Conditions for the spread of conspicuous warning signals: a numerical model with novel insights.

The initial evolution of conspicuous warning signals presents an evolutionary problem because selection against rare conspicuous signals is presumed to be strong, and new signals are rare when they first arise. Several possible solutions have been offered to solve this apparent evolutionary paradox, but disagreement persists over the plausibility of some of the proposed mechanisms. In this paper, we construct a deterministic numerical simulation model that allows us to derive the strength of selection on novel warning signals in a wide range of biologically relevant situations. We study the effects of predator psychology (learning, rate of mistaken attacks, and neophobia) on selection. We also study the how prey escape, predation intensity, number of predators, and abundance of different prey types affects selection. The model provides several important results. Selection on novel warning signals is number rather than frequency dependent. In most cases, there exists a threshold number of aposematic individuals below which aposematism is selected against and above which aposematism is selected for. Signal conspicuousness (which increases detection rate) and distinctiveness (which allows predator to distinguish defended from nondefended prey) have opposing effects on evolution of warning signals. A more conspicuous warning signal cannot evolve unless it makes the prey more distinctive from palatable prey, reducing mistaken attacks by predators. A novel warning signal that is learned quickly can spread from lower abundance more easily than a signal that is learned more slowly. However, the relative rate at which the resident signal and the novel signal are learned is irrelevant for the spread of the novel signal. Long-lasting neophobia can facilitate the spread of novel warning signals. Individual selection via the ability of defended prey to escape from predator is not likely to facilitate evolution of conspicuous warning signals if both the resident (cryptic) morph and the novel morph have the same escape probability. Predation intensity (defined as the proportion of palatable prey eaten by the predator) has a strong effect on selection. More intense predation results in strong selection against rare signals, but also strong selective advantage to common signals. The threshold number of aposematic individuals is lower when predation is intense. Thus, the evolution of warning signals may be more likely in environments where predation is intense. The effect of numbers of predators depends on whether predation intensity also changes. When predation intensity is constant, increasing numbers of predators raises the threshold number of aposematic individuals, and thus makes evolution of aposematism more difficult. If predation intensity increases in parallel with number of predators, the threshold number of aposematic individuals does not change much, but selection becomes more intense on both sides of the threshold.