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:
- 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?
- 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.
- 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)
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