[Maximum entropy principle and population genetic equilibrium].
A general mathematic model of population genetic equilibrium was constructed based on the maximum entropy principle. We proved that the maximum entropy probability distribution was equivalent to the Hardy-Weinberg equilibrium law. A population reached genetic equilibrium when the genotype entropy of the population reached the maximal possible value. In information theory, the entropy or the information content is used to measure the uncertainty of a system. In population genetics, we can use entropy to measure the uncertainty of the genotype of a population. The agreement of the maximum entropy principle and the hardy-Weinberg equilibrium law indicated that random crossing is an irreversible process, which increases the genotype entropy of the population, while inbreeding and selection decrease the genotype entropy of the population. In animal or plant breeding, we often use selection and/or inbreeding to decrease the entropy of a population, and use intercrossing to increase the entropy of the population. In this point of view, breeding is actually regulating the entropy of population. By applying the basic principle of informatics in population genetics, we revealed the biological significance of the genotype entropy and demonstrated that we can work over population genetic problems with the principles and methods of informatics and cybernetics.
Wang
Xiao-Long
XL
College of Marine Life Sciences, Ocean University of Qingdao, Qingdao 266003, China. xiaolong@ouqd.edu.cn
Yuan
Zhi-Fa
ZF
Guo
Man-Cai
MC
Song
Shi-De
SD
Zhang
Quan-Qi
QQ
Bao
Zhen-Min
ZM
D000818:Animals; D005075:Biological Evolution; D005828:Genetics, Population; D008957:Models, Genetic; D015233:Models, Statistical; D011336:Probability