Sure, let's break down the information and solve a likely question (since a specific question isn't stated, I'll assume you want to **calculate theotypic correlation T and W**). ### **Given Data** - \( \sigma^2_{BV_T} = 4 \) sec² - \( \sigma^2_{GCV_T} = 1 \) sec² - \( \sigma^2_{E_T} = 11 \) sec² - \( \sigma^2_{BV_W} = 100 \) rubles² - \( \sigma^2_{GCV_W} = \) rubles² - \( \sigma^2_{E_W} = 2,400 \) rubles² Covariances: - \( \text{cov}(BV_T, BV_W) = -2. \) sec·rubles - \( \text{cov}(E_T, E_W) = -118.8 \) sec·rubles - \( \text{cov}(P_T, P_W) = -120.8 \) sec·rubles --- ## **Step 1: Calculate Total Phenotypic Variances** Phenotypic variance for each trait is the sum of its genetic and environmental variances. - For \(T\): \[ \sigma^2_{P_T} = \sigma^2_{BV_T} + \sigma^2_{GCV_T} + \sigma^2_{E_T} \] \[ \sigma^2_{P_T} = 4 + 1 + 11 = 16 \text{ sec}^2 \] **Explanation:** We summed the breeding value, genetic combination value, and environmental variance for T. - For \(W\): \[ \sigma^2_{P_W} = \sigma^2_{BV_W} + \sigma^2_{GCV_W} + \sigma^2_{E_W} \] \[ \sigma^2_{P_W} = 100 + + 2,400 = 2,500 \text{ rubles}^2 \] **Explanation:** We summed the breeding value, genetic combination value, and environmental variance for W. --- ## **Step 2: Calculate the Phenotypic Correlation** The phenotypic correlation (\( r_P \)) between T and W is calculated as: \[ r_P = \frac{\text{cov}(P_T, P_W)}{\sqrt{\sigma^2_{P_T} \cdot \sigma^2_{P_W}}} \] Plugging in values: \[ r_P = \frac{-120.8}{\sqrt{16 \times 2,500}} \] \[ r_P = \frac{-120.8}{\sqrt{40,000}} \] \[ r_P = \frac{-120.8}{200} \] \[ r_P = -.604 \] **Explanation:** We divided the phenotypic covariance by the square root of the product of the phenotypic variances to get the correlation. --- ## **Final Answer** \[ \boxed{r_P = -.60} \] (Rounded to two decimal places.) The phenotypic correlation between time to swim 50 meters and lifetime winnings in Siberian racing muskrats is **-.60**. This indicates a moderate negative relationship: as swim time increases, lifetime winnings tend to decrease.