10.1 From Mendelian classes to a curve #
10.1.1 Continuous traits #
Height, yield, and blood pressure look bell-shaped because many loci each add a little and the environment blurs the steps. Fisher set this out in 1918. Every locus still segregates; the phenotype just stops being a clean report of any one of them.
A height measurement is not a test cross. Nutrition, temperature, and developmental noise sit in the environmental term. The physiology is Plant Physiology or Animal and Human Physiology. The variance partition is genetics.
10.1.2 Nilsson-Ehle and polygenic colour #
Nilsson-Ehle’s three-locus wheat colour still shows the Mendelian bones. White kernels, all three loci non-contributing, are (1/4)³ = 1/64, so coloured:white is 63:1, and the coloured class is graded by dose:
| Contributing alleles | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Count in 64 | 1 | 6 | 15 | 20 | 15 | 6 | 1 |
One additive locus gives 1:2:1; two give 1:4:6:4:1. With n loci there are 2n+1 dose classes. East’s tobacco flower length showed the curve that appears once more loci and more environment fill the gaps. The 9:7 and 15:1 ratios of Chapter 2 are what non-additive interaction looks like instead.
10.2 Heritability #
10.2.1 Variance components #
If genotype and environment do not covary or interact, V_P = V_G + V_E. Interaction is an extra term when that assumption fails. V_G = V_A + V_D + V_I: additive breeding values, dominance deviations, and epistasis. Offspring inherit alleles, not a parent’s diploid combination, so selection transmits V_A.
Broad-sense heritability is H² = V_G / V_P. Narrow-sense heritability is h² = V_A / V_P. Response uses h². The slope of offspring on the mid-parent estimates it; the slope on one parent estimates about half of it. Shared environment inflates the resemblance, which is the trap in Chapter 11.
10.2.2 What h² is and what it is not #
h² is a ratio of variances in one population in one range of environments. It is not the fraction of a person’s phenotype “caused by genes”, and a person does not have a heritability.
It changes if the environment or the segregating alleles change. A uniform environment can raise it by shrinking V_E; a genetically uniform population has h² = 0 because V_A = 0. It does not cap a shift of the mean under a new environment: height is substantially heritable within populations and has also risen across generations with nutrition. A value from one herd or country does not travel unchanged. It is not a ranking of groups, and a difference of means between groups is not what a within-population ratio measures.
10.2.3 Response to selection #
R = h² S. S is the mean of selected parents minus the population mean; R is the offspring mean minus that same original mean. Illustration, not a trial: mean 100, parents 120, so S = 20; if h² = 0.25, then R = 5 and the predicted offspring mean is 105.
The prediction is for one generation, the same environment, and this phenotype. Continued selection spends V_A and the response slows until h² is measured again. Mutation restores additive variance slowly. A genetic covariance, from pleiotropy or linkage disequilibrium, makes selection on one trait move another.
10.3 A chromosomal region and a trait #
The study of A chromosomal region and a trait provides fundamental principles governing cellular architecture, molecular interactions, and physiological regulation.
Chromosomal Structural Abnormality Robertsonian Translocation Icon
10.3.1 QTL mapping as an idea #
A quantitative trait locus is a region whose marker alleles travel with a difference in trait mean. Offspring that received the high parent’s marker allele are higher, on average, than the others. The marker is a landmark, not automatically the cause: linkage from Chapter 4, applied to a trait without classes.
More recombinants resolve a smaller interval. The region stays a region until a sequence inside it is shown to act. Marker technology is Biotechnology and Genetic Engineering; the statistics of dense markers are Bioinformatics. One QTL seldom accounts for all of h². Calling it “the gene for the trait” repeats the misuse of heritability.
10.4 Key terms, summary, and self-check #
Key terms. Polygenic; Nilsson-Ehle; V_A; breeding value; narrow-sense heritability; selection differential; response to selection; QTL.
Summary. Many additive loci plus environment turn Mendelian classes into a curve; three wheat loci still show doses 0 to 6 in 64ths. h² = V_A / V_P is a population variance ratio, not a personal percent-genetic and not a ceiling on a new environment. R = h²S predicts one generation from the additive part. A QTL is a chromosomal region associated with a trait difference, not yet a named gene.
Self-check.
1. Why is three-locus wheat colour both 63:1 and a graded series?
2. Why does selection transmit V_A rather than V_D?
3. Why can h² = 0.8 still allow a new environment to shift the mean?
4. Parents are 10 units above the mean and h² = 0.4. What is R?
5. Why is a real marker association not yet “the gene”?
