Lab 5:  In-class Exercise

Exponential Population Growth

Use Excel to complete the following exercises... 

1.  A population of 20 pheasants are introduced into an area in 1980. Under the favorable conditions present, there annual growth rate is 1.15 (i.e., lambda = 1.15).

a) Calculate the population size for the next 20 years (i.e., 1981 - 2000).

b) During this time, Fish and Game has been using distance sampling to estimate abundances.  By using this method, we know that the standard error of the log-scale abundance estimates is 0.1 (i.e., tau = 0.1).  Calculate one possibility for the observed, or estimated population abundances from 1981 to 2000.  To do this, you will need to generate random deviates and add them to each population size.

 

 

 

 

 

2.  Same as before, a population of 20 pheasants are introduced into an area in 1980.  For this scenario, we assume that environmental fluctuations (e.g., spring precipitation, winter snow, etc.) cause the annual growth rates to vary each year.  In this case, the average annual instantaneous growth rate is:  r  = ln[lambda = 1.1] = 0.0953 and the standard deviation of growth rates is 0.05 (i.e., sigma = 0.05).

1) Calculate 2 possibilities for the actual population size for the next 20 years (i.e., 1981 - 2000).

 

3.  For each of population abundance time series you generated in 1. and 2., estimate the growth rate

a) For the time series generated in 1., estimate lambda assuming that observation error is the only source of stochasticity.  Compare the true lambda (the one that generated the time series) to the estimated lambda.  Why are they different?

b) For the time series generated in 2., estimate lambda assuming that process noise is the only source of stochasticity.  Compare the true lambda (the one that generated the time series) to the estimated lambda.  Why are they different?

Revised: 22 September 2011