Batesian Mimicry Calculator

The Batesian Mimicry Calculator is an educational and research-oriented tool that estimates how effectively a harmless (Batesian) mimic is protected from predation by resembling a toxic or dangerous model species. The calculation follows classic frequency-dependent selection principles established in mimicry theory.

It combines elements from the mathematical models developed by Holling (1965), Brower & Brower (1970s), and especially the widely cited frequency-dependent predation risk equation popularized by Charlesworth & Charlesworth (1975) and later refined in many evolutionary ecology textbooks and papers (Ruxton et al. 2004, Speed & Turner 1999, Pfennig et al. 2001).

The core idea is simple yet powerful: the more common the toxic model is relative to the mimic, and the better the mimic resembles the model (low discrimination), the stronger the protection for the mimic. When mimics become too common, predators learn to ignore the warning signal → protection collapses.

Batesian mimicry is one of the most elegant and best-documented examples of evolutionary deception in nature. A palatable or harmless species gains protection by closely resembling a toxic, noxious, or dangerous model that predators have learned to avoid.

Classic textbook examples include:

• Viceroy butterfly mimicking the Monarch (Danaus plexippus)
• Many hoverflies mimicking stinging wasps and bees
• Coral snake mimicry rings (several harmless snake species mimicking venomous coral snakes)
• Harmless egg-eating snakes mimicking highly venomous species
• Numerous moth, beetle, and spider examples

The evolutionary stability of Batesian mimicry is strongly frequency-dependent — a fundamental insight first formalized mathematically in the 1970s. When mimics are rare, they receive almost free protection. When they become common, the warning signal loses credibility and the whole system can collapse (predators stop avoiding the pattern).

Understanding and quantifying this frequency-dependent dynamic is crucial in:

• Evolutionary ecology courses and textbooks
• Conservation biology (mimicry rings, coral snake patterns)
• Agroecology (mimicry-based pest control strategies, hoverfly predators)
• Science education and public understanding of natural selection

More resources and practical applications are available at Agri Care Hub.

Follow these steps to estimate protection in a Batesian mimicry system:

1. Model frequency (%) — how common is the toxic/dangerous model in the local predator environment?
2. Mimic frequency (%) — how common is the mimic compared to the total population of model + mimic individuals?
3. Predator learning rate — how quickly do predators learn to avoid the model after a bad experience? (higher = faster learning)
4. Discrimination ability — how easily can predators distinguish mimic from model? (0 = perfect mimic, 1 = very poor mimic)

Click “Calculate Mimic Protection & Risk” to see:

• Estimated % protection the mimic receives compared to a non-mimetic individual
• Relative predation risk compared to a situation with no mimicry
• Qualitative interpretation of mimicry quality and system stability

Most real-world values fall in these ranges:

• Model frequency: 5–40%
• Mimic frequency: 0.5–15% (usually much rarer than model)
• Learning rate: 0.4–0.85
• Discrimination: 0.05–0.40 for good mimics

Use the Batesian Mimicry Calculator when you want to:

• Understand frequency-dependent selection in the classroom
• Compare different mimic-model systems quantitatively
• Explore “how rare must a mimic stay?” questions
• Illustrate the breakdown of mimicry when mimics become too common
• Support student projects, theses, or citizen-science mimicry observations
• Visualize why perfect mimics are usually very rare in nature

It is especially useful in:

• Ecology & evolution university courses
• High-school advanced biology classes
• Science popularization blogs and websites
• Conservation discussions about mimicry rings
• Agroecological studies of hoverfly and other beneficial insect mimicry

The model implemented here is a simplified frequency-dependent protection function derived from classic theoretical papers on Batesian mimicry (most importantly Charlesworth & Charlesworth 1975, Speed 1993, Ruxton et al. 2004 “Avoiding Attack”).

Key assumptions:

• Predators learn from bad experiences with the model
• Protection is shared between model and mimic
• Protection decays when mimics become too common relative to models
• Discrimination error rate is constant

Important real-world factors NOT included in this simplified version:

• Spatial variation and predator generalization gradients
• Multiple predator species with different learning abilities
• Variation in model toxicity / aversiveness
• Multi-trait mimicry (color + pattern + behavior + odor)
• Density-dependent effects on predator attack rates
• Frequency-dependent changes in mimic morphology over generations

Despite these simplifications, the qualitative predictions match very well with field observations and experimental studies on hoverflies, coral snake mimics, butterfly mimicry rings, and many other systems.

For deeper reading we recommend:

• Ruxton, Sherratt & Speed (2004) — Avoiding Attack
• Pfennig et al. (2001) — Frequency-dependent Batesian mimicry
• Speed & Turner (1999) — Mathematical models of mimicry
• Wikipedia article on Batesian Mimicry