Müllerian Mimicry Calculator

The Müllerian Mimicry Calculator estimates the mutual survival benefit that toxic or noxious species gain when they share a similar warning (aposematic) pattern. It follows the frequency-dependent selection logic first described by Fritz Müller (1878–1879) and later formalized in modern evolutionary ecology (Fisher 1930, Turner 1984, Mallet 1999, Ruxton et al. 2004 “Avoiding Attack”).

Key principle: the more defended species share the same signal, the fewer predator attacks are needed to educate the predator population → each individual pays a lower “education cost” → average survival increases.

Müllerian mimicry is a mutualistic form of aposematism. Unlike Batesian mimicry (harmless → harmful), all participants are defended, so everyone benefits from convergence on the same warning signal.

Well-known real-world examples include:

• Heliconius butterfly mimicry rings (tiger / rayed patterns)
• Dendrobatid poison frogs (various bright rings)
• Social Hymenoptera (black-yellow wasps, bumblebees, some stingless bees)
• Many arctiid and ctenuchine moths
• True coral snake mimicry rings (some corals + corals)

Quantifying the strength of this mutual benefit helps explain:

• why certain warning patterns spread across many species
• stability of mimicry rings
• minimum number of species needed for strong reinforcement
• evolution of very widespread signals (black-yellow, red-black, etc.)

Learn more → Agri Care Hub | Müllerian Mimicry

1. Number of species sharing the warning pattern (2–12)
2. Relative frequency of your focal species within the guild (%)
3. Baseline mortality if the species had the signal alone (M₀)
4. Predator learning efficiency per aversive encounter (α)
5. Discrimination/generalization error rate between co-mimics (ε)

Click “Calculate Müllerian Benefit” to see:

• Mutual protection multiplier
• Reduced per-capita mortality
• Percent mortality reduction
• Qualitative strength of warning signal reinforcement

The calculator uses a simplified phenomenological model inspired by Müller (1879), Fisher (1930), Turner (1984), Mallet (1999), and especially the synthesis in Ruxton, Sherratt & Speed (2004) Avoiding Attack.

Approximate core relationship:

Protection ≈ (n ^ 0.65) × (f ^ -0.4) × (1 – ε) × (α / 0.2)

→ Mortality with mimicry = M₀ / (1 + scaled protection)

Limitations / simplifications:

• No spatial structure or predator memory decay
• Assumes constant learning rate and error rate
• No variation in toxicity among co-mimics
• No density-dependent attack rates
• No multi-predator or multi-trait effects

Despite these simplifications, the model reproduces the most important qualitative patterns observed in field studies, lab experiments, and theoretical work on Müllerian mimicry rings.