In a series of recent works it has been shown that a class of simple models
of evolving populations under selection leads to genealogical trees whose
statistics are given by the Bolthausen-Sznitman coalescent rather than by the
well known Kingman coalescent in the case of neutral evolution. Here we show
that when conditioning the genealogies on the speed of evolution, one finds a
one parameter family of tree statistics which interpolates between the
Bolthausen-Sznitman and Kingman's coalescents. This interpolation can be
calculated explicitly for one specific version of the model, the exponential
model. Numerical simulations of another version of the model and a
phenomenological theory indicate that this one-parameter family of tree
statistics could be universal. We compare this tree structure with those
appearing in other contexts, in particular in the mean field theory of spin
glasses