1. Calculate the dominant eigenvalue for the 2X2 matrix below.
1
1
0.8 0.8


2. What is the solution to Darwin’s elephant problem described below?
“ The elephant is reckoned to be the slowest breeder of all known animals, and I have
taken great pains to estimate its probable minimum rate of natural increase: it will be
safest to assume that it begins breeding when thirty years old, and goes on breeding
until ninety years old, bringing forth six young in the interval, and surviving till one
hundred years old: if this be so, after a period of from 740-750 years there would be
nearly nineteen million elephants alive, descended from the first pair.”
Hint: Construct a Leslie matrix for elephants, given the information Darwin had.
Rather than constructing a 90 X 90 matrix, consolidate the demographic parameters
into 10, 10-year age classes and use the techniques we learn in lab to estimate .
(Case Ch. 3).
3. What is the eventual geometric growth rate for a population with the following
2
0
0.5 0.8


Lefkovitch modified Leslie matrix?
4. Assume that the parameter estimates in the Leslie matrix below represent mean
values for fecundity and survival. Use the Normal (assume SD =0.3) and
Binomial random number generators in Poptools to project the population 20
years into the future. Calculate for each time step and the geometric mean rate
of population increase. How does the mean rate of increase compare to that for a
deterministic model?
 0 0 .8 1 
.5 0 0 0 


 0 .7 0 0 


 0 0 .8 .8 