Qualitative and quantitative inheritance
Qualitative vs quantitative traits, the multiple factor hypothesis, Nilsson-Ehle's wheat colour, estimating gene number, and transgressive segregation.
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Mendel's pea traits fell into neat classes: tall or dwarf, round or wrinkled, yellow or green. Most traits that farmers care about do not. Yield, height, days to flowering, grain weight, oil content and milk yield vary continuously, and an F2 population forms a bell-shaped curve rather than a few separate classes. For years after Mendel's work was rediscovered in 1900, many scientists doubted that Mendelian genes could explain continuous variation at all.
The answer, worked out between 1909 and 1918, is that continuous traits are controlled by many genes, each with a small effect, plus the environment. This multiple factor or polygenic model connects Mendelian genetics with the quantitative genetics that breeders use every day.
Comparing the two kinds of trait
| Feature | Qualitative traits | Quantitative traits |
|---|---|---|
| Variation | Discontinuous, in distinct classes | Continuous; measured, not counted |
| Genes | One or a few major genes (oligogenes) | Many genes with small effects (polygenes) |
| Effect of environment | Small | Large |
| Analysis | Ratios and chi-square | Means, variances, regression |
| Examples | Flower colour, awns, disease resistance from a major gene | Yield, height, maturity, grain weight, milk yield |
Some traits are threshold traits. They have an underlying continuous liability but appear in only two or a few classes. Disease incidence and twinning in cattle are examples: they appear only when the liability crosses a threshold.
Nilsson-Ehle's experiment
In 1909, the Swedish geneticist Herman Nilsson-Ehle crossed red-kernelled and white-kernelled wheat. The F1 was intermediate in colour. In different crosses, the F2 showed red to white ratios of 3 : 1, 15 : 1 and 63 : 1. The coloured kernels in each also ranged from dark to light red.
He explained this with two or three independent gene pairs with additive effects. Each "colour" allele (R1, R2, R3) adds the same amount of red, and the non-colour alleles add nothing. With two genes, the F2 has five colour classes, depending on whether a plant carries 4, 3, 2, 1 or 0 colour alleles, in the ratio 1 : 4 : 6 : 4 : 1. With three genes it has seven classes, in the ratio 1 : 6 : 15 : 20 : 15 : 6 : 1.
At about the same time, East (1910, 1916) showed similar results for corolla length in tobacco. In 1918, R. A. Fisher showed mathematically that many Mendelian genes acting together produce continuous variation and the correlations seen between relatives. That paper founded quantitative genetics.
Rules for polygenic inheritance
For n independent gene pairs with equal additive effects and no dominance, crossing two extreme parents gives:
How many genes?
A cross between a tall and a dwarf line gives 1,280 F2 plants, and 5 are as dwarf as the dwarf parent. The proportion is 5 ⁄ 1,280 = 1 ⁄ 256 = (1⁄4)4, so about four gene pairs control height in this cross. The F2 would show 2 × 4 + 1 = 9 classes. In practice, environmental variation blurs the classes together, so the counts give only a rough estimate.
A more general estimate is the Castle–Wright formula. It uses the difference between parental means and the genetic variance in the F2:
The estimate is a minimum. It assumes equal, additive, unlinked genes with all the "plus" alleles in one parent, which is rarely true.
Transgressive segregation
Sometimes F2 or later plants fall outside the range of both parents. This transgressive segregation happens when each parent carries some favourable alleles at different genes. For example, parent A might be AABBcc and parent B aabbCC, while some offspring are AABBCC. Breeders rely on it when they cross two good but different varieties hoping to find progeny better than either. Many high-yielding varieties came from such crosses.
Mapping polygenes
Polygenes are not mysterious; they are ordinary genes with small effects. With DNA markers, the regions that contain them can be mapped as quantitative trait loci (QTLs). Some QTLs turn out to have surprisingly large effects. Examples include the Sub1 locus for submergence tolerance in rice, qDTY loci for yield under drought, and the Gn1a and GW2 genes for grain number and grain weight. For traits with many tiny effects, breeders now use genomic selection.
Key points
- Qualitative traits are discontinuous, controlled by a few major genes and little affected by the environment. Quantitative traits are continuous, controlled by many genes and strongly affected by the environment.
- Nilsson-Ehle (1909) explained wheat kernel colour with additive gene pairs (ratios 3:1, 15:1 and 63:1); East studied tobacco corolla length; Fisher (1918) united Mendelian and quantitative genetics.
- For n additive genes: 2n + 1 classes; (1⁄4)n of the F2 resembles each extreme parent.
- The Castle–Wright formula estimates a minimum number of genes.
- Transgressive segregants fall outside the parental range and are a breeder's opportunity.
- QTLs are mapped regions that contain genes for quantitative traits.
What the exams ask
- Distinguish qualitative and quantitative traits.
- Explain Nilsson-Ehle's experiment and derive the 1 : 4 : 6 : 4 : 1 ratio.
- Calculate the number of genes from the proportion of extreme F2 plants.
- Define transgressive segregation and threshold traits.
- State the contribution of Fisher (1918).
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Is yield controlled by thousands of genes?
Effectively, yes. Yield depends on germination, growth, photosynthesis, stress tolerance, flowering, grain filling and more, and each process involves many genes. Genome studies usually find many small-effect loci for yield, which is why it responds slowly to selection and is predicted best with genome-wide markers.
Can a qualitative trait become quantitative?
The same trait can be either, depending on the genes involved. Disease resistance can come from a single major gene (qualitative, often race-specific) or from many minor genes (quantitative, often more durable). Plant height is qualitative when a single dwarfing gene such as Rht1 in wheat or sd1 in rice segregates, and quantitative otherwise.
Why does the F2 curve look normal even with few genes?
Environmental variation spreads each genotype class into its own small distribution, and these overlap and blur into a continuous curve. Even three or four genes plus normal field variation produce a curve very close to normal.
Sources
- Falconer, D. S. and Mackay, T. F. C. Introduction to Quantitative Genetics, 4th edition. Longman, 1996.
- Fisher, R. A. "The correlation between relatives on the supposition of Mendelian inheritance." Transactions of the Royal Society of Edinburgh 52, 399–433 (1918).
- Strickberger, M. W. Genetics, 3rd edition. Macmillan, 1985.
- Singh, B. D. Genetics, 3rd edition. Kalyani Publishers, 2019.
- Lande, R. "The minimum number of genes contributing to quantitative variation between and within populations." Genetics 99, 541–553 (1981).
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