Question 1 A single breeding pair of rabbits is introduced t

Question 1.

A single breeding pair of rabbits is introduced to Australia in 1900. Assume (for simplicity) that each pair can produce 4 offspring each year (2 male, 2 female). Also assume, that all births happen in the last hour of the last day each year and the parents die immediately after offspring are born.

a) How many rabbits are there after 10 years?

b) How many rabbits are there after 25 years?

If they have 20 offspring each year,

c) How many rabbits are there after 10 years?

d) How many rabbits are there after 25 years?

Question 2 Now, assume that rabbits reach sexual maturity instantly after being born and all can reproduce continuously (generations overlap). If each pair has 4 offspring and both parents die by the end of the year:

a)How many rabbits are there after 10 years?

b)How many rabbits are there after 25 years?

Question 3 Now, assume that the carrying capacity of the environment is K=1000. There are 6 offspring, both parents die as before.

What is the rabbit population when the growth rate of the rabbits each year is the largest? Use discrete logistic to answer:

a) How many rabbits are there after 2 years?

b) How many rabbits are there after 3 years?Please show work

Solution

Answer for Question 1

a) Since, the population is increasing in geometric progression, i.e 2,4,8,16....... and the initial number of rabbits was 2, then after 10 years, the total number of rabbits will be 2¹⁰.

b) Similarly, after 25 years, the total population will be 2²⁵.

c) After first year, there are 20 offspring (10 pairs). During the second year, they produce 10 X 20 = 200 offspring or 100 pairs. Thereon, the population is increasing in geometric progression. The population after 10 years is 2 X 10¹⁰

d. After 25 years, the population will be 20²⁵.