Measured Games · Paper 19 of 07 · Evolutionary ecology

Batesian mimicry

After H. W. Bates (1862); frequency dependence tested in the field by D. W. Pfennig, W. R. Harcombe and K. S. Pfennig (2001)

Abstract

A palatable species that resembles a defended one is protected only while predators keep meeting the real thing. As mimics become common relative to their model, predators encounter more edible copies, learn to attack the pattern, and the protection erodes. The frequency dependence runs through a third party's learning rather than through competition between the mimics themselves, and it predicts that mimicry should fail precisely where the model is scarce.

KeywordsBatesian mimicry · negative frequency dependence · predator learning · aposematism · field experiment

1Setup

Setup

Some animals advertise that they are dangerous with a conspicuous pattern, and predators learn to leave the pattern alone. That creates an opening. A harmless species that comes to resemble the dangerous one inherits the protection without paying for the defence.

The protection is not free, though, and not stable. It is borrowed from the predator's experience, and every harmless copy a predator eats teaches it that the pattern is worth attacking. The more successful the deception becomes, the less it works.

2The model

The model

# a defended model at frequency m, a palatable mimic at frequency b # predators cannot tell them apart and learn from what they eat P(an encounter with the pattern is edible) = b / (m + b) # a predator's willingness to attack tracks that proportion q → b / (m + b) tempered by how unpleasant the model is # the mimic's protection is whatever the predator still withholds mimic fitness ∝ 1 - q rising b lowers mimic fitness: negative frequency dependence # and the protection collapses entirely where the model is absent m → 0 → q → 1

The frequency dependence here does not run between the mimics. They do not compete with one another for anything. It runs through a third party's memory, which is what separates this from every other frequency-dependent model in the collection.

Figure 1Predator learning under mixed model and mimic populations

This figure needs JavaScript. The panels below are live simulations rather than images, so with scripting turned off they stay empty and the controls do nothing. Everything the figure demonstrates is also stated in the surrounding text: the model is given in full in section 2 and the result in section 3.

Predator's willingness to attack the pattern, as it learns

Mimic survival against the mimic-to-model ratio · hover to read any ratio

Encounters · filled markers were attacked

Attack probability Predicted equilibrium Mimic survival

Charts are focusable. With a chart focused, use the left and right arrow keys to read values along the horizontal axis.

Defended models per 100 prey

Mimics per 100 prey

How unpleasant the model is

Predator memory

Mimic to model ratio—

Attack probability—

Predicted—

Mimic survival—

Model survival—

Encounters0

Figure 1. A predator meets prey one at a time, cannot distinguish model from mimic, and updates its willingness to attack from what it swallows, so the attack rate is learned rather than set. Push the mimic count up and watch protection erode without anything about the mimic changing. Model absent is the field experiment: with no defended species present the pattern stops meaning anything and attacks go to certainty, which is what clay replicas outside the model's range actually experience.

3Results

Results

Bates (1862) described the resemblance and the puzzle from Amazonian butterflies. The modern account adds the frequency dependence: because protection comes from the predator's reluctance, and reluctance is maintained by unpleasant encounters, the mimic's advantage is a function of how often the predator is fooled relative to how often it is punished.

Two predictions follow, and they are the ones worth testing. Mimicry should be less effective where mimics are common relative to models, which bounds how abundant a mimic population can become. And mimicry should fail outright where the model is absent, because there is nothing sustaining the predator's aversion. The second is sharper, because it predicts a place rather than a proportion.

Unpalatability matters as well as abundance. A very unpleasant model buys the mimic more room, since a single bad experience does more work in the predator's memory than several good ones undo.

4Evidence

Evidence

The strongest field test uses the coral snake system. Pfennig, Harcombe and Pfennig (2001) put out plasticine replicas in natural habitat and recorded attacks by free-ranging predators. Ringed replicas matched the local mimic, scarlet kingsnakes where eastern coral snakes occur and Sonoran mountain kingsnakes where western coral snakes occur, while striped and plain brown replicas served as controls.

