遗传系统的中性和稳定平衡与Hardy-Weinberg原理：卡方检验的局限性和等位基因频率自相关函数的优点
Neutral and Stable Equilibria of Genetic Systems and The Hardy-Weinberg Principle: Limitations of the Chi-Square Test and Advantages of Auto-Correlation Functions of Allele Frequencies
摘要：
自群体遗传学建立以来，遗传平衡的概念（与经典力学非常相似）一直与哈代-温伯格（HW）原理相关联，目前的平衡识别假设是，如果在实验中观察到适当的卡方值（p<0.05），则HW公理有效。在这里，我们通过数值实验表明，考虑到人口的大合奏的一个位点/两个等位基因的遗传系统的卡方检验是不具有决定性的，可能会导致假阴性的随机交配群体和假阳性的非随机交配群体。因此，我们证实了统计检验不能用来推断遗传群体是否在HW条件下的逻辑陈述。此外，我们表明，在HW条件下，任何有限大小的人口在时间上的演变，根据什么可以被确定为中性动态的平衡的概念是无法达到任何实际目的。因此，在HW条件下，平衡性质是不可观察的。通过放宽随机交配的条件，我们证明了该动力学系统获得了渐近稳定平衡点的所有特征。因此，我们的研究结果表明，遗传系统中的平衡问题应接近非平衡统计物理学的密切类比，其可观测性应集中在动态量，如典型的衰变性质的等位基因自相关函数的时间。从这个角度来看，人们应该放弃遗传平衡的经典概念及其与HW比例的关系，并在寻找能够考虑这些系统的全部复杂性的群体遗传转化的统一一般原则的方向上进行开放式调查。
英文摘要：
Since the foundations of Population Genetics the notion of genetic equilibrium (in close analogy to Classical Mechanics) has been associated to the Hardy-Weinberg (HW) Principle and the identification of equilibrium is currently assumed by stating that the HW axioms are valid if appropriate values of Chi-Square (p<0.05) are observed in experiments. Here we show by numerical experiments with the genetic system of one locus/two alleles that considering large ensembles of populations the Chi-Square test is not decisive and may lead to false negatives in random mating populations and false positives in nonrandom mating populations. As a result we confirm the logical statement that statistical tests can not be used to deduce if the genetic population is under the HW conditions. Furthermore, we show that under the HW conditions populations of any finite size evolve in time according to what can be identified as neutral dynamics to which the very notion of equilibrium is unattainable for any practical purpose. Therefore, under the HW conditions equilibrium properties are not observable. We also show that by relaxing the condition of random mating the dynamics acquires all the characteristics of asymptotic stable equilibrium. As a consequence our results show that the question of equilibrium in genetic systems should be approached in close analogy to non-equilibrium statistical physics and its observability should be focused on dynamical quantities like the typical decay properties of the allelic auto correlation function in time. In this perspective one should abandon the classical notion of genetic equilibrium and its relation to the HW proportions and open investigations in the direction of searching for unifying general principles of population genetic transformations capable to take in consideration these systems in their full complexity.
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