
Müllerian mimicry is a natural phenomenon in which two or more well-defended
species
A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...
, often foul-tasting and sharing common
predator
Predation is a biological interaction in which one organism, the predator, kills and eats another organism, its prey. It is one of a family of common List of feeding behaviours, feeding behaviours that includes parasitism and micropredation ...
s, have come to
mimic
In evolutionary biology, mimicry is an evolved resemblance between an organism and another object, often an organism of another species. Mimicry may evolve between different species, or between individuals of the same species. In the simples ...
each other's
honest warning signals, to their
mutual benefit. The benefit to Müllerian mimics is that predators only need one unpleasant encounter with one member of a set of Müllerian mimics, and thereafter avoid all similar coloration, whether or not it belongs to the same species as the initial encounter. It is named after the
German Brazilian
German Brazilians (German language, German: ''Deutschbrasilianer'', Hunsrik: ''Deitschbrasiliooner'', ) refers to Brazilians of full or partial Germans, German ancestry. German Brazilians live mostly in the country's South Region, Brazil, South ...
naturalist
Fritz Müller
Johann Friedrich Theodor Müller (; 31 March 182221 May 1897), better known as Fritz Müller (), and also as Müller-Desterro, was a German biologist who emigrated to southern Brazil, where he lived in and near the city of Blumenau, Santa Cata ...
, who first proposed the concept in 1878, supporting his theory with the first
mathematical model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
of
frequency-dependent selection
Frequency-dependent selection is an evolutionary process by which the fitness (biology), fitness of a phenotype or genotype depends on the phenotype or genotype composition of a given population.
* In positive frequency-dependent selection, the fit ...
, one of the first such models anywhere in biology.
Müllerian mimicry was first identified in tropical
butterflies
Butterflies are winged insects from the lepidopteran superfamily Papilionoidea, characterized by large, often brightly coloured wings that often fold together when at rest, and a conspicuous, fluttering flight. The oldest butterfly fossi ...
that shared colourful wing patterns, but it is found in many groups of insects such as
bumblebee
A bumblebee (or bumble bee, bumble-bee, or humble-bee) is any of over 250 species in the genus ''Bombus'', part of Apidae, one of the bee families. This genus is the only Extant taxon, extant group in the tribe Bombini, though a few extinct r ...
s, and other animals such as
poison frogs and
coral snake
Coral snakes are a large group of elapid snakes that can be divided into two distinct groups, the Old World coral snakes and New World coral snakes. There are 27 species of Old World coral snakes, in three genera ('' Calliophis'', '' Hemibungar ...
s. 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
Convergence may refer to:
Arts and media Literature
*''Convergence'' (book series), edited by Ruth Nanda Anshen
*Convergence (comics), "Convergence" (comics), two separate story lines published by DC Comics:
**A four-part crossover storyline that ...
), 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 becomes, by degrees, the better-known bluffing of
Batesian mimicry
Batesian mimicry is a form of mimicry where a harmless species has evolved to imitate the warning signals of a harmful species directed at a predator of them both. It is named after the English naturalist Henry Walter Bates, who worked on butt ...
.
History
Origins

Müllerian mimicry was proposed by the German Brazilian
zoologist
Zoology ( , ) is the scientific study of animals. Its studies include the structure, embryology, classification, habits, and distribution of all animals, both living and extinct, and how they interact with their ecosystems. Zoology is one ...
and
naturalist
Natural history is a domain of inquiry involving organisms, including animals, fungi, and plants, in their natural environment, leaning more towards observational than experimental methods of study. A person who studies natural history is cal ...
Fritz Müller
Johann Friedrich Theodor Müller (; 31 March 182221 May 1897), better known as Fritz Müller (), and also as Müller-Desterro, was a German biologist who emigrated to southern Brazil, where he lived in and near the city of Blumenau, Santa Cata ...
(1821–1897). An early proponent of
evolution
Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...
