Fehr, Chapt. 3 Briggs and Knowles, Chapt. 5 & 6.

Variation due to the environment Variation within a crop species

Variation due to the environment Variation due to heredity

P = G + E + G x E

Variations in genetically uniform materials caused by varying environmental stresses are not transmitted to the progenies, and hence cannot be isolated by selection. Johannsen's experiments.

HERITABLE VARIATION (variation due to genotypes). If the character expression of two individuals could be measured in an environment exactly identical for both, differences in expression would result from genetic control. In this case E = 0, G x E = 0 or is pooled with G. Note it is very difficult to have E = 0.

In a genetically mixed population, variations that result from heritable causes are transmittable to the progeny.

Environmental and heritable variations in plants are not independent -- they frequently interact in their effect on the plant: G x E.

e.g., Chlorophyll mutants are often observed but chlorophyll will not function in normal seedlings unless seedlings are exposed to sufficient light.

A rust resistant variety of wheat may have no yield advantage over a rust susceptible variety in seasons unfavorable for the development of rust.

Inherent differences in the hardiness of winter barley varieties cannot be distinguished if the season is so mild that hardy and non-hardy cultivars survive the winter alike.

Selection of individual plants of oats for tillering capacity may be misleading unless the plants have comparable spacing. (Thinly spaced plants will have more plant nutrients and moisture available to them and will tiller more profusely than the plants growing in more crowded conditions.)

The exact genetic composition of a plant determines its genotype.

The appearance of the plant is its phenotype.

In cases of multiple alleles (forms) of a particular gene only 2 of the multiple allele will be present in a diploid cell. Note this will be different in polyploids (comment on allopolyploids vs. autopolyploids).

Simplest mode of inheritance of a character is that determined by a single gene.

Breeders' task is to identify those heritable variations which will be useful for the improvement of crop plants and to concentrate or combine genes for those characteristics into a variety.

Need a comprehensive knowledge of the mechanism of heredity and the principles upon which it operates.

• Qualitative . . .one or a few genes with distinct phenotypes, regardless of the environment.
• Quantitative . . .many genes with small effects and/or phenotype blurred by the environment
  such that classification of genotype from phenotype is difficult.

Qualitative traits are those in which the phenotypes can be distinctly separated into discrete categories or classes that do not overlap. Usually are considered as major genes.

Classification of individuals is easy (unambiguous).

Little variation from environmental interaction with genotype. Environment may affect the trait, but generally the effect is in a similar manner for both genotypes.

Level of dominance:

Determining the Mechanism of Heredity

Cross 2 plants that differ in a trait and breed true for the trait. Self the F₁ generation and study the segregation in the progeny (F₂).

Remember: phenotypic ratio 3 : 1 if complete dominance expressed; genotypic ratio 1 : 2 : 1 if incomplete dominance expressed.

These are the ratios expected if the trait is determined by a single gene.

If more than one locus is involved then can get 9:3:3:1 ratios or 27:9:9:3:9:3:3:1 ratios. These ratios can change with dominance and epistasis to 15:1 or 9:7, etc.

If have m segregating loci with two genes per loci then:

Can you explain this chart?

In a single cross (A x B) between pure (inbred) lines, then each parent should produce only one gamete and theoretically only one F₁ seed is needed to represent the hybrid. In practice, may need more than one F₁ plant to produce enough F₂ seed.

In a three-way cross (A x B) x C, then one gamete should represent C, but 2ⁿ gametes will be needed to represent A x B where n = number of segregating loci. Therefore should have 2ⁿ F₁ seed.

In a double cross hybrid (A x B) x (C x D), then will need 2ⁿ gametes to represent A x B and 2^m gametes to represent C x D where m = number of segregating loci. Therefore should have 2^{n + m} F₁ seed.

On the basis of the number of F₁ seed that is needed, most self-pollinated crop breeders effectively rely on single and three-way crosses. Double crosses are too much work and have too much variation in later generations.

PROGENY TEST: The most easily used breeding tool. Fits into the breeding program.

Make the cross: Grow and observe progeny.

The performance of the progeny is a better guide to the breeding behavior of the plant than the appearance of the plant itself. Why? Can have many more progeny than the parent plant. Can remove epistatic effects. Also the parent is often grown in one environment (no measurement of E or G x E). Finally, you are most interested identifying genotypes that are good for cultivars and inbreds, but also for future crosses as a parent.

TEST CROSS

Another method for identifying the genotype of the plant is to cross the plant in question to a homozygous recessive plant (difficulty is that you must know that your tester plant is homozygous recessive -- in this case observe the F₁ to help determine the dominance relationships) and observe the segregation in the testcross.

Note: In dioecious crops in which self-pollination is not possible, a test cross provides the only means of identifying the genotype of particular plants.

Test segregation ratios for fit to expected ratios via Chi Square test.

Genetic consequences of inbreeding:

Proportion of Heterozygotes: (1/2)ⁿ where n is the number of generations of selfing.

Note that S = selfing generations is one less than F = filial generations in self pollination. (i.e., S₁ = F₂).

Proportion of homozygotes: 1 - (1/2)ⁿ

Now consider the inbreeding in the 1, 2, 3, 4, and 5 generations of selfing:

Proportion of heterozygotes: 1/2, 1/4, 1/8, 1/16, 1/32

Proportion of homozygotes: 1/2, 3/4, 7/8, 15/16, 31/32

With multiple segregating loci (m):

Proportion of homozygotes:

Proportion of heterozygotes: 1 -- proportion of homozygotes

In a population: how to figure the number of plants that are homozygous and heterozygous for a number of traits
(see Allard p. 70-72): where n is the generations of selfing and m is the number of loci involved.

Definitions:

Penetrance -- the number of individuals that express a trait

Expressivity -- the level of expression

Now let's consider qualitative genetics empirically:

• You have made a cross between a powdery mildew resistant barley with a susceptible barley:

The F₁ is resistant, HENCE THE GENE (OR AT LEAST ONE OF THE GENES) is dominant.
In the F₂: 78 plants are resistant and 22 plants are susceptible.

3 R _ : 1 rr implies F3 families should be 1 RR : 2 segregating (3 : 1 ratios) : 1 rr. Also the F₁ test cross will be 1 Rr : 1 rr.

3 resistant : 3 susceptible implies 7 resistant : 8 segregating (3 : 1 and 13 : 3) : 1 susceptible. A test cross to a susceptible plant will probably give a 1 resistant: 1 susceptible (one loci for susceptibility is controlled by a dominant allele). Note the need for both tests. Also note that resistant progeny can be derived from susceptible segregating parents.

how to determine the proportion of plants in a population with three genes segregating in the F₅ with that are homozygous and heterozygous: