Mutation And Shannon Information Entropy

Based on the Shannon information entropy, this paper discusses the mutation in population genetics from four aspects:1 From the analysis on the entropy character of two pairs alleles equilibrium population, we get the following results:(1) The genotype information entropy and gametal information entropy of two pairs alleles equilibrium are the largest, that means, the largest information entropy distribution is the distribution of equilibrium population.(2) Among the equilibrium population, each position genotype is independent , the same is true for bisextral gametal. That means their interinformation is zero.(3) Among the equilibrium population, the degree of heterozygosity H and relative information entropy can be used for the measurement of population diversity. The relative information entropy reflects the information of all genotypes in the population and the degree of heterozygosity H reflects the information of heterogeneous species. So as the measurement of gene diversity, is superior to H. The simulated result by computer shows that the two are positively relative and their correlative modulus is 0.9747.(4) The non-equilibrium population, after random copulation for one generation, the information entropy of each position genotype reaches the largest; with the increase of random copulation generation, gametal information entropy increases generation after generation. It reaches the largest at the balanced state.(5) Among the equilibrium population, the information entropy of genotype is twice that of gamete. Gametal information entropy is equal to the sum of information entropy of the two loci's gene pool. 2 From the analysis on the entropy character of Shannon information entropy of neutral mutation gene, we get the following results:(1) In the frequent mutation , suppose the time for gene "A" and "a"'s frequency to reach 0.5 is . Before the time reach , the gene pool information entropy is continuously increasing. After that point, the gene pool information entropy is continuously decreasing. When the time is ,the gene pool information entropy reaches the maximum.(2) ) In the frequent mutation , the end gene "a" is fixed in population. When gene replacement happens, the information entropy cost offered by the population is .(3) In the reciprocating mutation, gene frequency's change with different time is a steady and balancing process. The balanced frequency is . The information entropy of gene pool at the balanced point is . The evolution result is stable diversity.(4) In the reciprocating mutation, when the initial frequency of gene "a" is below 0.5, the gene pool information entropy first continuously rises to and then decreases to ;When the former is equal to or bigger than 0.5 but below the balanced frequency , the gene pool information entropy continuously decreases to ; when the former is bigger than the latter, the gene pool information entropy continuously increases to ; when the former is equal to the latter, the gene pool information entropy dosen't change.(5) In the reciprocating mutation, during the changes from the initial point to the balanced point, the cost spent by the population is , among which is the population information entropy at the balanced point.3 From the analysis on the entropy character of Shannon information entropy of neutral mutation gene in the limited population, we get the following results:(1) In the random copulation population whose number is N, supposed the initial gene pool distribution is , the eventual result of gene random drift is that the population's genotype distributions is .(2) In the above population, the information entropy of the population decreases with time change.(3) In the above population, the population becomes steady with random drift. The cost of it is .4 From the study of the character of natural selection and steady diversity, we get the following results:(1) Suppose the gene pool of the initial population is , the selection modulus of the genotyp...