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Generalizing Fisher's "reproductive value": overlapping and nonoverlapping generations with competing genotypes
Summary
This study extends Fisher's reproductive value concept to Mendelian genetics. General systems are nonlinear, requiring infinite steps to calculate reproductive value, unlike simple dilute systems.
Area of Science:
- Population Genetics
- Mathematical Biology
Background:
- Fisher's 1930 linear eigenvector definition of reproductive value is limited to dilute systems with scale-free intensive ratios.
- Extending this definition is crucial for understanding complex genetic dynamics.
Purpose of the Study:
- To extend Fisher's reproductive value concept beyond linear, dilute systems.
- To apply this extension to standard Mendelian models.
Main Methods:
- Application of an established extension of reproductive value to Mendelian models.
- Analysis of dynamic relations as first-degree-homogeneous functions.
Main Results:
- General Mendelian systems are irreducibly nonlinear.
- Reproductive value functions for these systems are calculable only in an infinite number of steps.
- Exceptions include singular cases like the Hardy-Weinberg equilibrium.
Conclusions:
- The generalized reproductive value is applicable to standard Mendelian models.
- Nonlinearity necessitates iterative calculation for reproductive value in complex genetic systems.