We consider a nonlinear first order stochastic difference equation which may be viewed as a stochastic perturbation of {\it W. E. Ricker's} [J. Fish. Res. Bd. Can. 11, 559-623 (1954)] deterministic model of population growth. Numerical experiments seem to suggest that the corresponding Markov process has a stationary probability distribution but this is shown to be false by proving that the process is in fact null recurrent