Supplementary methods, figures, and results from Body size affects the evolution of hidden colour signals in moths

Many cryptic prey have also evolved hidden contrasting colour signals which are displayed to would-be predators. Given that these hidden contrasting signals may confer additional survival benefits to the prey by startling/intimidating predators, it is unclear why they have evolved in some species, but not in others. Here we have conducted a comparative phylogenetic analysis of the evolution of colour traits in the family Erebidae (Lepidoptera), and found that the hidden contrasting colour signals are more likely to be found in larger species. To understand why this relationship occurs, we present a general mathematical model, demonstrating that selection for a secondary defence such as deimatic display will be stronger in large species when (i) the primary defence (crypsis) is likely to fail as its body size increases and/or (ii) the secondary defence is more effective in large prey. To test the model assumptions, we conducted behavioural experiments using a robotic moth which revealed that survivorship advantages were higher against wild birds when the moth has contrasting hindwings and large size. Collectively, our results suggest that the evolutionary association between large size and hidden contrasting signals has been driven by a combination of the need for a back-up defence and its efficacy.