Long-term Response: 3. Adaptive Walks

One model for long-term evolution is an adaptive walk, a series of fixations of mutations that moves the trait mean toward some optimal value. The foundation for this idea traces back to Fisher's geometric model, which showed that mutations of large effect are favored when a trait is far from its optimal, while smaller effects are favored as it approaches the optimal value. Under fairly general conditions, this results in a roughly exponential distribution of fixed adaptive effects. An alternative to trait-based walks are walks in fitness space, motivated by considering a series of mutations to improve the fitness of a particular sequence. In such settings, extreme value theory also suggests a roughly exponential distribution, now of fitness (instead of trait) effects, for mutations fixed during the walk. Much of this theory offers at least partial experimental testing, and this chapter describes not only the theory, but also some of the empirical work testing the models.