  We present simple conditions under which the limiting genealogical process
associated with a class of interacting particle systems with non-neutral
selection mechanisms, as the number of particles grows, is a time-rescaled
Kingman coalescent. Sequential Monte Carlo algorithms are popular methods for
approximating integrals in problems such as non-linear filtering and smoothing
which employ this type of particle system. Their performance depends strongly
on the properties of the induced genealogical process. We verify the conditions
of our main result for standard sequential Monte Carlo algorithms with a broad
class of low-variance resampling schemes, as well as for conditional sequential
Monte Carlo with multinomial resampling.
