A single breeding pair of rabbits is introduced to Australia in 1900. Assume (fo

Question

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.

Now, assume that the carrying capacity of the environment is K=1000. There are 6 offspring, both parents die before the end of the year. 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?

Explanation / Answer

A single pair of Rabbits were introduced at first. so the number of Rabbits at first = 2 (1 pair)

assume that each pair can produce 4 offsprings i.e ( 2 male, 2 female) = 2 pairs of Rabbits in 1 year.

so, after the death of their parents, there will only be 2 pairs ( 4 rabbits ) left after 1 year.

2 pairs of rabbit will give birth to 8 rabbits ( 4 pairs) at the end of 2nd year.

seeing the trend we can see that the number of rabbits doubles each year.

A. at the end of 2 years the number of rabbits will be = 8.

B. at the end of 3 years the number of rabbits will be = 16.

we can put this into a simple equation.

suppose we want to find out the number of rabbits at the end of the Nth year so the equation will be 2n-1 .

comment for more clarifications.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.