Question

An inbred strain of plants has a mean height of \(24 \mathrm{cm}\). A second strain of the same species from a different peopraphic region also has a mean height of \(24 \mathrm{cm}\). When plants from the two strains are crossed together, the \(\mathrm{F}_{1}\) plants are the same height as the parent plants, However, the \(\mathrm{F}_{2}\) generation shows a wide range of heights;the majority are like the \(P_{1}\) and \(Y_{1}\) plants, but approximately 4 of 1000 are only \(12 \mathrm{cm}\) high and about 4 of 1000 are \(36 \mathrm{cm}\) high. (a) What mode of inheritance is occurring here? (b) How many gene pairs are involved? (c) How much does each gene contribute to plant height? (d) Indicate one possible set of genotypes for the original \(P_{1}\) parents and the \(P_{1}\) plants that could account for these results. (e) Indicate three possible genotypes that could account for \(\mathrm{F}_{2}\) plants that are \(18 \mathrm{cm}\) high and three that account for \(\mathrm{F}_{2}\) plants that are \(33 \mathrm{cm}\) high.

Short answer

Answer: The possible genotypes for 18 cm tall plants in the F2 generation are AaBb, aaBB, or AAbb. For 30 cm tall plants in the F2 generation, the possible genotypes are AABb, AaBB, or AABB.

Step-by-step solution

Determine the mode of inheritance.

Based on the given information, the mode of inheritance involved in this scenario is polygenic inheritance. Polygenic inheritance refers to the inheritance of multiple genes that control a single trait, such as height in this case.

Calculate the number of gene pairs involved.

In the \(F_{2}\) generation, approximately 4 plants out of 1000 show either a 12 cm or 36 cm height. Since these heights represent extreme values compared to the mean height of 24 cm, it indicates that each gene contributes a certain amount of height. The distribution suggests that there are two gene pairs involved, as there are three distinct height values (12, 24, 36) being observed, 4 extreme plants out of 1000, and 2 intermediate height values between the extreme heights.

Determine the contribution of each gene.

From this information, it can be determined that each gene contributes 6 cm to the plant's height. This is calculated as follows: the difference between the extreme heights (36 cm - 12 cm = 24 cm), divided by the number of gene pairs involved (2), resulting in 12 cm per gene pair. Each single gene in the pair will contribute half of that amount (12 cm / 2 = 6 cm).

Find possible genotypes for the original \(P_{1}\) parents and plants.

As both the original strains and the \(F_{1}\) plants have a height of 24 cm, they must have one of each type of gene. Therefore, a possible set of genotypes for the original \(P_{1}\) parents and plants is AABB, where the capital A and B are the additive genes that contribute to the plant height, and the original strains may have AAbb or aaBB genotypes.

Find possible genotypes for 18 cm and 33 cm tall plants in the \(F_{2}\) generation.

For 18 cm tall plants, the total contribution of height would be -6 cm from the mean height (24 cm). In this case, a possible set of three genotypes is: AaBb, aaBB, or AAbb. To reach a height of 33 cm (which is actually 30 cm, due to rounding), an additional contribution from both genes is needed, totaling 6 cm above the mean height. A possible set of three genotypes for 30 cm tall plants in the \(F_{2}\) generation would be: AABb, AaBB, or AABB.

Key concepts

Genetics

Genetics is the scientific study of heredity and the variation of inherited characteristics. It focuses on how traits are passed from parents to offspring through genes. Genes are the basic units of heredity, made up of DNA, and are responsible for guiding the development and functioning of all living organisms.

Every organism has a set of genetic instructions encoded in its DNA, which determine its physical and behavioral traits. These instructions are inherited from the organism's parents, with each parent contributing a set of genes to their offspring. The combination of genes from both parents can lead to variations in inherited traits, which is why siblings can look different from each other even though they have the same parents.

Understanding genetics is crucial for comprehending polygenic inheritance, which involves the interaction of multiple genes to influence a single trait. Each gene may have a small effect individually, but together, they can produce a wide range of outcomes in traits like plant height, skin color, or the risk of developing certain diseases. This complexity of genetic interactions is a fundamental concept in the study of biology and medicine.

Inherited Traits

Inherited traits are characteristics that are passed down from one generation to the next through the genetic information contained within an organism's DNA. Traits can include a wide range of features such as physical appearance, behavioral tendencies, and susceptibility to certain health conditions.

Some traits are determined by a single gene, while others, like those in the exercise, are the result of polygenic inheritance, where multiple genes influence the outcome. These traits often show a continuous range of variation within the population, such as the range of heights seen in the plant exercise.

Inherited traits are not always visible directly; some may lay dormant due to the dominance of other genes, or they may require specific environmental factors to be expressed. The study of how traits are inherited allows scientists to predict the likelihood of certain characteristics appearing in the offspring, understand the genetic diversity of populations, and explore ways to manage or treat hereditary disorders.

Gene Contribution

Gene contribution refers to the effect that each gene has on a particular trait. In polygenic inheritance, several genes contribute additively to the phenotype, which is the observable characteristic or trait of an organism.

For example, in the plant height exercise, each gene involved in determining plant height contributes a certain amount of centimeters. The calculation of gene contribution is essential for understanding the genetics behind quantitative traits, and it allows individuals to predict phenotypes based on genotypes. It also helps explain the variation within populations, such as the wide range of heights observed in the F2 generation of the plant cross.

Determining the specific contribution of each gene can be complex because it involves understanding both the genetics and the potential environmental factors that might influence trait expression. Nonetheless, it is a pivotal aspect of genetics that helps provide a comprehensive picture of how traits are transmitted and expressed in living organisms.