Biology subjects
Publications and source records attributed to Lev V. Kalmykov.
The main idea of this note is to show the most basic and purely mechanistic model of population growth, which has been used by us to create models of interspecific competition for verification of the competitive exclusion principle (1, 2). Our logical deterministic individual-based cellular automata model demonstrates a spatio-temporal mechanism of the S-shaped population growth.
Good science must be clearly transparent in its theories, models and experiments. Earlier David Tilman drew attention to the fact that ecologists investigate interspecific competition phenomenologically, rather than mechanistically. To create a mechanistic model of a complex dynamic system we need to logically describe interactions of its subsystems which lead to emergence of new properties on the macro-level. There are black-box, grey-box and white-box models of complex systems. Black-box models are completely nonmechanistic. We cannot investigate interactions of subsystems of such non-transparent model. A white-box model of a complex system has \"transparent walls\" and directly shows underlined mechanistic mechanisms - all events at micro-, meso-and macro-levels of the modeled dynamic system are directly visible at all stages. Grey-box models are intermediate. Basic ecological models are of black-box type, e.g. Malthusian, Verhulst, Lotka-Volterra models. These models are not individual-based and cannot show features of local interactions of individuals of competing species. That is why they principally cannot provide a mechanistic insight into interspecific competition. To create a white-box model we need a physical theory of the object domain and its intrinsic axiomatic system. On the basis of axiomatic system there is a possibility to logically generate a new knowledge by logical deterministic cellular automata. Understanding of biodiversity mechanisms is the global research priority. Only knowledge of mechanisms of interspecific interactions can allow us to efficiently operate in the field of biodiversity conservation. Obviously that such knowledge must be based on mechanistic models of species coexistence. In order to create a serviceable theory of biodiversity it is necessary to renew attempts to create a basic mechanistic model of species coexistence. But the question arises: Why ecological modelers prefer to use the heaviest black-box mathematical methods which cannot produce mechanistic models of complex dynamic systems in principle, and why they do not use simple and long-known pure logical deterministic cellular automata, which easily can produce white-box models and directly generate clear mechanistic insights into dynamics of complex systems?
The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. This principle was formulated incorrectly because of limitations of the traditional black-box models of interspecific competition. The principle is very important as the basis for understanding evolutionary processes. Our white-box multiscale models are based on logical deterministic individual-based cellular automata. This approach allows to provide an automatic deductive inference on the basis of a system of axioms and to get a direct holistic insight into the studied system. It is one of the most promising methods of artificial intelligence. Here on simplest models we show a mechanism of competitive coexistence which violates the known formulations of the competitive exclusion principle. We reformulate and generalize the competitive exclusion principle and explain why our formulations provide a solution of the biodiversity paradox. In addition, we propose a principle of competitive coexistence.\n\nGraphical abstract\n\nO_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=88 SRC=\"FIGDIR/small/006817_ufig1.gif\" ALT=\"Figure 1000\">\nView larger version (21K):\norg.highwire.dtl.DTLVardef@17f69c5org.highwire.dtl.DTLVardef@1f91196org.highwire.dtl.DTLVardef@f1ce70org.highwire.dtl.DTLVardef@12829e8_HPS_FORMAT_FIGEXP M_FIG C_FIG
The biodiversity paradox is the central problem in theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. This contradiction is the key subject of the long-standing and continuing biodiversity debates. The paradox impedes our insights into biodiversity conservation. Previously we proved that due to a soliton-like behaviour of population waves complete competitors can indefinitely coexist in one closed homogeneous habitat on one and the same limiting resource under constant conditions of environment, without any trade-offs and cooperations. As this fact violates the known formulations of the competitive exclusion principle we have reformulated the principle. Here we explain why this reformulation of the principle results in a solution of the biodiversity paradox. In addition, we generalize the competitive exclusion principle. Reasoning by contradiction, we formulate a generalized principle of competitive coexistence. These principles expand theoretical basis for biodiversity conservation and sustainable development.