Lab 5:  Problem Set

Exponential Population Growth

1.  Forty kokanee are introduced into a new lake/river system this year (2010), where they are expected to do well (Lambda = 1.12).

1a) Calculate the population size for the next 20 years (i.e., 2011 - 2030) assuming this population follows deterministic exponential growth.  Show your work for the first few years then use Excel for the rest. (2 points)

1b) Plot the population size through time (from the time of introduction) using both population size and the natural log of the population size versus time (i.e., on 2 separate graphs). Label your axes and provide a descriptive title for your graph(s). (2 points)

1c) On the same graph, plot one possibility for observed abundances based on using mark-recapture techniques to estimate abundance.  Assume that the error in these abundance estimates is tau = 0.4. (2 points)

1d) On a separate graph, plot 5 possibilities for actual population abundances assuming that there is environmental stochasticity that causes the annual growth rates to be different each year.  Assume that the mean instantaneous growth rate is  0.11 and the standard deviation of instantaneous growth rates is 0.15 (i.e., sigma = 0.15).   (4 points)

2.  Use the following time series of density for the Hawaiian Akepa to estimate the finite growth rate (lambda):  

Data from:  AkepaForest.xls

Year	Density (birds/hectare)
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007	1.461805 0.843124 0.809465 0.772998 0.696138 1.178799 0.798981 0.743477 0.734619 2.298882 1.682813 1.328402 0.898546 1.724918 1.539038 1.186112 1.438369 1.555484 0.886994 0.61843 0.942739

2a) Make a plot of time versus density.  (2 points)

2b) Assume that the population has grown (or declined) deterministically but that there is observation error in the time series.  Describe how you estimated lambda and indicate if the population is increasing or decreasing. (2 points)

2c) Assume that there is no error in the density estimates but that variation occurs due to environmental stochasticity.  Describe how you estimated lambda and indicate if the population is increasing or decreasing. (2 points)

2d) Are the conclusions from 2b and 2c the same?  What does this imply for the fate of the endangered Akepa?  You might be interested to know these are actual data, not made-up values! (4 points)

As usual, the problem set is due next week at the beginning of lab.

Revised: 22 September 2011