Text Assignment: Chapter 12, pages 358 - 364 (to start of Probability), and pages 371-376. The section on probability and chi square analysis (pages 364-371) will be the subject of the next two lectures.

Major concepts

• Principle of equal segregation (Mendel's first "law").
• Principle of independent assortment (Mendel's second "law").
• Punnett square.
  
• Forked line method.
  
• Product rule.
  
• Phenotypic ratios
  • Monohybrid cross, 3:1 phenotypic ratio
    
  • Dihybrid cross, 9:3:3:1 phenotypic ratio.
  • Trihybrid cross, 27:9:9:9:3:3:3:1 phenotypic ratio.
• Pedigrees
  • Standard symbols
  • Propositus, proposita
  • Mode of inheritance

DIHYBRID CROSSES

Principle of Equal Segregation: As discussed in the previous lecture, each parent has two "factors" (genes or alleles) for each inherited trait, and randomly contributes one or the other to each gamete, and thus to each of its progeny. This process of segregation of alleles into gametes is strictly random.

Principle of Independent Assortment: Each unlinked gene pair assorts independently into the offspring. Thus, among offspring that have received a particular allele at one locus, there will be a random assortment of alleles at a second unlinked locus. (This is only valid for genes that are not on the same chromosome and for genes on the same chromosome but so far apart that crossing over makes them appear unlinked).

Mendel's "laws": The principle of equal segregation and the principle of independent assortment are sometimes referred to as Mendel's first and second "laws". However, the term "law" is not really appropriate because of many exceptions due to phenomena such as linkage.

Product Rule: When two independent events occur simultaneously, their combined probability is equal to the product of their individual probabilities. Thus, if one-half of the gametes of a heterozygote receive a particular allele at the first genetic locus, one-half of those gametes will receive a particular allele at a second unlinked locus. Thus, for independent assortment, the probability that a gamete will contain a specific pair of alleles from two unlinked genetic loci is 1/2 x 1/2 = 1/4.

Punnett square: The Punnett square (introduced in the previous lecture) is a convenient method for analysis of the products of independent assortment of small numbers of unlinked genes. All possible pollen or sperm haploid genomes (haplotypes) are displayed along one dimension (for example, across the top). All possible female haploid genomes are displayed along the other dimension (for example, down the left side). The diploid genotypes that can be formed by fertilization events involving all of the possible combination of male and female gametes are displayed in the squares formed by the intersections of the vertical columns with the hortizontal rows. The predicted genotype is also usually included in the square with each of the genotypes. Genotypic or phenotypic ratios are then determined by counting all of the appropriate combinations. The Punnett square is a highly effective means for analyzing a dihybrid cross (figure 12.10), and also works reasonably well for a trihybrid cross (3 unlinked genes). However, it rapidly becomes extremely cumbersome as the number of unlinked events is increased.

9:3:3:1 phenotypic ratio: For a dihybrid cross (one that involves parents that are heterozygous for two unlinked loci), each parent will produce four different types of gametes. When these are combined in all possible combinations in a Punnett square, 16 different genotypic combinations are generated (figure 3.7). Because of independent assortment, 3/4 of these will exhibit the dominant phenotype for the first locus (yellow seeds) and 3/4 will also exhibit the dominant phenotype for the second locus (round seeds). Within the 3/4 with yellow seeds, there will be 3/4 whose seeds are round and 1/4 whose seeds are wrinkled. Similarly, within the 1/4 with green seeds, there will be 3/4 with round seeds and 1/4 with wrinkled seeds. When all of the multiplication is done, 9/16 of the seeds are round and yellow, 3/16 are round and green, 3/16 are yellow and wrinkled, and 1/16 are green and wrinkled. Thus, the phenotypic ratio from a dihybrid cross is 9:3:3:1. This can be verified by counting the squares on a Punnett square. In the ilustration that follows, the genotype is shown in each square, followed by the phenotype in parenthesis.

Forked line approach: For three or more unlinked events, Punnett squares, which do a complete genotypic analysis, tend to become quite cumbersome. With three unlinked genes, each parent can produce 8 different types of gametes, which generates 64 possible genotypic combinations, each depicted as a separate cell within the Punnett square. For four unllnked markers, there are 16 possible gametes from each parent and 256 cells in the complete Punnett square. It is therefore generally more effective to use the forked line approach, which is based on possible alternatives, rather than all possible fertilization events. The forked line can be based on phenotype, as shown below, or on genotype as shown in figure 12.12 of the textbook. Each branch point represents the expected distribution of phenotypes or genotypes at a particular locus. Multiplying the expected distributions at each of the branches across the diagram provides an easy calculation of the expected frequency of any particular phenotypic or genotypic combination. The example below is for phenotypic distribution when the parents are heterozygous at three unlinked loci in peas. Although this cross is set up so that each locus yields a 3:1 phenotypic ratio, other ratios can be employed, such as the 1:2:1 genotypic ratio in figure 12.12. It is also possible to have different crosses at different branches, such as a test cross (heterozygote x homozygous recessive) at one of the loci, which would yield a 1:1 ratio at that particular branch.

