Individual-based evolutionary simulation models are used alongside mathematical approaches as tools for investigating the selective pressures responsible for the origin and maintenance of animal warning displays and mimicry. The early chapters of the thesis review the literature on evolution and coevolution in general, as well as setting out a position on the use of computational models in science. The focus then moves to the evolution of warning displays and a review of the biological literature is presented, followed by an evolutionary simulation model. Bright warning displays of defended animals (those possessing a defence such as a sting or toxin) are among the most salient signalling systems in nature. Examples include black and yellow striped stinging wasps, bitter-tasting ladybird beetles, and brightly coloured, toxic butterflies: these conspicuous signals are thought to have evolved as a keep away warning to predators. A novel coevolutionary model (Sherratt, 2002a) regarding the evolution of warning displays is replicated and critiqued in detail. The results highlight the utility of a coevolutionary approach but also demonstrate that the theoretical account of the evolution of warning signals remains incomplete. The thesis then addresses open theoretical issues surrounding the evolution of mimicry (i.e., the adaptive resemblance of one species to another). A review of the biological literature is followed by an evolutionary simulation model. Mimicry is conventionally divided into two categories: Batesian and M¨ullerian. Batesian mimicry occurs when a species without a defence has evolved an appearance that is similar to that of a defended species. M¨ullerian mimicry occurs when two defended species evolve to mimic each other. M¨ullerian mimicries between multiple species are termed mimicry rings. The simulation is used to examine the evolution of such rings: first the model is used to look at whether multiple mimicry rings should be expected to form (as in nature), and second it is used to look at the effect of Batesian mimics on the evolution of mimicry rings. The simulation results show that mimicry rings can form because intermediate mutational forms (mutant prey that do not share the appearance of any ring) are at a selective disadvantage, and that Batesian mimics influence the evolution of M¨ullerian mimicry rings by encouraging those rings to converge. Finally, theories of warning signals and mimicry are brought together in a mathematical model that looks at whether animals with a defence might evolve traits that are difficult for undefended animals to exploit. This is the first model to implement both mimicry and conspicuous warning displays, and allows us to ask whether defended prey might have evolved conspicuous warning signals in order to shake off parasitic Batesian mimics. The results show that warning signals can, in theory, evolve in response to mimicry. The thesis concludes with a discussion of ways in which individual-based models could be used to take the investigation forward
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