A de Finetti diagram is a ternary plot

Ternary plot

A ternary plot, ternary graph, triangle plot, simplex plot, or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle...

 used in population genetics

Population genetics

Population genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...

. It is named after the Italian

Italy

Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

 statistician

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 Bruno de Finetti

Bruno de Finetti

Bruno de Finetti was an Italian probabilist, statistician and actuary, noted for the "operational subjective" conception of probability...

 (1906–1985) and is used to graph the genotype frequencies

Genotype frequency

In population genetics, the genotype frequency is the frequency or proportion In population genetics, the genotype frequency is the frequency or proportion In population genetics, the genotype frequency is the frequency or proportion (i.e. 0 In population genetics, the genotype frequency is the...

 of population

Population

A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...

s, where there are two allele

Allele

An allele is one of two or more forms of a gene or a genetic locus . "Allel" is an abbreviation of allelomorph. Sometimes, different alleles can result in different observable phenotypic traits, such as different pigmentation...

s and the population is diploid. It is based on an equilateral triangle, and Viviani's theorem

Viviani's theorem

Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from a point to the sides of an equilateral triangle equals the length of the triangle's altitude....

 concerning any point within the triangle, and the three lines from that point that are perpendicular to the sides of the triangle. The sum of the lengths of the lines is a fixed value, regardless of the position of the point. This value (the sum of the lengths) is set to be 1.

Applications in genetics

The de Finetti diagram has been put to extensive use in population genetics by A.W.F. Edwards in his book Foundations of Mathematical Genetics. In its simplest form the diagram can be used to show the range of genotype frequencies for which Hardy-Weinberg equilibrium is satisfied. A.W.F. Edwards and Chris Cannings extended its use to demonstrate the changes that occur in allele frequencies under natural selection

Natural selection

Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....

.

External links

• Online plotting of de Finetti diagrams for population genetics (also calculates Hardy Weinberg equilibrium statistics)