                    3/4 Full       = 27/64 YRF phenotype
                   /
                  3/4 Round
                 / \
                /   1/4 constricted = 9/64 YRf phenotype
               /
              3/4 Yellow
             / \
            /   \   3/4 Full        = 9/64 YrF phenotype 
           /     \ /
          /       1/4 Wrinkled
         /         \
        /           1/4 constricted = 3/64 Yrf phenotype
       /
YyRrFf x YyRrFf
       \
        \           3/4 Full        = 9/64 yRF phenotype
         \         /
          \       3/4 Round  
           \     / \
            \   /   1/4 constricted = 3/64 yRf phenotype 
             \ /
              1/4 green 
               \
                \   3/4 Full        = 3/64 yrF phenotype
                 \ /
                  1/4 wrinkled
                   \
                    1/4 constricted = 1/64 yrf phenotype .

27:9:9:9:3:3:3:1 ratio:. As can be seen in the forked line diagram above, a trihybrid cross yields a phenotypic ratio of 27:9:9:9:3:3:3:1. This reflects the phenotypes generated by the 64 genotypic combinations resulting from 8 different male gametes fertilizing 8 different female gametes. As can be seen from figure 12.12, a total of 27 different genotypes (3³) are involved in generating the 8 possible phenotypes (2³) in a trihybrid cross.

Absense of linkage: Mendel's original studies dealt only with genes in which there was complete dominance of one allele over the other. In addition, the genes he studied were all on separate chromosomes or else so far separated from one another on the same chromosomes so that they did not exhibit any detectable linkage to one another (Figure 12.13). One possible exception may be the locus with alleles that determine full versus constricted pods. Our textbook associates those traits with the P locus on Chromosome VI. However, last year's text (Klug and Cummings, Concepts of Genetics, 5th Edition -- Norlin Reserve) and the Mendel Web Glossary assign those traits to the V locus on chromosome IV, which is located close enough to the stem length locus Le (tall vs. dwarf) so that they should exhibit linkage. Mendel never reported experiments designed to demonstrate independent assortment of those two characteristics. This, together with the uncertainty about which locus he worked with makes it uncertain as to whether he never observed linkage or rejected it as a bad experiment that did not match the rest of his data.

Do we owe Mendelian genetics to a failed examination? Section 12.7 presents some background information about Mendel. In 1850, he failed an examination for teacher certification. He then enrolled in University courses in mathematics, physics, chemistry, and biology. The training he received in mathematics almost certainly set the stage for mathematical interpretation of his data, which was unusual in biology at the time.

Was Mendel too far ahead of his time? Mendel's studies were presented in meetings in 1865 and published in 1866. However, for a variety of reasons, including the popularity of the blending theory and Mendel's heavy reliance on mathematical calculations, which was unusual in the biology of that time period, they remained essentially unknown and unappreciated until about 1900, when the principles of inheritance and Mendel's earlier work were rediscovered. By the time of the rediscovery of Mendel's work, the behaviour of chromosomes in meiosis and their probable role as carriers of heredity were beginning to be reasonably well understood. Thus, Mendel's observations were suddenly recognized as being far ahead of their time and strongly supportive of the newly emerging viewpoints. The textbook goes through a number of the historical details that we will not have time to cover in class. You are strongly encouraged to read this section.

Did Mendel manipulate his data? Over the years, many critics have expressed the opinion that Mendel's data were better than would be expected statistically. The authors of our textbook present a number of reasons why they do not think this was the case.

Analysis of human inheritance: Because ethical considerations do not allow direct human experimentation, it is necessary to base the study of human inheritance on the results of existing family histories. This is done through the use of pedigree analysis of families where genetic traits of interest have appeared. Table 12.3 summarizes patterns of inheritance for a number of inherited diseases that have been discerned through the use of pedigree analysis. A standard set of symbols has been developed for stuch studies, as described below.

Standard symbols used in pedigree analysis: Figure 12.14 summarizes the symbols used for human pedigree analysis. An example of a pedigree for a dominant trait, brachydactyly, is presented in figure 12.15. In brief summary, the following symbols and conventions are employed:

• A square is used to indicate a male
• A circle is used to indicate a female
• A diamond is sometimes used to indicate an individual (or group of individuals) whose gender is not specified.
• A hortizontal line between a male and a female indicates a mating (or repeated matings of the same couple)
• Consanguinous matings, which are defined as matings between related individuals (for example cousins in figure 12.14), are shown with double hortizontal lines.
• A vertical line downward from the mating line connects it to the offspring of that mating.
• A second hortizontal line (the sibship line) joins together all of the progeny of the couple.
• The progeny are shown in birth order, left to right, with each connected to the sibship line with a vertical line.
• Branching of the vertical line indicates multiple births
• An individual who displays the phenotype whose inheritance is being followed is normally shown as a solid symbol (square or circle).
• Half shaded symbols are sometimes used to identify individuals known to be heterozygous carriers of recessive traits.
• When known, each individual's genotype may be written directly above or below his or her symbol.
• Generations are identified with Roman numerals at the left, starting with oldest generation included in the study.
• Within each generation, individuals are given arabic numbers across the pedigree from left to right. Note that this may include several different families (numbering of individuals has not been included the examples in out textbook)
• Any individual on the pedigree can be identified by the Roman numeral for the generation, followed by the arabic numeral for the individual in that generation.
• The individual whose phenotype first drew attention to a particular pedigree is referred to as the propositus if male, and proposita if female.
• The mode of inheritance is inferred from the pattern of phenotypic expression. For example, dominant inheritance requires that at least one of the parents must express the phenotype in question (as in figure 12.15), whereas neither parent of a homozygous recessive individual needs to express the recessive phenotype (figure 12.14).

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