It is currently unclear whether the amino acid substitutions that occur during protein evolution are primarily driven by adaptation, or reflect the random accumulation of neutral changes. When estimated from genomic data, the proportion of adaptive amino acid substitutions, called , was found to vary greatly across species, from nearly zero in humans to above 0.5 in Drosophila. These variations have been interpreted as reflecting differences in effective population size, adaptation being supposedly more efficient in large populations. Here, we investigate the influence of effective popu-lation size and other biological parameters on the rate of adaptive evolution by simulating the evolution of a coding sequence under Fisher’s geometric formalism. We explicitly model recurrent environmental changes and the subsequent adaptive walks, followed by periods of stasis during which purifying selection dominates. We show that, under a variety of conditions, the effective population size has only a moderate influence on , and an even weaker influence on the per generation rate of selective sweeps, modifying the prevalent view in current literature. The rate of environmental change and, interestingly, the dimensionality of the phenotypic space (organismal complexity) affect the adaptive rate more deeply than does the effective population size. We discuss the reasons why verbal arguments have been misleading on that subject and revisit the empirical evidence. Our results question the relevance of the “ ” parameter as an indicator of the efficiency of molecular adaptation. Key words: Fisher’s geometric model, population size, adaptive walk, extinction, amino acid substitution rate
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