Population Growth and Regulation - EE In Wisconsin



Population Growth and Regulation

Equation Sheet

Key

B= Birth rate (geometric) b= Birth rate (exponential)

D= Death rate (geometric) d= Death rate (exponential)

λ= Growth rate (geometric) r= Growth rate (exponential)

e= Logarithmic constant, found on calculator

N0= Initial population count N(t)= Final population count

t = time (usually in years) K= Carrying capacity

Equations:

Exponential Growth: N(t)=N0ert

Geometric Growth: N(t)=N0λt

Logistic equation: ΔN/Δt=rN(1-N/K)

Relationships:

Growth rate: r =b-d (exp) and λ=B-D (geo)

Relationship between exponential and geometric: λ=er

Name________________________

Hour_____

Ecology Population Studies

1. A population of mice reproduce at an exponential rate of 0.8. If the original population is 40 mice, what will the population be:

a. Next year?

b. 2 years

c. 20 years

2. A local population of ducks have a geometric population growth rate of 1.2. Their original population is 120 ducks. What will their population be:

a. Next year?

b. 2 years

c. 20 years

3. Suppose there is a population of 95 rabbits nearby. The habitat can support 120 rabbits. What will next years population be if the growth rate (r) is:

a. 0.5

b. 1.5

c. 0

d. -1

4. You have a cohort population of mice that you are monitoring. The population is diagrammed below:

Year Mice at beginning Mice born Mice killed by end of year

1 20 10 5

2 25 15 5

3 35 30 15

4 50 35 20

5 65 50 80

6 35 25 50

a. What is the birth rate for year

a. 2

b. 4

c. 6

b. What is the death rate for year

a. 2

b. 4

c. 6

c. What is the growth rate for year

a. 2

b. 4

c. 6

d. Assume the population follows an exponential growth rate. Use the average of the growth rates from year 2,4,and 6 in this problem. Using the total number of mice left at the end of year 6, which is 10 mice, what will the population be:

a. Next year?

b. The year after that?

5. Think back to the mice population game. How would the game be different if:

a. The carrying capacity was 150 instead of 100?

b. Each fox selected 20 pieces instead of 15?

c. Each fox needed only 3 mice instead of 5?

d. The mice tripled instead of doubled?

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