Independent Assortment: _{Mendel's testcrosses and Punnett squares}

Why Mendel's work was underappreciated

How could Mendel's important work have been all but forgotten for nearly a generation?

Perhaps part of the answer is that Mendel's studies did not appear novel. Horticulturalists had long published plant-breeding experiments that superficially resembled those of Mendel. For example in the 1800s, Thomas Andrew Knight published nearly 100 articles on the subject of horticulture, including an article about inheritance in pea plants, pre-dating Mendel's work by three decades. Those studies, however, did not include rigorous backcrossing of the starting plants to generate pure-breeding parental strains, nor were the number of different colored peas in the offspring carefully recorded. When Mendel tried to repeat Knight's experiments, he spent two years generating pure-breeding plants for each of the seven traits he followed, and then carefully counted plants with each trait after the parental plants were systematically crossed and then self-pollinated. Unlike Knight, Mendel employed a rigorous scientific strategy when devising his experiments. By assuring that he had pure-breeding plants to start, he made certain that his results were reproducible. In this way, Mendel's work was quite different from that before him. Mendel's decision to study discrete traits, to systematically cross-pollinate pure-breeding plants, and to keep count of all the offspring gave the reproducible 3:1 ratio of dominant to recessive traits, leading to what is now called Mendel's First Law, the Law of Segregation.

Another reason Mendel's work was not celebrated in his lifetime is that the scientific community failed to appreciate the powerful reductionist approach that Mendel took to the complex question of inheritance. Holistic and organismal approaches were in style when Mendel was performing his experiments. Most notable at the time was Charles Darwin's work, which examined biological specimens as whole entities, drawing conclusions from the sum total of their traits. However, Darwin's work was criticized because it offered no mechanism for how species variations could arise. Unlike Darwin, Gregor Mendel simplified the question he wanted to answer. Rather than asking "How do traits pass from parents to their offspring?" he pursued a more scientifically testable question, namely, "Can I describe and predict how one trait is passed to the next generation?" The answers he got by teasing the question apart illuminated the solutions to the more complex questions of inheritance. Through his meticulous experiments with peas, Mendel's work began to reveal how complex traits are passed on, and at the nexus of Mendel's and Darwin's observations is a model by which "descent with modification" could arise.

The Law of Independent Assortment

The power of Mendel's scientific approach can be seen in the work that led him to his Second Law, the Law of Independent Assortment. The Law of Independent Assortment states that different traits are inherited completely independently of one another. Yet how could Mendel have deduced this if he had no idea of the mechanism by which traits were inherited?

When looking at two traits simultaneously, Mendel observed the ratio of dominant and recessive hybrids for each trait, and discovered that the ratio of traits in the plants from such crosses arose as 9:3:3:1. Namely, 9 offspring showed both dominant traits, 3 offspring showed one dominant and one recessive trait, 3 offspring showed the complementary dominant and recessive mix, and 1 of every 16 progeny showed both recessive traits. As an example, consider the experiment in which Mendel crossed a plant with yellow round peas to a plant with green wrinkled ones. Just as dictated by his First Law of Segregation, Mendel observed that all the F1 progeny from such a cross had yellow round peas (the two dominant traits). Next, Mendel self-pollinated these F1 progeny and counted 315 yellow round peas, 101 yellow wrinkled ones, 101 green round peas, and 32 green wrinkled ones in the F2 generation. Finding those rare peas with traits completely different from the peas of the F1 plant may have initially surprised Mendel; however, the 9:3:3:1 ratio arose no matter which two traits he considered. What Mendel realized is that the mathematics behind the 9:3:3:1 ratio suggested independent inheritance. Consider two independent traits each governed by a dominant:recessive ratio of 3:1. If we cross those two ratios, the result of the cross is the 9:3:3:1 ratio that Mendel observed.

A Punnett square (seen in Figure 1) can be used to understand these dihybrid crosses. For the pure breeding plant with yellow and round peas, Mendel would have annotated the two dominant factors underlying these traits as YY and RR, respectively. By crossing this YYRR plant to a pure breeding plant with green, wrinkled peas, annotated yyrr, plants heterozygous for each factor (YyRr) would arise (the F1 generation). It does not matter which symbol is listed first, the presence of even one dominant factor gives rise to the dominant trait (see our Mendel and Inheritance module). Since each F1 plant has one dominant and one recessive factor for each of the two traits examined, they are called "dihybrids."

Mendel produced the F2 generation by self-pollinating the F1 dihybrid plants. Based on a model of independent heredity, Mendel predicted that each of the traits in the dihybrid would be equally represented in the cross. Namely, 1/2 the plants would donate the dominant form of the color trait (Y); of these, 1/2 would donate the dominant seed factor (R) and 1/2 would donate the recessive seed factor, thus resulting in either "YR" or "Yr" crosses. Similarly, the recessive form of the color trait (y) could equally well pass to the F2 generation paired with either seed shape factor, so yR and yr should make up the other 1/2 of the possible combinations. In other words, the combinations of traits that could be mixed to form the F2 generation were: ¼ YR, ¼ Yr, ¼ yR, and ¼ yr. Writing these combinations along the top and side bars of a Punnett square (Figure 2) reveals how the phenotype (physical appearance) ratio of 9:3:3:1 arose in the F2 generation.

The outcome that Mendel observed from his dihybrid crosses confirmed that each trait could be described by a pair of factors that segregated to form progeny (his First Law), and further suggested that factors for multiple traits segregated independently, thus forming the basis for Mendel's Second Law of Inheritance.

Testcrosses support Mendel's hypothesis

Mendel continued his methodical experiments to rigorously analyze his theory. To test his ideas about random and independent segregation of dihybrid factors, he tested the prediction that the combinations of inputs from the F1 (dihybrid) generation were equally represented, namely four combinations existed: YR, Yr, yR, and yr. He tested this by crossing the dihybrids F1 plants with purebred plants that were doubly recessive for each factor: yyrr. Given that the purebred plant could donate only one possible genotype (yr), Mendel was able to test his hypothesis. The term used to describe such an experiment is a "testcross," and Figure 3 below shows the predicted outcomes from such a cross.

Confirming his ideas of independent assortment, the outcome of the dihybrid testcrosses exhibited a ratio of 1:1:1:1 of each phenotype. The testcrosses powerfully supported Mendel's hypothesis regarding genetic contributions to the dihybrid cross and confirmed his notion that each factor in the dihybrid sorted independently.

Beyond Mendel

The rediscovery of Mendel's work in 1900 allowed the principles he described to be confirmed and extended. The scientists who rediscovered the research popularized Mendel's principles by working with peas and other plants such as corn. Soon inheritance patterns in other organisms were investigated. By 1902, animals were shown (by William Bateson) to inherit traits in Mendelian fashion. Non-Mendelian inheritance and phenotypes arising from multiple factors were later described, but the patterns that Mendel elucidated affected our understanding of heredity profoundly. Given that descriptions of the physical material of heredity (namely DNA) would not appear for years after Mendel's work, his intuitive and insightful scientific analyses are all the more remarkable.