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Related Experiment Videos

Generalizing Fisher's "reproductive value": Nonlinear, homogeneous, biparental systems.

P A Samuelson1

  • 1Department of Economics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.

Proceedings of the National Academy of Sciences of the United States of America
|December 1, 1977
PubMed
Summary

Biparental demographic models exhibit early linearity, allowing for a reproductive value function. This function captures population growth, incorporating the influence of both sexes for accurate predictions.

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Area of Science:

  • Population Dynamics
  • Mathematical Biology
  • Demographic Modeling

Background:

  • Biparental demographic models typically deviate from linear relationships.
  • Early population stages, before resource limitation and competition, can exhibit linear characteristics.

Purpose of the Study:

  • To define a reproductive value function for early-stage biparental demographic models.
  • To analyze the contribution of initial population structure to asymptotic exponential growth.
  • To generalize this function for systems of homogeneous-first-degree differential and difference equations.

Main Methods:

  • Development of a reproductive value function based on initial coordinates.
  • Analysis of generalized Fisher reproductive value, accounting for inter-sex numerical influence.

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  • Derivation of the function for systems of homogeneous-first-degree differential and difference equations.

    • Main Results:

    • A novel reproductive value function is defined for early-stage biparental models.
    • This function accurately recapitulates contributions to exponential population growth.
    • The generalized reproductive value is modified by the relative abundance of the other sex.

    Conclusions:

    • The defined reproductive value function provides insights into early population dynamics.
    • The function demonstrates growth from the outset at the asymptotic rate.
    • This approach offers a method for analyzing growth in homogeneous systems.