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The geometric-distance matrix of a molecular structure G is a real symmetric n x n matrix defined in the same way as a 2-D matrix. However, the matrix elements D ij will hold a collection of shortest Cartesian distances between i and j in G. Also known as topographic matrix, the geometric-distance matrix can be constructed from the known ...
Distance is often defined as the fraction of mismatches at aligned positions, with gaps either ignored or counted as mismatches. [1] Distance-matrix methods are frequently used as the basis for progressive and iterative types of multiple sequence alignment. The main disadvantage of distance-matrix methods is their inability to efficiently use ...
Figure 1: Genetic distance map by Cavalli-Sforza et al. (1994) [1] Genetic distance is a measure of the genetic divergence between species or between populations within a species, whether the distance measures time from common ancestor or degree of differentiation. [2] Populations with many similar alleles have small genetic distances.
In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points in k -dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them. That is. where denotes the Euclidean norm on ℝk.
Morphometrics (from Greek μορϕή morphe, "shape, form", and -μετρία metria, "measurement") or morphometry[5] refers to the quantitative analysis of form, a concept that encompasses size and shape. Morphometric analyses are commonly performed on organisms, and are useful in analyzing their fossil record, the impact of mutations on ...
t. e. In biology, phylogenetics (/ ˌfaɪloʊdʒəˈnɛtɪks, - lə -/) [1][2][3] is the study of the evolutionary history of life using genetics, which is known as phylogenetic inference. It establishes the relationship between organisms with the empirical data and observed heritable traits of DNA sequences, protein amino acid sequences, and ...
Distance geometry. Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between pairs of points. [1][2][3] More abstractly, it is the study of semimetric spaces and the isometric transformations between them. In this view, it can be considered as a ...
Phylogenetic comparative methods. Phylogenetic comparative methods (PCMs) use information on the historical relationships of lineages (phylogenies) to test evolutionary hypotheses. The comparative method has a long history in evolutionary biology; indeed, Charles Darwin used differences and similarities between species as a major source of ...