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 karyotypes of these chrysanthemums share the feature of having chromosome counts in sets of 9, indicating they are polyploid organisms. A variety with 27 chromosomes is sterile because it is a triploid organism, having three copies of each chromosome, which leads to irregular distribution of chromosomes during meiosis and the production of non-viable gametes.

Step-by-step solution

Observe the given numbers of chromosomes

Notice that all given numbers of chromosomes in these chrysanthemums are multiples of a basic set of 9: \(18 = 9 \times 2\), \(36 = 9 \times 4\), \(54 = 9 \times 6\), \(72 = 9 \times 8\), and \(90 = 9 \times 10\).

Describing the varieties genetically

Since all these varieties have chromosome counts that are multiples of 9, we can say that these varieties are polyploid. Polyploidy is a condition where an organism has more than two sets of chromosomes.

Identifying the karyotype feature

The common feature among the karyotypes of these varieties is that they contain a multiple of the basic set of 9 chromosomes. In other words, these karyotypes have chromosomes in sets of 9.

Explaining the sterility of 27-chromosome variety

The variety with 27 chromosomes can be represented as \(9 \times 3\). Since 3 is an odd number, this variety is a triploid organism, meaning it carries three copies of each chromosome. Triploid organisms are usually sterile because they cannot produce viable gametes due to irregular distribution of chromosomes during meiosis. In a triploid organism, the chromosomes cannot pair evenly during meiosis, leading to uneven distribution of genetic material and non-viable gametes. As a result, the 27-chromosome variety is sterile.