Analyzing the Model to Answer the Original Question

We have developed an appropriate model for the energy required by a crow to break open a whelk, on average. Now, we are in a position to answer the initial question posed on the first page: Can we explain the crows' behaviour in terms of optimal foraging theory?

Exercise 11: Complete the following optimization process:

a) Differentiate equation 8 with respect to height.

b) Set the derivative equal to zero and solve for H.

c) Insert the values you found for a and b, then discard the biologically irrelevant solution.

Exercise 12: Answer the following questions:

a) At what height is the energy expended minimized, on average?

b) Is your answer consistent with your earlier answers?

c) How confident are you with the answer?

Exercise 13: Can the tendency of the crows to fly to a height of around 5.6 m be explained in terms of optimal foraging theory? Discuss your ideas with your peers.