The History of Müllerian Mimicry

Attempts to explain what is now known as Müllerian mimicry were first made 135 years ago by German biologist Johann Friedrich Theodor (Fritz) Müller. Müller (1879) provided an evolutionary explanation to describe the phenomenon where two unpalatable species exhibit a similar appearance to each other. He was also the first person to present a “formal mathematical model to support an evolutionary hypothesis” (Sherratt, 2008, p. 682).

Müller (1879) hypothesised that if predators were required to learn from experience which prey items were distasteful, that two similarly distasteful prey items would benefit if they displayed similar appearances because this would reduce the number of individuals that die during the process where inexperienced predators ‘learn’ which prey items are distasteful. More specifically, Müller (1897) was saying a predator would only eat a given number of what they thought were a single distasteful species before they learned that they were distasteful regardless of whether it was in fact a single species or two species that mimicked each other (Sherratt, 2008).

Müller's formula explaining how it is beneficial for two poisonous species to have similar appearances (Source: Transactions of the Entomological Society of London. Image: Müller)

Using his proposed formula (pictured right) Müller (1879) put forward an explanation using two theoretical species in a community (Species A and Species B) and a theoretical number of individuals of a particular appearance must be eaten in the population before the predator species learns not to eat them. To put it simply, let’s pretend we are an animal who feeds on butterflies. When you are born you have absolutely no knowledge of what butterflies are good or bad tasting; all you know is that you have to eat butterflies. You eat a few butterflies but then you catch one that tastes revolting. You keep feeding, possibly thinking that it was just a dodgy butterfly. But then it happens again! This is another disgusting tasting butterfly that looks suspiciously similar to the last one that tasted bad.... For arguments sake, let’s say it takes you 5 attempts at eating that type of butterfly before you decide you will never eat a butterfly that looks like that again.

If there are two completely different species of bad tasting butterflies and one (Species A) is pretty small (eg. 2000 individuals) and the other (Species B) is relatively large (eg 10,000 individuals), 1 predator taking the same number of individuals out of both populations will make a larger difference in the smaller population than the larger one. For Species A, if we take into account for the entire population of predators and assume that there are 240 juveniles in the population each taking 5 individuals from a species, that is 1200 members of butterfly Species A that get eaten in one season. That equates to 60% of the population! If we compare that to Species B with 10,000 individuals, the predators still only take 1200 butterflies but it only equates to about 12% of the total population (See Figure 1).

Figure 1. Proportions of individuals eaten from two unpalatable
species that look different (Image: Summers)

Obviously, the larger population has the advantage here, but what if these two species looked similar? If a predator cannot tell the difference between them visually, they only need to remember one type of markings. If they eat one from Species A they will remember it and when they eat one from Species B they will see, what looks like to them, the same animal and avoid it also. This way, one predator only needs to eat five individuals from Species A or Species B and not five individuals from Species A and Species B. That equates to 1200 individuals from Species A or Species B and not 2,400 individuals from Species A and Species B combined.


Müller (1879) goes on to explain that when the predator takes individuals from species A and B thinking they are the same species, that the number of individuals eaten is dependent upon the number of individuals in each species and therefore the proportion taken from each species is e qual. In other words, the predator species will eat 200 individuals from Species A and 1,000 individuals B; 10% of each species’ initial population 

Figure 2. Proportions of individuals eaten from two unpalatable
species that look the same (Image: Summers)

References
Müller, F., 1879. Ituna and Thyridia; a remarkable case of mimicry in butterflies. Transactions of the Entomological Society  of London, pp. xx-xxix.

Sherratt, T. N., 2008. The Evolution of Müllerian Mimicry. Naturwissenschaften, 95(8), pp. 681-695.

Summers, K. M., 2014. Figure 1. Proportions of individuals eaten from two unpalatable species that look different photograph, viewed 31 March 2014.

Summers, K. M., 2014. Figure 2. Proportions of individuals eaten from two unpalatable species that look the same, photograph, viewed 31 March 2014.