Heritability and genetic advance
Heritability and genetic advance explained: variance components, broad and narrow sense, GCV and PCV, GA as % of mean, and a worked ANOVA example.
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A breeder looks at a field of wheat lines that differ in yield, height and grain weight, and has to decide which traits are worth selecting for. Some of the variation comes from genes and will be passed on. Some comes from soil, moisture and chance, and will vanish in the next generation. Heritability measures how much of the observed variation is genetic. Genetic advance predicts how much a trait will actually improve if the best plants are selected.
These two numbers, usually reported together with genotypic and phenotypic coefficients of variation, appear in thousands of plant breeding papers and almost every genetics exam.
Partitioning variance
The phenotype of a plant is its genotype plus the effect of the environment: P = G + E. If the two are independent, the variances add:
Additive variance comes from the average effects of alleles. It is what makes offspring resemble their parents, and it is the part that selection can reliably fix. Dominance and epistatic variance depend on particular combinations of alleles, which are broken up when gametes form. They matter for hybrids but are not reliably transmitted.
In practice there is also genotype × environment interaction (σ2GE). It is estimated when the same lines are tested over several locations or years.
Two kinds of heritability
Broad-sense heritability is the right measure for clonal crops and for selecting among pure lines, where whole genotypes are passed on intact. Narrow-sense heritability predicts response in sexually reproducing populations. It can be estimated from:
- parent–offspring regression: the slope on the mid-parent value equals h2ns, and the slope on one parent equals ½h2ns;
- half-sib or full-sib designs, such as North Carolina designs and diallel analysis;
- generation means analysis.
Heritability is not a fixed property of a trait. It depends on the population, the environment and the design. The same trait has higher heritability in a uniform research station plot than in a variable farmer's field.
Estimating components from a field trial
For g genotypes tested in a randomised block design with r replications, analysis of variance gives the mean squares for genotypes (Mg) and error (Me). Then:
Variation is often expressed relative to the mean, so that traits measured in different units can be compared:
- GCV (genotypic coefficient of variation) = (σG ⁄ x̄) × 100
- PCV (phenotypic coefficient of variation) = (σP ⁄ x̄) × 100
PCV is always larger than GCV. A small gap between them means the environment has little influence on the trait.
Genetic advance
The expected gain from selection is the breeder's equation applied to phenotypic standard deviation units:
Yield in 20 rice lines
Twenty lines are grown in three replications. The ANOVA gives Mg = 45 and Me = 9 (units: (g per plant)2), and the trial mean is 40 g per plant.
- σ2G = (45 − 9) ⁄ 3 = 12; σ2P = 12 + 9 = 21
- h2bs = 12 ⁄ 21 = 57% (moderate)
- σP = √21 = 4.58; GCV = √12 ⁄ 40 × 100 = 8.7%; PCV = 4.58 ⁄ 40 × 100 = 11.5%
- GA = 2.06 × 0.57 × 4.58 = 5.4 g, which is 13.5% of the mean (moderate)
Selecting the top 5% of lines is expected to raise yield per plant from 40 to about 45 g in the next generation.
Interpreting the results
The usual classification comes from Johnson, Robinson and Comstock (1955) for heritability and genetic advance, and from Sivasubramanian and Madhava Menon (1973) for GCV and PCV.
| Measure | Low | Moderate | High |
|---|---|---|---|
| Heritability | below 30% | 30–60% | above 60% |
| GA as % of mean | below 10% | 10–20% | above 20% |
| GCV and PCV | below 10% | 10–20% | above 20% |
Combining the two gives a hint about gene action:
- High heritability with high GA suggests mostly additive gene action, so simple selection will work well.
- High heritability with low GA suggests non-additive gene action (dominance and epistasis), so heterosis breeding may pay better.
- Low heritability with low GA means the trait is strongly affected by the environment. Selection should rely on replicated trials, family means or correlated traits.
Panse (1957) first pointed out the importance of considering heritability and GA together.
Key points
- σ2P = σ2G + σ2E; σ2G = σ2A + σ2D + σ2I.
- Broad-sense h2 = σ2G ⁄ σ2P; narrow-sense h2 = σ2A ⁄ σ2P. Only additive variance responds reliably to selection.
- From an RBD: σ2G = (Mg − Me) ⁄ r and σ2E = Me.
- GCV and PCV express variance relative to the mean; PCV is always at least as large as GCV.
- GA = k h2 σP, with k = 2.06 at 5% selection intensity.
- High heritability with high GA indicates additive gene action.
What the exams ask
- Define broad-sense and narrow-sense heritability.
- Calculate σ2G, h2, GCV, PCV and GA from ANOVA mean squares.
- State the selection differential for 5% intensity.
- Interpret combinations of heritability and genetic advance.
- Explain why heritability is specific to a population and environment.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Does high heritability mean the environment does not matter?
No. It means that, in that population and those conditions, most of the differences between individuals are genetic. A trait can be highly heritable and still respond strongly to fertiliser or irrigation. Heritability describes variation, not how much the trait itself depends on genes.
Why is yield heritability usually low?
Yield is controlled by many genes with small effects, and it integrates every stress the crop meets during the season. Environmental variance is therefore large compared with genetic variance. Breeders improve its effective heritability by testing in more replications, locations and years.
Can heritability exceed 1?
Not in theory. In practice, sampling error with small trials or negative variance estimates can give values above 1 or below 0. These are signs that the experiment was too small to estimate the components reliably.
Sources
- Falconer, D. S. and Mackay, T. F. C. Introduction to Quantitative Genetics, 4th edition. Longman, 1996.
- Johnson, H. W., Robinson, H. F. and Comstock, R. E. "Estimates of genetic and environmental variability in soybeans." Agronomy Journal 47, 314–318 (1955).
- Singh, R. K. and Chaudhary, B. D. Biometrical Methods in Quantitative Genetic Analysis. Kalyani Publishers, revised edition 1985.
- Burton, G. W. and DeVane, E. H. "Estimating heritability in tall fescue (Festuca arundinacea) from replicated clonal material." Agronomy Journal 45, 478–481 (1953).
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