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Muller's ratchet describes the irreversible accumulation of deleteriousmutations in asexual populations. In well-mixed populations the speed offitness decline is exponentially small in the population size, and any positiverate of beneficial mutations is sufficient to reverse the ratchet in largepopulations. The behavior is fundamentally different in populations withspatial structure, because the speed of the ratchet remains nonzero in theinfinite size limit when the deleterious mutation rate exceeds a criticalvalue. Based on the relation between the spatial ratchet and directedpercolation, we develop a scaling theory incorporating both deleterious andbeneficial mutations. The theory is verified by extensive simulations in oneand two dimensions.

Rare beneficial mutations cannot halt Muller's ratchet in spatial populations