Question

In a plant, fruit color is either red or yellow, and fruit shape is either oval or long. Red and oval are the dominant traits. Two plants, both heterozygous for these traits, were testcrossed, with the results shown in the following table. Determine the location of the genes relative to one another and the genotypes of the two parental plants. $$\begin{array}{lcc} & & \text { Progeny } \\ \text { Phenotype } & \text { Plant A } & \text { Plant B } \\ \text { red, long } & 46 & 4 \\ \text { yellow, oval } & 44 & 6 \\ \text { red, oval } & 5 & 43 \\ \text { yellow, long } & 5 & 47 \\ \text { Total } & 100 & 100 \end{array}$$

Short answer

Based on the analysis, the genotypes of the parental plants are RrOo, and there is evidence of linkage between the fruit color and fruit shape genes. The high chi-square values for both Plant A and Plant B indicate that these genes do not assort independently, and the dominant traits mainly appear together, suggesting that the genes are linked.

Step-by-step solution

Assign symbols for the genes

In this exercise, we have two traits: fruit color and fruit shape. Let's assign symbols for these traits: - R: red (dominant) - r: yellow - O: oval (dominant) - o: long Note that both parental plants are heterozygous for these traits, which means their genotypes are RrOo.

Determine the expected ratios for the progeny

For a dihybrid cross where both plants are heterozygous for both traits, we would expect a phenotypic ratio of 9:3:3:1 for the progeny if the genes are independently assorted. That is, the expected genotypic ratios would be: - 9 red, oval (R- O-): DOMINANT- DOMINANT - 3 red, long (R- oo): DOMINANT- RECESSIVE - 3 yellow, oval (rr O-): RECESSIVE- DOMINANT - 1 yellow, long (rr oo): RECESSIVE- RECESSIVE To apply these ratios to our problem and use them on a Chi-square test, we must adjust them to represent the percentages of each phenotype. To do this, we can consider that the ratios add up to 16 (9+3+3+1), and find the percentage for each phenotype by dividing each ratio by 16 and multiplying by the total number of progeny for each parental plant, which is 100.

Calculate the expected numbers and perform the Chi-square test

We now calculate the expected number of progeny for each phenotype considering the 9:3:3:1 ratio: - Red, long (DOM-REC): Expected = (3/16) * 100 = 18.75 - Yellow, oval (REC-DOM): Expected = (3/16) * 100 = 18.75 - Red, oval (DOM-DOM): Expected = (9/16) * 100 = 56.25 - Yellow, long (REC-REC): Expected = (1/16) * 100 = 6.25 Now, we perform the chi-square test using the formula: $$\chi ^{2}=\sum \frac{\left(\text {observed}-\text {expected}\right)^{2}}{\text {expected}}$$ For Plant A: $$\chi _{A} ^{2}=\sum \frac{\left(\text {observed}-\text {expected}\right)^{2}}{\text {expected}} = \frac{(46-18.75)^2}{18.75} + \frac{(44-18.75)^2}{18.75} + \frac{(5-56.25)^2}{56.25} + \frac{(5-6.25)^2}{6.25} = 29.07$$ For Plant B: $$\chi _{B} ^{2}=\sum \frac{\left(\text {observed}-\text {expected}\right)^{2}}{\text {expected}} = \frac{(4-18.75)^2}{18.75} + \frac{(6-18.75)^2}{18.75} + \frac{(43-56.25)^2}{56.25} + \frac{(47-6.25)^2}{6.25} = 29.07$$

Determine the conclusion

Both chi-square values are higher than the critical value for 3 degrees of freedom (7.815), which means that the null hypothesis (independent assortment) is rejected. It indicates that there is a linkage between the fruit color and fruit shape genes. The progeny numbers show that the dominant traits are mainly appearing together or along with the recessive traits, which further strengthens the assumption that the genes are linked. Now, we can report the genotypes of the parental plants and the gene linkage. Since both parental plants were heterozygous for these traits, their genotypes are RrOo. The high chi-square values demonstrate that the genes are linked, and the fruit color and fruit shape genes are not independently assorted.

Key concepts

Fruit Color Genetics

In genetics, understanding the inheritance of traits such as fruit color is essential. In this context, red fruit color is considered a dominant trait, represented by the allele 'R', while yellow is recessive, denoted by 'r'. This dominance means that if a plant has one 'R' allele, it will display red fruit, regardless of the second allele.
When dealing with plants heterozygous for fruit color (Rr), you will see a variety of expressions based on what other genetic traits they carry. For example, if both parental plants in a breeding experiment are Rr, the resulting offspring can exhibit either red or yellow fruit. Understanding which alleles are dominant or recessive allows geneticists to predict how traits are inherited across generations.
In practice, when crossing heterozygous plants, the combinations of alleles can give rise to distinct phenotypic ratios based on their dominance relationships. This foundational knowledge helps to unravel complex genetic linkages and better understand how traits can be linked across generations.

Phenotypic Ratios

Phenotypic ratios help in predicting the distribution of traits within offspring when certain genes are involved. For a classic dihybrid cross, where two traits with two alleles each (dominant and recessive) are considered, the expected phenotypic ratio is often 9:3:3:1.
This ratio suggests:

• 9 offspring will show both dominant traits (in this case, red, oval).
• 3 will exhibit the first dominant trait and second recessive trait (red, long).
• 3 will present the first recessive and second dominant trait (yellow, oval).
• 1 will show both recessive traits (yellow, long).

The idea here is that each trait is independently assorted, leading to predictable combinations. However, when actual results deviate significantly from this expectation, it suggests that there might be genetic linkage, meaning the genes are located close together on the same chromosome. In the given exercise, the observed phenotypic ratios deviate from the expected 9:3:3:1, indicating the genes for color and shape are linked.

Chi-Square Test in Genetics

The chi-square test is a statistical method used to compare the observed phenotypic ratios with the expected ratios.This helps in determining whether any deviation from the expected genetic outcome is due to chance or another factor.The formula for chi-square (\[\chi^2 = \sum \frac{(\text{observed} - \text{expected})^2}{\text{expected}}\]) compares observed values to expected values.
In genetic studies, when calculating chi-square, the null hypothesis assumes that traits are independently assorted, following the 9:3:3:1 ratio for two traits.
For both plants in the exercise, the chi-square value was 29.07, which is much higher than the critical value of 7.815 for 3 degrees of freedom. A high chi-square value leads us to reject the null hypothesis of independent assortment, suggesting that the genes are closely linked. This statistical tool is invaluable in genetics, as it provides evidence for or against genetic linkage, helping scientists draw more accurate conclusions about how traits are inherited and linked in organisms.