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Next: A little diversion Up: Two-locus population genetics Previous: Introduction

Gametic disequilibrium

One of the most important properties of a two-locus system is that it is no longer sufficient to talk about allele frequencies alone, even in a population that satisfies all of the assumptions necessary for genotypes to be in Hardy-Weinberg proportions at each locus. To see why consider this. With two loci and two alleles there are four possible gametes:1

Gamete $A_1B_1$ $A_1B_2$ $A_2B_1$ $A_2B_2$
Frequency $x_{11}$ $x_{12}$ $x_{21}$ $x_{22}$

If alleles are arranged randomly into gametes then,

\begin{eqnarray*}
x_{11} &=& p_1p_2 \\
x_{12} &=& p_1q_2 \\
x_{21} &=& q_1p_2 \\
x_{22} &=& q_1q_2 \quad ,
\end{eqnarray*}

where $p_1 = \hbox{freq}(A_1)$ and $p_2 = \hbox{freq}(A_2)$. But alleles need not be arranged randomly into gametes. They may covary so that when a gamete contains $A_1$ it is more likely to contain $B_1$ than a randomly chosen gamete, or they may covary so that a gamete containing $A_1$ is less likely to contain $B_1$ than a randomly chosen gamete. This covariance could be the result of the two loci being in close physical association, but it doesn't have to be. Whenever the alleles covary within gametes

\begin{eqnarray*}
x_{11} &=& p_1p_2 + D \\
x_{12} &=& p_1q_2 - D \\
x_{21} &=& q_1p_2 - D \\
x_{22} &=& q_1q_2 + D \quad ,
\end{eqnarray*}

where $D = x_{11}x_{22} - x_{12}x_{22}$ is known as the gametic disequilibrium.2 When $D \ne 0$ the alleles within gametes covary, and $D$ measures statistical association between them. It does not (directly) measure the physical association. Similarly, $D =
0$ does not imply that the loci are unlinked, only that the alleles at the two loci are arranged into gametes independently of one another.



Subsections
next up previous
Next: A little diversion Up: Two-locus population genetics Previous: Introduction
Kent Holsinger 2008-08-19