Lea-Coulson Formulation

Numerical Lea-Coulson examples show that lower replication capacity reduces the mode and spread of the mutant distribution. The expected number of mutants in Lea-Coulson matches the Luria-Delbruck expectation after setting gamma equal to alpha minus beta. Stochastic mutant extinction reduces Lea-Coulson escape probability relative to deterministic Luria-Delbruck dynamics when mutant death is present. The Lea-Coulson formulation combines deterministic wild-type dynamics with stochastic mutant birth-death dynamics. In Lea-Coulson, a mutant born at time s follows a birth-death process with birth rate alpha and death rate beta. Increasing mutant birth rate while keeping net growth fixed increases Lea-Coulson variance when mutant death is present.