Although the vast majority of research in evolutionary biology is focused on adaption, a general theory for the population-genetic mechanisms by which complex adaptations are acquired remains to be developed. The issue explored here is the procurement of novel traits that specifically require multiple mutations to achieve a fitness advantage. By highlighting the roles played by the forces of mutation, recombination, and random genetic drift, and drawing from observations on the joint constraints on these factors, the ways in which rates of acquisition of specific types of adaptations scale with population size are explored. These general results provide insight into a number of ongoing controversies regarding the molecular basis of adaptation, including the adaptive utility of recombination and the role of drift in the passage through adaptive valleys.adaptive evolution | complex traits | evolutionary rate | molecular evolution | recombination R ecent empirical observations imply that approximate scaling laws exist for several fundamental evolutionary forces (1-3). First, across the full domain of life, there is an inverse relationship between population density and organism size. This relationship bears importantly on the power of random genetic drift, which is expected to scale negatively (although not necessarily linearly) with total population size (4). Second, the recombination rate per physical distance on chromosomes scales inversely with genome size. This feature is a simple consequence of an apparent structural constraint across all sexually reproducing eukaryotes-the occurrence of approximately one crossover event per chromosome arm per meiosis, and the fact that most variation in genome size is associated with variation in chromosome size rather than chromosome number. Finally, the mutation rate per nucleotide site per generation scales negatively with the genetic effective size of a population, possibly because lineages more vulnerable to random genetic drift are less efficient at maintaining high-fidelity replication/repair machinery (3, 5). The fact that all three of these nonadaptive forces of evolution influence the efficiency of selection raises the question as to whether general scaling laws also exist for the exploitation of various pathways to adaptive evolution.The development of theory in this area is rendered difficult by the multidimensional nature of the problem. One strategy has been to ignore all deleterious mutations and to assume that selection is strong enough and mutation weak enough relative to the power of random genetic drift and recombination that evolution always proceeds by the sequential fixation of single mutations (e.g., refs. 6-11). Such an approach provides a useful entree into the evolutionary dynamics of rare adaptive mutations with large effects. Under these conditions, the expectations are clear-with larger numbers of mutational targets and a reduced power of random genetic drift, the rate of adaptation will increase with population size, although more slowly than ex...