Bulletin of Mathematical Biology

, Volume 62, Issue 2, pp 351–375

Rate estimation for a simple movement model


  • Emily Silverman
    • School of Natural Resources and EnvironmentUniversity of Michigan
  • Mark Kot
    • Department of MathematicsUniversity of Tennessee

DOI: 10.1006/bulm.1999.0159

Cite this article as:
Silverman, E. & Kot, M. Bull. Math. Biol. (2000) 62: 351. doi:10.1006/bulm.1999.0159


This paper introduces a simple stochastic model for waterfowl movement. After outlining the properties of the model, we focus on parameter estimation. We compare three standard least squares estimation procedures with maximum likelihood (ML) estimates using Monte Carlo simulations. For our model, little is gained by incorporating information about the covariance structure of the process into least squares estimation. In fact, misspecifying the covariance produces worse estimates than ignoring heteroscedasticity and autocorrelation. We also develop a modified least squares procedure that performs as well as ML. We then apply the five estimators to field data and show that differences in the statistical properties of the estimators can greatly affect our interpretation of the data. We conclude by highlighting the effects of density on per capita movement rates.

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© Society for Mathematical Biology 2000