Müllerian mimicry

Müllerian mimicry is a type of biological mimicry in which two or more well-defended species, often foul-tasting and sharing common predators, converge in appearance to mimic each other's honest warning signals. This convergence of appearance achieves the following benefit to species that undergo it: predators need only experience a single unpleasant encounter with any member of a set of Müllerian mimics in order to thereafter avoid all creatures of similar appearance, whether or not it is the same species as the initial encounter. A ring of distinct species is thereby protected from their mutual predators by attempted predation upon any one of its members. The phenomenon is named after the German-Brazilian naturalist Fritz Müller, who proposed the concept in 1878, supporting his theory with a mathematical model of frequency-dependent selection, one of the first such models to be deployed 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, as well as in other animals such as poison frogs and coral snakes. The mimicry need not be restricted to that detected by vision—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 among the several thousand species of velvet ants (which are all, in fact, types of wasp). Because the frequency of mimics in a given environment is positively correlated with an individual mimic's survival, the rarer mimics come to resemble commoner models, favouring both advergence and ever-larger rings of Müllerian mimicry. Where Müllerian mimics are not strongly protected by venom or other defences, honest Müllerian mimicry transforms incrementally into the better-known bluffing of Batesian mimicry.

History

Origins

Müllerian mimicry was proposed by Fritz Müller (1821–1897). 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 fraction of his life in Brazil, which Bates 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. Müller proposed a variety of other explanations. One was sexual selection—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 mathematical model

Müller's 1879 account was the earliest use 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, Müller then argued that, if the species are completely unalike they each lose n individuals. However, if they resemble each other, then species 1 loses ⁠a1n/a1+a2⁠ individuals, and species 2 loses ⁠a2n/a1+a2⁠ individuals. Species 1 therefore gains n-⁠a1n/a1+a2⁠ = ⁠a2n/a1+a2⁠ and species 2 similarly gains ⁠a1n/a1+a2⁠ in absolute numbers of individuals not killed. The proportional gain compared to the total population of species 1 is g1 = ⁠a2n/a1(a1+a2)⁠ and similarly for species 2 g2 = ⁠a1n/a2(a1+a2)⁠, giving the per head fitness gain of the mimicry when the predators have been fully educated. Hence, Müller concluded, the proportion g1:g2 was ⁠a2/a1⁠ : ⁠a1/a2⁠, which equals a22:a12, and the rarer species gains far more than the commoner one. The model is an approximation, and assumes the species are equally unprofitable. Later models are more complex. If one is more distasteful than the other, then the relative gains differ further, the less distasteful species benefiting more (as a square of the relative distastefulness) from the protection afforded by mimicry. Some have argued that some "Müllerian" mimicry may be "quasi-Batesian", or parasitic, rather than mutualistic. In "quasi-Batesian" mimicry, a weakly unpalatable species is proposed to gain protection from mimicry, while the strongly protected "model" species it mimics suffers greater predation as a result of the weakening of the average distastefulness of the mimetic pair. The assumption of a fixed number n to be attacked is a useful first step, but unlikely to perfectly reflect the effect of predators' memories. Müller also effectively assumed a step function, when a gradual change (a functional response) is more plausible.

Non-deceitful mimicry

Biologists have not always viewed the Müllerian mechanism as mimicry, both because the term was strongly associated with Batesian mimicry, and because no deception was involved—unlike the situation in Batesian mimicry, the aposematic signals given by Müllerian mimics are (unconsciously) honest. Earlier terms, no longer in use, for Müllerian mimicry included "homotypy", "nondeceitful homotypy" and "arithmetic homotypy".

Evolution

Aposematism, camouflage, and mimicry

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