Information Study On Relative Relation & Similarity Metric In Mendelian Population

This paper analyses relative relation and similarity metric of Mendelian population still further by Shannon entropy on the basis of the study on population genetics using information method. What's more, draw some conclusions following from the study: 1. the study on the relative relation in Mendelian population and the corresponding results: (1) the study on the kinship in one pair allele equilibrium population and the results: Dividing pro and con mating, chart the associated probability distribution between a female parental genotypes and its descendant genotypes, calculate the Shannon entropy separately and their associated genotype entropy and interentropy, define the information coefficient correlation of the female and its descendant as following: In the same way, define the information coefficient correlation of full antithetical couplet : The result is that the coefficient correlation of both the female and its descendant and full antithetical couplet is the constant 1 2 by statistics method. Thus the information coefficient correlation is better because it is the function of gene frequency. And population genetics also puts emphasis on the gene pool variety discipline. The descendant from generation to generation is gene. (2) the study on the kinship in multi-allele equilibrium population and the results: Firstly, matrix expression of associated probability distribution between the female genotypes and its descendant genotypes and between full antithetical couplets is given with the method of extended ITO. Probability matrixes of the condition I k ,Tk ,O kare the basic matrix. They are all k ( k + 1) 2square matrix. So the associated probability distribution between female and its descendant is given with each row of matrix Tk multiplied by p1 2 , 2p1p2,? ??,2p1pk ,p22,2p2p3,???,2pk?1pk,pk2; and that between full antithetical couplet is given with matrix 1 1 14 2 4??? = + +???k k kS S I T O multiplied by p1 2 , 2p1p2,? ??,2p1pk ,p22,2p2p3,???,2pk?1pk,pk2. Secondly, define the information coefficient correlation of the female and its descendant in multi-allele equilibrium population: I op = ln kI ? ( Pk ,k? O1)ln2 , 0 ≤Iop≤1 and the information coefficient correlation of full antithetical couplet : ( )( )( ) , 014111411 ≤≤+++?= =+∑sk kki iiiis IlnklnppplnpI 2. The information study on similarity metric between Mendelian population and the corresponding results: The information coefficient distance and the information coefficient similarity are constructed to measure the degree of gene mutation under the meaning of demonstrating genetic diversity by Shannon entropy, which should meet the given generally acknowledged truth about the distance and similarity. The definitions are: (1) mono-allele information coefficient distance: D ( X , Y ) = SS (( XX )) +? SS (( YY)) (2) mono-allele information coefficient similarity: R ( X , Y ) = 1 ? D ( X , Y ) = 1 ? SS (( XX )) +? SS (( YY)) (3) multi-allele information coefficient distance: ( , ) 1( , )11I Si jSD i je ee? ??= ? ? (4) multi-allele information coefficient similarity:Then prove their measure characteristic. On the basis of comparing the multi-allele information coefficient distance and the standard coefficient distance, point out the superiority of the former. Finally, compare the different results applying in actual cluster with the definitions above.