  We propose a truncation model for abundance distribution in the species
richness estimation. This model is inherently semiparametric and incorporates
an unknown truncation threshold between rare and abundant counts observations.
Using the conditional likelihood, we derive a class of estimators for the
parameters in the model by a stepwise maximisation. The species richness
estimator is given by the integer maximising the binomial likelihood when all
other parameters in the model are know. Under regularity conditions, we show
that the estimators of the model parameters are asymptotically efficient. We
recover the Chao$^{'}$s lower bound estimator of species richeness when the
model is a unicomponent Poisson$^{'}$s model. So, it is an element of our class
of estimators. In a simulation study, we show the performances of the proposed
method and compare it to some others.
