10.2 Rules of chance

Explain Mendel's principle of segregation. Objectives Explain Mendel's principle of segregation. Describe how probability applies to genetics. Contrast genotype and phenotype. Explain Mendel's principle of independent assortment. Key Terms hybrid monohybrid cross allele homozygous heterozygous dominant recessive Punnett square phenotype genotype testcross dihybrid cross

Mendel performed many experiments in which he tracked the inheritance of characters in pea plants, such as flower color and seed shape (pea shape). The results led him to formulate several hypotheses about inheritance

Mendel's Principle of Segregation In the language of genetics, the offspring of two different true-breeding varieties are called hybrids. The parental plants are called the P generation (P for parental), and the hybrid offspring are the F1 generation When the F1 plants self-fertilize or fertilize each other, their offspring are the F2 generation.

In one experiment, Mendel crossed purple-flowered pea plants with white-flowered pea plants. This is an example of a monohybrid cross, a pairing in which the parent plants differ in only one (mono) character. Mendel saw that the F1 hybrid plants were not a blend of purple and white. The F1 hybrids all had purple flowers, the same color as the purple-flowered parent. Was the factor for white flowers now lost as a result of the crossing?

By allowing the F1 plants to self-fertilize, Mendel found the answer to be no. About one fourth of the F2 plants had white flowers. Mendel concluded that the factor for white flowers did not disappear in the F1 plants. Instead, only the purple flower factor was affecting F1 flower color. He reasoned that the F1 plants must have carried two factors for the flower color character, one for purple and one for white. Today, Mendel's "factors" are called genes.

                                                                                                                                                                                                                          

Mendel used monohybrid crosses to investigate six other pea plant characters Each cross produced the same pattern. One of the two parent traits disappeared in the F1 generation, but then reappeared in about one fourth of the F2 offspring. From these results, Mendel developed four hypotheses.

There are alternative forms of genes There are alternative forms of genes. For example, the gene for flower color in pea plants exists in one form for purple and in another form for white. These alternative forms of genes are called alleles (uh LEELZ). For each inherited character, an organism has two alleles for the gene controlling that character, one from each parent. If the two alleles are the same, the individual is homozygous (hoh moh ZY gus) for that character. If the two alleles are different, the individual is heterozygous (het ur oh ZY gus).

When only one of the two different alleles in a heterozygous individual appears to affect the trait, that allele is called the dominant allele. And in such cases, the other allele that does not appear to affect the trait is called the recessive allele. In this book, a capital letter is used to represent the name of a dominant allele (in the flower color example, P). The lowercase version of the same letter is used to represent the recessive allele (p). The two alleles for a character segregate (separate) during the formation of gametes (sex cells), so that each gamete carries only one allele for each character. This is known as Mendel's principle of segregation. The union of gametes during fertilization reforms allele pairs in the offspring.

                                                                                                                                                                                                                                                                                              

Probability and Punnett Squares In a monohybrid cross of true-breeding (homozygous) purple-flowered and white-flowered plants, Mendel's hypotheses predict that each F1 plant will get the dominant purple-flower allele (P) from one parent and the recessive white-flower allele (p) from the other parent. Each F1 plant will be heterozygous: Pp. Then the F1 plants grow up and make gametes of their own. Each gamete receives only one allele for flower color, P or p, with equal likelihood.

As the F1 plants fertilize each other, gametes combine randomly and form zygotes with pairs of alleles. The likelihood of each specific pair forming is key to the inheritance pattern seen in the F2 generation. Consider the analogy of being handed two pennies. As you look at the two pennies, you will see 2 heads or 1 head and 1 tail or 2 tails. (Note that there are two different ways to get the outcome of 1 head and 1 tail.) The side shown by one coin is unaffected by the side shown by the other coin. But what is the probability of a particular combination occurring? For example, what is the probability that you will see 2 heads?

Punnett Squares You can build a table that shows the probability of each combination. List the probabilities for the first coin along the top of a piece of paper, and the probabilities for the second coin along the edge of the paper. Create a grid as shown in Figure 10-5. The probability of a particular combination is the product of the separate probabilities for each coin. For example, the probability of 2 heads showing is 1/2 x 1/2 = 1/4.

                                                                                                                                                                                                                                                                                              

In the same way, you can calculate the probabilities for different combinations of alleles resulting from a genetic cross. The gametes of the purple F1 flowers pair randomly, making the allele combinations in the F2 generation PP or Pp or pp This type of diagram that shows all possible outcomes of a genetic cross is called a Punnett square. You can use a Punnett square to predict probabilities of particular outcomes if you know the genetic makeup of both parents.

Genotype and Phenotype An observable trait (such as purple flowers) is called the phenotype (FEE noh type). The genetic makeup, or combination of alleles (such as PP), is called the genotype (JEE noh type). For the F2 plants, the ratio of plants with purple flowers to those with white flowers (3 purple : 1 white) is called the phenotypic ratio. The genotypic ratio is 1 PP : 2 Pp : 1 pp.

The Testcross What is the genotype of an organism that displays the dominant phenotype? Suppose, for example, that you have a purple-flowered pea plant. Its genotype could be either of two possibilities: PP or Pp. To determine whether the purple-flowered plant is homozygous (PP) or heterozygous (Pp), you need to perform what geneticists call a testcross. A testcross breeds an individual of unknown genotype, but dominant phenotype (your purple-flowered mystery plant) with a homozygous recessive individual—in this case, a white-flowered plant (pp )

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Mendel's Principle of Independent Assortment Two of the seven characters Mendel studied were qualities of the peas themselves: shape and color. From his monohybrid crosses, Mendel knew that round pea shape was dominant to wrinkled shape, and yellow color was dominant to green. What would be the result of a dihybrid cross—crossing organisms differing in two characters? Mendel crossed a true-breeding plant grown from a round yellow seed (genotype RRYY) with a true-breeding plant grown from a wrinkled green seed (genotype rryy). The first parent could only produce RY gametes. The other could only produce ry gametes. The union of these RY and ry gametes yielded hybrid peas heterozygous for both characters (RrYy). All peas had the dominant phenotype: They were round and yellow

                                                                                                                                                                                                                               

The hybrid peas grew into F1 plants, which Mendel allowed to self-fertilize. This produced four phenotypes of peas. Assuming there are four equally likely combinations of alleles in the gametes produced by the F1 generation—RY, rY, Ry, and ry—a Punnett square predicts a phenotypic ratio of 9 : 3 : 3 : 1

                                                                                                                                                                                                                                                     

Mendel tested his seven pea characters in various dihybrid combinations. The ratio of phenotypes in the F2 generation was always very close to the predicted ratio of 9 : 3 : 3 : 1. Based on these results Mendel proposed his principle of independent assortment. This principle states that during gamete formation in an F2 cross, a particular allele for one character can be paired with either allele of another character. For instance, in the above example, R can end up with either Y or y, and r can end up with either Y or y. The alleles for different genes are sorted into the gametes independently of one another.