A Lattice Model for Population Biology

  • H. Matsuda
  • N. Tamachi
  • A. Sasaki
  • N. Ogita
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 71)

Abstract

In statistical physics we study macroscopic properties of matter on the basis of constituent particles, and in theoretical population biology we study features of populations on the basis of behaviors of individuals or, more basically and generally, on the basis of properties of self-replicating entities such as genes or chromosomes. Let us refer to any object that we broadly regard as a unit of replication as a ‘replicon’, thereby extending the original meaning used by molecular geneticists. Each replicon has a definite genetic state and undergoes birth and death. Therefore, in addition to ‘attraction and repulsion’, interactions between replicons typically includes ‘attacking and helping’, which affects the birth and death of recipients. The particular mode of interaction depends on a replicon’s state. This state is inherited from its parent replicon, and we can therefore study what type of interaction is prevalent in a population by examining that population’s dynamics. This is simply the evolution of behavior by natural selection.

Keywords

Migration Helium 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyd, R. (1982) Density-dependent mortality and the evolution of social interactions. Anim. Behav. 30, 972–982.CrossRefGoogle Scholar
  2. Eshel, I. (1972) On the neighbor effect and the evolution of altruistic traits. Theor. Pop. Biol. 3, 258–277.CrossRefMathSciNetGoogle Scholar
  3. Felsenstein, J. (1975) A pain in the torus: some difficulties with models of isolation by distance. Amer. Nat. 967, 359–368.CrossRefGoogle Scholar
  4. Hamilton, W.D. (1964) The genetical evolution of social behavior. and II. J. Theor. Biol. 7, 1–16,CrossRefGoogle Scholar
  5. Hamilton, W.D. (1964) The genetical evolution of social behavior. and II. J. Theor. Biol. 7, 17–52.CrossRefGoogle Scholar
  6. Hamilton, W.D. (1972) Altruism and related Phenomena, mainly in social insects. Ann. Rev. Ecol. Syst. 3, 193–232.CrossRefGoogle Scholar
  7. Kimura, M. (1953) “Stepping ston” model of population. Ann. Rep. Natl. Inst. Genet. Japan 3, 63–65.Google Scholar
  8. Kimura, M. (1983) Diffusion model of intergroup selection, with special reference to evolution of an altruistic character. PNAS 80, 6317–6321.CrossRefMATHGoogle Scholar
  9. Kimura, M. and Weiss, G.H. (1964) The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49, 561–567.Google Scholar
  10. Lee, T.D. and Yang, C.N. (1952) Statistical theory of equations of state and phase transitions. II. lattice gas and Ising model.Google Scholar
  11. Matsubara, T. and Matsuda, H. (1956) A lattice model of liquid helium, I. Prog. Theor. Phys. 16, 569–582.CrossRefMATHGoogle Scholar
  12. Matsuda, H. (1981) The Ising model for population biology. Prog. Theor. Phys. 66, 1078–1080.CrossRefMATHMathSciNetGoogle Scholar
  13. Wilson, D.S. (1980) The natural selection of populations and communities. Menlo Park, California: Benjamin/Cummings Pub. Co.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • H. Matsuda
    • 1
  • N. Tamachi
    • 1
  • A. Sasaki
    • 1
  • N. Ogita
    • 2
  1. 1.Department of Biology, Faculty of ScienceKyushu UniversityFukuoka 812Japan
  2. 2.The Institute of Physical and Chemical ResearchWakoJapan

Personalised recommendations