Population Genetics. Matthew B. Hamilton

CHAPTER 2 Genotype frequencies

      2.1 Mendel's model of particulate genetics

In the nineteenth century, there were several theories of heredity, including inheritance of acquired characteristics and blending inheritance. Jean‐Baptiste Lamarck is most commonly associated with the discredited hypothesis of inheritance of acquired characteristics (although it is important to recognize his efforts in seeking general causal explanations of evolutionary change). He argued that individuals contain “nervous fluid” and that organs or features (phenotypes) employed or exercised more frequently attract more nervous fluid, causing the trait to become more developed in their offspring. His widely known example is the long neck of the giraffe, which he said developed because individuals continually stretched to reach leaves at the tops of trees. Later, Charles Darwin and many of his contemporaries subscribed to the idea of blending inheritance. Under blending inheritance, offspring display phenotypes that are an intermediate combination of parental phenotypes (Figure 2.1).

      From 1856 to 1863, the Augustinian monk Gregor Mendel carried out experiments with pea plants that demonstrated the concept of particulate inheritance. Mendel showed that phenotypes are determined by discrete units that are inherited intact and unchanged through generations. His hypothesis was sufficient to explain three common observations: (i) phenotype is sometimes identical between parents and offspring; (ii) offspring phenotype can differ from that of the parents; and (iii) “pure” phenotypes of earlier generations could skip generations and reappear in later generations. Neither blending inheritance nor inheritance of acquired characteristics are satisfactory explanations for all of these observations. It is hard for us to fully appreciate now, but Mendel's results were truly revolutionary and served as the very foundation of population genetics. The lack of an accurate mechanistic model of heredity severely constrained biological explanations of cause and effect up to the point that Mendel's results were “rediscovered” in the year 1900.

      It is worthwhile to briefly review the experiments with pea plants that Mendel used to demonstrate independent assortment of both alleles within a locus and of multiple loci, sometimes dubbed Mendel's first and second laws. We need to remember that this was well before the Punnett square, which originated in about 1905. Therefore, the conceptual tool we would use now to predict progeny genotypes from parental genotypes was a thing of the future. So, in revisiting Mendel's experiments, we will not use the Punnett square in an attempt to follow his logic. Mendel only observed the phenotypes of generations of pea plants that he had hand‐pollinated. From these phenotypes and their patterns of inheritance, he inferred the existence of heritable factors. His 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

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