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

Short answer: The chrysanthemum variety with 27 chromosomes is sterile because it is triploid, having three complete sets of chromosomes (3n). Triploid karyotypes often lead to sterility because during meiosis, the cells are unable to evenly divide the chromosomes, which is necessary for successful fertilization and offspring viability.

Step-by-step solution

Identifying the pattern of chromosome numbers

Observe that all the given chromosome numbers (\(18, 36, 54, 72,\) and \(90\)) are multiples of the basic set of nine chromosomes. The given sets can be represented as \(2\times9, 4\times9, 6\times9, 8\times9,\) and \(10\times9\).

Describing the genetic makeup of each variety

Since each variety is a multiple of the basic set of 9 chromosomes, we can describe these varieties genetically as diploid (\(2n\)), tetraploid (\(4n\)), hexaploid (\(6n\)), octoploid (\(8n\)), and decaploid (\(10n\)). The corresponding chromosome numbers are \(18\) for diploid, \(36\) for tetraploid, \(54\) for hexaploid, \(72\) for octoploid, and \(90\) for decaploid.

Identifying shared karyotype features

The karyotypes of each variety share the feature that they are all polyploid, meaning they have multiple complete sets of chromosomes. In the case of chrysanthemums, the basic set contains 9 chromosomes. The karyotypes share multiples of this basic chromosome set.

Sterility of the variety with 27 chromosomes

The variety with 27 chromosomes is observed to be sterile. This sterility can be explained by the fact that 27 is not a multiple of an even number of basic chromosome sets – it is represented as \(3\times9\). This variety would be triploid (\(3n\)), meaning it has three complete sets of chromosomes. Triploid karyotypes often lead to sterility because during meiosis, the cells are unable to evenly divide the chromosomes, which is required for successful fertilization and offspring viability.