The biological machinery of evolution can itself be subject to natural selection. Several mechanisms have been proposed through which this can happen. Here we argue that one of these—lineage selection—becomes a strong selective force when the time scale of fixation in the population is comparable to the time scale of adaptation. This implies that lineage selection will be enhanced by anything that slows down fixation; in particular, we expect its effects to be strong when populations are very large and when spatial diffusion is limited. To demonstrate this we construct a simple model of a spatially structured population evolving on a fixed, but infinite, fitness landscape. This landscape consists of a smooth, evolvable path surrounded by rugged local peaks. Our model exhibits an extremely strong dependence on population size: as its size is increased the population evolves along the smooth path, avoiding local peaks, for exponentially longer times. These results suggest that selection for evolvability might become an increasingly important force as we consider larger spatiotemporal scales, and in particular that it might help to explain the evolution of the modern cellular architecture from some previous, less evolvable state.