A note on density dependence in population models

One of the most studied phenomena in ecology is density dependent regulation. The model most frequently used to study this behaviour is the theta-logistic model. However, disagreement has developed within the ecology community pertaining to the interpretation of this model’s parameters, and thus as to appropriate values for the parameters to assume. In particular, the parameter θ$\theta$ has been allowed to take negative values, resulting in the ‘growth rate parameter’ estimated to be negative for species which are extant and exhibit no signs of becoming extinct in the short-term. Here we explain this phenomenon by formulating the theta-logistic model in the manner in which the original logistic model was formulated by Verhulst (1838), in doing so providing a simple interpretation of model parameters and thus restrictions on values the parameters may assume. We conclude that θ$\theta$ should (almost always) be restricted to values greater than −1$-1$. This has implications for studies assessing the form of density dependence from data. Additionally, another model appearing in the literature is presented which provides a more flexible model of density dependence at the expense of only one additional parameter.