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Critical mutation rate has an exponential dependence on population size

<28>As highlighted by E. O. Wilson, slowing the unnaturally high rate of species extinction is today's most important global challenge, necessitating an improved understanding of extinction factors. This paper reveals for the first time that as population size falls, the 'critical mutation rate' above which fitter alleles are lost transitions unexpectedly from near-constant (the previous assumption in evolutionary biology) to drop exponentially for small populations, leaving them spiralling toward extinction. This new understanding has great potential to aid population management and prevent extinctions. The model closely reproduces the less significant relationship between population size and 'error threshold'. EPSRC project EP/H031936/1.