Study On The Information Model Of Inbreeding Population

Population genetics which study mainly on genetic structure of biological population andits disciplinarian is the branch subject of genetics. From the aspect of gene standard,biological evolution is the change of genetic structure of population. The development ofpopulation genetics relates to the theory of biological evolution closely. Population geneticvariation is affected by many factors. It is difficult to solve many important problems only bythe observation or experiment to natural population or experimental population in evolution.So mathematical method is absolutely necessary to research on the degree of genetic variation,the evolutionary speed, and the limited condition. Mathematical model is the high summary about some property of a certain studyingsystem. Beforehand mathematical model in population genetics is basically statistic model.But in fact, hereditary process itself is the process of informational pass. So informationmodel should be also applied to the genetic science as another mathematical method. Since1998, Prof. Yuan Zhi-fa and Prof. Guo Man-cai et al. argue that Shannon entropy can be usedas the metrical indexof genetic diversity, providing a new method for the development ofpopulation genetics. The study will apply information model to further discuss some problemson inbreeding population. When information method is applied in the other subjects, although basic statisticproperty of information is the same, it holds special content in different subjects. In this study,the two principles following are observed from beginning to end: 1．We always suppose that reciprocal crosses are divided, and that the frequency ofreciprocal crosses is the same, when Shannon entropy and interentropy related to distributionof frequency are involved. 2．All information concepts, formula and limited condition in population genetics havenothing to do with the value of frequency. According to studying on inbreeding populationwith the information model, the mainIV 近亲繁殖群体的信息论模型研究results following are given: 1．Genotype entropy is monotonically decreasing and convex function by the genotypefrequency or inbreeding coefficient in inbreeding system. From the beginning of equilibriumpopulation of random mating system, in inbreeding system, its genotype entropy decreases bygeneration number, meeting: S(G1) = S(G0 ) 2 ≤ S(G) ≤ S(G0); after enough generations, thegenotype entropy decreases by generation becomes slower and slower, finally tends to fixedvalue, population reaches equilibrium of inbreeding; with the decrease of genotype entropy,the genetic diversity degree of population also decreases; the process that genotype entropytends to fixed value also is the process that population tends to inbreeding equilibrium. 2．Interentropy among gametes is monotonically increasing concave function bygenotype frequency or inbreeding coefficient. From the beginning of equilibrium of randommatting system, in inbreeding system, interentropy among gametes increases by generationnumber, meeting:0 ≤ I(X,Y) ≤ S(X ) = S(Y) = S(A) = S(G1) = S(G0) 2 ; after enough genera-tion, the interentropy among gametes increases by generation becomes slower and slower,finally tends to the fixed value, population reaches inbreeding equilibrium. 3．Associated genotype entropy between parents is monotonically decreasing function bygeneration number. Inter-entropy between parents is not always monotonically function aboutgeneration numbers, but meeting:0 ≤ I(GX (t),GY (t)) ≤ S(G0). 4．The associated entropy between a female genotypes and its descendant genotypes ismonotonic- ally decreasing function about generation number. From the beginning ofequilibrium of random mating system, inbreeding is given in mating proportion to w, inalternate generation, the associated entropybetween a female genotypes and its descendantgenotypes will decrease by generation, and...