最大信息熵原理与群体遗传平衡

建立了用最大信息熵原理推导群体遗传平衡定律的统一数学模型，并给出了模型的统一解，此解正是Hardy-Weinberg定律所给出的平衡群体的基因型频率，说明当群体信息熵达到最大时，群体基因型频率不再变化，即达到“平衡”。这证明了最大熵分布就是Hardy-Weinberg平衡分布。Hardy-Weinberg平衡定律与最大信息熵原理的内在一致性说明，杂交和随机交配是一个不可逆过程，使群体基因型信息熵增大，无序性增,是选择和近亲交配使群体的信息熵降低，有序性增加，育种过程实际就是调节群体信息熵的过程。过程信息熵的含义是表示一个概率分布的不确定性，最大熵原理意味着在一定的约束条件，选择具有最大不确定性的分布，从而其分布是最为随机的。最大熵原理在信息，工程，天文，地理，图像处理，模式识别等自然科学和社会科学领域都有广泛的成功应用，本文从群体遗传学角度证明了这一原理具有普遍适用性。熵是描述系统状态的函数，而最大熵原理则表明了系统发展变化的趋势，系统的最终状态必然是熵增加至最大值的状态，对于任何系统都是如此。因此，群体遗传系统的平衡定律可以统一用最大熵原理进行判定和描述；任意群体的基因型信息熵在随机交配世代传递时有不断增加的趋势；在一定约束条件下基因型信息熵达到最大值时，就称之为达到遗传平衡。本文将信息论原理应用于群体遗传学研究，揭示了基因信息熵的生物学意义，并表明可以用信息学和控制论的原理和方法来研究群体遗传学问题。

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.