Calculate Heritability from SAS Variance Components
Estimate broad-sense or narrow-sense heritability using variance components commonly exported from SAS PROC MIXED, PROC GLM, or PROC VARCOMP. This calculator supports plot-basis, entry-mean, and additive models.
How to calculate heritability with SAS variance components
Researchers, plant breeders, animal breeders, and quantitative geneticists often use SAS to estimate variance components before translating those values into heritability. If you are searching for a practical way to calculate heritability SAS results, the key is understanding that SAS usually gives you the building blocks rather than the final heritability value itself. In most workflows, PROC MIXED, PROC GLM, or PROC VARCOMP estimates random-effect variance components such as genotype variance, genotype x environment variance, and residual error variance. Heritability is then computed from those components using a formula matched to the study design.
At its core, heritability measures the proportion of observable phenotypic variation that can be attributed to genetic variation within a defined population and environment. It does not describe how genetically determined an individual is, and it does not remain fixed across populations, locations, or years. Instead, it is a population-level statistic. That is exactly why a well-specified SAS model matters: if the model captures the design correctly, the resulting variance components are much more useful for reliable heritability estimates.
What SAS outputs are typically used?
When analysts say they want to calculate heritability from SAS, they usually mean one of three situations:
- Broad-sense heritability on a plot basis for early-stage screening or simple trials.
- Broad-sense heritability on an entry-mean basis for replicated multi-environment trials, especially in plant breeding.
- Narrow-sense heritability when additive genetic variance is available from pedigree, mating design, genomic relationship, or animal model analyses.
In SAS output, these are often represented as:
- σ²g: genetic or genotype variance
- σ²ge: genotype x environment interaction variance
- σ²e: residual or error variance
- Va: additive genetic variance
- Vp: total phenotypic variance
The three most common heritability formulas
Use the formula that matches the level at which selection or inference is being made.
- Broad-sense heritability on a plot basis
H² = σ²g / (σ²g + σ²ge + σ²e) - Broad-sense heritability on an entry-mean basis
H² = σ²g / (σ²g + σ²ge/e + σ²e/(re)) - Narrow-sense heritability
h² = Va / Vp
The entry-mean basis formula is especially common in multi-location and multi-year breeding trials because it discounts environmental noise by the number of environments and replications. As those counts increase, residual noise contributes less to the denominator, often increasing the estimated heritability of line means.
Step-by-step example using SAS-style variance components
Assume SAS returns the following random-effect estimates for a replicated trial:
- Genotype variance, σ²g = 12.4
- Genotype x environment variance, σ²ge = 6.1
- Residual variance, σ²e = 18.7
- Environments, e = 3
- Replications, r = 4
For broad-sense heritability on an entry-mean basis:
H² = 12.4 / (12.4 + 6.1/3 + 18.7/(4 x 3))
This becomes:
H² = 12.4 / (12.4 + 2.033 + 1.558) = 12.4 / 15.991 = 0.775
So the estimated broad-sense heritability is approximately 0.78, which is generally interpreted as a high heritability estimate for the mean performance of entries under this design. That does not mean the trait is immune to environmental effects. It means that, after averaging over environments and replications, genetic differences explain a relatively large share of the remaining phenotypic variation among entries.
How to interpret low, moderate, and high heritability
Heritability is context dependent, but many applied programs use rough interpretation bands to support breeding or research decisions:
- Low heritability: below 0.30. Environmental noise and non-additive effects may dominate, so direct phenotypic selection is often less efficient.
- Moderate heritability: 0.30 to 0.60. Genetic signal is present, but design quality and repeated testing strongly affect selection accuracy.
- High heritability: above 0.60. Genetic differences are easier to detect, especially when means are estimated from replicated designs.
These cutoffs are not universal. A high heritability estimate in one population can fall in another if genetic diversity narrows or environmental heterogeneity increases. Likewise, a well-replicated and balanced design may raise the heritability of entry means even when plot-level heritability is only moderate.
