  In this paper, we consider stochastic versions of three classical growth
models given by ordinary differential equations (ODEs). Indeed we use
stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential
equations as models. We assume that each stochastic differential equation (SDE)
has some crucial parameters in the drift to be estimated and we use the Maximum
Likelihood Estimator (MLE) to estimate them. For estimating the diffusion
parameter, we use the MLE for two cases and the quadratic variation of the data
for one of the SDEs. We apply the Akaike information criterion (AIC) to choose
the best model for the simulated data. We consider that the AIC is a function
of the drift parameter. We present a simulation study to validate our selection
method.
  The proposed methodology could be applied to datasets with continuous and
discrete observations, but also with highly sparse data. Indeed, we can use
this method even in the extreme case where we have observed only one point for
each path, under the condition that we observed a sufficient number of
trajectories. For the last two cases, the data can be viewed as incomplete
observations of a model with a tractable likelihood function; then, we propose
a version of the Expectation Maximization (EM) algorithm to estimate these
parameters. This type of datasets typically appears in fishery, for instance.
