The law of features independent assortment

Mendel’s work was not limited to single-trait crosses. In his writings, Mendel wondered whether the patterns he had detected in the single trait crosses would apply to crosses involving multiple traits. He decided to test his ideas using a two-trait (or dihybrid) cross. Mendel chose the traits of seed shape and seed color for his first experiment. He recognized from his single-trait crosses that yellow seed color was dominant to green, and round seed shape was dominant to wrinkle. To facilitate analysis of his crosses, he assigned the following symbols to the traits:

A—round seed shape

a—wrinkled seed shape

B—yellow seed color

b—green seed color

This concept of assigning the dominant trait a capital letter, and the recessive variant of the trait the lower case of the same letter, is still used in many genetic systems. In his cross, Mendel followed the same pattern as he did in the single trait cross. First he obtained two true-breeding lines of pea plants. The first produced round and yellow seeds (AB using Mendel’s symbols), while the second produced wrinkled and green seeds (symbol: ab). When these were crossed, 100 percent of the seeds produced in the first generation were round and yellow. This was not surprising, since in the single-trait crossed both round and yellow were shown to be dominant. When he crossed two members of the first generation, he obtained 556 seeds in the second generation, all of which fell into one of four figured classes. The seeds were either round yellow or round green, or wrinkled yellow or wrinkled green. This represented all the possible combinations from the parents, but only if the traits were acting independent from one another. In other words, seed color was independent from seed shape, and these traits assorted independently in the offspring. This concept serves as the basis of Mendel’s law of independent assortment, or Second Law of Heredity.

An examination of the number of seeds in each class indicates that the offspring are not distributed evenly among the classes. Mendel recognized that there was a distinct ratio present in the second generation seeds. The seeds with two dominant traits, round and yellow, were represented 9/16 of the time. There were two classes of seeds that possessed only one of the dominant traits: round and green and wrinkled and yellow. Each of these was present in approximately 3/16 of the offspring. In comparison, there were relatively few seeds displaying the two recessive traits (wrinkled and green). These only occurred 1/16 of the time.

Mendel’s Experiments with Two-Trait (Dihybrid Crosses)

(Courtesy of Ricochet Productions)

By the laws of probability, the probability of getting independent events is equal to the sum of their individual probabilities. If we dissect a two-trait cross into two one-trait crosses, then the probability of getting a recessive trait in the second generation is 1 in 4 (1/4). Thus the probability of two recessive traits getting is equal to the product of their individual probabilities (1/4 for seed shape × 1/4 for seed color), or 1/16. This is exactly what Mendel observed in his two-trait cross.

Mendel recognized that a single cross was not a verification of his ideas, so he designed additional crosses under the same parameters. All of these yielded similar results, providing an additional verification of his law of independent assortment.

Mendel’s paper, “Experiments in Plant Hybridization” (1865) was published in the Br.unn Scientific Society Proceedings. Mendel’s work had almost no influence on the scientific community of the time, and quickly fell into obscurity. However, 35 years later, the scientific world caught up to Mendel.