  The mathematical analysis of these models is non-trivial. The most general and uncontroversial theoretical result to date is that progressively larger populations are required for safety in the face of demographic, environmental, and random catastrophic stochasticity. Moreover, because of the structural uncertainly of these models, apparently slight differences in assumptions and techniques routinely lead to widely divergent predictions. This can be illustrated using the well-studied example of the Yellowstone grizzlies. In 1994 Foley constructed a model for this population incorporating environmental stochasticity alone and depending on the intrinsic growth rate of the population and the carrying capacity of the  environment.[30]  The model's prediction augured well for the grizzlies: with a reasonable value for the carrying capacity and the measured value for the intrinsic growth rate, the expected time to extinction was about 12,000 years. In 1997 Foley constructed another model incorporating both demographic and environmental stochasticity but with the option of setting either part equal to  0.[31]  When this model is solved with the demographic stochasticity equal to 0 (a case not analyzed by Foley), it should give the same result as the 1994 model. It does not. It predicts a much lower expected time to  extinction.[32]