Acta Biotheoretica

, Volume 61, Issue 4, pp 499–519 | Cite as

A General Method for Modeling Population Dynamics and Its Applications

Original Article

Abstract

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.

Keywords

Population growth Organism growth Population growth equation Growth scenarios Extinction, sustainability, J-curve S-curve 

References

  1. Blount ZD, Boreland CZ, Lenski RE (2008) Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli. Proc Natl Acad Sci USA 105:7899–7906CrossRefGoogle Scholar
  2. Chester MA (2012) Fundamental principle governing populations. Acta Biotheor 60:289–302CrossRefGoogle Scholar
  3. Crow JA (1971) The epic of Latin America. Doubleday & Company Inc, New YorkGoogle Scholar
  4. Fantes PA (1977) Control of cell size and cycle time in Schizosaccharomyces pombe. J Cell Sci 24:51–67Google Scholar
  5. Jorgensen P, Tyers M (2004) How cells coordinate growth and division. Curr Biol 14:1014–1027CrossRefGoogle Scholar
  6. 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
  7. Matos MP (2011) Dynamics, games and science II. Springer-Verlag, BerlinGoogle Scholar
  8. Neal D (2004) Introduction to population biology. Cambridge University Press, CambridgeGoogle Scholar
  9. Nebel BJ, Wright RT (1993) Environmental science: the way the world works. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  10. Pramanik J, Keasling JD (1997) Stoichiometric model of Escherichia coli metabolism: incorporation of growth-rate dependent biomass composition and mechanistic energy requirements. Biotechnol Bioeng 56:398–421CrossRefGoogle Scholar
  11. Shestopaloff YK (2012a) General law of growth and replication, growth equation and its applications. Biophys Rev Lett 7(1, 2):71–120CrossRefGoogle Scholar
  12. 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
  13. Shestopaloff YK (2012c) Predicting growth and finding biomass production using the general growth mechanism. Biophys Rev Lett 7(3):177–195Google Scholar
  14. Shestopaloff AY, Neal RM (2013) MCMC for non-linear state space models using ensembles of latent sequences. http://www.utstat.toronto.edu/~alexander/
  15. Sveiczer A, Novak B, Mitchison JM (1996) The size control of fission yeast revisited. J Cell Sci 109:2947–2957Google Scholar
  16. Thieme HR (2003) Mathematics in population biology (Princeton Serious in mathematical and computational biology). Princeton University Press, Princeton, NJGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Research & Development Lab, Segmentsoft Inc.TorontoCanada

Personalised recommendations