USA Biology Olympiad (USABO) Practice Exam

If two inbred plant strains both average 24 cm in height, what fraction of the F2 plants will be 27 cm in height?

1. 28/256

2. 56/256

3. 40/256

4. 64/256

The correct answer is: 56/256

When two inbred plant strains with the same average height of 24 cm are crossed, the resulting F1 generation will also be uniform in traits due to the lack of genetic variation. When these F1 generation plants are self-pollinated to create the F2 generation, new combinations of traits can arise due to segregation and recombination of alleles. For height specifically, we can utilize a simple model assuming that height is controlled by a number of additive alleles. If we hypothesize that the average height of 24 cm corresponds to a specific genotype and that reaching 27 cm represents a common variation occurring due to the contribution of dominant alleles, we can use the concept of a normal distribution. The F2 plants will show variation around the average height of 24 cm due to the genetic segregation of alleles. In a typical genetic model involving height, a certain fraction of the plants will approximately reach heights above the average. In this scenario, 27 cm is a relatively small increment above the average, thus the fraction of plants that could achieve this height is determined by the spread of the phenotypes in the F2 generation. One can typically expect that a specific fraction of plants will attain each height based on variation in traits. For heights