, Müller offered the first explanation for resemblance between certain
butterflies
Butterflies are winged insects from the lepidopteran superfamily Papilionoidea, characterized by large, often brightly coloured wings that often fold together when at rest, and a conspicuous, fluttering flight. The oldest butterfly fossi ...
that had puzzled the English naturalist
Henry Walter Bates
Henry Walter Bates (8 February 1825 – 16 February 1892) was an English natural history, naturalist and explorer who gave the first scientific account of mimicry in animals. He was most famous for his expedition to the Tropical rainforest ...
in 1862. Bates, like Müller, spent a significant part of his life in
Brazil
Brazil, officially the Federative Republic of Brazil, is the largest country in South America. It is the world's List of countries and dependencies by area, fifth-largest country by area and the List of countries and dependencies by population ...
, 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
Sexual selection is a mechanism of evolution in which members of one sex mate choice, choose mates of the other sex to mating, mate with (intersexual selection), and compete with members of the same sex for access to members of the opposite sex ...
, 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
Sexual dimorphism is the condition where sexes of the same species exhibit different Morphology (biology), morphological characteristics, including characteristics not directly involved in reproduction. The condition occurs in most dioecy, di ...
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
Evolutionary ecology lies at the intersection of ecology and evolutionary biology. It approaches the study of ecology in a way that explicitly considers the evolutionary histories of species and the interactions between them. Conversely, it can ...
, 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
individuals,
and species 2 loses
individuals.
Species 1 therefore gains
and species 2 similarly gains
in absolute numbers of individuals not killed.
The proportional gain compared to the total population of species 1 is
and similarly for species 2
, giving the per head fitness gain of the mimicry when the predators have been fully educated.
Hence, Müller concluded, the proportion g1:g2 was
, which equals , 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
Deception is the act of convincing of one or many recipients of untrue information. The person creating the deception knows it to be false while the receiver of the information does not. It is often done for personal gain or advantage.
Tort of ...
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
Müllerian mimicry relies on aposematism
Aposematism is the Advertising in biology, advertising by an animal, whether terrestrial or marine, to potential predation, predators that it is not worth attacking or eating. This unprofitability may consist of any defenses which make the pr ...
, or warning signals. Dangerous organisms with these honest signals are avoided by predators, which quickly learn after a bad experience not to pursue the same unprofitable prey again. Learning
Learning is the process of acquiring new understanding, knowledge, behaviors, skills, value (personal and cultural), values, Attitude (psychology), attitudes, and preferences. The ability to learn is possessed by humans, non-human animals, and ...
is not actually necessary for animals which instinct
Instinct is the inherent inclination of a living organism towards a particular complex behaviour, containing innate (inborn) elements. The simplest example of an instinctive behaviour is a fixed action pattern (FAP), in which a very short to me ...
ively avoid certain prey; however, learning from experience is more common. The underlying concept with predators that learn is that the warning signal makes the harmful organism easier to remember than if it remained as well camouflage
Camouflage is the use of any combination of materials, coloration, or illumination for concealment, either by making animals or objects hard to see, or by disguising them as something else. Examples include the leopard's spotted coat, the b ...
d as possible. Aposematism and camouflage are in this way opposing concepts, but this does not mean they are mutually exclusive. Many animals remain inconspicuous until threatened, then suddenly employ warning signals, such as startling eyespots, bright colours on their undersides or loud vocalizations. In this way, they enjoy the best of both strategies. These strategies may also be employed differentially throughout development. For instance, large white butterflies are aposematic as larva
A larva (; : larvae ) is a distinct juvenile form many animals undergo before metamorphosis into their next life stage. Animals with indirect development such as insects, some arachnids, amphibians, or cnidarians typically have a larval phase ...
e, but are Müllerian mimics once they emerge from development as adult
An adult is an animal that has reached full growth. The biological definition of the word means an animal reaching sexual maturity and thus capable of reproduction. In the human context, the term ''adult'' has meanings associated with social an ...
butterflies.
