Question

Male voles pair with either a single female (monogamous) or with two females (polygynous) during a given breeding season. The probability of a male being polygynous in a breeding season is 0.2. The reproductive success (number of offspring) of monogamous males is 2, and of polygynous males is 3. A male’s expected reproductive success in a breeding season is \_\_\_\_\_\_\_\_\_\_\_. (Round off to one decimal place)

Hint:

To calculate expected values: 1. Multiply each outcome by its probability. 2. Add the results to obtain the weighted average. 3. Ensure probabilities sum to 1 for accurate calculations.

Answer 1

Step 1: Understand the expected reproductive success formula. The expected reproductive success (\(E\)) is calculated as the weighted average of the reproductive successes of the two groups, using their respective probabilities: \[ E = (P_{\text{monogamous}} \times \text{Success}_{\text{monogamous}}) + (P_{\text{polygynous}} \times \text{Success}_{\text{polygynous}}) \] where: - \(P_{\text{monogamous}} = 1 - P_{\text{polygynous}} = 1 - 0.2 = 0.8\), - \(\text{Success}_{\text{monogamous}} = 2\), - \(\text{Success}_{\text{polygynous}} = 3\), and - \(P_{\text{polygynous}} = 0.2\). Step 2: Substitute the values and calculate. \[ E = (0.8 \times 2) + (0.2 \times 3) \] \[ E = 1.6 + 0.6 = 2.2 \]