  We study limits for the detection and estimation of weak sinusoidal signals
in the primary part of the mammalian auditory system using a stochastic
Fitzhugh-Nagumo (FHN) model and an action-reaction model for synaptic
plasticity. Our overall model covers the chain from a hair cell to a point just
after the synaptic connection with a cell in the cochlear nucleus. The
information processing performance of the system is evaluated using so called
phi-divergences from statistics which quantify a dissimilarity between
probability measures and are intimately related to a number of fundamental
limits in statistics and information theory (IT). We show that there exists a
set of parameters that can optimize several important phi-divergences
simultaneously and that this set corresponds to a constant quiescent firing
rate (QFR) of the spiral ganglion neuron. The optimal value of the QFR is
frequency dependent but is essentially independent of the amplitude of the
signal (for small amplitudes). Consequently, optimal processing according to
several standard IT criteria can be accomplished for this model if and only if
the parameters are ``tuned'' to values that correspond to one and the same QFR.
This offers a new explanation for the QFR and can provide new insight into the
role played by several other parameters of the peripheral auditory system.
