  Honest signals and cues have been observed as part of interspecific and
intraspecific communication among animals. Recent theories suggest that
existing signaling systems have evolved through natural selection imposed by
predators. Honest signaling in the interspecific communication can provide
insight into the evolution of anti-predation techniques. In this work, we
introduce a deterministic three-stage, two-species predator-prey model, which
modulates the impact of honest signals and cues on the interacting populations.
The model is built from a set of first principles originated from signaling and
social learning theory in which the response of predators to transmitted honest
signals or cues is determined. The predators then use the signals to decide
whether to pursue the attack or save their energy for an easier catch. Other
members from the prey population that are not familiar with signaling their
fitness observe and learn the technique. Our numerical bifurcation analysis
indicates that increasing the predator's search rate and the corresponding
assimilation efficiency gives a journey from predator-prey abundance and
scarcity, a stable transient cycle between persistence and near-extinction, a
homoclinic orbit pointing towards extinction, and ultimately, a quasi-periodic
orbit. A similar discovery is met under the increment of the prey's intrinsic
birth rate and carrying capacity. When both parameters are of sufficiently
large magnitudes, the separator between honest signal and cue takes the similar
journey from a stable equilibrium to a quasi-periodic orbit as it increases. In
the context of modeling, we conclude that under prey abundance, transmitting
error-free honest signals leads to not only a stable but also more predictable
predator-prey dynamics.

Populations and Evolution;Dynamical Systems