© 2018 Aaron A. King.

A Leslie matrix model for orcas

In class, I described to you a study on orca population dynamics that estimated survival and fecundity in a population of the marine mammals [1]. The population was divided into four stage classes: yearlings, juveniles, reproductive adults, and post-reproductive adults. With these classes, the estimated 1-year projection matrix for the population is
yearling juvenile adult post-reproductive
yearling 0.0000 0.0043 0.1132 0.0000
juvenile 0.9775 0.9111 0.0000 0.0000
adult 0.0000 0.0736 0.9534 0.0000
post-reproductive 0.0000 0.0000 0.0452 0.9801

In this challenge, you will use this information to make projections of the orca population and to examine which life stages are most important to the continued viability of the population.

Specific tasks:

  1. Construct long-term projections of the population size and structure, assuming that the projection matrix continues to be accurate into the indefinite future. Describe your projections.
  2. Show how the dominant eigenvalue and eigenvector of the projection matrix give information on the growth rate and stable age structure of the population.
  3. Assume that, by creation and enforcement of marine hunting regulations, you would be able to reduce the mortality of any one life stage by up to 90% relative to its current value. Assume that the ratio of the fraction of animals moving to the next stage class to that remaining in the same stage class remains the same. Assume also that the change of hunting regulations does not affect fecundity. Which life stage should you protect? Explain your reasoning.

Be sure to explain your reasoning carefully at every stage. Your goal should be that a first-year biology student without any previous knowledge of projection matrices or eigenvalues should be able to follow your reasoning.

Important Note: You will turn in each draft of your report via the course Canvas site. Upload both the Rmarkdown document and a PDF version of your report. Choose the filenames according to the following formula: Challenge_X-Y.Z where X is the challenge problem number, Y is the draft number (1, 2, or 3), and Z is the appropriate extension (.Rmd or .pdf).

References

1. Brault S, Caswell H (1993) Pod-specific demography of killer whales (Orcinus orca). Ecology 74: 1444–1454. doi:10.2307/1940073.