Selective advantage
Many different prey of the same predator could all employ their own warning signals, but this would make no sense for any party. If they could all agree on a common warning signal, the predator would have fewer detrimental experiences, and the prey would lose fewer individuals educating it. No such conference needs to take place, as a prey species that just so happens to look a little like an unprofitable species will be safer than its conspecifics, enabling natural selection
Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the Heredity, heritable traits characteristic of a population over generation ...
to drive the prey species toward a single warning language. This can lead to the evolution
Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...
of both Batesian and Müllerian mimicry, depending on whether the mimic is itself unprofitable to its predators, or just a free-rider. Multiple species can join the protective cooperative, expanding the mimicry ring. Müller thus provided an explanation for Bates' paradox; the mimicry was not, in his view, a case of exploitation by one species, but rather a mutualistic arrangement, though his mathematical model indicated a pronounced asymmetry.[
]
Relationship to Batesian mimicry
The Müllerian strategy is usually contrasted with Batesian mimicry
Batesian mimicry is a form of mimicry where a harmless species has evolved to imitate the warning signals of a harmful species directed at a predator of them both. It is named after the English naturalist Henry Walter Bates, who worked on butt ...
, in which one harmless species adopts the appearance of an unprofitable species to gain the advantage of predators' avoidance; Batesian mimicry is thus in a sense parasitic
Parasitism is a close relationship between species, where one organism, the parasite, lives (at least some of the time) on or inside another organism, the host, causing it some harm, and is adapted structurally to this way of life. The ent ...
on the model's defences, whereas Müllerian is to mutual benefit. However, because comimics may have differing degrees of protection, the distinction between Müllerian and Batesian mimicry is not absolute, and there can be said to be a spectrum between the two forms.
Viceroy butterflies and monarch
A monarch () is a head of stateWebster's II New College Dictionary. "Monarch". Houghton Mifflin. Boston. 2001. p. 707. Life tenure, for life or until abdication, and therefore the head of state of a monarchy. A monarch may exercise the highest ...
s (types of admiral butterfly) are both poisonous Müllerian mimics, though they were long thought to be Batesian. Mitochondrial DNA
Mitochondrial DNA (mtDNA and mDNA) is the DNA located in the mitochondrion, mitochondria organelles in a eukaryotic cell that converts chemical energy from food into adenosine triphosphate (ATP). Mitochondrial DNA is a small portion of the D ...
analysis of admiral butterflies shows that the viceroy is the basal lineage of two western sister species in North America. The variation in wing patterns appears to have preceded the evolution of toxicity, while other species remain non-toxic, refuting the hypothesis that the toxicity of these butterflies is a conserved characteristic from a common ancestor.
Non-visual mimicry
Müllerian mimicry need not involve visual
The visual system is the physiological basis of visual perception (the ability to detect and process light). The system detects, transduces and interprets information concerning light within the visible range to construct an image and buil ...
mimicry; it may employ any of the sense
A sense is a biological system used by an organism for sensation, the process of gathering information about the surroundings through the detection of Stimulus (physiology), stimuli. Although, in some cultures, five human senses were traditio ...
s. For example, many snakes share the same auditory warning signals, forming an auditory Müllerian mimicry ring. More than one signal may be shared: snakes can make use of both auditory signals and warning coloration.
Negative frequency-dependent selection
There is a negative correlation between the frequency of mimics and the "survivability" of both species involved. This implies that it is reproductively beneficial for both species if the models outnumber the mimics; this increases the negative interactions between predator and prey.[
]
Genetics
Some insight into the evolution of mimetic color mimicry in Lepidoptera in particular can be seen through the study of the Optix gene. The Optix gene is responsible for the ''Heliconius
''Heliconius'' comprises a colorful and widespread genus of brush-footed butterflies commonly known as the longwings or heliconians. This genus is distributed throughout the tropical and subtropical regions of the New World, from South America ...
