Females of the yellow dung fly mate with multiple males, and the sperm of different males compete to fertilize her eggs. The last male to mate usually gains a disproportionate number of fertilizations. A laboratory study examined fertilization using male and female flies from two different populations, one in Switzerland and the other in the U.K. Each female was mated to two males, one from each population (for half of females of each type, the U.K. male was second; for the other half, the Swiss male was second). DNA fingerprinting was then used to determine the percentage of offspring fathered by the second male in each mating.

Question 12: What parametric method would you use to test for influences of mother’s population of origin and father’s population of origin on male fertilization success?
Group of answer choices:
1. Two-way t-test
2. One-factor ANOVA
3. Two-factor ANOVA
4. Generalized difference test

Question 13: If the assumptions of your chosen test were not met, what would be your next step in the analysis?
Group of answer choices:
1. Perform a linear regression.
2. Conduct a two-way Wilcoxon test.
3. Redefine the hypothesis.
4. Transform the data.

For Question 12, the appropriate parametric method to use in this case is the Two-factor ANOVA (Analysis of Variance), which corresponds to option 3 from the given choices.

Explanation:

What is Two-factor ANOVA?
It is a statistical test used to determine the effect of two different categorical independent variables on a continuous dependent variable.
Why use Two-factor ANOVA here?
In this scenario, you are testing for influences of two variables: the mother's population of origin (first factor) and the father's population of origin (second factor), on the dependent variable, which is the male fertilization success (measured as the percentage of offspring fathered by the second male). Since you have two categorical factors and you are interested in understanding how these factors influence the fertilization success, a Two-factor ANOVA is the correct choice.

For Question 13, if the assumptions of the Two-factor ANOVA were not met, the next step in the analysis would be to transform the data, which corresponds to option 4.

Explanation:

Why transform the data?
Transforming data, such as applying a logarithmic transformation or a square root transformation, can help meet the assumptions of normality and homogeneity of variances required for ANOVA tests. If this step does not resolve the issues, other non-parametric tests may be considered, but initially, trying to make the data fit the assumptions is a logical first step.

In summary, use Two-factor ANOVA for the given biogeographical study to analyze male fertilization success. If the assumptions are not met, consider transforming the data to help meet these assumptions.