Ecology Letters (2010) 13: 744–753
Many animals use bright colouration to advertise their toxicity to predators. It is now well established that both toxicity and colouration are often variable within prey populations, yet it is an open question whether or not brighter signals should be used by the more toxic members of the population. We therefore describe a model in which signal honesty can easily be explained. We assumed that prey toxicity is environmentally conferred and variable between individuals, and that signalling bears a cost through attracting the attention of predators. A key assumption is that predators know the mean toxicity associated with each signalling level, so that the probability of attack for each signal value declines as mean toxicity associated with that signal increases. The probability of death given attack for each individual, however, declines with the precise value of its own toxicity, and prey must evolve the optimal level of signal to match the toxicity level that they acquire from their environments. At the start of our simulations there is no signalling system, as neither prey nor predators have biases that favour signal diversification. Over evolutionary time, however, a positive correlation emerges between signal strength and the mean toxicity associated with each signal level. When stability is reached, predators change their behaviour so that they now tend to avoid prey that signal conspicuously. In addition to predicting within-species signal reliability, our model can explain the initial evolution of aposematic displays without the need to assume special biases in predators.