Question

A genetics experiment on characteristics of tomato plants provided the following data on the numbers of 'offspring expressing four phenotypes¹⁶ Phenotype Frequency tall, cut-leaf 926 dwarf, cut-leaf 293 tall, potato-leaf 288 dwarf, potato-leaf 104 total 1611 State the hypotheses to test that theoretically the four phenotypes will appear in the proportion 9:3.3:1

Answer 1

The student's question is concerned with verifying the observed phenotypes of tomato plants against the expected 9:3:3:1 Mendelian ratio. A chi-square test can be used to analyze the data to determine if the hypothesis that the data fits the Mendelian ratio is true, while acknowledging that smaller sample sizes could increase variation from the expected ratio.

Step-by-step explanation:

The question focuses on an experiment with tomato plants to determine if the observed phenotypic frequencies align with the expected Mendelian ratio of 9:3:3:1 which is typical when two heterozygous genes are involved. To determine the consistency of the data with the Mendelian principles, you can calculate the expected frequency of each phenotype if the genes assort independently. For example, if you have 1611 plants in total, the expected numbers for each phenotype following a 9:3:3:1 ratio would be:

• 9/16 tall, cut-leaf
• 3/16 dwarf, cut-leaf
• 3/16 tall, potato-leaf
• 1/16 dwarf, potato-leaf

Using a chi-square test, one can analyze whether the observed ratios significantly deviate from the expected ratios. The hypothesis to test would be that the observed frequencies do not significantly differ from the expected 9:3:3:1 ratio, implying that the traits are inherited according to Mendel's laws. If fewer plants were used, the statistical variation could increase, possibly leading to more deviation from the expected ratio.