Müllerian mimicry

Müllerian mimicry is a natural phenomenon in which two or more unprofitable (often, distasteful) species, that may or may not be closely related and share one or more common predators, have come to mimic each other's honest warning signals, to their mutual benefit, since predators can learn to avoid all of them with fewer experiences. It is named after the German naturalist Fritz Müller, who first proposed the concept in 1878, supporting his theory with the first mathematical model of frequency-dependent selection, one of the first such models anywhere in biology. Müllerian mimicry was first identified in tropical butterflies that shared colourful wing patterns, but it is found in many groups of insects such as bumblebees, and other animals including poison frogs and coral snakes. The mimicry need not be visual; for example, many snakes share auditory warning signals. Similarly, the defences involved are not limited to toxicity; anything that tends to deter predators, such as foul taste, sharp spines, or defensive behaviour can make a species unprofitable enough to predators to allow Müllerian mimicry to develop. Once a pair of Müllerian mimics has formed, other mimics may join them by advergent evolution (one species changing to conform to the appearance of the pair, rather than mutual convergence), forming mimicry rings. Large rings are found for example in velvet ants. Since the frequency of mimics is positively correlated with survivability, rarer mimics are likely to adapt to resemble commoner models, favouring both advergence and larger Müllerian mimicry rings. Where mimics are not strongly protected by venom or other defences, honest Müllerian mimicry grades into bluffing Batesian mimicry. Müllerian mimicry was proposed by the German zoologist and naturalist Johann Friedrich Theodor Müller (1821–1897), always known as Fritz. An early proponent of evolution, Müller offered the first explanation for resemblance between certain butterflies that had puzzled the English naturalist Henry Walter Bates in 1862. Bates, like Müller, spent a significant part of his life in Brazil, as described in his book The Naturalist on the River Amazons. Bates conjectured that these abundant and distasteful butterflies might have been caused to resemble each other by their physical environment. Müller had also seen these butterflies first hand, and like Bates had collected specimens, and he proposed a variety of other explanations. One was sexual selection, namely that individuals would choose to mate with partners with frequently-seen coloration, such as those resembling other species. However, if as is usual, females are the choosers, then mimicry would be seen in males, but in sexually dimorphic species, females are more often mimetic. Another was, as Müller wrote in 1878, that 'defended species may evolve a similar appearance so as to share the costs of predator education.' Müller's 1879 account was one of the earliest uses of a mathematical model in evolutionary ecology, and the first exact model of frequency-dependent selection. Mallet calls Müller's mathematical assumption behind the model 'beguilingly simple'. Müller presumed that the predators had to attack n unprofitable prey in a summer to experience and learn their warning coloration. Calling a1 and a2 the total numbers of two unprofitable prey species, then, Müller argued, if the species are completely unalike they each lose n individuals. However, if they resemble each other, then species 1 losesa1n/a1+a2 individuals,and species 2 losesa2n/a1+a2 individuals. Species 1 therefore gainsn-a1n/a1+a2 = a2n/a1+a2and species 2 similarly gainsa1n/a1+a2 in absolute numbers of individuals not killed. The proportional gain compared to the total population of species 1 isg1 = a2n/a1(a1+a2)and similarly for species 2g2 = a1n/a2(a1+a2), giving the per head fitness gain of the mimicry when the predators have been fully educated.