Density independent (geometric) population growth model: N t = N 0 * t where: N

Question

Density independent (geometric) population growth model:

Nt = N0 * t

where:

Nt = population size at time t

N0 = starting population size

= lambda (population growth rate)

Use the above geometric growth model to solve the following for a starting population size of 10 plants that reproduce annually.

1a. If the population size can increase by 15% every year ( = 1.15), approximately what will the population size be in t = 10 years?

1b. Using your population size answer from 1a. and the same , in how many more years will this population approximately double in size?

Question 2. Exponential population growth model:

Nt = N0 * erm*t

where:

Nt = population size at time t

N0 = starting population size

e = 2.7183 (Euler’s number)

rm = estimated rate of increase

Use the above exponential growth model to solve the following for a (not so) get rich quick scheme to breed worms in your apartment and sell them as fishing bait. You start your project with only five individuals.

2a. If your estimated rate of increase (rm) is 0.19 per day, what will your population size be in t = 10 days?

2b. If your estimated rate of increase (rm) is 0.19 per day, what will your population size be in t = 30 days?

From your answers to 2a and 2b, the exponential nature of the increase in your worm population should be clear. However, in another 30 days you find that your population increase has leveled off (i.e., looks more like an S-shaped curve)

2c. What is the name of this type of growth curve?

2d. Assume that you have raised your earthworms in a defined area such as a fish tank. Name the constraint on population growth that your worms have probably reached, and describe one likely mechanism behind this constraint.

Explanation / Answer

1 ) a)

Nt = N0 * ^t

here    = 1.15 , N0 = 10

hence at t = 10 years

Nt =10*(1.15)^10

= 40.455577

b) suppose after t years this happen

then

2 N0 = N0 * (1.15)^t

hence

2 = 1.15 ^t

so t = 4.95948 years

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