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Generalizing Fisher's "reproductive value": Nonlinear, homogeneous, biparental systems
1Department of Economics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
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.
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.
- 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.