Although we have discussed exaggeration mostly in terms of its implications for the costs
of signals and the increased probability of responses (correct detections) by receivers,
Signal Detection Theory identifies an additional consequence of exaggeration:
diminishing returns for a signaler. As a signal becomes more detectable to receivers,
the probabilities of errors by receivers decrease asymptotically toward 0 and the
probability of correct detections increases towards 1. In the later stages of this
process, any further increase in a receiver's threshold would result in progressively
fewer additional correct detections and more additional missed detections. As receivers'
thresholds stabilized, further exaggeration of signals would yield little or no increase
in benefits for them.
Selection on receivers for increasing thresholds would thus progressively decrease.
Even if further exaggeration of signals had little or no cost, selection on signalers for
further exaggeration would also progressively decrease as a result of the diminishing
returns from improved performance of receivers. Although high costs of false alarms and
noisy discriminations could result in the evolution of highly fastidious receivers and
extravagant exaggeration of signals, both receivers and signalers eventually reach a
point of diminishing returns.
Eventually an equilibrium between diminishing benefits and augmenting costs of
exaggeration would put an end to further exaggeration of a signal. Furthermore, these
diminishing returns suggest that this equilibrium would be reached at a point short of
perfect discriminability of signals by intended receivers. At this equilibrium,
receivers would make some mistakes, and signals would sometimes fail to evoke the
intended response. Receivers would have evolved optimal, not ideal, performance, and
signals would have evolved optimal, not complete, efficacy. Both receivers and signalers
would have adapted to the constraints of environmental noise on signal detection or
discrimination. We should therefore avoid a naive expectation that evolution leads to
signals that are always detectable by receivers or receivers that never make mistakes.
At a signal-detection balance, ideal signals and ideal receivers would not exist.
It seems likely that most communication is poised in such a signal-detection
balance. If so, the properties of communication would be difficult to understand without
an investigation of all the constraints on optimal performance of receivers and on
optimal detectability or discriminability of signals. Noise, as much as costs and
benefits of signals or responses, would determine the properties of communication.