Paternity Calculation
Equilibrium Test
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Equilibrium Test Print E-mail

In 1908 the englishman G. H. Hardy and the german W. Weinberg independently concluded that, in the absence of factors which cause mutation or selection, the relationships between the allelic frequencies and the genotypic frequencies in a population remain stable between generations, forming an equilibrium. This became known as the Hardy-Weinberg Equilibrium (HWE).

The HWE uses the following laws of Mendel:

"Law of segregation": inherited characteristics are transmitted equally by each of both parents and, instead of becoming mixed, they are maintained separate. That is, each characteristic is determined by a pair of instructions, such that the “dominant” instructions determine the appearance of the progeny while the “recessive” instructions remain latent. (The recessive characteristics only appear when both instructions in a pair are recessive.)

"Law of independent variation": the transmission of characteristics by each parent is governed by the laws of probability; dominant characteristics are not transmitted with greater probability than recessive ones. The different characteristics are also transmitted independently of one another: instructions determining, for instance, eye colour are independent of those controlling gender.

The allelic and genotypic frequencies are maintained constant throughout generations but, if some factor causes disequilibrium, in the next generation this disequilibrium will disappear and the allelic and genotypic frequencies will reach a new equilibrium.

In disequilibrium there is a variation between the allelic and genotypic frequencies, reflecting the mechanism of evolution of the species.

Consequently the frequencies do vary between generations.
This variation in frequencies perturbs the convergence of methods to calculate the probability of paternity, making it necessary to take into account the causal factors or use genetic markers (loci) that are maintained in HWE throughout successive generations.

To test whether a marker is in equilibrium means, more precisely, to apply a statistical test in which the hypothesis is that the marker is in equilibrium.
One method to test if a marker is in HWE was created by Montoya-Delgado et al., itself being based on the Bayesian significance test devised by Pereira e Stern. This test method has been applied and is available here to subscribers of GenomiCalc.