values than models without displacement for both monkeys (Mann–Whitney U tests with Bonferroni correction, n = 1000, α = 0.0029; Monkey A: p < 1.0e−235; Monkey B: p < 1.0e−300).

Notably, the models slope ~ 1 + velocity + duration (Model 4; Mann–Whitney U tests with Bonferroni correction, n = 1000, α = 0.0029; Monkey A: p = 6.544e−238; Monkey B: p = 1.020e−317) and slope ~ 1 + duration (Model 2; Mann–Whitney U tests with Bonferroni correction, n = 1000, α = 0.0029; Monkey A: p = 1.228e−245; Monkey B: p = 8.046e−320) had significantly lower mean adjusted R² values than the model with displacement as the sole predictor (Model 3), further highlighting the dominant role of displacement in explaining variations in psychometric function slope.

Additionally, we examined the linear regression models (n = 13) that included duration, displacement, and velocity as main effects (Model 7: slope ~ 1 + velocity + duration + displacement). For Monkey A, neither duration (coefficient estimate = 0.030, standard error = 0.32, t = 0.094, p = 0.927) nor velocity (coefficient estimate = − 0.003, standard error = 0.003, t = − 1.219, p = 0.251) had a significant effect on slope. Similarly, for Monkey B, duration (coefficient estimate = − 0.214, standard error = 0.219, t = − 0.976, p = 0.350) did not significantly predict slope, though velocity showed a marginally significant effect (coefficient estimate = − 0.005, standard error = 0.002, t = − 2.370, p = 0.037). In contrast, displacement had the strongest influence on slope for both monkeys, with significant effects observed in Monkey A (coefficient estimate = 0.019, standard error = 0.004, t = 5.238, p = 3.798e−4) and Monkey B (coefficient estimate = 0.030, standard error = 0.003, t = 10.226, p = 5.911e−7).

Since increasing stimulus duration beyond 0.367 s resulted in only minimal improvements in sensitivity to auditory motion direction (Figs. 3, 4, 5b, and c), we reanalyzed the data using only trials with durations of 0.367 s or longer (Fig. 6c and d). This allowed us to assess whether the influence of duration observed in earlier models was primarily driven by shorter-duration trials.

When focusing on longer-duration conditions, the effect of duration weakened. The duration-only model (Model 2) was not significant for either monkey (Monkey A: coefficient estimate = 0.594, standard error = 0.456, t = 1.301, p = 0.22; Monkey B: coefficient estimate = 0.517, standard error = 0.641, t = 0.806, p = 0.437). In contrast, velocity became a stronger predictor, as the velocity-only model (Model 1) was significant under these conditions (Monkey A: coefficient estimate = 0.013, standard error = 0.004, t = 3.75, p = 0.003; Monkey B: coefficient estimate = 0.020, standard error = 0.004, t = 5.584, p = 1.64e−4).

Despite this shift, models that included displacement continued to explain significantly more variance than those that excluded it (Mann–Whitney U tests with Bonferroni correction, n = 1000, α = 0.0029; Monkey A: p = 0; Monkey B: p < 2.9e−320). These findings suggest that the greater influence of duration relative to velocity observed in the full dataset (Fig. 6a and b) was primarily driven by trials with shorter durations.

Discussion

Although some cortical and subcortical structures are responsive to auditory motion, how they represent and process motion remains debated. This study provides evidence as to whether auditory motion perception relies on specialized motion detectors or infers motion through sequential sound location processing. While velocity, duration, and displacement play distinct roles in each mechanism, their relative contributions to motion perception were previously unexplored. Overall, our results suggest that the duration, displacement, and velocity of an auditory motion stimulus all have the capacity to influence sensitivity to motion direction. However, out of the three tested motion parameters, displacement was found to have the greatest effect on lateral (leftward vs. rightward) direction perception. Additionally, the impact of duration or velocity also depended on the duration of the stimulus. For short duration (i.e., less than 0.367 s) stimuli, duration was more influential than velocity. For longer-duration stimuli, velocity was the more impactful motion parameter. These results suggest that there is a duration threshold between 0.133 and 0.367 s, beyond which longer stimulus durations do not facilitate accurate auditory motion direction perception.

These results provide supporting evidence for the snapshot mechanism for auditory motion perception, in which displacement cues are weighted more heavily than velocity cues. With such a mechanism, “snapshots” of auditory stimulus location are sampled at different points in time over the duration of the stimulus using sound localization cues such as ITDs and ILDs, and velocity is then inferred from the displacement of the sound source between snapshots. In such a model, duration and displacement information alone would be sufficient to support auditory motion processing. Our findings show that displacement alone accounted for the most variance across both model sets, while duration alone explained the most variance when including stimuli of 0.367 s or less, supporting this theory.

