In the first part of the paper I will present a brief review on the Hardy–Weinberg equilibrium and it’s formulation in projective algebraic geometry. In the second and last part I will discuss examples and generalizations on the topic.

Panmixia is a key issue in maintaining genetic diversity, which facilitates evolutionary potential during environmental changes. Additionally, conservation biologists suggest the importance of avoiding small or subdivided populations, which are prone to losing genetic diversity. In this paper, computer simulations were performed to the genetic drift of neutral alleles in random mating populatio...

Amethod of complexity control in multinomial mixture modeling of multiple-marker genotype data, imposing the Hardy-Weinberg equilibrium (HWE) between the genotype values, is studied. This is a very natural restriction and known to hold at population level under modest assumptions. The hypothesis under study is that imposing this restriction will prevent overfitting and lead to a better model. T...

Traditionally population genetics precludes the use of the same genetic individual more than once in Hardy-Weinberg (HW) based calculations due to the model's explicit assumptions. However, when applied to clonal plant populations this can be difficult to do, and in some circumstances, it may be ecologically informative to use the ramet as the data unit. In fact, ecologists have varied the defi...

Deviations from Hardy-Weinberg equilibrium (HWE) can indicate inbreeding, population stratification, and even problems in genotyping. In samples of affected individuals, these deviations can also provide evidence for association. Tests of HWE are commonly performed using a simple chi2 goodness-of-fit test. We show that this chi2 test can have inflated type I error rates, even in relatively larg...