10.8: Population Models Practice Exercises

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Put your knowledge and comprehension to the test with these practice problems! Some of these questions may require you to use a calculator and draw out models while you practice. Be sure to complete all questions included in each section before you click "Answer" for that section because the answers for all the questions in that section will be revealed together.

General Population Growth Equation \(\PageIndex{1}\)

Your ecology class starts the semester out with a student population of 42. By the end of the semester, two students dropped out of the college, one student dropped the class, one student died on a fieldtrip, and five students joined the course late. What is the class population at the end of the semester?

\[N_{t+1} = N_t + B_t - D_t + I_t- E_t \nonumber \]

Answer: \(N_t\) = 42 + (0-1) + (5-3) = 43 students

Choosing the Right Model \(\PageIndex{2}\)

Which type of model (exponential, logistic, geometric, Leslie Matrix) belongs at each point in this figure?

Answer

a) Leslie Matrix Model

b) Logistic Model

c) Geometric Model

d) Exponential Model

Reading Results \(\PageIndex{3}\)

How does the population change under the following conditions (increase, decrease, or remain stable)?

1) λ = 1.02

2) \(R_0\) = 1

3) N > K

4) r = -0.10

Answer

1) increase

2) remains stable

3) decrease (population overshoots carrying capacity)

4) decrease

Geometric Model \(\PageIndex{4}\)

Given \(N_t\) (population size at initial time) = 500, B = 300, and D = 350, calculate λ.

1) Is this population increasing, decreasing, or stable?

2) What will the population be in 10 years? What about in 30 years?

Answer

1) \(N_{t+1}\) = \(N_t\) + B –D = 500 + 300 – 350 = 450

λ = \(N_{t+1}\) / \(N_t\) = 450/500 = 9/10 = 0.9

Since λ < 1, the population is decreasing.

2) \(N_{t+1}\) = \(N_0\) λ t

N10 = 500*(0.9)10 = 174

N30 = 500*(0.9)30 = 21

Exponential Model \(\PageIndex{5}\)

A new species you are studying has continuous reproduction in a newly invaded habitat. The species’ population is still growing without limit.

1) If the initial population size is 3000, and the growth rate is 0.02, what is the expected population in 25 years? How about in 50 years?

2) If at \(t_0\), the population size is 500, and r = 0.035, how many years until the population reaches 4,000 individuals?

Answer

1) \(N_t\) = \(N_0\) e t r

\(N_0\) = 3000, r = 0.02

N25 = 3000*e(25)(0.02) = 4,946

N50 = 3000*e(50)(0.02) = 8,154

2) Population doubling time = 70/3.5 = 20: 20 years to reach 1000 individuals, 40 years to reach 2000 individuals, 60 years to reach 4000 individuals.