A General Method for Modeling Population Dynamics and Its Applications
- 196 Downloads
Studying populations, be it a microbe colony or mankind, is important for understanding how complex systems evolve and exist. Such knowledge also often provides insights into evolution, history and different aspects of human life. By and large, populations’ prosperity and decline is about transformation of certain resources into quantity and other characteristics of populations through growth, replication, expansion and acquisition of resources. We introduce a general model of population change, applicable to different types of populations, which interconnects numerous factors influencing population dynamics, such as nutrient influx and nutrient consumption, reproduction period, reproduction rate, etc. It is also possible to take into account specific growth features of individual organisms. We considered two recently discovered distinct growth scenarios: first, when organisms do not change their grown mass regardless of nutrients availability, and the second when organisms can reduce their grown mass by several times in a nutritionally poor environment. We found that nutrient supply and reproduction period are two major factors influencing the shape of population growth curves. There is also a difference in population dynamics between these two groups. Organisms belonging to the second group are significantly more adaptive to reduction of nutrients and far more resistant to extinction. Also, such organisms have substantially more frequent and lesser in amplitude fluctuations of population quantity for the same periodic nutrient supply (compared to the first group). Proposed model allows adequately describing virtually any possible growth scenario, including complex ones with periodic and irregular nutrient supply and other changing parameters, which present approaches cannot do.
KeywordsPopulation growth Organism growth Population growth equation Growth scenarios Extinction, sustainability, J-curve S-curve
The author thanks Alexander Shestopaloff for discussions, feedback and editing efforts, and reviewers for valuable comments.
- Crow JA (1971) The epic of Latin America. Doubleday & Company Inc, New YorkGoogle Scholar
- Fantes PA (1977) Control of cell size and cycle time in Schizosaccharomyces pombe. J Cell Sci 24:51–67Google Scholar
- Maaloe O, Kjeldgaard NO (1966) Control of macromolecular synthesis; a study of DNA, RNA, and protein synthesis in bacteria. W. A. Benjamin, New YorkGoogle Scholar
- Matos MP (2011) Dynamics, games and science II. Springer-Verlag, BerlinGoogle Scholar
- Neal D (2004) Introduction to population biology. Cambridge University Press, CambridgeGoogle Scholar
- Nebel BJ, Wright RT (1993) Environmental science: the way the world works. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
- Shestopaloff YK (2012b) Growth and replication of living organisms. General law of growth and replication and the unity of biochemical and physical mechanisms, 2nd edn. AKVY Press, TorontoGoogle Scholar
- Shestopaloff YK (2012c) Predicting growth and finding biomass production using the general growth mechanism. Biophys Rev Lett 7(3):177–195Google Scholar
- Shestopaloff AY, Neal RM (2013) MCMC for non-linear state space models using ensembles of latent sequences. http://www.utstat.toronto.edu/~alexander/
- Sveiczer A, Novak B, Mitchison JM (1996) The size control of fission yeast revisited. J Cell Sci 109:2947–2957Google Scholar
- Thieme HR (2003) Mathematics in population biology (Princeton Serious in mathematical and computational biology). Princeton University Press, Princeton, NJGoogle Scholar