Additive Genetic Variance Calculator

The Additive Genetic Variance Calculator estimates additive genetic variance from heritability and phenotypic variance to inform breeding and selection decisions.

About the Additive Genetic Variance Calculator

This tool focuses on additive genetic variance, often written as Va. Additive effects are the predictable contributions of alleles that sum across loci. They are the part breeders and evolutionary biologists rely on to forecast response to selection.

The calculator accepts common inputs from quantitative genetics. You can enter phenotypic variance, regression slopes, or variance components from family or mixed models. It then returns Va, narrow-sense heritability (h2), and related checks. It is designed for traits measured on continuous scales, such as height, mass, yield, or timing.

The interface supports different study designs. You can work from parent–offspring regression, half-sib or sire models, or direct mixed-model variance estimates. Clear outputs and unit notes help you compare across datasets and populations.

How the Additive Genetic Variance Method Works

Quantitative traits vary for genetic and environmental reasons. Total phenotypic variance (Vp) can be partitioned into components. The additive part (Va) matters because it passes predictably from parents to offspring. We estimate Va using study designs that separate genetic signals from noise.

• Variance decomposition: Partition Vp into Va plus dominance (Vd), epistasis (Vi), environment (Ve), and other terms.
• Parent–offspring regression: The slope of offspring on mid-parent equals narrow-sense heritability (h2).
• Half-sib or sire model: Variance among offspring of different sires reflects one-quarter of Va in many designs.
• Mixed models (REML): Fit random additive genetic effects using a pedigree or genomic relationship matrix to estimate Va.
• Breeder’s equation: Use observed response to selection (R) and selection differential (S) to infer h2, then Va.

Each approach makes different assumptions. Regression methods assume linear inheritance and no assortative mating bias. Family designs assume random mating and known family structure. Mixed models assume the relationship matrix is correct and that residuals are well behaved. The calculator shows which assumptions apply to your choice.

Formulas for Additive Genetic Variance

The core idea is straightforward: narrow-sense heritability is the fraction of phenotypic variance due to additive effects. From that, we compute Va. Several designs give equivalent paths to these values.

• Total variance: Vp = Va + Vd + Vi + Ve + Vgxe (if modeled) + measurement error. Narrow-sense heritability: h2 = Va / Vp.
• From h2: Va = h2 × Vp.
• Parent–offspring regression: h2 = slope of offspring on mid-parent. If regressing on a single parent, h2 = 2 × slope.
• Half-sib (sire) design: Va = 4 × σ²(sire). This assumes dams are unique to sires and effects are balanced.
• Response to selection: h2 = R / S, where R is the shift in mean in offspring, and S is the selection differential in parents. Then Va = h2 × Vp in the base population.
• Mixed model (REML): Va is the estimated variance component for the random additive genetic effect. Then h2 = Va / (Va + Vr), where Vr is the residual plus any other modeled non-additive components included in Vp.

Standard errors can be propagated with the delta method. For example, SE(h2) depends on SE(Va) and SE(Vp). Mixed-model software often reports SEs directly. The calculator can accept either raw components or h2 to compute the rest.

Inputs, Assumptions & Parameters

Choose the workflow that matches your data. The calculator supports common inputs from family, regression, and mixed-model studies. You can enter summary statistics or component estimates.

• Phenotypic variance (Vp) of the trait, in the trait’s units squared (for example, cm², kg², days²).
• Either h2 or Va. If you provide one, the calculator will compute the other using Vp.
• Regression slope of offspring on mid-parent (or on a single parent), if using the regression method.
• Variance components from family designs, such as σ²(sire) for half-sib designs, or Va from REML.
• Sample sizes for families or pairs, to support plausibility checks and optional confidence intervals.

Values must make biological sense. h2 ranges from 0 to 1. Va cannot be negative; small negative estimates from sampling are treated as zero. Vp must be positive. If units differ across inputs, convert them before running the calculation to avoid nonsense results.

Using the Additive Genetic Variance Calculator: A Walkthrough

Here’s a concise overview before we dive into the key points:

1. Select your method: regression, half-sib/sire, mixed model, or direct h2 to Va conversion.
2. Enter the trait’s Vp and units. If you used standardized data, note that Vp may be 1.
3. Provide the required method-specific input (for example, slope, σ²(sire), or Va from REML).
4. Optional: add sample sizes for quality checks and confidence intervals if supported.
5. Review assumptions listed for your chosen method and confirm they match your design.
6. Click Calculate to view Va, h2, and any derived quantities.

These points provide quick orientation—use them alongside the full explanations in this page.

Example Scenarios

Plant height in a greenhouse: You measured 300 offspring and their parents. Phenotypic variance Vp is 64 cm². The regression slope of offspring height on mid-parent height is 0.40. Thus h2 = 0.40, and Va = 0.40 × 64 = 25.6 cm². Interpretation: about 40% of height variation is additive, and the expected response to selection is proportional to this value. What this means: selection on height should yield moderate, predictable gains in this population under similar conditions.

