The central point of DCA is to interpret the J_{ij} (which can be represented as a q\times q matrix if there are q possible symbols) as direct couplings. If two positions are under joint evolutionary pressure (for example to maintain a structural bond), one might expect these couplings to be large because only sequences with fitting pairs of symbols should have a significant probability. On the other hand, a large correlation between two positions does not necessarily mean that the couplings are large, since large couplings between e.g. positions i,j and j,k might lead to large correlations between positions i and k , mediated by position j . In fact, such indirect correlations have been implicated in the high false positive rate when inferring protein residue contacts using correlation measures like mutual information.
