  We consider a family of models describing the evolution under selection of a
population whose dynamics can be related to the propagation of noisy traveling
waves. For one particular model, that we shall call the exponential model, the
properties of the traveling wave front can be calculated exactly, as well as
the statistics of the genealogy of the population. One striking result is that,
for this particular model, the genealogical trees have the same statistics as
the trees of replicas in the Parisi mean-field theory of spin glasses. We also
find that in the exponential model, the coalescence times along these trees
grow like the logarithm of the population size. A phenomenological picture of
the propagation of wave fronts that we introduced in a previous work, as well
as our numerical data, suggest that these statistics remain valid for a larger
class of models, while the coalescence times grow like the cube of the
logarithm of the population size.