Dairy cattle milk yield: A sire model on 2,500 daughters across many herds estimates σ²(sire) = 1,500 kg². Phenotypic variance Vp is 12,000 kg² after standard herd-year-season adjustments. Under a half-sib design, Va = 4 × 1,500 = 6,000 kg². Narrow-sense heritability h2 = Va / Vp = 6,000 / 12,000 = 0.50. What this means: additive genetics explain half the yield variation, so selection on breeding values should be effective.

Limits of the Additive Genetic Variance Approach

Additive models are powerful but not complete. Real traits can show dominance, epistasis, genotype-by-environment interaction, and non-linear effects. These can bias estimates if not addressed in design or modeling.

• Non-additive effects: Ignoring dominance or epistasis can inflate or deflate Va.
• Environmental structure: Shared environments within families can mimic genetic signals.
• Population specificity: Va and h2 apply to a defined population and environment, not to all contexts.
• Measurement error: Noisy phenotypes increase Vp and lower h2 even if Va is unchanged.
• Assortative mating or inbreeding: These change covariance patterns and can bias regression methods.

Use study designs and mixed models that address these limits where possible. Report the population, environment, and model so others can interpret your estimates correctly.

Units & Conversions

Variance depends on units. If you measure height in centimeters instead of meters, Vp and Va change by the square of the conversion. Heritability h2 is unitless, but Va is not. We denote additive genetic variance as Va and phenotypic variance as Vp. Keep units consistent across inputs before calculating.

Apply conversions to the raw trait values first, then recompute Vp. Because variance scales with the square of the unit change, check any converted Va against the new Vp to keep h2 consistent. Record the final units with your results.

Tips If Results Look Off

Strange outputs usually come from unit mix-ups, small samples, or mismatched designs. Scan your inputs and assumptions before rerunning.

• Confirm that all trait values use the same unit across families and time points.
• Check that Vp > 0 and h2 is between 0 and 1.
• If using regression, verify that you used mid-parent for the slope, not a single parent.
• In sire models, confirm that dams are not shared across sires unless the model accounts for it.
• If Va is slightly negative from REML, treat it as zero and examine model specification.

When in doubt, run a quick sensitivity check. Adjust one input at a time to see how Va and h2 respond. This can reveal which component needs closer review.

FAQ about Additive Genetic Variance Calculator

What is the difference between additive and dominance variance?

Additive variance (Va) comes from allele effects that sum across loci. Dominance variance (Vd) comes from interactions between alleles at the same locus. Only Va transmits predictably from parents to offspring under random mating.

Is narrow-sense heritability the same as broad-sense heritability?

No. Narrow-sense heritability (h2) is Va divided by Vp. Broad-sense heritability (H2) is all genetic variance (Va + Vd + Vi) divided by Vp. They can differ a lot for traits with strong dominance or epistasis.

How large should my sample be to estimate Va?

Larger is better. Many studies target hundreds of individuals or families. Precision depends on design, trait variability, and how well you control environments. Mixed models with relationship matrices also benefit from bigger datasets.

Why did the calculator give a zero or negative Va?

Sampling noise or model misspecification can yield small negative estimates. Biologically, Va cannot be negative. The tool sets such values to zero and recommends checking inputs, design, and residual structure.

Glossary for Additive Genetic Variance

Additive genetic variance (Va)

The component of trait variance due to additive effects of alleles. It predicts response to selection and underlies narrow-sense heritability.

Phenotypic variance (Vp)

Total observable variance of a trait in a population. It includes genetic, environmental, and measurement sources of variation.

Narrow-sense heritability (h2)

The proportion of Vp explained by Va. It is unitless and ranges from 0 to 1 under standard scaling.

Dominance variance (Vd)

Variance arising from interactions between alleles at the same locus. It is not transmitted additively to offspring.

Epistatic variance (Vi)

Variance caused by interactions among alleles at different loci. It can be complex and context dependent.

Parent–offspring regression

A method that estimates h2 from the slope of offspring phenotype on parental phenotype. Using mid-parent gives the cleanest estimate.

Half-sib (sire) design

A family design where many dams are mated to each sire. Variance among sire families estimates a fraction of Va.

Genomic relationship matrix (GRM)

A matrix that captures realized genetic relatedness from markers. It supports mixed-model estimates of Va via REML.

Sources & Further Reading

Here’s a concise overview before we dive into the key points:

• Nature Education: Quantitative Traits—What Is Heritability?
• Visscher et al. 2008: Heritability in the genomics era (Nat Rev Genet, open access version)
• Wikipedia: Heritability (overview of h2, H2, and variance components)
• AnimalGenome.org: Heritability FAQ for animal breeding
• Evolution textbook online: Quantitative genetics and selection

These points provide quick orientation—use them alongside the full explanations in this page.