Fundamental Theorem of Natural Selection

  title={Fundamental Theorem of Natural Selection},
  author={C. C. Li},
  • C. Li
  • Published 1 April 1967
  • Mathematics, Biology
  • Nature
FISHER1 in 1930 stated his “fundamental theorem of natural selection” in the form: “The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.” Later, Fisher2 restated his theorem more clearly: “The rate of increase in the average fitness of a population is equal to the genetic variance of fitness of that population”. The “genetic variance” in the foregoing statements is the linear or additive component of the fitness variance in… 

Fundamental Theorem of Natural Selection

Li's description of his formula for the rate of change of mean fitness in a population as the “fundamental theorem of natural selection” is criticized on the grounds that Fisher's derivation of the fundamental theorem used overlapping generations, whereas Li uses separate generations.


  • J. Crow
  • Mathematics
    Evolution; international journal of organic evolution
  • 2002
The effectiveness of reproductive‐value weighting and the theorem in integrated form is discussed, and an optimum principle, analogous to least action and Hamilton's principle in physics, is discussed.

Fundamental Theorem of Natural Selection

The fundamental theorem of natural selection, V′ − V ≥ 0, where V and V′ represent, in successive discrete generations, the mean fitness at a single diallelic locus in a random mating diploid population, has already been proved by Moran.

The basic theorems of natural selection: A naïve approach

The theorem is expounded for selection, the same in both sexes, on single autosomal loci, in diploids, and some special cases will be derived, and the theorem will be extended to some less restricted cases.

Inbreeding and the fundamental theorem of natural selection

The purpose of this note is to examine some of the properties of the change in average fitness as a function of the gene frequency when there is inbreeding in the case of a genetical system consisting of two alleles at a single locus with constant differential viability parameters.

A Fundamental Theorem of Natural Selection for Sex Linkage or Arrhenotoky

  • D. Hartl
  • Biology
    The American Naturalist
  • 1972
In computer-simulated populations undergoing random mating, the additive variance is a good approximation to actual fitness changes over a wide range of selection intensities.

Fundamental theorem of natural selection in two loci

The premises in which Fisher's fundamental theorem holds in a two locus system are explored and the results of a recent investigation by Ewens are examined.

The Price equation




On the change of population fitness by natural selection2 3

A general equation for the role of additive, dominance, and epistatic components of fitness in determining the rate of change in population fitness is given and claims that this law should hold the same position among the biological sciences as the second law of thermodynamics in physical sciences.

The Stability of an Equilibrium and the Average Fitness of a Population

The effect of intra-population selection on gene frequency in a large random mating population has been examined and it was emphasized that they cannot be used as a basis for comparison between two separate populations under two different environments.

Fundamental Theorem of Natural Selection

LI1 has pointed out that Fisher's fundamental theorem of natural selection does not apply exactly in a discrete-generation random-mating situation unless there is no dominance in fitness, and that the mean fitness cannot decrease from generation to generation for a single diallelic locus.

The Genetic Variance of Autotetraploids with Two Alleles.

  • C. Li
  • Biology, Medicine
  • 1957
The author examines the simple but important case of two alleles in more detail and through an alternative method, zliz.

The spread of a gene in natural conditions in a colony of the moth Panaxia dominula L.

The time has now come when an account can be given of the ecological side of the work, though the experimental breeding is still in progress, and several more seasons must elapse before it is possible to report upon it in detail.

Repeated Linear Regression and Variance Components of a Population with Binomial Frequencies

It is well known that X = np and = npq. Now suppose that there is a concomitant variate Y that takes the value Y0 when X = 0, takes the value Y1 when X = 1, and so on. Therefore, fi is also the