Modeling Age Structured Populations
Theoretical Ecology: BIOL765
Department of Biological Sciences
University of South Carolina, Columbia, SC, 29208
September 5, 2000
Examine the age structured population model in one of the papers. Find the
population growth rate (lambda), the stable age distribution, the
reproductive value distribution, and the elasticity of growth rate with
respect to each of the elements in the projection matrix. Use the Brault
and Caswell worksheet as a template for your analysis. You will need to
change the matrix at the top of the worksheet to match that of your paper,
and will have to make sure that the sizes and indices of the matrices used
in the worksheet are the proper sizes.
Do your estimates of lambda match those of the author? If not, why not?
Do your estimates of stable age distribution and elasticity match those
of the author?
See if you can determine how population numbers would change over 4 time
intervals, using data from the paper. To do this, you will need to do
matrix multiplication to project the population from one time to the next.
To multiply matrices use the Maple command A:=evalm(A1 &* A2);
where A is the result of multiplying matrices A1 and A2
together. This command is used a couple of times in the Brault and Caswell worksheet.
You should produce a short written description of your results, which can
be incorporated into your maple worksheet. A 5-minute presentation of your
results will be made to the class by each group.
Papers:
Pascarella, J & CC Horvitz. 1998. Hurricane disturbance and the population
dynamics of a tropical understory herb: megamatrix elasticity analysis.
Ecology 79:547-563.
Pick a patch type in Table 4 and determine lambda and elasticity values.
Compare with results in Table 5. How do stable stage distributions compare
to the figures?
Watson, IW, M Westoby & A McR Holm. 1997. Continuous and episodic components
of demographic change in arid zone shrubs: models of two Eremophila
species from Western Australia compared with published data on other species.
Journal of Ecology 85:833-846.
Pick one site and compare two different kinds of years. Calculate
lambda for each type of year, and compare with the results in Table 3.
Bulak, JS, DS Wethey & MG White. 1995. Evaluation of management options for
a reproducing striped bass population in the Santee-Cooper system, South
Carolina. North American Journal of Fisheries Management 15:85-94.
Use the data in Table 2: the columns labelled P and F are the survival and
fecundity values used in the matrix.
Barlow, J & PJ Clapham. 1997. A new birth-interval approach to estimating
demographic parameters for humpback whales. Ecology 78: 535-546.
Use the data in Table 2 to create the Leslie Matrix. Does your estimate of
growth rate agree with the authors'? What are the elasticities of growth rate
to changes in fecundity at various ages? How good are the estimates of
fecundity at those ages?
Levin, LA, H Caswell, KD DePatra & EL Creed. 1988. Life table consequences
of larval development mode: intraspecific comparison of planktotrophy and
lecithotrophy. Ecology 68: 1877-1886.
Pick either the lecithotrophic or planktotrophic form and examine it.
Valdaverde, T & J Silvertown. 1998. Variation in the demography of a woodland
understorey herb (Primula vulgaris) along the forest regeneration
cycle: projection matrix analysis. Journal of Ecology 86:545-562.
Pick a population and compare your values of lambda, and sensitivity and
elasticity with those of the author.