A de Finetti diagram is a

ternary plot A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle 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 equi ...

used in

population genetics Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...

. It is named after the

Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...

statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...

Bruno de Finetti Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability. The classic exposition of his distinctive theory is the 1937 "La prévision: ...

(1906–1985) and is used to graph the

genotype frequencies Genetic variation in populations can be analyzed and quantified by the frequency of alleles. Two fundamental calculations are central to population genetics: allele frequencies and genotype frequencies. Genotype frequency in a population is the n ...

population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...

s, where there are two

allele An allele (, ; ; modern formation from Greek ἄλλος ''állos'', "other") is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution. ::"The chro ...

s and the population is

diploid Ploidy () is the number of complete sets of chromosomes in a cell, and hence the number of possible alleles for autosomal and pseudoautosomal genes. Sets of chromosomes refer to the number of maternal and paternal chromosome copies, respectively ...

. It is based on an

equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each othe ...

, and

Viviani's theorem Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from ''any'' interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. It is a theorem commonly employed in various ma ...

: the sum of the perpendicular distances from ''any'' interior point to the sides of said triangle is a constant equal to the length of the triangle's

altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...

Applications in genetics

The de Finetti diagram is used extensively in A.W.F. Edwards' book ''Foundations of Mathematical Genetics''. The sum of the lengths, representing allele frequencies, is set to be 1. In its simplest form the diagram can be used to show the range of genotype frequencies for which Hardy–Weinberg equilibrium is satisfied (the curve within the diagram). A. W. F. Edwards and

Chris Cannings Chris is a short form of various names including Christopher, Christian, Christina, Christine, and Christos. Chris is also used as a name in its own right, however it is not as common. People with the given name * Chris Abani (born 1966), N ...

extended its use to demonstrate the changes that occur in allele frequencies under

natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charle ...

References

* Cannings C., Edwards A. W. F. (1968) "Natural selection and the de Finetti diagram" ''Ann Hum Gen'' 31:421–428 * Edwards, A.W.F. (2000) ''Foundations of Mathematical Genetics 2nd Edition'', Cambridge University Press.

External links

Online plotting of ''de Finetti'' diagrams for population genetics
(also calculates Hardy Weinberg equilibrium statistics) Population genetics Diagrams {{Mathapplied-stub

Applications in genetics

See also

References

External links