Comparison table: common trait heritability ranges
The following values reflect widely reported approximate ranges from genetics and breeding literature. Actual estimates vary by population, environment, and model specification.
| Trait | Species or context | Typical heritability range | Practical interpretation |
|---|---|---|---|
| Human height | Population genetics studies | 0.60 to 0.80 | Strong genetic contribution, though nutrition and health still matter. |
| Body mass index | Human epidemiology | 0.40 to 0.70 | Moderate to high heritability with substantial environmental influence. |
| Milk yield | Dairy cattle | 0.25 to 0.35 | Genetics matter, but management and environment remain major drivers. |
| Kernel weight | Maize and wheat breeding | 0.50 to 0.80 | Usually favorable for direct selection in replicated trials. |
| Grain yield | Multi-environment crop trials | 0.20 to 0.60 | Highly sensitive to environment and GxE, especially at plot level. |
Notice how yield traits often exhibit lower heritability than more structurally defined traits such as height or kernel weight. That is one reason breeders rely heavily on replication, multi-environment testing, and mixed models when evaluating yield performance.
Comparison table: how design affects heritability of means
One of the most important practical lessons in calculating heritability from SAS is that experimental design changes the denominator. The table below uses the same variance components, σ²g = 12.4, σ²ge = 6.1, and σ²e = 18.7, and shows how changing environments and replications affects broad-sense heritability on an entry-mean basis.
| Environments (e) | Replications (r) | Effective denominator | Estimated H² |
|---|---|---|---|
| 1 | 2 | 12.4 + 6.1 + 18.7/2 = 27.85 | 0.445 |
| 1 | 4 | 12.4 + 6.1 + 18.7/4 = 23.175 | 0.535 |
| 3 | 2 | 12.4 + 6.1/3 + 18.7/6 = 17.55 | 0.707 |
| 3 | 4 | 12.4 + 6.1/3 + 18.7/12 = 15.991 | 0.775 |
| 5 | 4 | 12.4 + 6.1/5 + 18.7/20 = 14.555 | 0.852 |
This pattern explains why entry-mean heritability is often much higher than plot-basis heritability. As replication and environmental coverage improve, random noise is averaged out and the genetic signal becomes more stable.
Common mistakes when using SAS outputs to calculate heritability
- Using the wrong formula for the design. Plot-basis and entry-mean heritability answer different questions.
- Ignoring genotype x environment interaction. In multi-environment trials, dropping σ²ge can overstate heritability.
- Confusing broad-sense and narrow-sense heritability. Broad-sense includes additive, dominance, and epistatic contributions. Narrow-sense isolates additive variance relevant to response to selection.
- Plugging in negative variance estimates without review. Mixed-model outputs can occasionally produce small negative estimates because of sampling or model constraints. These often require boundary treatment or model revision.
- Treating heritability as universal. A value computed in one population, year, or management system does not automatically transfer elsewhere.
How SAS procedures fit into heritability analysis
In many practical workflows, PROC MIXED is preferred because it handles random effects cleanly and can estimate variance components under unbalanced data structures. PROC GLM is still useful in balanced settings or teaching contexts, but mixed models are usually more flexible for modern breeding data. PROC VARCOMP can also estimate variance components, though analysts often move to mixed-model frameworks when they need greater control over covariance structures or repeated measures.
A standard multi-environment breeding analysis may treat genotype as random, environment as either fixed or random depending on the inference target, and block or replication nested within environment as random. Once those components are estimated, heritability can be calculated externally using a calculator like the one above or directly in SAS with a derived expression.
Authoritative references for deeper study
If you want to validate formulas or expand your understanding of quantitative genetics and variance components, these sources are worth reviewing:
Best practices for reporting heritability
When you publish or present heritability estimated from SAS, report more than the final number. Include the population studied, the environments or years sampled, the exact SAS procedure used, the random and fixed effects, and whether the estimate is on a plot basis or entry-mean basis. If possible, provide standard errors or confidence intervals. This extra transparency makes the estimate interpretable and reproducible.
It is also wise to state the intended use of the statistic. For example, broad-sense heritability may be ideal for clone selection or early-stage line testing, whereas narrow-sense heritability is usually more informative for predicting response to selection under additive inheritance. The number itself is useful, but the breeding context is what turns it into a decision tool.
Final takeaway
To calculate heritability SAS results correctly, start by identifying the relevant variance components and matching them to the proper formula. For replicated multi-environment trials, broad-sense heritability on an entry-mean basis is often the most informative measure because it reflects the reliability of genotype means after averaging over noise. For pedigree or genomic models focused on additive inheritance, narrow-sense heritability is usually the better metric. The calculator above helps you move from raw variance components to a clear estimate, interpretation, and charted breakdown in a few seconds.