  Interpretation of empirical results based on a taxa's lifetime distribution
shows apparently conflicting results. Species' lifetime is reported to be
exponentially distributed, whereas higher order taxa, such as families or
genera, follow a broader distribution, compatible with power law decay. We show
that both these evidences are consistent with a simple evolutionary model that
does not require specific assumptions on species interaction. The model
provides a zero-order description of the dynamics of ecological communities and
its species lifetime distribution can be computed exactly. Different behaviors
are found: an initial $t^{-3/2}$ power law, emerging from a random walk type of
dynamics, which crosses over to a steeper $t^{-2}$ branching process-like
regime and finally is cutoff by an exponential decay which becomes weaker and
weaker as the total population increases. Sampling effects can also be taken
into account and shown to be relevant: if species in the fossil record were
sampled according to the Fisher log-series distribution, lifetime should be
distributed according to a $t^{-1}$ power law. Such variability of behaviors in
a simple model, combined with the scarcity of data available, cast serious
doubts on the possibility to validate theories of evolution on the basis of
species lifetime data.
