Thesis (M.S., Statistical Sciences) -- University of Idaho, 2016 | We studied the limits of estimability of stochastic versions of the Gompertz model of density dependent population growth when the models are expanded to include an environmental covariate. The stochastic versions were the Gompertz model with process noise (GPN) and the Gompertz state space model (GSS) containing both process noise and observation error. Simulation trials and maximum likelihood estimates of the parameter values show that when sample size is low (n=10) the addition of the covariate in the GPN model causes estimability to break down, but the GPN model performs adequately for longer time series. In most cases studied, the GSS model with a covariate has extremely high estimate variance, estimates often covering the entire range of possible values of the parameter of interest. These results represent severe limitations to the use of covariates with the GPN and GSS models and do not bode well for larger state space and other hierarchical models used in modern statistics.