BIOS 6150: Ecology
Dr. S. Malcolm
Biological Sciences
Week 4: The Logistic Equation & population modelling:
Populus exercise 1 - Population Growth models:
For 20 points (10x2) towards the total of 100 for computer session questions
(this may be handed in at the end of class, or next week).
See: Alstad, Don. 2001. Basic Populus models of ecology. Prentice Hall, NJ, 144
pages; and http://www.cbs.umn.edu/populus/index.html
Name:
A. Using the density independent exponential model for discrete
generations:
1) What values of λ (=R) make the population increase geometrically?
2) What values of λ (=R) make the population decrease geometrically?
3) What values of λ (=R) make the population remain the same?
BIOS 6150: Ecology
Dr. Stephen Malcolm
Populus exercise 1
page - 1
B. Using the density independent exponential model for continuous
generations:
4) What values of r (=ln λ) make the population increase geometrically?
5) What values of r (=ln λ) make the population decrease geometrically?
6) What values of r (=ln λ) make the population remain the same?
7) If r = 0.5, what value of λ will give exactly the same exponential rate of
population increase (demonstrate this graphically with both the
discrete and continuous models)?
C. Using the Logistic Population Growth model:
8) For the continuous model with N0 = 10 and r = 0.5, what is the
population size after 10 generations?
9) How does the answer to 8) compare with population size after 10
generations for the same values from the density-independent
growth model? What term in the model has generated this
difference?
10) Using time lags in the logistic population growth can you generate
population fluctuations? If so, at what reproductive values (r or λ)
do you see monotonic damping, and at what values do you see
damped oscillations?
BIOS 6150: Ecology
Dr. Stephen Malcolm
Populus exercise 1
page - 2