Question

4.   Temperature-dependent sex determination, where temperatures experienced during embryonic/larval development determine the sex of the offspring, has been observed in reptiles and fish. In a certain species of sea turtle, increased temperature during egg development results in a 40% decrease in males, while a decreased temperature results in a 10% increase in males.
a.   Early spring temperatures are predicted to increase with a probability of 0.55, while there is a probability of 0.30 that there will be a no change and a probability of 0.15 of a temperature decrease. What is the expected change in the number of males?
b.   If the 40% decrease in males was an overestimate, and instead was actually a 20% decrease, what is the expected change in the number of males?

Answer 1

a.

Probability of increase in temperature = 0.55

Increase in males with increase in temperature = -0.40

Probability of decrease in temperature = 0.15

Increase in males with decrease in temperature = 0.10

Assuming there would be no increase in males with no change in temperature.

Expected change in the number of males = 0.55 * -0.40 + 0.30 * 0 + 0.15 * 0.10 = -0.205 = -20.5%

Thus, we expect 20.5% decrease in males.

b.

If the increase in males with increase in temperature is -0.20, then

Expected change in the number of males = 0.55 * -0.20 + 0.30 * 0 + 0.15 * 0.10 = -0.095 = -9.5%

Thus, we expect 9.5% decrease in males.