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Recombination is a powerful evolutionary force that merges historically distinct genotypes. But the extent of recombination within many organisms is unknown, and even determining its presence within a set of homologous sequences is a difficult question. Here we develop a new statistic, [[PHI].sub.w] that can be used to test for recombination. We show through simulation that our test can discriminate effectively between the presence and absence of recombination, even in diverse situations such as exponential growth (star-like topologries) and patterns of substitution rate correlation. A number of other tests, Max [X.sup.2], NSS, a coalescentbased likelihood permutation test (from LDHat), and correlation of linkage disequilibrium (both [r.sup.2] and |D'|) with distance, all tend to underestimate the presence of recombination under strong population growth. Moreover, both Max [X.sup.2] and NSS falsely infer the presence of recombination under a simple model of mutation rate correlation. Results on empirical data show that our test can be used to detect recombination between closely as well as distantly related samples, regardless of the suspected rate of recombination. The results suggest that [[PHI].sub.w] is one of the best approaches to distinguish recurrent mutation from recombination in a wide variety of circumstances.

Consider a v v (0; 1) matrix A with exactly k ones in each row and each column. A is (n){stable, if it does not contain any n submatrix with exactly one 0. If A is (n){stable, n 2, then under suitable conditions on A, v k n k(n-1)+(-2) -2. The case of equality leads to new and substantive connections with block designs. The previous bound and characterization of (2){stable matrices follows immediately as a special case. [ABSTRACT FROM AUTHOR]