'' butterflies' signature red wing patterns that help it signal to predators that it is toxic. By sharing this coloration with other poisonous red winged butterflies the predator may have pursued previously, the Heliconius butterfly increases its chance of survival through association. By mapping the genome of many related species of ''Heliconius'' butterflies "show that the cis-regulatory evolution of a single transcription factor can repeatedly drive the convergent evolution of complex color patterns in distantly related species…". This suggests that the evolution of a non-coding piece of DNA that regulates the transcription of nearby genes can be the reason behind similar phenotypic
In genetics, the phenotype () is the set of observable characteristics or traits of an organism. The term covers the organism's morphology (physical form and structure), its developmental processes, its biochemical and physiological propert ...
coloration between distant species, making it hard to determine if the trait is homologous or simply the result of convergent evolution
Convergent evolution is the independent evolution of similar features in species of different periods or epochs in time. Convergent evolution creates analogous structures that have similar form or function but were not present in the last comm ...
.
Two step evolution
One proposed mechanism for Müllerian mimicry is the "two step hypothesis". This states that a large mutational leap initially establishes an approximate resemblance of the mimic to the model, both species already being aposematic. In a second step, smaller changes establish a closer resemblance. This is only likely to work, however, when a trait is governed by a single gene, and many coloration patterns are certainly controlled by multiple genes.
Advergence versus mutualism
The mimic poison frog '' Ranitomeya (Dendrobates) imitator'' is polymorphic, with a striped morph that imitates the black and yellow striped morph of '' Ranitomeya variabilis'', a spotted morph that imitates the largely blue-green highland spotted morph also of ''R. variabilis'', and a banded morph that imitates the red and black banded '' Ranitomeya summersi''.[
''R. imitator'' has thus apparently evolved in separate populations to resemble different targets, i.e. it has changed to resemble (adverged on) those target species, rather than both ''R. imitator'' and the other species mutually converging in the way that Müller supposed for tropical butterflies.
Such advergence may be common. The mechanism was proposed by the entomologist F. A. Dixey in 1909 and has remained controversial; the evolutionary biologist James Mallet, reviewing the situation in 2001, suggested that in Müllerian mimicry, advergence may be more common than convergence. In advergent evolution, the mimicking species responds to predation by coming to resemble the model more and more closely. Any initial benefit is thus to the mimic, and there is no implied mutualism, as there would be with Müller's original convergence theory. However, once model and mimic have become closely similar, some degree of mutual protection becomes likely.] This theory would predict that all mimicking species in an area should converge on a single pattern of coloration. This does not appear to happen in nature, however, as ''Heliconius'' butterflies form multiple Müllerian mimicry rings in a single geographical area. The finding implies that additional evolutionary forces are probably at work.
Mimicry complexes
bumblebee
A bumblebee (or bumble bee, bumble-bee, or humble-bee) is any of over 250 species in the genus ''Bombus'', part of Apidae, one of the bee families. This genus is the only Extant taxon, extant group in the tribe Bombini, though a few extinct r ...
s are Müllerian mimics, with effective stings and similar warning coloration
Aposematism is the Advertising in biology, advertising by an animal, whether terrestrial or marine, to potential predation, predators that it is not worth attacking or eating. This unprofitability may consist of any defenses which make the pr ...
">
File:Bombus terrestris (Buff-tailed bumblebee) - queen - Flickr - S. Rae.jpg, '' Bombus terrestris''
File:Bombus lucorum - Centaurea scabiosa - Keila.JPG, '' Bombus lucorum''
File:Bombus hortorum queen - Echium vulgare - Keila.jpg, '' Bombus hortorum''
File:Tree bumblebee (RLs) (34742598795).jpg, ''Bombus hypnorum
The tree bumblebee or new garden bumblebee (''Bombus hypnorum'') is a species of bumblebee common nthe European continent and parts of Asia. Since the start of the twenty-first century, it has spread to Great Britain and Ireland. These bum ...
''
Müllerian mimicry often occurs in clusters of multiple species called rings. Müllerian mimicry is not limited to butterflies, where rings are common; mimicry rings occur among
s. Bumblebees ''
'' are all aposematically coloured in combinations, often stripes, of black, white, yellow, and red; and all their females have stings, so they are certainly unprofitable to predators. There is evidence that several species of bumblebees in each of several areas of the world, namely the American West and East coasts, Western Europe, and Kashmir, have converged or adverged on mutually mimetic coloration patterns. Each of these areas has one to four mimicry rings, with patterns different from those in other areas.