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In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram. In game theory [2] and convex optimization, [3] it is often called a simplex plot. In a ternary plot, the values of the three variables a, b, and c must sum to some constant, K. Usually, this constant is represented as 1.0 or 100%.
Mixtures of the three gasses are usually depicted in a triangular diagram, known as a ternary plot. Such diagrams are available in the speciality literature. [1] [2] [3] The same information can be depicted in a normal orthogonal diagram, showing only two substances, implicitly using the feature that the sum of all three components is 100 ...
A de Finetti diagram. The curved line is the expected Hardy–Weinberg frequency as a function of p.. 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.
Derivation of ternary plots from Cartesian coordinates, drawn by CMG Lee. (1) shows a point P(a,b,c) in a 3-dimensional Cartesian plane. In (2), if a + b + c = K, and a, b and c are non-negative, P is restricted to the triangle bounded by A, B and C. In (3), the axes are rotated to give an isometric view (the triangle appears equilateral).
For a representation of ternary equilibria a three-dimensional phase diagram is required. Often such a diagram is drawn with the composition as a horizontal plane and the temperature on an axis perpendicular to this plane. To represent composition in a ternary system an equilateral triangle is used, called Gibbs triangle (see also Ternary plot).
A three-component compatibility diagram will depict the stable phase of each pure component as the point at each corner of a ternary diagram. Additional points in the diagram represent other pure phases, and lines connecting pairs of these points represent compositions at which the two phases are the only phases present.
Compositional data in three variables can be plotted via ternary plots. The use of a barycentric plot on three variables graphically depicts the ratios of the three variables as positions in an equilateral triangle .
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 .