These exercises ask you to plot the expected time to extinction using
the analytical model for the length of phase two of the mutation
buildup. Gnuplot, which allows users to define their own functions
and then plot them in two or three dimensions,
is a good tool for this exercise.

Plot , the expected number of generations in phase
two of the mutation buildup, as a function of population size (K).
Limit the range of K to .
Plot three different curves, using values of R = 2, R = 3, and R = 4.
The three curves should show an increasing time to extinction for
larger values of R. For the other model parameters, use
and ; these are realistic values derived from
field studies of a variety of different plants and animals.

There is an interesting interaction between s, the average
effect per mutation, and the expected time to extinction. If mutations
are relatively harmless (values of s smaller than .0001), then organisms can carry quite a few
mutations and still survive, and it will take a long time for
sufficient mutations to accumulate to start affecting the health
of the whole population. On the other hand, if mutations are
relatively severe (s larger than 0.25) a single mutation is enough
to kill an individual, which in turn implies it is very unlikely
that any mutations will be passed to the next generation, and
thus the buildup of mutations will take a long time. In this case,
for large
enough values of s no mutations will accumulate and the population
will never go extinct (from genetic causes alone). For the
meltdown to occur, the selection coefficient must be in the
right range.
Plot as a function of s in the range ,
using a fixed value of K = 50 and . Again plot three
curves, for R = 2, R = 3, and R = 4. At what value of s
is the population most vulnerable?