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Optimal neural population coding of an auditory spatial cue


A sound, depending on the position of its source, can take more time to reach one ear than the other. This interaural (between the ears) time difference (ITD) provides a major cue for determining the source location1,2. Many auditory neurons are sensitive to ITDs3,4, but the means by which such neurons represent ITD is a contentious issue. Recent studies question whether the classical general model (the Jeffress model5) applies across species6,7. Here we show that ITD coding strategies of different species can be explained by a unifying principle: that the ITDs an animal naturally encounters should be coded with maximal accuracy. Using statistical techniques and a stochastic neural model, we demonstrate that the optimal coding strategy for ITD depends critically on head size and sound frequency. For small head sizes and/or low-frequency sounds, the optimal coding strategy tends towards two distinct sub-populations tuned to ITDs outside the range created by the head. This is consistent with recent observations in small mammals6,7. For large head sizes and/or high frequencies, the optimal strategy is a homogeneous distribution of ITD tunings within the range created by the head. This is consistent with observations in the barn owl8,9,10. For humans, the optimal strategy to code ITDs from an acoustically measured distribution depends on frequency; above 400 Hz a homogeneous distribution is optimal, and below 400 Hz distinct sub-populations are optimal.

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Figure 1: Key features of model.
Figure 2: Optimal distributions of tuning curves for coding IPDs.
Figure 3: Probability distributions of IPDs at different frequencies for three human subjects.


  1. Rayleigh, L. On our perception of sound direction. Phil. Mag. 13, 214–232 (1907)

    Article  Google Scholar 

  2. Wightman, F. L. & Kistler, D. J. The dominant role of low-frequency interaural time differences in sound localisation. J. Acoust. Soc. Am. 91, 1648–1661 (1992)

    ADS  CAS  Article  Google Scholar 

  3. Kuwada, S. & Yin, T. C. T. Binaural interaction in low-frequency neurons in inferior colliculus of the cat. I. Effects of long interaural delays, intensity, and repetition rate on interaural delay function. J. Neurophysiol. 50, 981–999 (1983)

    CAS  Article  Google Scholar 

  4. Yin, T. C. T. & Chan, J. C. K. Interaural time sensitivity in medial superior olive of cat. J. Neurophysiol. 64, 465–488 (1990)

    CAS  Article  Google Scholar 

  5. Jeffress, L. A. A place theory of sound localisation. J. Comp. Physiol. Psychol. 41, 35–39 (1948)

    CAS  Article  Google Scholar 

  6. McAlpine, D., Jiang, D. & Palmer, A. R. A neural code for low-frequency sound localization in mammals. Nature Neurosci. 4, 396–401 (2001)

    CAS  Article  Google Scholar 

  7. Brand, A., Behrend, O., Marquardt, T., McAlpine, D. & Grothe, B. Precise inhibition is essential for microsecond interaural time difference coding. Nature 417, 543–547 (2002)

    ADS  CAS  Article  Google Scholar 

  8. Takahashi, T. & Konishi, M. Selectivity for interaural time difference in the owl's midbrain. J. Neurosci. 6, 3413–3422 (1986)

    CAS  Article  Google Scholar 

  9. Wagner, H., Takahashi, T. & Konishi, M. Representation of interaural time difference in the central nucleus of the barn owl's inferior colliculus. J. Neurosci. 7, 3105–3116 (1987)

    CAS  Article  Google Scholar 

  10. Coles, R. B. & Guppy, A. Directional hearing in the barn owl (Tyto alba). J. Comp. Physiol. A 163, 117–133 (1988)

    CAS  Article  Google Scholar 

  11. Joris, P. X., Smith, P. H. & Yin, T. C. T. Coincidence detection in the auditory system: 50 years after Jeffress. Neuron 21, 1235–1238 (1998)

    CAS  Article  Google Scholar 

  12. Henning, G. B. Detectability of interaural delay in high-frequency complex waveforms. J. Acoust. Soc. Am. 55, 84–90 (1974)

    ADS  CAS  Article  Google Scholar 

  13. Bernstein, L. R. & Trahiotis, C. Lateralization of sinusoidally amplitude-modulated tones: Effects of spectral locus and temporal variation. J. Acoust. Soc. Am. 78, 514–523 (1985)

    ADS  CAS  Article  Google Scholar 

  14. Skottun, B. C., Shackleton, T. M., Arnott, R. H. & Palmer, A. R. The ability of inferior colliculus neurons to signal differences in interaural delay. Proc. Natl Acad. Sci. USA 98, 14050–14054 (2001)

    ADS  CAS  Article  Google Scholar 

  15. Shackleton, T. M., Skottun, B. C., Arnott, R. H. & Palmer, A. R. Interaural time difference discrimination thresholds for single neurons in the inferior colliculus of Guinea pigs. J. Neurosci. 23, 716–724 (2003)

    CAS  Article  Google Scholar 

  16. Brunel, N. & Nadal, J. P. Mutual information, Fisher information, and population coding. Neural Comput. 10, 1731–1757 (1998)

    CAS  Article  Google Scholar 

  17. Bala, A. D., Spitzer, M. W. & Takahashi, T. T. Prediction of auditory spatial acuity from neural images on the owl's auditory space map. Nature 424, 771–774 (2003)

    ADS  CAS  Article  Google Scholar 

  18. Wagner, H., Mazer, J. A. & von Campenhausen, M. Response properties of neurons in the core of the central nucleus of the inferior colliculus of the barn owl. Eur. J. Neurosci. 15, 1343–1352 (2002)

    Article  Google Scholar 

  19. Carr, C. E. & Konishi, M. Axonal delay lines for time measurement in the owl's brainstem. Proc. Natl Acad. Sci. USA 85, 8311–8315 (1988)

    ADS  CAS  Article  Google Scholar 

  20. Kapfer, C., Seidl, A. H., Schweizer, H. & Grothe, B. Experience-dependent refinement of inhibitory inputs to auditory coincidence-detector neurons. Nature Neurosci. 5, 247–253 (2002)

    CAS  Article  Google Scholar 

  21. Domnitz, R. H. & Colburn, H. S. Lateral position and interaural discrimination. J. Acoust. Soc. Am. 61, 1586–1598 (1977)

    ADS  CAS  Article  Google Scholar 

  22. Dayan, P. & Abbot, L. F. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, Cambridge, Massachusetts, 2001)

    Google Scholar 

  23. Bethge, M., Rotermund, D. & Pawelzik, K. Optimal short-term population coding: When Fisher information fails. Neural Comput. 14, 2317–2351 (2002)

    CAS  Article  Google Scholar 

  24. Culling, J. F. & Summerfield, Q. Measurements of the binaural temporal window using a detection task. J. Acoust. Soc. Am. 103, 3540–3553 (1998)

    ADS  Article  Google Scholar 

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We thank C. Rasmussen for the algorithm ‘Minimize’. This work was supported by a MRC Career Establishment Grant to D.M and a MRC BioInformatics Studentship to N.S.H.

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Correspondence to David McAlpine.

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Harper, N., McAlpine, D. Optimal neural population coding of an auditory spatial cue. Nature 430, 682–686 (2004).

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