The contrast is stark. Where the venomous model was present, about 8 per cent of ringed replicas were attacked. Where it was absent, about 65 per cent were. The design is unusually clean because the prey are identical objects differing only in pattern, so predator behaviour is the only thing that varies, and the result is the prediction the theory most needs: protection exists only where something sustains it.

Harper and Pfennig (2007) then asked how the precision of the copy varies across the model's range, and found something the naive version of the theory does not predict. Mimicry is most precise where models are rare but still present, not where they are abundant. The explanation offered is that predators facing a rare but deadly model cannot afford mistakes and so attack anything imperfect, which sharpens selection on the mimic; where models are common, predators avoid the pattern generally and sloppy copies get away with it.

The older laboratory tradition, beginning with Brower's experiments feeding birds palatable and unpalatable butterflies, established the learning mechanism and the frequency dependence under controlled conditions.

5Limitations

Limitations

The textbook example turned out to be wrong, and it is worth knowing. The viceroy butterfly was for decades presented as the classic Batesian mimic of the monarch, until Ritland and Brower showed the viceroy is itself unpalatable, making the relationship Müllerian rather than Batesian. Two defended species converging is a different game with different dynamics: there the resemblance helps both parties and the frequency dependence runs the other way.

The model also treats predators as a single learner with one memory. Real communities contain many predator species with different experience, different sampling rates and different tolerance for the toxin, and mimicry that fails against one may work against another.

The simple version also assumes mimics and models meet the same predators in the same places at the same time. Where they are separated in season or microhabitat, the arithmetic of relative frequency stops applying even when both appear in the same census.

Coral snake mimicry in particular was contested for a long time, because the observed distribution and abundance of the snakes did not sit comfortably with what mimicry theory predicted. A phylogenetic analysis across New World snakes has since given strong support to the mimicry account, while also finding that shifts between mimetic and cryptic colouration happen in both directions and unexpectedly often. That challenges the picture of mimicry as a stable endpoint, and the model on this page, which has no way for a mimic to stop being one, does not represent it.

References

Bates, H. W. (1862). Contributions to an insect fauna of the Amazon valley. Lepidoptera: Heliconidae. Transactions of the Linnean Society of London, 23(3), 495–566. https://doi.org/10.1111/j.1096-3642.1860.tb00146.x
Brower, J. V. Z. (1958). Experimental studies of mimicry in some North American butterflies: Part I. The monarch, Danaus plexippus, and viceroy, Limenitis archippus archippus. Evolution, 12(1), 32–47. https://doi.org/10.2307/2405902
Harper, G. R., & Pfennig, D. W. (2007). Mimicry on the edge: Why do mimics vary in resemblance to their model in different parts of their geographical range? Proceedings of the Royal Society B: Biological Sciences, 274(1621), 1955–1961. https://doi.org/10.1098/rspb.2007.0558
Pfennig, D. W., Harcombe, W. R., & Pfennig, K. S. (2001). Frequency-dependent Batesian mimicry. Nature, 410(6826), 323. https://doi.org/10.1038/35066628
Ritland, D. B., & Brower, L. P. (1991). The viceroy butterfly is not a Batesian mimic. Nature, 350(6318), 497–498. https://doi.org/10.1038/350497a0
Davis Rabosky, A. R., Cox, C. L., Rabosky, D. L., Title, P. O., Holmes, I. A., Feldman, A., & McGuire, J. A. (2016). Coral snakes predict the evolution of mimicry across New World snakes. Nature Communications, 7, Article 11484. https://doi.org/10.1038/ncomms11484
Ruxton, G. D., Allen, W. L., Sherratt, T. N., & Speed, M. P. (2018). Avoiding attack: The evolutionary ecology of crypsis, aposematism, and mimicry (2nd ed.). Oxford University Press.

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