Discrimination of alternative response relations using the
Iso-Response Method. (a and b) A hypothetical two-dimensional
stimulus space is spanned by the variables s1 and s2. The
drawn surfaces represent the response r(s1,s2) for two
different models, which take the linear (a) and quadratic sum
(b) as the argument of a sigmoid non-linearity. Although the
two input-output scenarios are fundamentally
different, both produce exactly the same one-dimensional
response functions r(s1) and r(s2), respectively, as seen by
the black areas at the sides of the surface blocks.
Furthermore, any measurement along a radial direction, as is
common in physiological experiments, will produce similar
sigmoid response curves in both cases, as seen by the thick
black lines running along the surfaces. The iso-response
manifolds r=const (here: one-dimensional curves) below the
surface plots, however, give a clear signature of the
different underlying processes. (c) Iso-firing-rate curves for
an auditory neuron stimulated by superpositions of two pure
tones. The measured pairs of amplitudes s1 and s2
corresponding to a firing rate r of 150 Hz are shown together
with the iso-firing-rate curves for the two scenarios which
now correspond to sound-amplitude integration (a) and
sound-energy integration (b), respectively. The straight line
for the amplitude hypothesis deviates systematically from the
data, whereas the ellipse obtained from the energy hypothesis
provides an excellent fit. The different scales on the axes
reflect the strong frequency dependence of the neuron's sound
sensitivity. (d) As expected from the sound-energy model,
iso-response lines for different output firing rates are
scaled ellipses.
From Benda et al. 2007,
as modified from

Gollisch et al. 2002.