In recent years, many authors have attempted to determine whether local processes (such as competitive exclusion) result in local species richness below that of a local community assembled only by dispersal from a larger regional species pool. To do this they hypothesize that no local processes are significant and that local communities are assembled by dispersal only (Dispersal Assembly Hypothesis or DAH). Some authors have presumed that a prediction of this hypothesis is that, if many regions of similar ecological type (e. g., grassland, temperate deciduous forest, etc.) are compared then local richness will be the same fixed proportion of regional richness, across all regions. To compare this putative prediction with observed data, they plot local richness on the vertical axis vs. regional richness on the horizontal axis and discover how well a straight line fits: if it fits well then they accept the hypothesis and they take the slope as an estimate of the fixed proportion; if it fits poorly (usually by curving down for larger regional pools), then they reject the hypothesis and they presume that local processes are significant. In the present paper, I hypothesize DAH, and for each of two different species relative abundance distributions and predict, by simulation, the probability distribution of species richness in a local community, for a full spectrum of local community sample sizes. The plot of the expected values of these predicted distributions vs. regional richness (for a constant local sample size) and vs. increasing local sample size (for constant regional richness) is not a straight line in either case, but always curves downward. Thus, a straight line (proportional sampling) is never a prediction of DAH, so that looking for straight lines in data plots is irrelevant to testing DAH. Finally, I describe how to compare these predictions to observed data to test whether local processes significantly limit local species richness.