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6 changes: 3 additions & 3 deletions Chapters/Population_structure.tex
Original file line number Diff line number Diff line change
Expand Up @@ -246,9 +246,9 @@ \subsection{Assignment Methods}
We have genotype data from unlinked $S$ biallelic loci for $K$ populations. The
allele frequency of allele $A_1$ at locus $l$ in population $k$ is denoted by
$p_{k,l}$, so that the allele frequencies in population 1 are $p_{1,1},\cdots
p_{1,L}$ and population 2 are $p_{2,1},\cdots p_{2,L}$ and so on.
p_{1,S}$ and population 2 are $p_{2,1},\cdots p_{2,S}$ and so on.

You genotype a new individual from an unknown population at these $L$ loci. This individual's genotype at locus $l$ is $g_l$, where $g_l$ denotes the number of copies of allele $A_1$ this individual carries at this locus ($g_l=0,1,2$).
You genotype a new individual from an unknown population at these $S$ loci. This individual's genotype at locus $l$ is $g_l$, where $g_l$ denotes the number of copies of allele $A_1$ this individual carries at this locus ($g_l=0,1,2$).
%JRI: is this formally the definition of a set? should if be $g_l={0,1,2}$ ?

The probability of this individual's genotype at locus $l$ conditional on coming from population $k$, i.e. their alleles being a random HW draw from population $k$, is
Expand All @@ -261,7 +261,7 @@ \subsection{Assignment Methods}
\end{cases}
\end{equation}

Assuming that the loci are independent, the probability of the individual's genotype across all S loci, conditional on the individual coming from population $k$, is
Assuming that the loci are independent, the probability of the individual's genotype across all $S$ loci, conditional on the individual coming from population $k$, is
\begin{equation}
P(\textrm{ind.} | \textrm{pop k}) = \prod_{l=1}^S P(g_l | \textrm{pop k}) \label{eqn_assignment}
\end{equation}
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