Analytical Expressions for the Eigenvalues and Confidence Intervals Arising from a 3-Stage Wildlife Population Matrix Thesis uri icon



  • Thesis (M.S., Statistical Sciences) -- University of Idaho, 2016 | We used the well-known symbolic solution for the roots of a cubic polynomial to derive expressions for the dominant and subdominant eigenvalues of a 3-stage population projection matrix. The resulting expressions were used in conjunction with the delta method to obtain symbolic asymptotic confidence limits for the eigenvalues to aid in understanding how errors in the demographic rates are propagated into population growth and volatility. The projection matrix corresponds to a generic life history of many wildlife populations containing juvenile, sub adult, and adult stages. In the formulas, the four demographic parameters (three stage survival probabilities and the adult fecundity) collapse into two superparameters (adult recruitment and survival). Because the eigenvalues and their uncertainties depend on just two fundamental parameters, focusing sampling efforts on the two superparameters could produce greater efficiencies in sampling for growth rate estimation. The eigenvalue results presented here will be useful in population viability analysis, population recovery planning, translocation planning, and hunting/harvest management.

publication date

  • June 1, 2016