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On second order sensitivity for stage-based population projection matrix models.

Dominic McCarthy1, Stuart Townley, Dave Hodgson

  • 1School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter, EX4 4QE, UK. D.Mc-Carthy@ex.ac.uk

Theoretical Population Biology
|July 16, 2008
PubMed
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We present a simple method to identify life-history changes in population models that cause accelerating population growth. This involves calculating convexity using a new formula derived from the transfer function.

Area of Science:

  • Ecology
  • Population Dynamics
  • Mathematical Biology

Background:

  • Population projection matrices are crucial for understanding population dynamics.
  • Identifying factors that influence population growth rates is essential for ecological management.
  • Previous methods may not fully capture the nuances of accelerating growth patterns.

Purpose of the Study:

  • To introduce a straightforward method for detecting life-history perturbations that lead to accelerating population growth.
  • To establish a mathematical framework for quantifying the convexity of population growth rate dependence on perturbations.
  • To investigate the interplay between stasis and growth probabilities in stage-structured populations.

Main Methods:

  • Derivation of a novel formula for calculating the convexity of population growth rate sensitivity.

Related Experiment Videos

  • Utilizing the transfer function of a perturbed system to compute this convexity.
  • Application of the method to stage-structured population projection matrices.

    • Main Results:

    • A simple method for identifying life-history perturbations causing accelerating population growth is presented.
    • The method quantifies accelerating growth through the convexity of the growth rate's dependence on perturbations.
    • A new formula for calculating convexity, based on the second sensitivity of the growth rate, is derived.

    Conclusions:

    • The developed method provides a clear way to identify specific life-history perturbations that accelerate population growth.
    • The formula offers a new tool for analyzing the relationship between perturbation effects and population growth dynamics.
    • This approach enhances the understanding of factors influencing population stability and change in structured populations.