Significance of matches increases with evolutionary distance. Median p-values for the positive (black squares) and negative (white triangles or white triangle points) sets of binding sites for (a) Gal4p and (b) Rpn4p at different evolutionary distances represented by comparing S. cerevisiae to different subsets of the available species. For both factors, as evolutionary distance increases, the median p-value of the functional matches decreases, indicating that they are less likely to have appeared by chance. Conversely, the median p-value of the nonfunctional matches (negative set, white symbols) increases. These observations agree with our predictions for the behavior of the p-values (solid traces) under either the HB evolution for the motif or HKY evolution for the background. There is little difference between these predictions and similar ones that assume that all the comparisons were pairwise (dotted traces).