A Central Limit Theorem for the Driver Site Frequency Spectrum

Source abstract

We consider a supercritical two-type continuous-time linear birth-death process with mutation and selection, in which wild-type individuals give rise to mutant offspring with a larger net-growth rate. We previously had obtained first-order law of large number results for the driver site frequency spectrum. We return to obtain a second-order central limit theorem, in which we show stable convergence of a scaling of the deviation of the SFS from its first-order limit. We provide a central limit theorem at both large detection times and sizes. Then, we apply these results to obtain confidence intervals for a class of consistent estimators for the fitness advance.