Abstract： Mathematical population models are constructed based on plausibleexplicit and implicit biological assumptions. While it is easy to incorporate explicitassumptions correctly in the models, those implicit ones are often ill treated or forgot-ten. Indeed, this happens to some well known models in the literature and examplesof such will be mentioned and discussed. For a model to be logically credible, we mustdo our best to ensure that all assumptions are incorporated correctly and consistently.To this end, we exam a simple set of criteria proposed by Arditi and Michalski in 1996.For patchy models, we add an additional criterion to their list. We also add some important criteria in other specific situations and comment on modelling of single speciesgrowths. Following criteria of Arditi and Michalski and other well accepted biological assumptions, we introduce some interesting three dimensional predator-dependent(ratio-dependent) population models. We also discuss various aspects of modellingpopulation fluctuations.