Memchord

\[D_{Memchord} = \sqrt{ \sum_{j=1}^{S_T} \left ( \frac{S_{Aj}}{\sqrt{S_A}} - \frac{S_{Bj}}{\sqrt {S_B}} \right )^2 }\]

where \(S_{T}\) is the total number of OTUs
where \(S_{Aj}\) is 1 if the abundance of the jth OTU in sample a is greater than zero, otherwise 0.
where \(S_{Bj}\) is 1 if the abundance of the jth OTU in sample b is greater than zero, otherwise 0.
where \(S_{a}\) is the number of nonzero OTUs in sample a.
where \(S_{b}\) is the number of nonzero OTUs in sample b.