Discussion on Foraging

Read Bulmer, p. 102-104 on Foraging Theory

1. In equation (1) there are several terms.  Define and explain
each of the terms.  You may find it useful to create an example
for yourself.  For example, you might describe the terms using
bees, cows, wolves, or your favorite critter.







2.  Discuss why an animal might want to maximize its rate of
energy gain.







3. In your calculus class you should have learned about how
derivatives can be used to find the maximum (or minimum)
of a function.  If you did not, then it is time to pull out your
calculus book for a refresher.

(a) Find the derivative of Equation (1) with respect to t.  Notice
that the function g depends on t, it is not a constant.  If you don't
understand what to do at this point then make some explicit choice
for g(t), say t*t + 2t+6.  Then find the derivative of equation (1).






(b) Recall that our goal is to find the maximum of the function R.
Armed with the derivative of Equation (1) we are ready to set the
derivative equal to zero to obtain the maximum.  Do this and solve
the equation for g'(t).  You should obtain Equation (2).





4. Graph the function, -1 + 2t -2t*t, that Bulmer gives as the function
that produced the graph in Figure 6.1.  If you know how to use a
computer graphing package then use it,  otherwise use graph paper.
You should see that the function can't be the one in the figure.  Next
try the function that is handwritten on the page.  It should look like the
one in the figure.






5. Invent some g(t) functions and explain what there shape inplies about
the gain of energy with time.  Don't worry about doing this with equations,
rather, just draw them and explain what they mean.