A Liebig’s Principle of Limiting Factors based Single-Species Population Growth Model

Abstract

In this contribution, we propose a single-species population growth model formulated using ideas emanating from Liebig’s principle of limiting factors. The inherent natural natality rate determines by the minimum between the size of the population and that of a resource on which the population depends for sustenance. Moreover, emulating the unrestricted population growth assumption, we hypothesise that the associating natural mortality rate is proportional to population size. We also consider that the external feeding resource's consumption rate varies directly proportional to the natural growth rate of the population. In this delivery, we present a qualitative study of the associated trajectories and fitting results based on data on populations growing under experimental or natural conditions. The possible phase configurations include regimes with stable equilibria, sigmoidal growth, extinction, or stationarity. All study cases confirmed that the offered model entails high reproducibility of observed variation patterns while supplying remarkable interpretative capabilities. The proposed model also allows simultaneous identification of the population size trajectory and the resource abatement function. One phase of Liebig’s limiting factors principle-driven model can consistently mimic population size abatement to extinction. Such a feature misses improved in regularly conceived S-shaped population growth models.