Linkage disequilibrium¶
Linkage disequilibrium statistics are computed by two methods,
stats.pairwise_LD()
and stats.matrix_LD()
.
The available statistics are:
The statistics listed in the table below are available as methods or attributes of this class. The documentation provides more information regarding the usage.
Code 
Statistic 
Equation 
Reference 


Standard linkage disequilibrium 
1 


Lewontin’s \(D'\) 
2 


Correlation coefficient 
3 


Correlation coefficient 
3 
Reference
Lewontin and Kojima (Evolution 1960 14:458472).
Lewontin (Genetics 1964 49:4967).
Hill and Robertson (Theor. Appl. Genet. 1968 38:226231).
To compute linkage disequilibrium statistics, we assume pair of alleles at two different sites that are respectively at relative frequencies \(p_1\) and \(p_2\) while the genotype constituted by the two alleles is at frequency \(p_{12}\). The standard linkage disequilibrium is:
The standardized linkage disequilibrum is computed as:
where:
\(k = p_1 p_2\) if \(D\) < 0 and \(p_1 p_2 < (1p_1) (1p_2)\),
\(k = (1p_1) (1p_2)\) if \(D\) < 0 and \(p_1 p_2 \ge (1p_1) (1p_2)\),
\(k = p_1 (1p_2)\) if \(D\) > 0 and \(p_1 (1p_2) < (1p_1) p_2\), and
\(k = (1p_1) p_2\) otherwise.
Finally, the pairwise correlation coefficient \(r^2\) is computed as follows: