1. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 1. Mendel’s dihybrid crosses Mendel went on to analyze the descendants of pure lines that differed in two characters. Mendel went on to analyze the descendants of pure lines that differed in two characters. Here we need a general symbolism to represent genotypes including two genes. If two genes are on different chromosomes, the gene pairs are separated by a semicolon, for example, A /a ; B /b. If they are on the same chromosome, the alleles on one chromosome are written adjacently and are separated from those on the other chromosome by a slash, for example, A B /a b or A b /a B. Here we need a general symbolism to represent genotypes including two genes. If two genes are on different chromosomes, the gene pairs are separated by a semicolon, for example, A /a ; B /b. If they are on the same chromosome, the alleles on one chromosome are written adjacently and are separated from those on the other chromosome by a slash, for example, A B /a b or A b /a B. An accepted symbolism does not exist for situations in which it is not known whether the genes are on the same chromosome or on different chromosomes. For this situation, we will separate the genes with a dot, for example, A /a ·B /b. A double heterozygote, A /a · B /b, is also known as a dihybrid. From studying dihybrid crosses (A /a · B /b × A /a · B /b ), Mendel came up with another important principle of heredity. An accepted symbolism does not exist for situations in which it is not known whether the genes are on the same chromosome or on different chromosomes. For this situation, we will separate the genes with a dot, for example, A /a ·B /b. A double heterozygote, A /a · B /b, is also known as a dihybrid. From studying dihybrid crosses (A /a · B /b × A /a · B /b ), Mendel came up with another important principle of heredity.

2. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 2. Yellow/green-round/wrikled seeds The two specific characters that he began working with were seed shape and seed color. The two specific characters that he began working with were seed shape and seed color. To perform a dihybrid cross, Mendel started with two parental pure lines. One line had yellow, wrinkled seeds; because Mendel had no concept of the chromosomal location of genes, we must use the dot representation to write this genotype as Y /Y · r /r. The other line had green, round seeds, the genotype being y /y · R /R. To perform a dihybrid cross, Mendel started with two parental pure lines. One line had yellow, wrinkled seeds; because Mendel had no concept of the chromosomal location of genes, we must use the dot representation to write this genotype as Y /Y · r /r. The other line had green, round seeds, the genotype being y /y · R /R. The cross between these two lines produced dihybrid F1 seeds of genotype R /r · Y /y, which he discovered were round and yellow. The cross between these two lines produced dihybrid F1 seeds of genotype R /r · Y /y, which he discovered were round and yellow. This result showed that the dominance of R over r and of Y over y was unaffected by the presence of heterozygosity for either gene pair in the R /r · Y /y dihybrid. This result showed that the dominance of R over r and of Y over y was unaffected by the presence of heterozygosity for either gene pair in the R /r · Y /y dihybrid.

3. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 3. DiHybrid-cross F 2 ratios Next Mendel made the dihybrid cross by selfing the dihybrid F1 to obtain the F 2 generation. The F 2 seeds were of four different types in the following proportions: Next Mendel made the dihybrid cross by selfing the dihybrid F1 to obtain the F 2 generation. The F 2 seeds were of four different types in the following proportions: What could be the explanation? Mendel added up the numbers of individuals in certain F 2 phenotypic classes to determine if the monohybrid 3:1 F2 ratios were still present. He noted that, in regard to seed shape, there were 423 round seeds (315+108) and 133 wrinkled seeds (101+32). This result is close to a 3:1 ratio. Next, in regard to seed color, there were 416 yellow seeds (315+101) and 140 green (108+32), also very close to a 3:1 ratio. The presence of these two 3:1 ratios hidden in the 9:3:3:1 ratio was undoubtedly a source of the insight that Mendel needed to explain the 9:3:3:1 ratio, because he realized that it was nothing more than two independent 3:1 ratios combined at random.

4. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 4. Visualizing the 9:3:3:1 ratio One way of visualizing the random combination of these two ratios is with a branch diagram, as follows: One way of visualizing the random combination of these two ratios is with a branch diagram, as follows: The combined proportions are calculated by multiplying along the branches in the diagram because, for example, 3/4 of 3/4 is calculated as 3/4 × 3/4, which equals 9/16 These multiplications give us the following four proportions: The combined proportions are calculated by multiplying along the branches in the diagram because, for example, 3/4 of 3/4 is calculated as 3/4 × 3/4, which equals 9/16 These multiplications give us the following four proportions:

5. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 5. The Punnett square The four female gametic types will be fertilized randomly by the four male gametic types to obtain the F2, and the best way of showing this graphically is to use a 4×4 grid called a Punnett square, which is depicted in Figure 2-10. Grids are useful in genetics because their proportions can be drawn according to genetic proportions or ratios being considered, and thereby a visual data representation is obtained. In the Punnett square in Figure 2-10, for example, we see that the areas of the 16 boxes representing the various gametic fusions are each one-sixteenth of the total area of the grid, simply because the rows and columns were drawn to correspond to the gametic proportions of each. As the Punnett square shows, the F2 contains a variety of genotypes, but there are only four phenotypes and their proportions are in the 9:3:3:1 ratio. The four female gametic types will be fertilized randomly by the four male gametic types to obtain the F2, and the best way of showing this graphically is to use a 4×4 grid called a Punnett square, which is depicted in Figure 2-10. Grids are useful in genetics because their proportions can be drawn according to genetic proportions or ratios being considered, and thereby a visual data representation is obtained. In the Punnett square in Figure 2-10, for example, we see that the areas of the 16 boxes representing the various gametic fusions are each one-sixteenth of the total area of the grid, simply because the rows and columns were drawn to correspond to the gametic proportions of each. As the Punnett square shows, the F2 contains a variety of genotypes, but there are only four phenotypes and their proportions are in the 9:3:3:1 ratio.

6. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 6. Mendel’s trihybrid experiment Mendel submitted his principle of independent assortment to a further test. He tested the segregation ratios of the F2 progeny from parental plants that were simultaneously pure for three characters: Mendel submitted his principle of independent assortment to a further test. He tested the segregation ratios of the F2 progeny from parental plants that were simultaneously pure for three characters: In Mendel’s own words: “This experiment was made in precisely the same way as the previous one. Among all the experiments it demanded the most time and trouble. From 24 hybrids, 687 seeds were obtained in all. From these, 639 plants fruited in the following year.

7. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 7. Mendel’s original results “The whole expression contains 27 terms. Of these, 8 are constant in all characters, and each appears on the average 10 times; 12 are constant in two characters, and hybrid in the third; each appears on the average 19 times; 6 are constant in one character and hybrid in the other two; each appears on the average 43 times. One form appears 78 times and is hybrid in all of the characters. The ratios 10:19:43:78 agree so closely with the ratios 10:20:40:80, or 1:2:4:8 that this last undoubtedly represents the true value”. These 639 plants were backcrossed with the triple-recessive parental line, so that Mendel was able to classify them by genotype and not only by phenotype. He presented the following table:

8. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 8. Punnett’s square of Mendel’s trihybrid crosses We can easily interpret Mendel’s trihybrid experiment using the Punnett square: We can easily interpret Mendel’s trihybrid experiment using the Punnett square: Colors distinguish the four classes of genotypes identified by Mendel: 1)Plants homozygous for all traits (red); 2)Plants homozygous for two traits and heterozygous for one (pale blue); 3)Plants heterozygous for two traits and homozygous for one (pink); 4)Plants heterozygous for all three traits (yellow).

9. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 9. Mendel’s series 1:2:4:8 Examining the Punnett square, we can see that:  each of the 8 different red genotypes appears in the table only once, so that each has a probability of 1/64;  each of the 12 different pale-blue genotypes appears in the table twice, so that each occurs with probability 2/64 or 1/32;  each of the 6 pink genotypes appears in the table four times, so that each occurs with probability 4/64 or 1/16;  the unique yellow genotype appears in the table eight times, so that its probability is 8/64 or 1/8. Summing these probabilities together for each class we find the series 1:2:4:8 that Mendel correctly recognized and allowed him to confirm the law of independent segregation.

10. Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini 10. Chi-square analysis of Mendel’ tri-hybrid crosses Reasoning in modern terms, we can test the independent segregation of the three loci investigated by Mendel by means of chi-square analysis Reasoning in modern terms, we can test the independent segregation of the three loci investigated by Mendel by means of chi-square analysis Expected values of each genotype is obtained by mutiplying its probability (1/8, 1/16, 1/32, or 1/64) by the total number of observation (639). Expected values of each genotype is obtained by mutiplying its probability (1/8, 1/16, 1/32, or 1/64) by the total number of observation (639). The final chi-square value of 15.3 is not significant of deviation from the expected values (P > 0.05). The final chi-square value of 15.3 is not significant of deviation from the expected values (P > 0.05).