Solutions to Foraging Problems

1) For these problems, calories are a measure of energy (E), the time it takes to consume the item is the handling time (h), and the cost of the food is the search time (S).

a) Profitability of BigMac = E/h = 563/9 = 62.556

Profitability of BigMac = E/h = 220/4.5 = 48.889

Profitability of BigMac = E/h = 144/5 = 28.8

So the BigMac has the highest profitability

b) The best formula to use for this problem is:

S_BM > (E_BM/E_F)(h_F) ≠ (h_BM)

2.75 > (563/220)(4.5) ≠ 9

2.75 > 11.52 ≠ 9

2.75 > 2.52

Since the cost of the BigMac (or the search time for the BigMac) is greater than the other side of the inequality, fries should be included in the lunch.

Another alternative is to use the same formula, but rearranged.

E_current/h_current > E_other / (S_other + h_other)

with fries as current and the BigMac as other

220/4.5 > 563/(2.75+9)

48.889 > 47.915

Again, since the profitability of the fries is greater than the profitability of finding (paying for) and consuming the BigMac, fries should be included.

c) The formula to use in answering this question is the multiple prey choice

formula.

E₃/h₃ > (E₁ + E₂)/(S₁ + h₁ + S₂ + h₂)

144/5 > (563 + 220)/(2.75 + 9 + 1.29 + 4.5)

28.8 > 783/17.54

28.8 > 44.64

Because the profitability of the coke does not exceed the net profitability of all higher ranking prey, it should never be included in the diet.

2)

a) Marginal value theorem graph

b) Many experiments could explore the optimal copulation time

in this system. I saw two main ideas proposed in the homework set. The first involved varying the number of males in relation to the number of females. Adding more males should increase competition and, therefore, increase the time it takes for a male to access a female. This will create a longer optimal copulation time than a condition with few males or no other males. The second commonly proposed study involved setting different distances between dung piles. An increase in distance would increase the time between copulations. Again, you would expect to see longer optimal copulation times as distance between dung piles (and females) increased.

3) a) In the wet season, when food is abundant, the tamarins are most likely to

display a utility function than shows diminishing returns (risk averse). In

the dry season, the tamarins should show a utility function with

accelerating returns (risk prone).

b) Potential long term responses to variation in the environment include:

torpor, hibernation, fat storage, caching, hording, and agriculture.