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I am following the original genomic control article - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.167.8448&rep=rep1&type=pdf
What's the role of $p_i$ in the article? It says that $p_i$ denotes the frequency of $A_i$ allele in population. Is it derived from Hardy-Weinberg equilibrium?
I would like to know how I should calculate $p_1$ for a specific data set.
I have not read the article but in general the allele frequency is pretty much the easiest statistics to compute from population genetics data.
The allele frequency $p_i$ of the allele $A_i$ is the relative frequency of this allele $A_i$ in the population. In other words, it is the counts of haplotypes having the allele $A_i$ divided by the total number of haplotypes. For the specific case of diploid organisms, this frequency is the count of allele $A_i$ divided by twice the number of individuals.
Consider for example the following data, where we have two alleles in the population, $A$ and $B$. Each individual is denoted by its two haplotypes separated by '|'. For example individual A|B is heterozygous.
A|B A|A A|A A|A B|B A|B A|B A|A A|A A|A A|A A|B A|A A|B
In this population there are $7$ Bs over 14 individuals. That makes a allele frequency for B of $\frac{7}{28} = \frac{1}{4}$.
Of course, if you have genotype frequencies, you could - making a number of assumptions - calculate the allele frequency using Hardy-Weinberg but typically from empirical data, you don't need to go through that.
More information about Hardy-Weinberg rule at the post Solving Hardy Weinberg problems.