When modeling data from all conditions, the model with velocity as the only independent variable was not significant. This indicates that for the range of velocities, durations, and displacements included in our experiment, velocity information alone is not sufficient to account for monkeys’ sensitivity to auditory motion direction. It is therefore unlikely that a velocity detector mechanism for auditory motion processing exists. Interestingly, our modeling results for longer duration stimuli (> 0.367 s) show pairing of velocity information with displacement and/or duration information yielded mean adjusted R² values as high or higher than those of displacement information alone. Nevertheless, if a velocity detector mechanism were to dominate motion processing, listeners’ behavior would have to be highly sensitive to velocity without necessarily being sensitive to displacement and duration.

At least for neocortical structures, it appears highly likely that sound-source locations are encoded through a distributed representation, rather than via a direct topographic mapping of auditory space onto individual neurons with discrete receptive fields⁴². Indeed, studies of sound localization in cats show localization to be more accurate when based on spike patterns that consistently preserve detailed spike timing, compared to relying solely on spike counts^43,44. In such a scenario, individual neurons have been labeled as “panoramic localizers,” containing spatial information within the dynamics of their firing patterns, which are part of a network that builds the distributed code of space. Such neurons may also play an integral role in the computation of auditory motion, with the spiking patterns not only signifying spatial location but also the change in location over time. The current results argue for displacement being a key parameter in this distributed computation.

Our findings align with a previous psychophysical study which found that the speed of an auditory stimulus is a secondary cue, used only when distance and duration information are unreliable³⁰. The results in their study, however, suggest that listeners were most sensitive to duration rather than displacement. This may be due to differences in stimulus and task design between the two studies. The stimulus in the aforementioned study used auditory motion stimuli based on head-related transfer functions (HRTFs), so the motion contained only interaural time differences as a cue to stimulus location, unlike the present experiment, which predominantly manipulated interaural level differences (and spectral cues) between two displaced speakers. Moreover, their use of a different task, one in which listeners are presented with three stimuli on each trial and asked to choose which is unique, introduces an additional temporal component to the task due to the sequential presentation of stimuli on each trial. The prominence of timing information within their design likely accounts for the subjects’ heightened sensitivity to duration over displacement. In contrast, in the present study, monkeys were required to respond to an inherently spatial feature of the stimulus–its direction. Because displacement is a spatial stimulus attribute, it is likely more directly tied to the perception of direction compared to duration–a temporal stimulus attribute. Therefore, in the current work, displacement more strongly influenced the monkeys’ decisions as opposed to duration. Hence, the task the listener is performing is an important factor in whether they are more sensitive to duration versus displacement information.

Our behavioral results alone can’t adjudicate between competing theories of how auditory motion is processed in the brain. Nonetheless, there are valuable insights to be gained from previous neurophysiological studies of auditory motion. A number of those using non-primate animal models have evaluated the claim that there are specialized auditory motion detector neurons at subcortical and cortical auditory structures^{1, 2, 3, 4, 5, 6–7,45}. Numerous studies have used dynamic motion stimuli, in particular, binaural beats, to suggest sensitivity to auditory motion direction and velocity beginning at the earliest binaural center in the brainstem–the superior olivary complex (SOC); however, no studies to date have done so in NHP^{46, 47–48}. Binaural beats occur when two tones (or amplitude modulations) of slightly different frequencies are presented separately to each ear through headphones. Manipulating the difference between the frequencies over time can simulate auditory motion because the beat–an illusory tone that results from the summation of the diotic stimuli–seems to move through virtual auditory space. Some have argued that SOC neurons’ sensitivity to binaural beats does not necessarily mean they encode motion as a distinct feature and may simply reflect moment-to-moment changes in static spatial cues (ITDs/ILDs)⁴⁷. However, since the results of our study suggest that the sequential sampling of static spatial cues is sufficient for auditory motion processing under a large range of stimulus velocities, durations, and displacements, it is possible that the SOC is the first structure in the ascending auditory pathway to contribute to the perception of auditory motion along the azimuthal plane. Since binaural beats differ greatly from true auditory motion, future studies of SOC activation in the presence of more ecologically valid auditory motion stimuli such as those used in the present experiment are needed to further elucidate its role in auditory motion processing.

Studies have addressed the possibility of auditory motion encoding in the inferior colliculus (IC)^1,2,8 and in the optic tectum of the barn owl³. These studies complement the rich literature on auditory spatial maps in the barn owl^49,50 and the great degree of convergence from brainstem nuclei on the IC^49,50. Differences in stimulus configurations complicate generalization across studies. Moreover, studies are equivocal with regard to the presence or absence of motion-selective responses in the IC, with some suggesting apparent motion responses are simply the result of spatial masking (i.e. that the preceding stimulus elicits adaptation or suppression)^1,51 and other studies suggesting that the presence of directional selectivity is sufficient to underpin auditory motion perception^1,52. However, even the presence of spatial direction selectivity in the IC has been questioned⁵³, and was qualified with the term “directional sensitivity” by Ingham et al.¹. Additionally, no studies to date have recorded from primate IC in the presence of auditory motion stimuli. Thus, future neurophysiological studies are needed to conclusively define the role of the inferior colliculus in auditory spatial and motion processing.

