The role of adaptation is a fundamental question in molecular evolution. Theory predicts that species with large effective population sizes should undergo a higher rate of adaptive evolution than species with low effective population sizes if adaptation is limited by the supply of mutations. Previous analyses have appeared to support this conjecture because estimates of the proportion of nonsynonymous substitutions fixed by adaptive evolution, α, tend to be higher in species with large N(e). However, α is a function of both the number of advantageous and effectively neutral substitutions, either of which might depend on N(e). Here, we investigate the relationship between N(e) and ω(a), the rate of adaptive evolution relative to the rate of neutral evolution, using nucleotide polymorphism and divergence data from 13 independent pairs of eukaryotic species. We find a highly significant positive correlation between ω(a) and N(e). We also find some evidence that the rate of adaptive evolution varies between groups of organisms for a given N(e). The correlation between ω(a) and N(e) does not appear to be an artifact of demographic change or selection on synonymous codon use. Our results suggest that adaptation is to some extent limited by the supply of mutations and that at least some adaptation depends on newly occurring mutations rather than on standing genetic variation. Finally, we show that the proportion of nearly neutral nonadaptive substitutions declines with increasing N(e). The low rate of adaptive evolution and the high proportion of effectively neutral substitution in species with small N(e) are expected to combine to make it difficult to detect adaptive molecular evolution in species with small N(e).