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De Finetti Diagram
A de Finetti diagram is a ternary plot used in population genetics. It is named after the Italian statistician Bruno de Finetti (1906–1985) and is used to graph the genotype frequencies of populations, where there are two alleles and the population is diploid. It is based on an equilateral triangle, and Viviani's theorem: 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. 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 extended its use to demonstrate the changes that occur in allele frequencies under na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Finetti Diagram
A de Finetti diagram is a ternary plot used in population genetics. It is named after the Italian statistician Bruno de Finetti (1906–1985) and is used to graph the genotype frequencies of populations, where there are two alleles and the population is diploid. It is based on an equilateral triangle, and Viviani's theorem: 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. 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 extended its use to demonstrate the changes that occur in allele frequencies under na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 math competitions, secondary school mathematics examinations, and has wide applicability to many problems in the real world. Proof This proof depends on the readily-proved proposition that the area of a triangle is half its base times its height—that is, half the product of one side with the altitude from that side.Claudi Alsina, Roger B. Nelsen: ''Charming Proofs: A Journey Into Elegant Mathematics''. MAA 2010, , p. 96 () Let ABC be an equilateral triangle whose height is ''h'' and whose side is ''a''. Let P be any point inside the triangle, and ''u, s, t'' the distances of P from the sides. Draw a line from P to each of A, B, and C, forming three triangles PAB, PBC, and PCA. Now, the areas of these triangles are \frac, \frac, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy Weinberg
Hardy may refer to: People * Hardy (surname) * Hardy (given name) * Hardy (singer), American singer-songwriter Places Antarctica * Mount Hardy, Enderby Land * Hardy Cove, Greenwich Island * Hardy Rocks, Biscoe Islands Australia * Hardy, South Australia, a locality * Cape Hardy, a headland in South Australia * Hardy Inlet, Western Australia Canada * Hardy Township, Ontario, Canada, administered by the Loring, Port Loring and District, Ontario, services board * Port Hardy, British Columbia * Hardy, Saskatchewan, Canada, a hamlet United States * Hardy, Arkansas, a city * Hardy, California, an unincorporated community * Hardy, Iowa, a city * Hardy, Kentucky, an unincorporated community * Hardy, Mississippi, an unincorporated community * Hardy, Montana, an unincorporated community * Hardy, Nebraska, a village * Hardy, Virginia, an unincorporated community * Hardy County, West Virginia * Hardy Dam, Michigan * Hardy Lake, Indiana, a state reservoir * Hardy Pond, Massachusetts * H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wahlund Effect
In population genetics, the Wahlund effect is a reduction of heterozygosity (that is when an organism has two different alleles at a locus) in a population caused by subpopulation structure. Namely, if two or more subpopulations are in a Hardy–Weinberg equilibrium but have different allele frequencies, the overall heterozygosity is reduced compared to if the whole population was in equilibrium. The underlying causes of this population subdivision could be geographic barriers to gene flow followed by genetic drift in the subpopulations. The Wahlund effect was first described by the Swedish geneticist Sten Wahlund in 1928. Simplest example Suppose there is a population P, with allele frequencies of A and a given by p and q respectively (p + q = 1). Suppose this population is split into two equally-sized subpopulations, P_1 and P_2, and that all the ''A'' alleles are in subpopulation P_1 and all the ''a'' alleles are in subpopulation P_2 (this could occur due to drift). Then, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Diagram
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 equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram. In game theory, it is often called a simplex plot.Karl Tuyls, "An evolutionary game-theoretic analysis of poker strategies", ''Entertainment Computing'' January 2009 , p. 9 Ternary plots are tools for analyzing compositional data in the three-dimensional case. In a ternary plot, the values of the three variables , , and must sum to some constant, . Usually, this constant is represented as 1.0 or 100%. Because for all substances being graphed, any one variable is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Charles Darwin popularised the term "natural selection", contrasting it with selective breeding, artificial selection, which in his view is intentional, whereas natural selection is not. Genetic diversity, Variation exists within all populations of organisms. This occurs partly because random mutations arise in the genome of an individual organism, and their offspring can inherit such mutations. Throughout the lives of the individuals, their genomes interact with their environments to cause variations in traits. The environment of a genome includes the molecular biology in the Cell (biology), cell, other cells, other individuals, populations, species, as well as the abiotic environment. Because individuals with certain variants of the trait tend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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), Nigerian author * Chris Abrahams (born 1961), Sydney-based jazz pianist *Chris Adams (other), multiple people * Chris Adcock (born 1989), English internationally elite badminton player * Chris Albright (born 1979), American former soccer player *Chris Alcaide (1923–2004), American actor *Chris Amon (1943–2016), former New Zealand motor racing driver *Chris Andersen (born 1978), American basketball player * Chris Anderson (other), multiple people *Chris Angel (wrestler) (born 1982), Puerto Rican professional wrestler * Chris Anker Sørensen (born 1984), Danish cycler *Chris Anstey (born 1975), Australian basketball player * Chris Anthony, American voice actress *Chris Antley (1966–2000), champion American jockey *Chri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Altitude (triangle)
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the ''extended base'' of the altitude. The intersection of the extended base and the altitude is called the ''foot'' of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as ''dropping the altitude'' at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. Thus, the longest altitude is perpendicular to the shortest side of the triangle. The altitudes are also related to the sides of the triangle through the trigonometri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Principal properties Denoting the common length of the sides of the equilateral triangle as a, we can determine using the Pythagorean theorem that: *The area is A=\frac a^2, *The perimeter is p=3a\,\! *The radius of the circumscribed circle is R = \frac *The radius of the inscribed circle is r=\frac a or r=\frac *The geometric center of the triangle is the center of the circumscribed and inscribed circles *The altitude (height) from any side is h=\frac a Denoting the radius of the circumscribed circle as ''R'', we can determine using trigonometry that: *The area of the triangle is \mathrm=\fracR^2 Many of these quantities have simple r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram. In game theory, it is often called a simplex plot.Karl Tuyls, "An evolutionary game-theoretic analysis of poker strategies", ''Entertainment Computing'' January 2009 , p. 9 Ternary plots are tools for analyzing compositional data in the three-dimensional case. In a ternary plot, the values of the three variables , , and must sum to some constant, . Usually, this constant is represented as 1.0 or 100%. Because for all substances being graphed, any one variable is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diploidy
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, in each homologous chromosome pair, which chromosomes naturally exist as. Somatic cells, tissues, and individual organisms can be described according to the number of sets of chromosomes present (the "ploidy level"): monoploid (1 set), diploid (2 sets), triploid (3 sets), tetraploid (4 sets), pentaploid (5 sets), hexaploid (6 sets), heptaploid or septaploid (7 sets), etc. The generic term polyploid is often used to describe cells with three or more chromosome sets. Virtually all sexually reproducing organisms are made up of somatic cells that are diploid or greater, but ploidy level may vary widely between different organisms, between different tissues within the same organism, and at different stages in an organism's life cycle. Half ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
