  Muller's ratchet describes the irreversible accumulation of deleterious
mutations in asexual populations. In well-mixed populations the speed of
fitness decline is exponentially small in the population size, and any positive
rate of beneficial mutations is sufficient to reverse the ratchet in large
populations. The behavior is fundamentally different in populations with
spatial structure, because the speed of the ratchet remains nonzero in the
infinite size limit when the deleterious mutation rate exceeds a critical
value. Based on the relation between the spatial ratchet and directed
percolation, we develop a scaling theory incorporating both deleterious and
beneficial mutations. The theory is verified by extensive simulations in one
and two dimensions.

Populations and Evolution;Statistical Mechanics