Question

population Problems

A species of finches on the Galapagos Island has a geometric growth pattern. The island has 25 000 finches in the first year. In the same year, there are 5000 births and 3500 deaths. What is the geometric growth rate Calculate the population after 5 years A population of walruses on an island in the South Pacific Ocean shows continuous growth.

The carry capacity of the environment is 10 000 and r = 0.5. What is the rate of growth for populations of 100, 1000 and 2000 walruses.

The Metro Toronto Zoo has an endangered species called the Eastern cougar. A pair of cougars have a fecundity of 5 offspring per year where all offspring survive to reproductive age (2.5 per parent per generation). Explain the type of growth Calculate the number of cougars after 5 years and 9 years.

In the summer, the Ottawa University has many pigeons. A grade 12 biology student decided to estimate the population size. She noticed that when she fed the pigeons in the atrium of Morriset Library, the same amount always returned. She devised a way to tag them. The first week she tagged 55 pigeons by luring them and feeding them. The second week she recaptured 45 pigeons and of those only 8 had the original tag. Estimate the population size.

A group of biology students are assisting a researcher from the University of Toronto on a project. They are trying to determine the growth rate of frogs in a marsh near Owen Sound. There are 200 frogs in the first year. By the time the students are in grade 12, 40 frogs were born, 90 died and 5 frogs immigrated. Determine the growth rate Do you think that tracking the frogs for one year is sufficient for this researcher?

An eager graduate student at Carleton, counts geese in the marshes off the Ottawa river. In 2004, they counted 2500 geese. During the next year, 500 goslings hatched, 45 immigrated, 200 died and 30 emigrated. Determine the following: Population change in individuals, in % and per capita The expected size of the population after 2, 4 and 8 years, given unlimited resources The doubling time, where r = 0.1725 Assuming a carrying capacity of 4235 geese, when will the geese population reach carrying capacity under ideal conditions?

if possible i would appreciate an answer in a text form not handwritten. thank you

Answer 1

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1. A species of finches on the Galapagos Island has a geometric growth pattern. The island has 25 000 finches in the first year. In the same year, there are 5000 births and 3500 deaths. What is the geometric growth rate Calculate the population after 5 years.

Population size = 25000 = N

Number of births = 5000

Number of deaths = 3500

Increase in population size = 5000 - 3500 = 1500

We know the below formula

dN/dt = rN

where dN/dt is the change in population size ; r is the geometric growth rate and N is the population size.

So , 1500 = r x 25000

r = 1500/ 25000 = 0.06

2. The carry capacity of the environment is 10 000 and r = 0.5. What is the rate of growth for populations of 100, 1000 and 2000 walruses.

Formula for logistic growth :

dN/dt = rN(K-N) / K where K= carrying capacity and N = population size

For population of N = 100

dN/dt = 0.5 x 100 (10000 - 100) / 10000

= 50 x x9990 / 10000

= 50 x 0.99 = 49.5 ~ 50

Rate of growth = 50 / 10000 = 0.005

For population of N = 1000

dN/dt = 0.5 x 1000 (10000 - 1000) / 10000

= 500 x 9000 / 10000

= 500 x 0.9

= 450

Rate of growth = 450 / 10000 = 0.045

For population of N = 2000

dN/dt = 0.5 x 2000 (10000 - 2000)/10000

= 1000 x 8000 / 10000

= 1000 x 0.8 = 800

Rate of growth = 800 / 10000 = 0.08

3.The Metro Toronto Zoo has an endangered species called the Eastern cougar. A pair of cougars have a fecundity of 5 offspring per year where all offspring survive to reproductive age (2.5 per parent per generation). Explain the type of growth Calculate the number of cougars after 5 years and 9 years.

Here it is assumed that no offspring dies and every offspring survives to reproductive age. In addition, the parents in the previous generation also mate and reproduce along with offsprings of next generation

If the fecundity rate is 2.5 per parent per generation, this implies that the growth rate is 2.5.

This type of growth is called exponential growth .

Formula for population size after t years is :

N1= (1+r) x N0 = (1 + 2.5) x 2 = 3.5 x 2 = 7\

N2 = (1 + r) x N1 = (1 + 2.5) x 7 = 24.5

Similarly

N3 = 24. 5 x 3.5 = 85.75

N4 = 85.75 x 3.5 = 300.125

N5 = 300.125 x 3.5 = 1050.4375 ~ 1050

N6 = 1050.4375 x 3.5 = 3676.53125

N7 = 3676.53125 x 3.5 = 12867.86

N8 = 12867.86 x 3.5 = 45037.5078 ~ 45038

4. In the summer, the Ottawa University has many pigeons. A grade 12 biology student decided to estimate the population size. She noticed that when she fed the pigeons in the atrium of Morriset Library, the same amount always returned. She devised a way to tag them. The first week she tagged 55 pigeons by luring them and feeding them. The second week she recaptured 45 pigeons and of those only 8 had the original tag. Estimate the population size.

We know that in capture recapture method , the formula for population size (N) is :

N = M x n / m where M = number of members intially captured and tagged

n = number of individuals recaptured

m = number of individuals which were tagged in the recapture

So N = 55 x 45 / 8 = 2475 / 8 = 309.375 ~ 309.

Thus the population size is 309.

PS -I am unable to solve the rest of the questions due to time constraints. Please do repost the other questions.