A white-box model of S-shaped and double S-shaped single-species population growth

Lev V. Kalmykov, Vyacheslav L. Kalmykov

Complex systems may be mechanistically modelled by white-box modeling with using logical deterministic individual-based cellular automata. Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models). Most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka-Volterra models. In black-box models, the individual-based (mechanistic) mechanisms of population dynamics remain hidden. Here we mechanistically model the S-shaped and double S-shaped population growth of vegetatively propagated rhizomatous lawn grasses. Using purely logical deterministic individual-based cellular automata we create a white-box model. From a general physical standpoint, the vegetative propagation of plants is an analogue of excitation propagation in excitable media. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We have investigated mechanisms of the single-species population growth limited by habitat size, intraspecific competition, regeneration time and fecundity of individuals in two types of boundary conditions and at two types of fecundity. Besides that, we have compared the S-shaped and J-shaped population growth. We consider this white-box modeling approach as a method of artificial intelligence which works as automatic hyper-logical inference from the first principles of the studied subject. This approach is perspective for direct mechanistic insights into nature of any complex systems.