Question

Certain varieties of chrysanthemums contain \(18,36,54,72,\) and 90 chromosomes; all are multiples of a basic set of nine chromosomes. How would you describe these varieties genetically? What feature do the karyotypes of each variety share? A variety with 27 chromosomes has been discovered, but it is sterile. Why?

Short answer

Answer: The chrysanthemum variety with 27 chromosomes is sterile because it has an odd number of chromosome sets, which can lead to complications during the process of meiosis. Proper pairing of chromosomes is not possible with an odd number of chromosome sets, resulting in a failure of reproduction and, consequently, sterility.

Step-by-step solution

Determine the genetic descriptions of chrysanthemum varieties

Chrysanthemum varieties contain \(18, 36, 54, 72,\) and \(90\) chromosomes, and all are multiples of a basic set of \(9\) chromosomes. These varieties can be described genetically by the formula \(9n\), where \(n\) is an integer.

Describe the karyotypes of each variety

Each variety has a karyotype that is a multiple of the basic set of 9 chromosomes. This means that the karyotypes share the same basic chromosomal structure, since they all have 9 chromosomes in common.

Analyze the sterile variety with 27 chromosomes

Since 27 is also a multiple of the basic set of 9 chromosomes (\({9\times3}\)), this variety shares the same basic chromosomal structure as the other varieties. However, the difference lies in the number of chromosome sets present. All the given varieties have even numbers of chromosomes in sets (\(2, 4, 6, 8,\) and \(10\)). On the other hand, the variety with 27 chromosomes has an odd number of chromosome sets (\({9\times3}\)).

Explain the sterility of the variety with 27 chromosomes

The variety with 27 chromosomes is sterile because it has an odd number of chromosome sets, which can lead to complications during the process of meiosis, or cell division. During meiosis, chromosomes pair up to form homologous pairs, which are eventually separated into daughter cells to ensure the correct number of chromosomes in the offspring. However, in the case of an odd number of chromosome sets, proper pairing is not possible, resulting in a failure of reproduction and, consequently, sterility.