markovian
Kryazhimskiy S, Tkačik G & Plotkin JB 2009 The dynamics of adaptation on correlated fitness landscapes. PNAS 106:18638-18643.
- we assume that the mutation rate is sufficiently small that, at most, one mutant segregates in the population at any time
- the population is essentially always monomorphic
- in this limit, the adaptive walk of the population is described by a continuous-time, continuous-space Markov chain
- in contrast to the "greedy" adaptive walks typically studied in the literature on rugged fitness landscapes (3, 4), the adaptive walks studied here never stop
- even if a population reaches a local fitness maximum, a deleterious mutation will eventually fix, and the walk will continue
- the assumption of weak mutation, although restrictive, has been used in previous literature and provides a reasonable starting point for future research
- relaxing this assumption presents substantial mathematical complications and introduces entirely new phenomena, such as clonal interference
- we must first have a solid understanding of adaptation dynamics under weak mutation before proceeding to incorporate these additional effects
- without a theory of weak mutation, we would be unable to disentangle the effects of the fitness landscape itself from the effects of clonal interference
- neutral networks are important for adaptation only when a population can use them to quickly access previously inaccessible beneficial mutations
- this regime only occurs when the population is polymorphic
- i.e. when θ > 1
- a monomorphic population can explore the neutral network only very slowly, by substituting neutral mutations
