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?

Solution

Number of rabbits at the begining = 2 ( 1 pair).

Nuber of rabbits produced each year by each pair = 4 ( 2 males & 2 females) ie 2 pairs.

Number of rabbits produced during first year will be , 4 (2 pairs) because parents die after the birth of their offsprings.

These 2 pairs will produce 8 rabbits (4 pairs) in the second year.

That means each year number of rabbit pairs become double.

Number of rabbits produced during third year = 16 ( 8 pairs).

(A) Therefore number of rabbits produced after 10 years will be =

(2)10 pairs = (2×2×2×2×2×2×2×2×2×2 )pairs = 1024 pairs.

Therefore 1024 pairs of rabbit will be produced after 10 years.

(B) Number of rabbit pairs produced after 25 years will be

(2)25 = 33,554,432.