  We consider weighted particle systems in which new generations are re-sampled
from current particles with probabilities proportional to their weights. This
covers a broad class of sequential Monte Carlo methods, widely used in applied
statistics. We consider the genealogical tree embedded into such particle
system. When the time is reversed, the particle system induces a partition
valued family of processes (partitions on the leaves of the genealogical tree).
Our aim here is to give a counterexample to a well known formula describing the
transition probabilities of this process.
