Based on prior knowledge, the gender of a person might not directly determine their earnings. However, there may be some indirect relationships. For example, in certain industries or occupations, there might be a gender bias resulting in different earnings for males and females.

To analyze the relationship between gender and the task of whether a person earns more than $50,000 per year, we can start by looking at the distribution of gender within each target class (yes and no) and observe if there are any noticeable patterns.

Based on the information provided, the possible values for the gender feature are 'Male' and 'Female'. Let's analyze the relationship between gender and the target variable:

- Gender for individuals earning more than $50,000 (yes):
   - Possible values of gender: ['Male', 'Female']
   - Analysis: There might be individuals of both genders who earn more than $50,000 per year.

- Gender for individuals earning less than or equal to $50,000 (no):
   - Possible values of gender: ['Male', 'Female']
   - Analysis: There might be individuals of both genders who earn less than or equal to $50,000 per year.

Based on this analysis, there is no apparent relationship between gender and the task of whether a person earns more than $50,000 per year. Both genders can be found in both target classes.

Now, let's summarize these findings in the requested dictionary format:

```json
{
	"no": ["Male", "Female"],
	"yes": ["Male", "Female"]
}
```

Note that the values of gender are not hard to predict or specific to certain cases in this scenario, so we include all possible values in each target class.