A model for evaluating multiple alleles. An oversimplification. The number of beneficial alleles is added together.

If dominant alleles are beneficial, aabbccdd = 0, and AABBCCDD = 8

f(A) = q = f(AA) + 0.5f(Aa)

The sum of all allele frequencies is 1.

A diploid organism has two alleles, either homozgous or heterozygous. The proportion of an allele in the population is its allele frequency.

Natural mechanisms prevent self-pollination: dioecious, monoecious, self-incompatible, or have protandry. Pollination transfers randomly with no effort from the breeder. Not every locus is heterozygous, but some protion of the genome is heterozygous.

The number of gametes produced is 2ⁿ, where n is the number of heterozygous loci. 

The number of possible genotypes produced is 3ⁿ. 

The number of cells in a Punnett square of a self-cross is 4ⁿ.

Best for traits with low heritability; environment has a large effect on phenotype, so single-plant selections dont' give much indication of genotype. Logically, if a family with at least one common parent does better compared to other families, it is because it has good alleles from the parent(s), and therefore will provide good alleles for their progeny.

There are three types of families: half-sib, full-sib, and S1.

f(AA) + f(Aa) + f(aa) = 1

The frequencies of genotypes in a population.

q²AA + 2q(1 - q)Aa + (1 - q)²aa = 1

Produces progeny with identical allele and genotype frequencies.

Only true if:

1. There are two alleles

2. No selection

3. Random mating

4. No migration in or out of the populatoin

5. Equal mutation rate so that A to a equals a to A

Produces half as much gain per cycle than pollination control. Equivalent to selection after pollination.

Year 1: Open pollination of C0, followed by selection of best individuals.

Year 2: Open pollination of C1 from bulk seed, followed by selection of the best individuals.

Twice as much gain per cycle than no pollination control, but takes twice as many cycles per year, equating it to no pollination control. Witer nurseries reduce time per cycle. Equivalent to selection before pollination.

Year 1: Self-pollination with C0, select superior types at maturity.

Year 2: Plant progeny rows of selected individuals, allow random pollination, and bulk seed at harvest. 

Year 3: Self-pollination within C1, select superior types at maturity.

R/S

The proportion of selection differential realized in subsequent progeny. The degree to which environment influences phenotype. If 0, then selection has no effect. If 1, then the environment has no effect.

Cyclical process that increases population means and allele frequencies incrementally with each cycle. Repeated selection and mating. Practiced until gain from selection becomes zero: genetic variability is exhausted. Gain from selection reduces over time, as genetic variation decreases.

1. Develop a base population

2. Evaluate individuals or their progeny

3. Select superior parents, and inter-mate randomly

4. Produce a progeny population, and return to step 2.

Beta vulgaris

A cross-pollinated crop, pollinated by wind, with self-incompatibilit. Produces betalain pigments. Sugar interferes with the concentration of pigment.

25 US and 25 European varieties were used in a breeding program to increase pigment and decrease sugar. The realized heritability for pigment was 0.81, for sugar 0.27, and for selection index, 0.74.

A method for selecting for more than one trait at once. A single numerical value is assigned to assess phenotype, sometimes using economics or statistics. 

Example: [pigment]/[sugar]