Epistasis and Genetic Interaction Calculator

Calculate epistasis coefficients and genotype-phenotype map statistics for genetic interactions.

Fitness of wild-type (wt) (relative fitness)

Fitness of single mutant A (fA)

Fitness of single mutant B (fB)

Fitness of double mutant AB (fAB)

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What Epistasis Measures

Epistasis is the departure of a double mutant's fitness from what the two single mutants predict independently. Under a multiplicative model, independent effects multiply.

ε = f_AB − (f_A × f_B)

ε	Type	Interpretation
< 0	Negative (synergistic)	Double mutant worse than predicted
≈ 0	None	Genes act independently
> 0	Positive (buffering)	Double mutant better than predicted

The sign carries mechanistic information. Positive epistasis usually means the genes act in the same pathway — once one step is broken, breaking a second in the same chain adds little. Negative epistasis suggests parallel pathways, each buffering the loss of the other until both fail.

Synthetic Lethality and Why It Matters Clinically

The extreme case of negative epistasis is synthetic lethality: neither mutation alone is lethal, but together they are. This is the basis of an entire class of cancer therapy.

Tumour genotype	Drug target	Outcome
BRCA1/2 mutant	PARP inhibitor	Tumour cells die
BRCA wild-type	PARP inhibitor	Cells survive — normal tissue spared

BRCA-deficient cells have lost homologous recombination repair. Inhibiting PARP removes the alternative single-strand break repair route, and the combination is lethal. Normal cells retain BRCA function and survive — which is what gives the therapy its selectivity.

Why Model Choice Changes the Answer

Whether an interaction counts as epistatic depends on the null model used. The multiplicative model above is standard for fitness, but additive and minimum models are also used and can classify the same data differently.

This is not a technicality — published epistasis maps from different groups have disagreed substantially for this reason. The model should always be stated alongside the results.

Worked Examples

Example 1: Negative epistasis: fAB=0.5, expected=0.72

ε=-0.22 (observed < expected)

Result: Synthetic lethality — double mutant worse than expected

Cancer drug combinations: synthetic lethality (PARP + BRCA)

Example 2: Positive epistasis: fAB=0.85, expected=0.72

ε=+0.13 — buffering

Result: Pathways redundant — second mutation compensates

Genetic robustness / canalization

Example 3: Why BRCA plus PARP is selective

BRCA-mutant tumour, PARP inhibitor

Result: Tumour dies, normal tissue survives

Tumour cells have lost homologous recombination; blocking PARP removes the backup repair route. Normal cells retain BRCA and tolerate the drug.

Example 4: Positive epistasis in a shared pathway

Two mutations in the same linear pathway

Result: ε > 0

Once the first step is broken the pathway is already non-functional, so breaking a second step downstream adds little further cost.

Common Mistakes

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Assuming the sign alone identifies pathway relationships

Positive epistasis often indicates a shared pathway and negative suggests parallel ones, but exceptions are common. Genetic interaction is evidence, not proof.

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Using an additive model for fitness data

Fitness effects generally combine multiplicatively. An additive null classifies many independent gene pairs as epistatic.

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Treating synthetic lethality as an absolute

Most synthetic lethal interactions are quantitative rather than binary, and depend heavily on genetic background and environment.

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Not stating the null model

Multiplicative, additive and minimum models classify the same data differently. Published interaction maps have disagreed for exactly this reason.

Frequently Asked Questions

Synthetic lethality applications?

Exploit negative epistasis for cancer therapy. BRCA1/2 mutant tumors: sensitive to PARP inhibitors (normal cells: two repair pathways, cancer: only one). Essentiality screen: KO both genes → cell death. Systematic genetic interaction maps (E-MAP, SGA) reveal pathway architecture.

Epistasis in evolution?

Negative epistasis: mutation accumulation more lethal → purging. Positive epistasis: more tolerant of multiple mutations → mutationally robust. Sign epistasis: double mutant better than either single → bypasses fitness valleys. Important for evolvability and speciation (Bateson-Dobzhansky-Muller incompatibilities).

What does negative epistasis mean?

The double mutant is less fit than the product of the single mutants predicts. It often indicates parallel pathways that buffer each other.

What is synthetic lethality?

An extreme negative interaction where neither mutation alone is lethal but the combination is. PARP inhibitors in BRCA-mutant cancer exploit this.

Why does positive epistasis suggest a shared pathway?

Because if one step is already broken, breaking another in the same chain adds little further damage. The second mutation has less effect than independence predicts.

Does the null model matter?

Substantially. Multiplicative, additive and minimum models classify the same interactions differently, so the model must be stated with any epistasis result.