We study the evolution of large but finite asexual populations evolving in
fitness landscapes in which all mutations are either neutral or strongly
deleterious. We demonstrate that despite the absence of higher fitness
genotypes, adaptation takes place as regions with more advantageous
distributions of neutral genotypes are discovered. Since these discoveries are
typically rare events, the population dynamics can be subdivided into separate
epochs, with rapid transitions between them. Within one epoch, the average
fitness in the population is approximately constant. The transitions between
epochs, however, are generally accompanied by a significant increase in the
average fitness. We verify our theoretical considerations with two analytically
tractable bitstring models.Comment: 16 pages, 4 eps figures, Latex (academic press style file), submitted
to the Bulletin of Mathematical Biolog
