you did problem 2 wrong look it over again using the picture i uploaded

Let's carefully review and solve Problem 2 again using the information provided in the uploaded image.

### Question 2: Revised Solution

**Given:**
- After the invasive tree with cream-colored bark is introduced, you survey the sloth population again.
- The new population data after 150 generations is:
  - 75 sloths with black fur (AA or Aa)
  - 225 sloths with beige fur (aa)
  - Total population = 300

**Hypothesis:**
- Sloths with black fur (dominant phenotype) are more easily seen by predators against the lighter bark, leading to higher predation rates for them.
- Therefore, the hypothesis is that the frequency of the recessive allele (a) will increase over time.

**Revised Step-by-step Solution:**

1. **Determine the frequency of the recessive genotype (aa):**

   Given that there are 225 beige-furred sloths (aa), the frequency of the recessive genotype (aa) is:

   \[
   q^2 = \frac{\text{Number of recessive individuals (aa)}}{\text{Total population}} = \frac{225}{300} = 0.75
   \]

2. **Calculate \(q\), the frequency of the recessive allele (a):**

   \[
   q = \sqrt{q^2} = \sqrt{0.75} \approx 0.866
   \]

3. **Calculate \(p\), the frequency of the dominant allele (A):**

   Since \(p + q = 1\),

   \[
   p = 1 - q = 1 - 0.866 = 0.134
   \]

4. **Calculate the frequency of each genotype:**

   - **Homozygous dominant (AA):** \(p^2 = (0.134)^2 \approx 0.018\)
   - **Heterozygous (Aa):** \(2pq = 2 \times 0.134 \times 0.866 \approx 0.232\)
   - **Homozygous recessive (aa):** \(q^2 = 0.75\)

5. **Show your work (frequencies):**

   - Frequency of AA: 0.018
   - Frequency of Aa: 0.232
   - Frequency of aa: 0.75

### Conclusion for Question 2

The hypothesis that the recessive allele (a) would become more common is **supported**. The frequency of the recessive allele (a) increased significantly to 0.866, while the frequency of the dominant allele (A) decreased to 0.134. This supports the idea that black-furred sloths are more likely to be preyed upon due to their visibility against the lighter bark, allowing the beige-furred (aa) sloths to survive and reproduce more successfully.

Would you like further clarification on any part of the solution? Here are 5 related questions you might find helpful:

1. How do you interpret allele frequency changes in a population under selective pressure?
2. What other factors besides predation might affect the allele frequencies in this scenario?
3. How can genetic diversity be preserved in small populations with changing environments?
4. What are some real-world examples of allele frequency shifts due to environmental changes?
5. How can we calculate the expected number of individuals for each genotype in a future generation?

**Tip:** When analyzing population genetics problems, always reassess your hypothesis based on the data given to ensure that your conclusions align with the observed trends.

Explore a detailed analysis of allele frequency changes in a sloth population after the introduction of a tree with cream-colored bark. Understand how selective pressures affect genetic diversity and the prevalence of dominant and recessive alleles.

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