## Info

The probability of an offspring from this cross having genotype aabbccddee is now easily obtained by using the multiplication rule: 1/4 X 1/4 X 1/2 X 1/2 X 1/4 = 1/256. This calculation assumes that genes at these five loci all assort independently.

### Concepts

A cross including several characteristics can be worked by breaking the cross down into single-locus crosses and using the multiplication rule to determine the proportions of combinations of characteristics (provided the genes assort independently).

### The Dihybrid Testcross

Let's practice using the branch diagram by determining the types and proportions of phenotypes in a dihybrid testcross between the round and yellow F1 plants (Rr Yy) that Mendel obtained in his dihybrid cross and the wrinkled and green plants (rryy) (Figure 3.13). Break the cross down into a series of single-locus crosses. The cross Rr X rr yields 1/2 round (Rr) progeny and 1/2 wrinkled (rr) progeny. The cross Yy X yy yields 1/2 yellow (Yy) progeny and 1/2 green (yy)

Round, yellow

Wrinkled, green x

RrYy

Expected proportions for first character

Expected proportions for second character

Expected proportions for first character

/ Yy Yellow rryy

Expected proportions for both characters

RrYy X rr yy

/ Rr Round

/ rr Wrinkled m

/ Yy Yellow

Green

Yellow

Green Green

Rr Yy

Rr yy

Round, green rr Yy

Wrinkled, yellow rr yy

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

progeny. Using the multiplication rule, we find the proportion of round and yellow progeny to be 1/2 (the probability of round) X 1/2 (the probability of yellow) = 1/4. Four combinations of traits with the following proportions appear in the offspring: 1/4 RrYy, round yellow; 1/4 Rryy, round green; 1/4 rrYy, wrinkled yellow; and 1/4 rryy, wrinkled green.

### Trihybrid Crosses

The branch diagram can also be applied to crosses including three characters (called trihybrid crosses). In one tri-hybrid cross, Mendel crossed a pure-breeding variety that possessed round seeds, yellow endosperm, and gray seed coats with another pure-breeding variety that possessed wrinkled seeds, green endosperm, and white seed coats (Figure 3.14). The branch diagram shows that the expected phenotypic ratio in the F2 is 27:9:9:9:3:3:3:1, and the numbers that Mendel obtained from this cross closely fit these expected ones.

In monohybrid crosses, we have seen that three genotypes (RR, Rr, and rr) are produced in the F2. In dihybrid crosses, nine genotypes (3 genotypes for the first locus X 3 genotypes for the second locus = 9) are produced in the F2:

Expected proportions for first trait

Rr x Rr

Cross nr

Cross nr

/ rr Wrinkled x