From the discrete to the continuous: Relationships and results for single-species population models

To be useful, and therefore successful, a model of single-species population dynamics should be: a satisfactory description of the experimental and natural settings; useful for opening new doors of understanding of population dynamics; and capable of incorporation into more complex models of intra- and inter-specific interaction. In this paper, we compare the qualitative and quantitative features of several simple one-species 'density-functional' population models. Furthermore, we derive novel analytic results pertaining to various regimes of population behaviour and investigate in detail the relationships between different types of mathematical functionality. We propose and critique novel models, generated in both ad hoc and systematic fashion from existing population functionals.