Corrections (with my apologies!) . . .
Figure 3 -- the vertical axis should be labeled "1 - Cumulative
corrected version of Figure 8 (with correct labels for the panels)
corrected version of Figure 10 (with correct labels for the lines) --
notice that the published corrigendum for Figure 10 (below) is itself incorrect!
Figure 12 -- the key for the symbols in each plot should have the circle and the square interchanged
Page 964, the second and third lines from the bottom should read, "...
the optimal threshold is low when these parameters are high.
A high threshold is termed 'adaptive choosiness' ..."
Corrigendum published by Behaviour 2014 (doi:10.1163/1568539X-00003063O)
20 January 2015
Mathematica 8 .nb file for the calculations in this article
Communication in noise differs in a fundamental way from communication without noise,
because a receiver faces four possible outcomes every time it checks its input.
These outcomes present inevitable trade-offs for a receiver in adjusting its threshold
for response. A signaler also faces trade-offs, in this case between costs and
benefits as the exaggeration of signals increases. Furthermore, a receiver's and
signaler's performances are mutually interdependent.
The utility of a receiver's threshold depends on the signaler's exaggeration (the level
of the signal in relation to the level of noise), and the utility of a signaler's
exaggeration depends on the receiver's threshold. Diminishing returns for both
receiver and signaler suggest the possibility of a joint evolutionary equilibrium for a
receiver's threshold and a signaler's exaggeration.
The present analysis combines previous expressions for the utility of a receiver's
threshold ( Ur ) and the utility of a signaler's exaggeration ( Us ) in order to
explore the possibility of this joint equilibrium. Utilities for both parties
are expressed as survival X fecundity, an approximate measure of the spread of genes
associated with a phenotype. Thus, Ur and Us, as functions of both the
receiver's threshold (t) and the signaler's exaggeration (e), represent the adaptive
landscapes for each party, and the reciprocal partial
derivatives of these utilities ( dUr/de and dUs/dt ) approximate the selection
gradients for the receiver's threshold and the signaler's exaggeration.
With parameters for both the receiver's and the signaler's performances set to plausible
values for many cases of mate choice, the resulting analysis shows that there exists a
joint optimum for the receiver's threshold and the signaler's exaggeration. This
optimum is a Nash equilibrium at which neither party can do better by a unilateral change
in behavior. In some conditions, the equilibrium for communication in mate choice
occurs at a higher threshold and higher exaggeration than the equilibrium for
communication with warning signals.
In general, these results indicate that the normal situation for communication in noise
is honesty with deception -- honesty on average but with instances of disadvantageous
outcomes for receivers or signalers. Furthermore, the relationship between honesty
and costs is more complex than currently recognized. Most important, the joint
optimum for receiver and signaler indicates that communication in noise cannot escape the
problems created by noise. Noise is an inevitable component of communication, and
perfection in communication is not expected in natural conditions.