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Since the foundations of Population Genetics the notion of geneticequilibrium (in close analogy to Classical Mechanics) has been associated tothe Hardy-Weinberg (HW) Principle and the identification of equilibrium iscurrently assumed by stating that the HW axioms are valid if appropriate valuesof Chi-Square (p<0.05) are observed in experiments. Here we show by numericalexperiments with the genetic system of one locus/two alleles that consideringlarge ensembles of populations the Chi-Square test is not decisive and may leadto false negatives in random mating populations and false positives innonrandom mating populations. As a result we confirm the logical statement thatstatistical tests can not be used to deduce if the genetic population is underthe HW conditions. Furthermore, we show that under the HW conditionspopulations of any finite size evolve in time according to what can beidentified as neutral dynamics to which the very notion of equilibrium isunattainable for any practical purpose. Therefore, under the HW conditionsequilibrium properties are not observable. We also show that by relaxing thecondition of random mating the dynamics acquires all the characteristics ofasymptotic stable equilibrium. As a consequence our results show that thequestion of equilibrium in genetic systems should be approached in closeanalogy to non-equilibrium statistical physics and its observability should befocused on dynamical quantities like the typical decay properties of theallelic auto correlation function in time. In this perspective one shouldabandon the classical notion of genetic equilibrium and its relation to the HWproportions and open investigations in the direction of searching for unifyinggeneral principles of population genetic transformations capable to take inconsideration these systems in their full complexity.

frontiers in genetics

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