Tools for Demographic Analyses

• Analysis of projection matrices can be conducted with a great variety of tools: Matlab, Excel spreadsheets, programming in Basic or canned software like Ramas or Vortex.  On this page, I  provide some basic tools for doing conventional analyses.  Most of the analyses provide worked through examples for a matrix model presented in the following paper:     
  Hiraldo, F., J.J. Negro, J.A. Donazar and P. Gaona. 1996. A demographic model for a population of the endangered Lesser Kestrel in southern Spain.  Journal of Applied Ecology 33: 1085-1093.
  
  
• MATLAB is a mathematics program that allows manipulation of matrix population models based on Leslie or Lefkovitch projection matrices. I have written a series of macros for Matlab (Student version, Rel. 11) that do several different matrix calculations.  I have worked with these to my satisfaction but there still could be errors.  Please let me know if you have troubles.
  
  • To run these files:
    1. Cut and paste the text into an ASCII file and save it into a directory on your computer.
    2. Start-up Matlab and locate the directory that the file is in.
    3. Run the macro by typing the name as a command. E.g., type "basic".
    
  • Basic.m: For any matrix of values, basic.m will calculate the rate of population change (lambda), the damping ratio (rho), the stable age distribution (w), the reproductive values (v), and the sensitivity (S) and elasticity (E) of each of the cells in the matrix.  Examples are included for the Lesser Kestrel, Loggerhead Turtles and Killer Whales.
    
  • Lower.m: The elements of a population matrix are often expressions that include the product or sum of multiple demographic rates. It may be desirable to have separate estimates of the elasticity of each rate instead of an overall sum. Lower.m is an example of Matlab code that calculates the 'lower-level' sensitivities and elasticities for the Lesser Kestrel.  Lower.m illustrates the use of symbolic notation.
    
  • Random.m: In a life table response experiment (LTRE), a projection matrix of vital rates appears as the response variable in an experimental design.  Random.m is Matlab program that provides a worked through example of a random design for Killer Whales.  A set of 18 matrices for different pods of whales are a random sample from some distribution of possible treatments.  This program yields the contributions of the different vital rates and their covariances to the variance in the rate of population change of the pods.
    
  • Lsa.m: This program is an example of a Life-stage Simulation Analysis (LSA). It bootstraps random draws from a matrix, collects all of the variables and estimates of lambda, and then conducts linear regression on the output to calculate R-square values for each variable in the matrix.
  
  
• Excel spreadsheets and @RISK. The basic matrix calculations done in Matlab can also be performed in standard Excel spreadsheets using the power method.  @RISK is an add-on for Excel that can be used to extend these models for stochastic populations. It contains a variety of distributions and graphing functions that make programming quite convenient.
  
  • Kestrel.xls is an Excel 2000 file that provides a worked through example for a 2x2 matrix model of the Lesser Kestrel.  Documentation for the calculations are provided on the spreadsheets and this file could be modified to fit matrices of other sizes.
  
  
• Programming languages.  Matrix calculations can also be performed with various programming languages including Basic and SAS.  One of the best books currently available is: 
  Ebert, T.A. 1999.  Plant and Animal Populations: Methods in Demography  Academic Press, New York.  Basic programs are included at the end of each chapter and are available at Cornered Rat Software.
  
  
• VORTEX and RAMAS are two software packages that can be used to model stochastic models for age- and stage-structured populations. Both have been widely used in conservation biology, but permit little control over the model. Comparative studies that use these and other packages for analyses of population viability sometimes come up with different answers, depending on how density-dependence is treated.  As black box programs, they have less utility than the approaches above.

• Analysis of Marked Animal Encounters: Notes from a course offered by Gary White at Colorado State. A good background into the fundamental concepts underlying mark-recapture statistics. Note that the special fonts needed by Adobe Acrobat are available online at the bottom of the website.
  
  
• Program MARK: Developed by Gary White, the best program for mark-recapture statistics currently available. Also available at Evan Cooch's mirror site. Mark-recapture models that previously required different programs have now been incorporated into Program MARK. A second edition of the user manual is now available (Go to "Select a Chapter"). An online discussion forum is also available for questions.
  
  
• Program RELEASE: Developed by Gary White, and available from the Patuxent Software Archive. RELEASE is a utility that can be used to test for pseudoreplication and heterogeneity in mark-recapture data, often as a preliminary step to more detailed analyses with MARK. It tests goodness-of-fit to a CJS model: phi(grp*time), p(grp*time).
  
  
• Program CONTRAST: Developed by Jim Hines and John Sauer, available at the Patuxent Software Archive. This DOS program is handy because it allows posthoc comparisons of survival estimates. Input simply requires the estimates of survival and their standard errors or a variance-covariance matrix. It can be used to compare estimates published in the literature, or for testing Mayfield estimates.
  
  
• Lebreton et al. (1992. Ecol. Monog. 62:67-118) provide a number of examples for mark-recapture modelling..  These now classic examples are available from the CNRS ftp site in France (AA=swift, ED=dipper, LV=lizard, PR=flamingo, RD=roe deer).

• Colorado State Software: Gary White, Colorado State. This site includes downloadable versions of the software developed at Colorado.
  
  
• Patuxent Software Archive: Maintained by Jim Hines, USGS. This site includes downloadable versions of most of the software developed by the Patuxent group.
  
  
• Software for Population Analysis: Evan Cooch, Cornell University. This site features nice capsule summaries of the software currently available for mark-recapture analyses.
  
  
• Wildlife Ecology Software Server: Illinois Natural History Survey. A mixed bag of a variety of software applications for analysis of ecological data.
  
  
• Electronic Textbook: An online statistics textbook that includes lucid discussion of some complex topics.
  
  
• HyperStat Online: An introductory statistics website.
  
  
• Introduction to SAS: A nice introduction to SAS statistical package from a course offered at Cornell University.

Kansas State University | Division of Biology