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Another look at the eigenvalues of a population matrix model.

Brenda Hanley1,2, Patrick Connelly1, Brian Dennis2,3

  • 1Cornell Wildlife Health Lab, Department of Population Medicine and Diagnostic Sciences, Cornell University, Ithaca, NY, United States of America.

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|November 19, 2019
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Summary

Population matrix models help resource management by calculating growth rates. New software, IsoPOPd, visualizes how survival and fertility vital rates influence population growth, simplifying complex interactions for better management strategies.

Keywords:
Asymptotic growth rateBalance equationCharacteristic equationDominant eigenvalueInteractive softwareLefkovitch matrixLeslie matrixProjection matrixWildlife

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Area of Science:

  • Ecology
  • Population Dynamics
  • Mathematical Biology

Background:

  • Population matrix models are crucial for resource management, estimating population growth rates via dominant eigenvalues.
  • Understanding the relationship between life history traits and population growth rates can be complex.
  • Vital rates (survival, fertility) are key inputs, but their interactions complicate predictions.

Purpose of the Study:

  • To introduce interactive software (IsoPOPd) for visualizing the contribution of vital rates to population growth.
  • To simplify the understanding of how population matrix models link life history traits to growth rates.
  • To demonstrate the application of the software in evaluating management interventions.

Main Methods:

  • Utilized the characteristic equation to develop the IsoPOPd software.
  • Developed interactive visualizations to display the influence of survival and fertility on population growth.
  • Applied the software to a 3-stage matrix model of white-tailed deer population dynamics.

Main Results:

  • IsoPOPd effectively displays how vital rates contribute to the finite rate of growth.
  • The software aids in understanding higher-order interactions among vital rates.
  • The study illustrated how management interventions impact population growth using the software.

Conclusions:

  • IsoPOPd provides a valuable tool for exploring population dynamics and the effects of management.
  • The software enhances the interpretability of population matrix models for ecological management.
  • The underlying mathematical principles are applicable to matrix models of any size.