and the total number of species Stotal and the
parameter b (which controls the rate at which
identifications accumulate) are unknown and
to be estimated. By this approach, Paxton
predicted that 47 large marine species remain
to be discovered.
Numerous mathematical functions have
been used to fit discovery records. A problem
with this is that different functions can fit the
observed part of the record equally well yet have
very different asymptotes. To avoid this problem,
the form of the model can be based on an
explicit consideration of the process by which
species are discovered. Briefly, one such model
assumes that the identification of a species
represents the first event in a non-stationary
Poisson process (essentially a process in which
events happen with different time intervals
between them – see box). Its rate function is
proportional to a function g(t) common to
all species. This function reflects how species
discovery effort has varied over time. The
constant multiplying g(t) in the rate function
is then allowed to vary from species to species
according to an exponential distribution to
reflect differences in observability between
species. (It may be easier to spot surface species
than deep-sea ones.) Using an exponentially