Population Genetics. Matthew B. Hamilton

experiments were actually both logical and clever, but are now taken for granted since the basic mechanism of particulate inheritance has long since ceased to be an open question. It was Mendel who established the first and most fundamental prediction of population genetics: expected genotype frequencies.

Mendel used pea seed coat color as a phenotype he could track across generations. His goal was to determine, if possible, the general rules governing the inheritance of pea phenotypes. He established “pure”‐breeding lines (meaning plants that always produced progeny with phenotypes like themselves) of peas with both yellow and green seeds. Using these pure‐breeding lines as parents, he crossed a yellow‐ and a green‐seeded plant. The parental cross and the next two generations of the progeny are shown in Figure 2.2. Mendel recognized that the F1 plants had an “impure” phenotype because of the F2 generation plants, of which three‐quarters had yellow and one‐quarter had green seed coats.

Figure 2.1 The model of blending inheritance predicts that progeny have phenotypes that are the intermediate of their parents. Here, “pure” blue and white parents yield light blue progeny, but these intermediate progeny could never themselves be parents of progeny with pure blue or white phenotypes identical to those in the P1 generation. Crossing any shade of blue with a pure white or blue phenotype would always lead to some intermediate shade of blue. By convention, in pedigrees, females are indicated by circles and males by squares while “P” refers to parental and “F” to filial.

Figure 2.2 Mendel's crosses to examine the segregation ratio in the seed coat color of pea plants. The parental plants (P1 generation) were pure breeding, meaning that if self‐fertilized all resulting progeny had a phenotype identical to the parent. Some individuals are represented by diamonds since pea plants are hermaphrodites and can act as a mother, a father, or can self‐fertilize.

Figure 2.3 Mendel self‐pollinated (indicated by curved arrows) the F2 progeny produced by the cross shown in Figure 2.2. Of the F2 progeny that had a yellow phenotype (3/4 of the total), 1/3 produced all progeny with a yellow phenotype and 2/3 produced progeny with a 3 : 1 ratio of yellow and green progeny (or 3/4 yellow progeny). Individuals are represented by diamonds since pea plants are hermaphrodites.

His insightful next step was to self‐pollinate a sample of the plants from the F2 generation (Figure 2.3). He considered the F2 individuals with yellow and green seed coats separately. All green‐seeded F2 plants produced green progeny and thus were “pure” green. However, the yellow‐seeded F2 plants were of two kinds. Considering just the yellow F2 seeds, one‐third were pure and produced only yellow‐seeded progeny, whereas two‐thirds were “impure” yellow since they produced both yellow‐ and green‐seeded progeny. Mendel combined the frequencies of the F2 yellow and green phenotypes along with the frequencies of the F3 progeny. He reasoned that three‐quarters of all F2 plants had yellow seeds, but these could be divided into plants that produced pure yellow F3 progeny (one‐third) and plants that produced both yellow and green F3 progeny (two‐thirds). So, the ratio of pure yellow to impure yellow in the F2 was (1/3 × 3/4 =) 1/4 pure yellow to (2/3 × 3/4 =) 1/2 “impure” yellow. The green‐seeded progeny comprised one‐quarter of the F2 generation and all produced green‐seeded progeny when self‐fertilized, so that (1 × 1/4 green =) 1/4 pure green. In total, the ratios of phenotypes in the F2 generation were 1 pure yellow : 2 impure yellow : 1 pure green or 1 : 2 : 1. Mendel reasoned that “the ratio of 3 : 1 in which the distribution of the dominating and recessive traits take place in the first generation therefore resolves itself into the ratio of 1 : 2 : 1 if one differentiates the meaning of the dominating trait as a hybrid and as a parental trait” (quoted in Orel 1996). During his work, Mendel employed the terms “dominating” (which became dominant) and “recessive” to describe the manifestation of traits in impure or heterozygous individuals.

      With the benefit of modern symbols of particulate heredity, we could diagram Mendel's monohybrid cross with pea color in the following way.

P1	Phenotype	Yellow × green
	Genotype	GG	Gg
	Gametes produced	G	G
F1	Phenotype	All “impure”yellow
	Genotype	Gg
	Gametes produced	G, g

      A Punnet square could be used to predict the phenotypic ratios of the F2 plants

	G	G
G	GG	Gg
G	Gg	Gg

F2	Phenotype	3 Yellow : 1 green
	Genotype	GG	Gg	Gg
	Gametes produced	G	G, g	G

      and another Punnet square could be used to predict the genotypic ratios of the two‐thirds of the yellow F2 plants

	G	G
G	GG	Gg
G	Gg	Gg

      Mendel’s first