6 Jan 13: Geometric growth

6.1 Reading

Vandermeer, J.H., Goldberg, D.E., 2013. Population Ecology: First Principles (Second Edition). Princeton University Press, Princeton, United States. p1-3. Link

• Von Foerster human population become effectively infinite on Nov 13 2026

• Lilly pads replicate once per week. If it take a year for 1/2 a pond to be covered, when will it be completely covered? See also the wheat and chessboard

• \(N_{t+1} = \lambda N_t\) equation 3 in Vandermeer and Goldberg. For what values of \(\lambda\) will the population size, \(N_t\), grow?

• \(N_t = N_0 \lambda^t\) is equation 4 in Vandermeer and Goldberg (but written more generally). With \(N_0 > 0\) sketch a graph of \(N_t\) for different values of \(\lambda\). If \(N_0 = 0\), sketch a graph of \(N_t\).

• If \(N_0 = 1.1\) individuals per km\(^2\), \(\lambda = 2\), what is is the population size at time \(t = 10\)?

• Consider population growth of pheasants on Protection Island. If we were to apply the geometric growth model to the pheasant population, what are some assumptions? How might this affect our parameterization (i.e., our estimate of \(\lambda\)) for the pheasant population?

• How can we understand what \(\lambda\) is in a population that has births and deaths?