Linkage disequilibrium between loci
LD was studied using \({\overset{\overline{}}{r}}_{d}\) (Agapow & Burt, 2001). The mean correlation coefficient (r ) of genetic distance (d ) between unordered alleles at \(n\) loci ranged from 0 to 1. This metric has the advantage of limiting the dependency of the correlation coefficient on the number of alleles and loci and is well suited to studies of partially clonal populations.
\begin{equation} {\overset{\overline{}}{r}}_{d}=\frac{V_{D}-\sum_{j=1}^{j=n}\text{var}_{j}}{2\sum_{j=1}^{j=n}{\sum_{k>j}^{k=n}\sqrt{\text{var}_{j}.\text{var}_{k}}}}\nonumber \\ \end{equation}
with\(V_{D}=\frac{\sum_{a,b\neq a}^{\nu}D_{a,b}^{2}-\frac{\left(\sum D_{a,b}\right)^{2}}{\nu}}{\nu}\)and\(\text{var}_{j}=\frac{\sum{d^{2}-\frac{\left(\sum d\right)^{2}}{\nu}}}{\nu}\)
where \(D\) is the number of loci at which two individuals, \(a\) and\(b\), differ (the genetic distance between two individuals over all their loci), \(d\) is the number of different alleles between two individuals at locus \(j\) (for diploids, \(d\) can be 0, 1 or 2), andν is the number of unique possible pairs of individuals \(a\) and\(b\), where \(b\neq a\), within a population.