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 Mendel's breeding experiments.

 Independent assortment of alleles.

 Independent segregation of loci.

 Some common genetic terminology.

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 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 “law”: Predicts independent segregation of alleles at a single locus: two copies of a diploid locus (a pair of alleles that make a diploid genotype) segregate independently into gametes so that in a large number of gametes half carry one allele and the other half carry the other allele.

Individual pea plants obviously have more than a single phenotype, and Mendel followed the inheritance of other characters in addition to seed coat color. In one example of his crossing experiments, Mendel tracked the simultaneous inheritance of both seed coat color and seed surface condition (either wrinkled [“angular”] or smooth). He constructed an initial cross among pure‐breeding lines identical to what he had done when tracking seed color inheritance, except now there were two phenotypes (Figure 2.4). The F2 progeny appeared in the phenotypic ratio of 9 round/yellow : 3 round/green : 3 wrinkled/yellow : 1 wrinkled/green.

How did Mendel go from this F2 phenotypic ratio to the second law? He ignored the wrinkled/smooth phenotype and just considered the yellow/green seed color phenotype in self‐pollination crosses of F2 plants just like those for the first law. In the F2 progeny, 12/16 or three‐quarters had a yellow seed coat and 4/16 or one‐quarter had a green seed coat, or a 3 yellow : 1 green phenotypic ratio. Again using self‐pollination of F2 plants like those in Figure 2.3, he showed that the yellow phenotypes were (1/3 × ¾) one‐quarter pure and (2/3 × ¾) one‐half impure yellow. Thus, the segregation ratio for seed color was 1 : 2 : 1 and the wrinkled/smooth phenotype did not alter this result. Mendel obtained an identical result when considering instead only the wrinkled/smooth phenotype and ignoring the seed color phenotype.

Mendel concluded that a phenotypic segregation ratio of 9 : 3 : 3 : 1 is the same as combining two independent 3 : 1 segregation ratios of two phenotypes since (3 : 1) × (3 : 1) = 9 : 3 : 3 : 1. Similarly, the multiplication of two (1 : 2 : 1) phenotypic ratios will predict the two phenotype ratios (1 : 2 : 1) × (1 : 2 : 1) = 1 : 2 : 1 : 2 : 4 : 2 : 1 : 2 : 1. We now recognize that dominance in the first two phenotype ratios masks the ability to distinguish some of the homozygous and heterozygous genotypes, whereas the ratio in the second case would result if there was no dominance. You can confirm these conclusions by working out a Punnett square for the F2 progeny in the two‐locus case.

Figure 2.4 Mendel's crosses to examine the segregation ratios of two phenotypes, seed coat color (yellow or green) and seed coat surface (smooth or wrinkled), in pea plants. The stippled pattern indicates wrinkled seeds, while the solid color indicates smooth seeds. The F2 individuals exhibited a phenotypic ratio of 9 round‐yellow: 3 round‐green: 3 wrinkled‐yellow: 1 wrinkled‐green.

Mendel’s second “law”: Predicts independent assortment of multiple loci: during gamete formation, the segregation of alleles of one locus is independent of the segregation of alleles of another locus.

Mendel performed similar breeding experiments with numerous other pea phenotypes and obtained similar results. Mendel described his work with peas and other plants in lectures and published it in 1866 in the Proceedings of the Natural Science Society of Brünn in German where it went unnoticed for nearly 35 years. However, Mendel's results were eventually recognized, and his paper was translated into several languages. Mendel's rediscovered the hypothesis of particulate inheritance was also bolstered by evidence from microscopic observations of chromosomes during cell division that led Walter Sutton to propose in 1902 that chromosomes are the physical basis of heredity, supported by results obtained independently by Theodor Boveri at around the same time (see Crow and Crow 2002).

Much of the currently used terminology was coined as the field of particulate genetics initially developed. Therefore, many of the critical terms in genetics have remained in use for long periods of time. However, the meanings and connotations of these terms have often changed as our understanding of genetics has also changed.

Unfortunately, this has led to a situation where words can sometimes mislead. A common example is equating gene and allele. For example, it is commonplace for news media to report scientific breakthroughs where a “gene” has been identified as causing a particular phenotype, often a debilitating disease. Very often what is meant in these cases is that a genotype or an allele with the phenotypic effect has been identified. Both unaffected and affected individuals all possess the gene, but they differ in their alleles and therefore in their genotype. If individuals of the same species really differed in their gene content (or loci they possessed), that would provide evidence of additions or deletions to genomes. For an interesting discussion of how terminology in genetics has changed – and some of the misunderstandings this can cause, see Judson (2001).

Gene: A unit of particulate inheritance; in contemporary usage, it usually means an exon or series of exons, or a DNA sequence that codes for an RNA or protein.

Locus (plural loci, pronounced “low‐sigh”): Literally “place” or location in the genome; in contemporary usage, it is the most general reference to any sequence or genomic region, including non‐coding regions.

Allele: A variant or alternative form of the DNA sequence at a given locus.

Genotype: The set of alleles possessed by an individual at one locus; the genetic composition of an individual at one locus or many loci.

Phenotype: The morphological, biochemical, physiological, and behavioral attributes of an individual; synonymous with character and trait.

Dominant: Where the expressed phenotype of one allele takes precedence over the expressed phenotype of another allele. The allele associated with the expressed phenotype is said to be dominant. Dominance is seen on a continuous scale that includes “complete” dominance (one allele completely masks the phenotype of another allele so that the phenotype of a heterozygote is identical to a homozygote for the dominant allele) and “partial” or “incomplete” dominance (masking effect is incomplete so that the phenotype of a heterozygote is intermediate to both homozygotes) and includes over‐ and under‐dominance (phenotype is outside the range of phenotypes seen in the homozygous genotypes). The lack of dominance (heterozygote is exactly intermediate to the phenotypes of both homozygotes) is when the effects of alleles are additive, a situation sometimes termed “codominance” or “semi‐dominance.”

Recessive: The expressed phenotype of one allele is masked by the expressed phenotype of another allele. The allele associated with the concealed phenotype is said to be recessive.