Two opposing patterns of meta-community organization are nestedness and negative species co-occurrence. Both patterns can be quantified with metrics that are applied to presence-absence matrices and tested with null model analysis. Previous meta-analyses have given conflicting results, with the same set of matrices apparently showing high nestedness (Wright et al. 1998) and negative species co-occurrence (Gotelli and McCabe 2002). We clarified the relationship between nestedness and co-occurrence by creating random matrices, altering them systematically to increase or decrease the degree of nestedness or co-occurrence, and then testing the resulting patterns with null models. Species co-occurrence is related to the degree of nestedness, but the sign of the relationship depends on how the test matrices were created. Low-fill matrices created by simple, uniform sampling generate negative correlations between nestedness and co-occurrence: negative species co-occurrence is associated with disordered matrices. However, high-fill matrices created by passive sampling generate the opposite pattern: negative species co-occurrence is associated with highly nested matrices. The patterns depend on which index of species co-occurrence is used, and they are not symmetric: systematic changes in the co-occurrence structure of a matrix are only weakly associated with changes in the pattern of nestedness. In all analyses, the fixed-fixed null model that preserves matrix row and column totals has lower type I and type II error probabilities than an equiprobable null model that relaxes row and column totals. The latter model is part of the popular nestedness temperature calculator, which detects nestedness too frequently in random matrices (type I statistical error). When compared to a valid null model, a matrix with negative species co-occurrence may be either highly nested or disordered, depending on the biological processes that determine row totals (number of species occurrences) and column totals (number of species per site).