GoalPredict the offspring of a cross that follows two traits at once, using a 16-box Punnett square and the ratio 9 : 3 : 3 : 1.
New words
Mendel’s second law · when two traits are followed together, each pair of alleles separates independently into the gametesdihybrid cross · a cross that follows two traits at the same timegenetic diversity · the variety of genes and traits among the individuals of a species
Explanation
Mendel also followed two traits together, for example seed shape (round R, wrinkled r) and seed colour (yellow Y, green y). His second law says that each pair of alleles separates independently into the gametes. Cross a pure round yellow plant with a pure wrinkled green plant: RRYY × rryy gives an F₁ that is all RrYy, round and yellow. When two F₁ plants are crossed, each makes four kinds of gametes with equal chance: RY, Ry, rY and ry. So the Punnett square has 4 × 4 = 16 boxes. The phenotypes come out in the ratio 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green. Count one trait at a time and the old law returns: round 12 and wrinkled 4 is 3 : 1, and yellow 12 and green 4 is also 3 : 1. Because of independent assortment, each human also has a unique mix of genes; genetic diversity helps a species survive when conditions change. The 9 : 3 : 3 : 1 ratio is a probability, so real counts are only close to it.
Gametes of RrYy: pick one allele from each pair. R with Y, R with y, r with Y, r with y: four gametes, RY, Ry, rY and ry, each with chance 1/4. Two parents each make 4 kinds, so there are 4 × 4 = 16 boxes.
With 160 F₂ seeds we expect 9 : 3 : 3 : 1 in sixteenths. One sixteenth is 160 ÷ 16 = 10 seeds, so about 90 round yellow, 30 round green, 30 wrinkled yellow and 10 wrinkled green. Check: 90 + 30 + 30 + 10 = 160.
Peas: T tall (dominant), t short; G green pods (dominant), g yellow pods. TtGg × TtGg gives 9 tall green-podded : 3 tall yellow-podded : 3 short green-podded : 1 short yellow-podded. So 9/16 are tall with green pods. Among 64 offspring: 36 : 12 : 12 : 4.
HhBb × hhbb (hairy and blue are dominant traits of an invented plant). The cross gives four equal phenotypes, 1 : 1 : 1 : 1: HhBb, Hhbb, hhBb and hhbb. Each is 1/4 of the offspring.
Class activity
Two coins for two traits. Coin A is the shape gene (heads R, tails r) and coin B is the colour gene (heads Y, tails y). Each parent is RrYy. Toss both coins twice for each offspring (once for each parent) and record the four phenotypes for 32 offspring. About 18 : 6 : 6 : 2 is expected for 32, but your counts will only come close. Then colour a 4 × 4 grid on squared paper by phenotype.
Practice
1
List the four kinds of gametes of the plant AaBb.
AB, Ab, aB and ab.
2
In a dihybrid cross of two heterozygous plants, how many boxes does the Punnett square have?
