  Multitype branching processes with immigration in one type are used to model
the dynamics of stage-structured plant populations. Parametric inference is
first carried out when count data of all types are observed. Statistical
identifiability is proved together with derivation of consistent and
asymptotically Gaussian estimators for all the parameters ruling the population
dynamics model. However, for many ecological data, some stages (i.e. types)
cannot be observed in practice. We study which mechanisms can still be
estimated given the model and the data available in this context. Parametric
inference is investigated in the case of Poisson distributions. We prove that
identifiability holds for only a subset of the parameter set depend- ing on the
number of generations observed, together with consistent and asymptotic
properties of estimators. Finally, simulations are performed to study the
behaviour of the estimators when the model is no longer Poisson. Quite good
results are obtained for a large class of models with distributions having mean
and variance within the same order of magnitude, leading to some stability
results with respect to the Poisson assumption.
