Abstract
Since the foundations of Population Genetics the notion of genetic equilibrium (in close analogy with Classical Mechanics) has been associated with 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 χ2 (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 χ2-test is not decisive and may lead to false negatives in random mating populations and false positives in non-random mating populations. This result confirms the logical statement that statistical tests cannot be used to deduce if the genetic population is under the HW conditions. Furthermore, we show that under the HW conditions populations of any 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 the identification of equilibrium properties needs a different approach and the use of more appropriate concepts. 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.
Highlights
IntroductionIn the 1930s the synthetic theory proposed that under the Hardy– Weinberg (HW) conditions genetic systems attain an “equilibrium” state characterized by the genotype frequency proportions obtained directly from the allele frequencies as stated in the HW relation above
In his letter to the Editor of Science Hardy (1908) showed that under specific conditions the simple two allele system (A, a) has the property that the allele frequencies (p, q) determine the genotype frequencies (AA, aa, Aa) obeying proportions given by the simple well-known relation p2 + q2 + 2pq = 1
This definition of equilibrium in genetic systems became part of the well-known Hardy– Weinberg (HW) Principle (Hartl and Clarke, 2007) which formally states that: “If a genetic population is such that (1) organisms are diploid, (2) reproduction is sexual, (3) generations do not overlap, (4) mating is random, (5) the size of the population is significantly large, (6) allele frequencies are equal in the sexes, and (7) there is no migration, mutation, or selection, the genotype frequencies in the population are given by weighted products of the allele frequencies
Summary
In the 1930s the synthetic theory proposed that under the Hardy– Weinberg (HW) conditions genetic systems attain an “equilibrium” state characterized by the genotype frequency proportions obtained directly from the allele frequencies as stated in the HW relation above. This definition of equilibrium in genetic systems became part of the well-known HW Principle (Hartl and Clarke, 2007) which formally states that: “If a genetic population is such that (1) organisms are diploid, (2) reproduction is sexual, (3) generations do not overlap, (4) mating is random, (5) the size of the population is significantly large, (6) allele frequencies are equal in the sexes, and (7) there is no migration, mutation, or selection, the genotype frequencies in the population are given by weighted products of the allele frequencies.
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