While auditory motion processing beyond primary auditory cortex has not been thoroughly investigated in animal models, studies in macaques have shown that sensitivity to static spatial information increases from A1 to the caudomedial (CM) and caudolateral (CL) belt areas^{54, 55–56} which suggests that motion sensitivity could exist along such a gradient. Moreover, human fMRI studies have implicated the planum temporale, which contains areas homologous to macaque areas CM and CL, in auditory motion processing^57,58. Studies have also characterized how auditory cortical neurons are sensitive to dynamic sound localization cues^4,5,59. As described previously, some of these results can be explained by spatial masking, which Poirier et al.³⁶ addressed in their neuroimaging study by creating auditory motion stimuli and collecting primary auditory cortex responses to spectrotemporal and stationary control stimuli to regress these sound features out of the putative motion response. Their results suggest that BOLD responses in the primary auditory cortex do not exhibit true motion direction selectivity, but can instead be accounted for by simpler spectral and temporal sound features.

Our findings align with the broader conceptual framework that auditory spatial representations are dynamically reconstructed through coordinate transformations incorporating head and eye position signals⁶⁰. Just as a previous study has argued for a supramodal, world-centered encoding of static sound location–dependent on integrating multiple sensory signals–our results support a snapshot mechanism for auditory motion perception, wherein direction is inferred through successive samples of static spatial information. Both studies reinforce the view that auditory motion and spatial location rely on dynamic transformations of sensory input rather than on dedicated motion-selective mechanisms.

It is important to acknowledge that displacement, duration, and velocity are mathematically interdependent (i.e., velocity = displacement / duration), which inherently constrains the extent to which they can be manipulated independently. While our experimental design strategically varied which parameter was held constant across condition sets, complete orthogonality is mathematically impossible. To address this, we implemented a condition structure that allowed for systematic covariation and employed linear regression modeling with cross-validation to disentangle the unique contributions of each parameter. This approach substantially reduced confounding effects and enhanced interpretability, though some residual covariation remains. Unlike in visual motion stimuli, such as random dot kinematograms (RDKs) in which displacement can be varied independently by replotting dots, auditory motion stimuli such as the one used in this study do not permit such manipulations due to the continuous nature of sound propagation. Thus, although our design markedly minimized parameter confounds, the inherent linkage between motion components should still be considered when interpreting the results.

Our study focused on auditory motion in the horizontal (azimuthal) plane, but future work should consider how motion perception might differ in other spatial dimensions, such as vertical or radial (looming/receding) trajectories. Unlike azimuthal localization, which primarily relies on binaural cues like interaural time and level differences (ITDs and ILDs), elevation and depth perception depend more on monaural spectral cues shaped by the pinna and head-related transfer functions^10,11. These distinct cue profiles may shift how motion parameters like velocity, displacement, and duration are weighted. For example, looming stimuli–sounds that increase in intensity over time–elicit stronger orienting responses in rhesus monkeys than receding sounds, but only when the stimulus is tonal rather than broadband⁶¹. This suggests a spectrally dependent, adaptive bias for detecting approaching sounds. Moreover, looming and receding motions often carry different behavioral relevance than lateral motion, especially in contexts involving self-motion or environmental navigation. Additionally, studies have shown that allowing monkeys to move their heads improves spatial localization accuracy and reduces response variability, potentially altering the weighting or availability of certain spatial cues⁶². In our study, head restraint was necessary for future neurophysiological recordings and consistent stimulus delivery, but may have limited access to some dynamic localization cues. It is therefore possible that with a broader range of stimulus parameters, vertical or radial motion, and/or under free-listening conditions, the relative influence of motion cues could differ. These contextual factors should be considered when generalizing our findings beyond the specific lateral, head-restrained conditions tested here.

Our results suggest that auditory motion processing primarily relies on the displacement of the sound source when monkeys were asked to judge the direction of auditory motion. This finding supports the snapshot model of auditory motion perception, in which auditory motion direction is inferred through sequential processing of sound location. Future studies implementing a similar task design during simultaneous neural recordings would be beneficial to further elucidate the mechanisms used to process auditory motion.

Acknowledgements

The authors would like to acknowledge Mary Feurtado for assistance with procedures involving anesthesia, Jackson Mayfield for technical assistance, Wesley Williams for assistance with data collection, and Bruce Williams and Roger Williams for building experimental hardware. The authors thank Dr. Andrew Tomarken for his advice on statistical analyses and modeling, as well as Dr. Gregory DeAngelis for helpful guidance throughout the experiment. Finally, the authors would like to acknowledge the National Institutes of Health, the National Eye Institute, and the National Science Foundation for funding this research through the following grant support: NIH F31EY035167 and NSF DGE-1922697 to A.M.S.

Author contributions

A.M.S., M.T.W., and R.R. designed and planned the experiments. A.M.S. collected the data, performed the analysis and modeling, and wrote the manuscript. M.T.W. and R.R. edited the manuscript. All authors revised and approved the final version of the manuscript.

Data availability

The datasets generated during and/or analysed during this study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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