How bright and how nasty: explaining diversity in warning signal strength

The conspicuous displays that warn predators of defenses carried by potential prey have been of interest to evolutionary biologists from the time of Wallace and Darwin to the present day. Although most studies implicitly assume that these "aposematic" warning signals simply indicate the presence of some repellent defense such as a toxin, it has been speculated that the intensity of the signal might reliably indicate the strength of defense so that, for example, the nastiest prey might "shout loudest" about their unprofitability. Recent phylogenetic and empirical studies of Dendrobatid frogs provide contradictory views, in one instance showing a positive correlation between toxin levels and conspicuousness, in another showing a breakdown of this relationship. In this paper we present an optimization model, which can potentially account for these divergent results. Our model locates the optimal values of defensive traits that are influenced by a range of costs and benefits. We show that optimal aposematic conspicuousness can be positively correlated with optimal prey toxicity, especially where population sizes and season lengths vary between species. In other cases, optimal aposematic conspicuousness may be negatively correlated with toxicity; this is especially the case when the marginal costs of aposematic displays vary between members of different populations. Finally, when displays incur no allocation costs there may be no single optimum value for aposematic conspicuousness, rather a large array of alternative forms of a display may have equal fitness.