On ecological modelling problems in the context of resolving the biodiversity paradox

The biodiversity paradox has been a long-standing enigma in theoretical ecology. It emerged as a contradiction between the competitive exclusion principle and the natural species richness. There are two competing ecological theories which try to explain this issue: niche theory and neutral theory. The problem is that both theories are based on nontransparent models which ignore local interactions between individuals and cannot provide an understanding of interspecific competition mechanisms. Mathematical models of complex systems may be of three general types: black-box, grey-box and white-box models. Classical ecological models – Malthusian, Verhulst and Lotka–Volterra models are of black-box type. Black-box models are nonmechanistic. They cannot help to create a mechanistic ecological theory as they do not provide a direct insight into individual-based mechanisms. Here we make some critical notes on the recent attempts to resolve the paradox by black-box and grey-box approaches. We critically discuss a contribution of the neutral theory and the attempts to solve the paradox by methods of the classical quantum mechanics. These attempts are rather ineffective due to the lack of mechanicalness and likely lead to more confusion than clarity in understanding of biodiversity mechanisms. We also discuss our solution to the biodiversity paradox through a verification of the competitive exclusion principle with using the white-box approach to mathematical modelling of competitive coexistence.