A white-box model of population growth
- Published
- Accepted
- Subject Areas
- Biophysics, Computational Biology, Ecology, Mathematical Biology, Computational Science
- Keywords
- population dynamics, complex systems, cellular automata, white-box modeling, individual-based modeling, population growth curves, autowaves, population waves
- Copyright
- © 2014 Kalmykov et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ PrePrints) and either DOI or URL of the article must be cited.
- Cite this article
- 2014. A white-box model of population growth. PeerJ PrePrints 2:e762v1 https://doi.org/10.7287/peerj.preprints.762v1
Abstract
Background. Integration of reductionist and holistic approaches is one of the great challenges for mathematical modeling. Mathematical models of complex systems are divided into black-box, white-box and grey-box types. A black-box model is completely nonmechanistic as internal mechanisms of a modeled complex system are hidden. A white-box model demonstrates direct mechanisms of functioning of a complex system. It holistically shows all events at microlevel, mesolevel and macrolevel of a modeled system at all stages of its dynamics. Earlier we have used the white-box modeling for verification and reformulation of the competitive exlusion principle. Here we investigate our white-box model of single-species population dynamics. This is fundamentally important because most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka-Volterra models. Methods. Our white-box model of single-species population growth is a purely logical deterministic individual-based cellular automata model. A biological prototype of the model is a vegetative propagation of rhizomatous lawn grasses. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We also investigate different size and structure of the habitat and two types of fecundity. Results. We have created and investigated a logical white-box model of an ecosystem with one species. This model demonstrates mechanisms of the S-shaped and double S-shaped population growth. We have investigated population growth limited by different factors, in particular by resources, habitat structure, intraspecific competition, lifetime of individuals, regeneration time and fecundity of individuals. We have compared the S-shaped curves with J-shaped curves of population growth. Conclusion. We present a basic white-box model of population dynamics which combines reductionist and holistic approaches. Integration of reductionist and holistic approaches is provided by the simultaneous modeling of both part-whole and cause-effect relations in complex system. We consider this holystic multi-level white-box modeling approach as a method of artificial intelligence which works as hyper-logical automatic deductive inference that provides direct mechanistic insights into complex systems. The white-box modeling by logical deterministic cellular automata is a perspective way for investigation not only of population dynamics but also of any complex systems.
Author Comment
This is a submission to PeerJ for peer review.
Supplemental Information
Movie S1: Monte Carlo simulation. Torus-lattice. Hexagonal neighborhood
Every Monte Carlo simulation consisted of 100 repeated experiments with different initial positioning of an individual on the lattice. Here are shown five repeated experiments. The lattice is uniform, homogeneous and limited. It consists of 23x23 sites available for occupation by individuals. The lattice is closed on the torus and the neighborhood is hexagonal.
Movie S2: Monte Carlo simulation. The lattice has a boundary. Hexagonal neighborhood
Every Monte Carlo simulation consisted of 100 repeated experiments with different initial positioning of an individual on the lattice. Here are shown five repeated experiments. The lattice is uniform, homogeneous and limited. It consists of 23x23 sites available for occupation by individuals. The lattice has a boundary and the neighborhood is hexagonal.
Movie S3: Monte Carlo simulation. Torus-lattice. Tripod neighborhood
Every Monte Carlo simulation consisted of 100 repeated experiments with different initial positioning of an individual on the lattice. Here are shown five repeated experiments. The lattice is uniform, homogeneous and limited. It consists of 23x23 sites available for occupation by individuals. The lattice is closed on the torus and the neighborhood is tripod.
Movie S4: Monte Carlo simulation. The lattice has a boundary. Hexagonal neighborhood
Every Monte Carlo simulation consisted of 100 repeated experiments with different initial positioning of an individual on the lattice. Here are shown five repeated experiments. The lattice is uniform, homogeneous and limited. It consists of 23x23 sites available for occupation by individuals. The lattice has a boundary and the neighborhood is tripod.
Movie S5: S-shaped population growth with short phase of decelerating growth
The lattice size which is available for occupation consists of 50x50 sites. Cellular automata neighborhood is hexagonal and the lattice is closed on the torus.
Movie S6: S-shaped population growth with sharp transition to long phase of decelerating growth
The lattice size which is available for occupation consists of 50x50 sites. Cellular automata neighborhood is hexagonal and the lattice has a boundary.
Movie S7: Double S-shaped population growth
The lattice size which is available for occupation consists of 50x50 sites. Cellular automata neighborhood is tripod and the lattice is closed on the torus.
Movie S8: S-shaped population growth with very long deceleration phase
The lattice size which is available for occupation consists of 50x50 sites. Cellular automata neighborhood is tripod and the lattice has a boundary.