Question

Please show all work for full credit!

When performing calculations, round numbers to 3 decimal places

The California Condor (Gymnogyps californianus) is a critically endangered species. In 1991, 48 adults individuals were released in the wild from the captive breeding program. In 2016, there were approximately 323 individuals in existence.

1.Calculate r for this time frame, assuming a continuous and constant growth rate (2 pts).

2.What is the doubling time of this population (2 pts)?

3. 30 rabbits are introduced onto a small island at the beginning of 2000.

4. If this population has an annual exponential growth rate (lambda) of 1.18 on the island, what was the population size at the beginning of 2010 (2 pt)? Assume discrete growth

5. At the beginning of 2017 (2 pt)?

6. The black-footed ferret (Mustela nigripes) may be downgraded to threatened status (from endangered) once it reaches a total population size of 1300 animals in the wild. If this population has been growing exponentially since 1991 at r = 0.02, calculate when it would be downgraded to threatened status, given a population of 300 animals in the wild in 2015 (2 pt). Assume continuous growth.

Answer 1

Answer :)

Frist, we calculate net generations that happened during the given time.

N_t =N₀ X 2ⁿ

Here N_t is the population after t time. N₀ is the initial population and n is the number of generations.

Therefore,

N_t =N₀ X 2ⁿ

232 = 48 x 2ⁿ

2ⁿ = 4.83

Taking log on both sides

Log 2ⁿ = log 4.83

n Log 2 = log 4.83

n x 0.3 = 0.68

n = 0.68/0.3

n = 2.26

Therefore, total generations are 2.26.

Answer 1:)

Net reprodcutive rate r =n/t

The time t = 2016-1991

The time t = 25

Net reprodcutive rate r =2.26 / 25

Net reprodcutive rate r =0.09

Answer 2:)

Doubling time = 0.693/r

Doubling time = 0.693 / 0.09

Doubling time = 7.7 years

Answer 4:)

To calculate the net population size, we need the following formula:

N_t =N₀ X e^rt

First, we calculate the population size in 2001; the time is 9 years.

N_t =48 X e^{0.09x 9}

N_t =48 X 2.25

N_t =108

Now, they add 30 more into the population in 2001.

Therefore, the present population size in 2001 is 138.

Now, calculate the net population size in 2010; the time is 9 years.

N_t =N₀ X λ^t

Here λ is the exponential growth rate.

N_t =138 X 1.18⁹

N_t =138 X 4.44

N_t =612.7

N_t =613 (approx)

Answer 5:)

At the beginning of 2017:

Total time from 2001 to 2017 t = 16 years.

N_t =138 X 1.18¹⁶

N_t =138 X 14.13

N_t =1949.9

N_t =1950 (approx)