Mendel’s Second Law (A Quick Review)
To analyze the segregation of two traits (e.g., colour, wrinkle) at the same time, in the same individual, Mendel crossed a pure breeding line of green, wrinkled peas with a pure breeding line of yellow, round peas to produce F1 progeny that were all green and round, and which were also dihybrids; they carried two alleles at each of two loci (Figure 8.2.1).
If the inheritance of seed color was truly independent of seed shape, then when the F1 dihybrids were crossed to each other, a 3:1 ratio of one trait should be observed within each phenotypic class of the other trait (Figure 8.2.1). Using the product law, we would therefore predict that if ¾ of the progeny were green, and ¾ of the progeny were round, then ¾ × ¾ = 9/16 of the progeny would be both round and green. Likewise, ¾ × ¼ = 3/16 of the progeny would be both round and yellow, and so on. By applying the product rule to all these combinations of phenotypes, we can predict a 9:3:3:1 phenotypic ratio among the progeny of a dihybrid cross, if certain conditions are met, including the independent segregation of the alleles at each locus. Indeed, 9:3:3:1 is very close to the ratio Mendel observed in his studies of dihybrid crosses, leading him to state his Second Law, the Law of Independent Assortment, which we now express as follows: two loci assort independently of each other during gamete formation.
Assumptions of the 9:3:3:1 Ratio
Both the product rule and the Punnett Square approaches showed that a 9:3:3:1 phenotypic ratio is expected among the progeny of a dihybrid cross such as Mendel’s RrYy × RrYy. In making these expectations, we assumed that:
- Both loci assort independently;
- One allele at each locus is completely dominant; and
- Each of four possible phenotypes can be distinguished unambiguously, with no interactions between the two genes that would alter the phenotypes.
Deviations from the 9:3:3:1 phenotypic ratio may indicate that one or more of the above conditions has not been met. For example, Linkage of the two loci results in a distortion of the ratios expected from independent assortment. Also, if complete dominance is lacking (e.g., co-dominance or incomplete dominance) then the ratios will also be distorted. Finally, if there is an interaction between the two loci such that the four classes cannot be distinguished (which is the topic under consideration in this chapter), the ratio will also deviate from 9:3:3:1.
Modified ratios in the progeny of a dihybrid cross can, therefore, reveal useful information about the genes being investigated. Such interactions lead to Modified Mendelian Ratios.
- Figure 8.2.1 Mendel 3b by Miguelferig, CC0 1.0 Public Domain Dedication, via Wikimedia Commons
- Figure 8.2.2 Original by Deyholos (2017), CC BY-NC 3.0, Open Genetics Lectures
Deyholos, M. (2017). Figure 6. A Punnett square showing the results of the dihybrid cross [digital image]. In Locke, J., Harrington, M., Canham, L. and Min Ku Kang (Eds.), Open Genetics Lectures, Fall 2017 (Chapter 17, p. 4). Dataverse/ BCcampus. http://solr.bccampus.ca:8001/bcc/file/7a7b00f9-fb56-4c49-81a9-cfa3ad80e6d8/1/OpenGeneticsLectures_Fall2017.pdf