Fish and Wildlife Population Ecology  - Dr. Edward O. Garton

 

Matrix Projection Lab Exercise

WLF543
Brian Gilbert

 Matrix projections are an extremely useful and valuable way to investigate population dynamics.  This exercise will introduce concepts of matrix projection and investigate differences in prediction using deterministic and stochastic models.  These data are based on a population reconstruction from harvested deer on private timber lands in Western Washington where virtually every deer harvested passed through a check station and was sampled.  Harvest rates have varied over the study period.  Female harvest was primarily through antlerless permit seasons until recent years when additional harvest has occurred in archery and muzzleloader seasons.  To reduce browse conflicts, a major reduction effort was made in 1983 and 1984, followed by moderate to heavy harvest through 2000.  Buck harvest has been heavy throughout the study area, however antler point restrictions were instituted in 1987 to increase mature buck representation.  We will review basic matrix projection approaches and then project the population size and compare to known abundance values.

 Access the data on the S: drive under the WLF/543/PROJECTION subdirectory and download the data set:  matrix_projection_deer.xls

After familiarization with the modeling files conduct two separate simulation exercises: 

  1. Deterministic Age Matrix Projections:  Use the first 10 years of age class data to estimate vital rates and then project population size and composition from 1990 through 2000.  In the initial projection, use average values for vital rates.  Then conduct the same projection exercise, but assign vital rates pertinent to the eras discussed above relating to harvest intensity and season structure.

      Queston:  Which projection gave estimates in total population size closest to the reconstructed values?  Which projection portrayed composition most effectively?  Why do you think this is?

        Question:  What are the effects of using time specific vital rates in the projections versus using average values over the initial period?  How could you improve the projections even more? 

  1. Deterministic Stage Matrix Projections:  Again use the first 10 years of stage class data to estimate vital rates and project population size and composition from 1990 through 2000.  Use average rates for the initial projections, and then follow up with projections using era specific vital rates.

            Question:  Which projection gave the best estimates in total population size (as compared to reconstruction estimates)?  Why was the relationship between the two projection approaches (i.e. with average rates and then with era specific rates) were better or worse than those using an age class matrix?

              Question:  What advantages does a stage matrix offer a manager over an age based matrix?  What disadvantages?  (hint:  think about the types of data needed and the characteristics of projection estimates you investigated above)

  

Extra Credit:  If you think this stuff is really cool and just can’t stand to stop, continue on with an investigation of a stochastic projection approach. 

  1. Stochastic Projections:  Conduct two projections using 1) the age based matrix and 2) the stage matrix, however use stochastic estimates for vital rates rather than deterministic ones.  Use what you think are the best estimates of vital rates for projection.

        Question:  How did using stochastic vital rates affect the projection results?  Why do you think this occurred?

       Question:  How could you improve the stochastic version of the projection? (hint:  think about other data that are likely available such as weather, timber harvest, etc)