  We show that genealogical trees arising from a broad class of non-neutral
models of population evolution converge to the Kingman coalescent under a
suitable rescaling of time. As well as non-neutral biological evolution, our
results apply to genetic algorithms encompassing the prominent class of
sequential Monte Carlo (SMC) methods. The time rescaling we need differs
slightly from that used in classical results for convergence to the Kingman
coalescent, which has implications for the performance of different resampling
schemes in SMC algorithms. In addition, our work substantially simplifies
earlier proofs of convergence to the Kingman coalescent, and corrects an error
common to several earlier results.
