The model for coalescence is a start. It makes reasonable sense to
suggest that in a population of 
cracks the number of
coalescences can be modelled by a binomial. The implicit
assumptions that go along with this include the fact that a
coalescence is an event which consists of exactly two cracks
merging (or dying) and one crack being born. Where three cracks
are observed at 
and only one is extant at 
, this is
described adequately as the combination of two coalescences under
this model. That is that two of the initial cracks die, a new
crack is born and then subsequently the new crack dies with the
third crack and a crack is born from these two. Of course the
intermediate crack is not observed.
The information on which the data is based is just the number of
coalescences in a particular time interval. The 
are a
function of 
, and this needs further examination. The fact
that 
differs from 
raises questions as to how the
true underlying rate should be modelled across the time interval,
and indeed how real the relationship is. Also, the times of
coalescence determine how the cracks grow up to and after
coalescence, and these are not observed, but nor are they
modelled.
Further investigation of the nature of coalescence was undertaken in the examination of a joint model for coalescence and growth.