Introduction
Plant and animal populations display variation for practically all measurable traits — for example, plant height, days to flowering, grain yield, oil content, or disease resistance. These differences (phenotypic variation) arise from genetic causes (differences in the hereditary material) and environmental causes (differences in soil, climate, management). For effective selection and breeding, a breeder must know how much of the observed variation is transmissible (genetic) and how much is environmental. This is quantified by heritability and by the expected improvement from selection quantified as genetic advance.
1. Components of Variance
Phenotypic variance (Vp) is the total observed variation and can be partitioned as:
Vp = Vg + Ve + Vge
Definitions:
Vg — Genetic variance (variation due to genotype differences)
Ve — Environmental variance (variation due to environment)
Vge — Genotype × Environment interaction variance (differences in relative performance of genotypes across environments)
Further partitioning of genetic variance:
Vg = Va + Vd + Vi
Va = Additive genetic variance (effects of individual alleles that add up)
Vd = Dominance variance (interaction between alleles at the same locus)
Vi = Epistatic (interaction) variance (interactions between genes at different loci)
Biological meaning: Additive variance is most important for selection because it is transmitted predictably from parents to offspring. Dominance and epistatic variance can create heterosis or specific combining ability but are less predictable in simple selection schemes.
2. Heritability — Concept and Types
General definition: Heritability is the proportion of phenotypic variance that is attributable to genetic variance.
Broad-sense heritability (H2):
H2 = Vg / Vp
Narrow-sense heritability (h2):
h2 = Va / Vp
Interpretation:
H2 tells how much of the observed variation is genetic (total genetic effects). h2 tells how much is due to additive genetic effects — the component most directly useful for predicting response to selection.
Numerical scale: Heritability ranges from 0 to 1 (or 0%–100%). Values near 0 indicate environmental control; values near 1 indicate strong genetic control of phenotypic differences.
3. Estimation of Heritability
Common methods:
a) Parent–offspring regression: Slope of regression of offspring phenotype on mid-parent phenotype approximates h2.
b) Analysis of variance (ANOVA) from designs: Use replicated trials, randomization and block designs to partition variance components and estimate Vg, Ve and Vge. For example, in a randomized complete block design with r replications and g genotypes:
Mean square for genotypes (MSg) and mean square for error (MSe) are obtained from ANOVA. One can estimate variance components as:
Vg = (MSg - MSe)/r
Ve = MSe
Example: If MSg = 150, MSe = 50, and r = 3, then Vg = (150 - 50)/3 = 33.33 and Vp = Vg + Ve = 33.33 + 50 = 83.33. Thus H2 = 33.33/83.33 = 0.4 (40%).
Note: Estimating Va (additive variance) specifically requires mating designs such as half-sib/full-sib analysis, diallel crosses or parent–offspring regressions under controlled conditions.
4. Genetic Advance (Expected Genetic Gain)
Definition: Genetic advance (GA) is the expected improvement in trait mean of the selected population over the base population after one generation of selection.
Formula:
GA = k · h2 · σp
Where:
k = Selection differential (a function of selection intensity; e.g., for top 5% selected, k ≈ 2.06)
h2 = Narrow-sense heritability (Va/Vp)
σp = Phenotypic standard deviation (= sqrt(Vp))
Expressing GA relative to mean:
GA% = (GA / µ) × 100, where µ is population mean.
Interpretation: GA quantifies how many units (or what percentage) we can expect the mean to increase when selecting the top proportion of individuals. It depends on selection intensity, the heritability (particularly additive variance), and the amount of phenotypic variability available.
5. Joint Interpretation: Heritability and Genetic Advance
Heritability indicates the proportion of variation that is genetic. Genetic advance indicates the absolute improvement obtainable under a specific selection regime. Their joint patterns are highly informative:
| Heritability | Genetic Advance | Implication for Breeding |
|---|---|---|
| High | High | Trait under additive gene action — phenotypic selection is effective (e.g., plant height, seed weight). |
| High | Low | Non-additive gene effects (dominance/epistasis) — use hybrid breeding, recurrent selection or exploit heterosis. |
| Low | High | Rare; may indicate special interactions or measurement issues. Selection predictions are uncertain — investigate further. |
| Low | Low | Strong environmental influence — selection based on phenotype will be inefficient; improve management or use progeny testing. |
6. Worked examples
Example 1 — Calculating heritability from ANOVA:
A breeder conducts an experiment with 20 genotypes and 3 replications. ANOVA gives MSg = 200 and MSe = 80.
