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.and the probability of each trait is determined.

Expected proportions for both traits

.and the probability of each trait is determined.

| The individual traits and the associated probabilities are then combined by using the branch method.

| The individual traits and the associated probabilities are then combined by using the branch method.

These proportions are determined from the cross in part a.

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These proportions are determined from the cross in part a.

Wrinkled

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1/4 yy Lrr

rryy

3.12 A branch diagram can be used for determining the phenotypes and expected proportions of offspring from a dihybrid cross (RrYy x RrYy).

proportion of progeny with wrinkled and green seeds is

Branch diagrams are a convenient way of organizing all the combinations of characteristics (Figure 3.12b). In the first column, list the proportions of the phenotypes for one character (here, 3/4 round and 1/4 wrinkled). In the second column, list the proportions of the phenotypes for the second character (3/4 yellow and 1/4 green) next to each of the phenotypes in the first column: put 3/4 yellow and 1/4 green next to the round phenotype and again next to the wrinkled phenotype. Draw lines between the phenotypes in the first column and each of the phenotypes in the second column. Now follow each branch of the diagram, multiplying the probabilities for each trait along that branch. One branch leads from round to yellow, yielding round and yellow progeny. Another branch leads from round to green, yielding round and green progeny, and so on. The probability of progeny with a particular combination of traits is calculated by using the multiplicative rule: the probability of round (3/4) and yellow (3/4) seeds is 3/4 X 3/4 = 9/16. The advantage of the branch diagram is that it helps keep track of all the potential combinations of traits that may appear in the progeny. It can be used to determine phenotypic or genotypic ratios for any number of characteristics.

Using probability is much faster than using the Punnett square for crosses that include multiple loci. Genotypic and phenotypic ratios can quickly be worked out by combining, with the multiplication rule, the simple ratios in Tables 3.2 and 3.3. The probability method is particularly efficient if we need the probability of only a particular phenotype or genotype among the progeny of a cross. Suppose we needed to know the probability of obtaining the genotype Rryy in the F2 of the dihybrid cross in Figure 3.11. The probability of obtaining the Rr genotype in a cross of Rr X Rr is 1/2 and that of obtaining yy progeny in a cross of Yy X Yy is 1/4 (see Table 3.3). Using the multiplication rule, we find the probability of Rryy to be 1/2 X 1/4 = 1/8.

To illustrate the advantage of the probability method, consider the cross AaBbccDdEe X AaBbCcddEe. Suppose we wanted to know the probability of obtaining offspring with the genotype aabbccddee. If we used a Punnett square to determine this probability, we might be working on the solution for months. However, we can quickly figure the probability of obtaining this one genotype by breaking this cross into a series of single-locus crosses:

Cross

Progeny genotype aa bb cc dd ee

Probability

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