  We apply recently developed inference methods based on general coalescent
processes to DNA sequence data obtained from various marine species. Several of
these species are believed to exhibit so-called shallow gene genealogies,
potentially due to extreme reproductive behaviour, e.g. via Hedgecock's
"reproduction sweepstakes". Besides the data analysis, in particular the
inference of mutation rates and the estimation of the (real) time to the most
recent common ancestor, we briefly address the question whether the genealogies
might be adequately described by so-called Beta coalescents (as opposed to
Kingman's coalescent), allowing multiple mergers of genealogies.
  The choice of the underlying coalescent model for the genealogy has drastic
implications for the estimation of the above quantities, in particular the
real-time embedding of the genealogy.
