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Researches in 1900's on cooperative population dynamics

협력형 개체 수 동역학에 대한 1900년대 연구

  • Received : 2020.03.30
  • Accepted : 2020.06.08
  • Published : 2020.06.30

Abstract

Cooperative behavior may seem contrary to the notion of natural selection and adaptation, but is widely observed in nature, from the genetic level to the organism. The origin and persistence of cooperative behavior has long been a mystery to scientists studying evolution and ecology. One of the important research topics in the field of evolutionary ecology and behavioral ecology is to find out why cooperation is maintained over time. In this paper we take a historical overview of mathematical models representing cooperative relationships from the perspective of mathematical biology, which studies population dynamics between interacting biological groups, and analyze the mathematical characteristics and meanings of these cooperative models.

Keywords

References

  1. W. C. ALLEE, Animal Aggregations: A Study in General Sociology, University of Chicago, Chicago, 1931.
  2. W. C. ALLEE, The Social Life of Animals, Heinemann, London, 1938.
  3. R. AXELROD, The Evolution of Cooperation, Basic Books, Ann Arbor, 1981.
  4. F. BRAUER & C. CASTILLO-CHAVEZ, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, Heidelberg, 2000.
  5. J. BULL & W. HARCOMBE, Population Dynamics Constrain the Cooperative Evolution of Cross-Feeding, PLoS ONE, Vol. 4, no. 1, January 2009.
  6. H. CRONIN, The Ant and the Peacock, Cambridge University Press, 1991.
  7. C. DARWIN, On the origin of species, J. Murray, London, 1859.
  8. C. DARWIN, The Descent of Man, and Selection in Relation to Sex, J. Murray, London, 1871.
  9. H. I. FREEDMAN, Deterministic Mathematical Models in Population Ecology, Marcel Dekker, New York, 1980.
  10. A. HALLOWAY, M. MALONE & J. BROWN, The Population Dynamics of Obligately Cooperative Species Are Inherently Unstable, preprint on bioRxiv, Oct. 26, 2017; https://doi.org/10.1101/208934
  11. W. D. HAMILTON, The genetical evolution of social behavior. I and II, Journal of Theoretical Biology 7 (1964), 1-52, . https://doi.org/10.1016/0022-5193(64)90038-4
  12. C. HOLLING, The components of predation as revealed by a study of small-mammal predation of the European pine sawfly, Can. Entomol. 91 (1959), 293-320. https://doi.org/10.4039/Ent91293-5
  13. C. HOLLING, The characteristics of simple type of predation and parasitism, Canadian Entomologist 91 (1959), 385-398. https://doi.org/10.4039/Ent91385-7
  14. C. HOLLING, The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Entomol. Soc. Can. 45 (1965), 3-60.
  15. M. KOT, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, UK, 2001.
  16. A. J. LOTKA, Elements of Physical Biology, Williams and Wilkins, Baltimore, 1925.
  17. R. MAY & A. MCLEAN, Theoretical Ecology: Principles and Applications, 3rd ed., Oxford University Press, 2007.
  18. J. D. MURRAY, Mathematical biology, Springer-Verlag, Heidelberg, 1989.
  19. M. A. NOWAK & K. SIGMUND, Evolution of indirect reciprocity by image scoring, Nature 393 (1998), 573-577. https://doi.org/10.1038/31225
  20. M. ROSENZWEIG, Paradox of enrichment: destabilization of exploitation ecosystems in ecological time, Science 171 (1971), 385-387. https://doi.org/10.1126/science.171.3969.385
  21. U. SEGERSTRALE, Defenders of the Truth: The Battle for Science in the Sociobiological Debate and Beyond, Oxford University Press, 2000.
  22. S. A. SHIM, Mathematical models for population changes of two interacting species, Journal for History of Mathematics 25(1) (2012), 45-56.
  23. V. VOLTERRA, Variations and fluctuations of the number of individuals in animal species living together, 1926., Translated by R.N. Chapman, Animal Ecology, 409-448, McGraw-Hill, New York, 1931.