Fisher's Malthusian parameter and reproductive value

@article{Price1972FishersMP,
  title={Fisher's Malthusian parameter and reproductive value},
  author={GEORGE R. Price and Cedric A. B. Smith},
  journal={Annals of Human Genetics},
  year={1972},
  volume={36}
}
An explanation is given of Fisher's ‘Malthusian parameter’m (= Lotka's ‘rate of increase’) and ‘reproductive value’v. It is pointed out that there is a flaw in fisher's mathemathics due to his neglect of changes in population charactersitcs under natural selection, with the result that m equals the logarithmic rate of change of the total reproductive value of a population. A modified definition is given that does have this property. however, for practical uses in population genetic it may be… 

Biological Fitness and the Fundamental Theorem of Natural Selection

Fisher’s fundamental theorem of natural selection is proved satisfactorily for the first time, resolving confusions in the literature about the nature of reproductive value and fitness and the relevance of the newly understood theorem to five current research areas is discussed.

Fisher's fundamental theorem of natural selection revisited.

  • S. Lessard
  • Biology
    Theoretical population biology
  • 1997
This work considers a wide range of models, from discrete-time selection models with nonoverlapping generations to continuous-time models with overlapping generations and age effects on viability and fecundity, which is the original framework for Fisher's fundamental theorem.

Malthusian parameters, reproductive values and change under selection in self fertilizing age-structured populations

  • E. Pollak
  • Mathematics
    Journal of mathematical biology
  • 2004
If the number of individuals of each sort of ancestor is multiplied by its reproductive value and the products are summed, the result is the total value, which is Vij(t) for genotype AiAj, where mij is the Malthusian parameter for AiAJ.

Gene frequency and fitness change in an age‐structured population

  • J. Crow
  • Biology
    Annals of human genetics
  • 1979
Fisher's system of reproductive value weighting, whereby each age group is assigned a weight purported to measure its contribution to the ancestry of future generations, was suggested by him as a way

Generalizing Fisher's "reproductive value": linear differential and difference equations of "dilute" biological systems.

  • P. Samuelson
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1977
The present linear analysis prepares the way for generalizing reproductive value to nonlinear systems involving first-degree-homogeneous relationships.

The genetical theory of kin selection

Fisher's genetical paradigm is used to demonstrate the generality of Hamilton’s rule and to clarify links between different studies, and to emphasize the need to distinguish between general kin‐selection theory that forms the foundations of social evolution, and streamlined kin-selection methodology that isused to solve specific problems.

Class Structure, Demography, and Selection: Reproductive-Value Weighting in Nonequilibrium, Polymorphic Populations

  • S. Lion
  • Environmental Science
    The American Naturalist
  • 2018
It is shown that reproductive values can be defined as time-dependent weights satisfying dynamical demographic equations that depend only on the average between-class transition rates over all genotypes, which yields a simple Price equation where the nonselective effects of between- class transitions are removed from the dynamics of the trait.

Defining fitness in an uncertain world

The recently elucidated definition of fitness employed by Fisher in his fundamental theorem of natural selection is combined with reproductive values as appropriately defined in the context of both

Another Way to Calculate Fitness from Life History Variables: Solution of the Age-Structured Logistic Equation

The basis for the model is the logistic equation, which, it is argued, applies more generally than is commonly appreciated, and support is offered for the utility of this paradigm.

References

SHOWING 1-8 OF 8 REFERENCES

Extension of covariance selection mathematics

  • G. Price
  • Mathematics
    Annals of human genetics
  • 1972
The mathematics given here applies not only to genetical selection but to selection in general, intended mainly for use in deriving general relations and constructing theories, and to clarify understanding of selection phenomena, rather than for numerical calculation.

Selection and Covariance

THIS is a preliminary communication describing applications to genetical selection of a new mathematical treatment of selection in general.

A n IntroductiOra to P o p l a t h Genetic8 Theory

  • 1970

The Genetid Theory of Naturd Selection, 2nd ed

  • New York: Dover Publications. Lo%, A. J. (1925). Elements of P h y s i d Biology. Baltimore: Williams end Wdkins. PRICE, G. R
  • 1958

Extension of covariance selection mathematics. An& of Human Genetics 335,485-90

  • 1972

The Genetid Theory of Naturd Selection

  • 1958

The Benetid Theory of Natural Selection

  • 1930

Elements of P h y s i d Biology

  • 1925