Abstract.— Adaptation is characterized by the movement of a population toward a many-character optimum, movement that results in an increase in fitness. Here I calculate the rate at which fitness increases during adaptation and describe the curve giving fitness versus time as a population approaches an optimum in Fisher's model of adaptation. The results identify several factors affecting the speed of adaptation. One of the most important is organismal complexity—complex organisms adapt more slowly than simple ones when using mutations of the same phenotypic size. Thus, as Fisher foresaw, organisms pay a kind of cost of complexity. However, the magnitude of this cost is considerably larger than Fisher's analysis suggested. Indeed the rate of adaptation declines at least as fast as n-1, where n is the number of independent characters or dimensions comprising an organism. The present results also suggest that one can define an effective number of dimensions characterizing an adapting species.