The neoclassical theory of population dynamics in spatially homogeneous environments. (I) Derivation of universal laws and monotonic growth

A neoclassical theory is proposed for the growth of populations in a spatially homogeneous environment. The proposed theory derives from first principles while extending and unifying the existing theories by addressing all the cases, where the existing theories fall short in recovering qualitative as well as quantitative features that appear in experimental data. These features include in some cases overshooting and oscillations, in others the existence of a Lag Phase at the initial growth stages, as well as an inflection point in the ln curve of the population number, i.e., a logarithmic inflection point referred here as Lip. The proposed neoclassical theory is derived to recover the logistic growth curve as a special case. It also recovers results of a classical experiment reported by Pearl (Quart. Rev. Biol. II(4) (1927) 532-548) featuring growth followed by decay. Comparisons of the solutions obtained from the proposed neoclassical equation with experimental data confirm its quantitative validity, as well as its ability to recover a wide range of qualitative features captured in experiments. This is the first non-autonomous system proposed so far that is shown to capture all these effects.