Vg = (MSg - MSe)/r = (200 - 80)/3 = 40. Ve = MSe = 80. Vp = 40 + 80 = 120. Thus H2 = 40/120 = 0.333 (33.3%).
Example 2 — Genetic advance calculation:
Suppose a trait in a crop has µ = 50 units, Vp = 120 (as above) so σp = sqrt(120) = 10.954. If estimated narrow-sense heritability h2 = 0.25 and selection intensity for top 10% plants corresponds to k = 1.76, then:
GA = k · h2 · σp = 1.76 · 0.25 · 10.954 ≈ 4.81 units.
GA% = (4.81 / 50) × 100 ≈ 9.62% — the breeder expects about 9.6% improvement in one generation by selecting the top 10% lines.
7. Crop-specific examples and implications
Wheat — Plant height: Often shows high h2 and high GA because additive genes largely control height. Direct selection is effective.
Rice — Grain yield: Complex trait with moderate heritability often due to large environmental influences and non-additive gene action. Genetic advance is often low; therefore, breeders use multi-environment testing, selection indices, and heterosis breeding.
Groundnut — Oil content: Usually shows high heritability and high GA — simple selection can improve oil percentage effectively.
Maize — Grain yield per plant: Sometimes low h2 and low GA for yield per plant, but hybrids exploit dominance and specific combining ability to increase yield.
8. Factors influencing estimates and practical considerations
Experimental design and sample size: Poor design, low replication and small sample sizes bias variance estimates. Use appropriate designs (RCBD, lattice) with adequate replication.
Environmental uniformity: Greater environmental heterogeneity inflates Ve and reduces heritability estimates. Manage environments or use controlled conditions where appropriate.
Genetic background: Heritability estimates are population-specific. Different germplasm sets can yield different h2 values for the same trait.
G×E interactions: Large genotype-by-environment interactions complicate selection and reduce expected gains unless selection is conducted across target environments.
Measurement precision: Poor phenotyping increases error variance. Improve measurement tools and standardize protocols.
9. Breeding strategies guided by heritability and genetic advance
When h2 and GA are high: Use direct phenotypic selection — mass selection, pedigree selection or single-seed descent are effective.
When h2 is high but GA is low: Non-additive gene action dominates — consider hybrid breeding, recurrent selection for combining ability, or exploitation of heterosis.
When h2 is low: Improve experimental precision, use progeny testing, estimate combining ability, or adopt selection indices combining multiple traits.
When environmental variance is large: Use multi-environment trials, adjust for covariates (e.g., soil fertility), or use BLUP and mixed-model methods to separate genetic effects.
10. Advanced topics (brief)
Quantitative genetics in modern breeding: Mixed model approaches (REML/BLUP) estimate genetic values while accounting for unbalanced data and complex designs. These methods provide more accurate genetic parameter estimates in modern breeding programs.
Genomic heritability: With genomic data, "genomic heritability" (the proportion of phenotypic variance explained by markers) can be estimated. This aids genomic selection by predicting breeding values using marker data.
Selection indices: Combining traits into selection indices allows simultaneous improvement of multiple traits and can increase expected genetic gain for a breeding objective.
Conclusion
Heritability and genetic advance form a complementary pair of parameters that guide practical plant breeding decisions. Heritability quantifies the extent of genetic control over phenotypic variation; genetic advance quantifies the expected improvement under a defined selection scheme. Their joint interpretation tells breeders whether to use simple phenotypic selection, heterosis exploitation, progeny testing, or modern genomic selection tools.
References & Further reading
Textbooks and classical references on quantitative genetics and plant breeding (examples):
- Falconer, D. S. & Mackay, T. F. C. (1996). Introduction to Quantitative Genetics.
- Allard, R. W. (1999). Principles of Plant Breeding.
- Burton, G. W. & DeVane, E. T. (1953). Estimation of heritability in plant breeding studies.
