The theta-logistic is unreliable for modelling most census data

Summary
1.The theta-logistic is a simple and flexible model for describing how the growth rate of a popula-tion slows as abundance increases. Starting atrm(taken as the maximum population growth rate),the growth response decreases in a convex or concave way (according to the shape parameterh)tozero when the population reaches carrying capacity.
2.We demonstrate that fitting this model to census data is not robust and explain why. The param-etershandrmare able to play-off against each other (providing a constant product), thus allowingboth to adopt extreme and ecologically implausible values.
3.We use simulated data to examine: (i) a population fluctuating around a constant carrying capac-ity (K); (ii) recovery of a population from 10% of carrying capacity; and (iii) a population subject tovariation inK. We show that estimates of extinction risk depending on this or similar models aretherefore prone to imprecision. We refute the claim that concave growth responses are shown todominate in nature.
4.As the model can also be sensitive to temporal variation in carrying capacity, we argue that theassumption of a constant carrying capacity is both problematic and presents a fruitful direction forthe development of phenomenological density-feedback models.