Skip to main content

Cycling in Simple Genetic Systems: II. The Symmetric Cases

  • Conference paper
Dynamical Systems

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 287))

Abstract

Sewall Wright’s adaptive landscape is the picture we all use to visualize the dynamics of evolution, at least at the microlevel. Imagine a flat plane each point of which represents a genetic state of the gene pool of a population. Upon this plane is erected a continuous topography whose height above a point describes the degree of adaptedness, or fitness, associated with the corresponding genetic state. The dynamic assumption is that natural selection moves the population upward, in the direction of increasing fitness, with equilibria at local maxima or more general critical points of the fitness function.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Akin, E. (1979), The geometry of population genetics, Lecture Notes in Biomathematics, No. 31 (Springer-Verlag, Berlin).

    Google Scholar 

  • Akin, E. (1982), Cycling in simple genetic systems, J. Math. Biology, 13, 305–324.

    Article  Google Scholar 

  • Akin, E. (1983), Hopf Bifurcation in the Two Locus Genetic Model, Memoir No. 284 (Amer. Math. Soc., Providence, RI).

    Google Scholar 

  • Antoneili, P. and Strobeck, C. (1977), The geometry of random drift I. Stochastic distance and diffusion, Adv. Appl. Prob., 9, 238–249.

    Article  Google Scholar 

  • Ewens, W. (1969), With additive fitness, the mean fitness increases, Nature, 221, 1076.

    Article  Google Scholar 

  • Hastings, A. (1981), Stable cycling in discrete-time genetic models, Proc. Natl. Acad. Sci. USA, 78, 7224–7225.

    Article  Google Scholar 

  • Karlin, S. and Feldman, M. (1970), Linkage and selection: Two locus symmetric viability models, Theoret. Pop. Biology, 1, 39–71.

    Article  Google Scholar 

  • Kun, L. and Lyubich, Yu. (1979), Convergence to equilibrium under the action of additive selection in a multilocus muitiailelic population, Soviet Math. Dokl. (AMS translations), 6, 1380–1382.

    Google Scholar 

  • Losert, V. and Akin, E. (1983), Dynamics of games and genes: Discrete versus continuous time, J. Math. Biology, 17, 241–251.

    Article  Google Scholar 

  • Lyubich, Yu., Maistrovskii, G., and Ol’khovskii, Yu. (1980), Selection-induced convergence to equilibrium in a single-locus autosomal population, Problems Inform. Transmission, 16, 66–75.

    Google Scholar 

  • Marsden, J. and McCracken, M. (1976), The Hopf Bifurcation and its Applications (Springer-Verlag, Berlin).

    Book  Google Scholar 

  • Moran, P. (1964), On the nonexistence of adaptive topographies, Ann. Human Genet., 27, 383–393.

    Article  Google Scholar 

  • Shahshahani, S. (1979), A New Mathematical Framework for the Study of Linkage and Selection, Memoir No, 211 (Amer. Math. Soc., Providence, RI).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Akin, E. (1987). Cycling in Simple Genetic Systems: II. The Symmetric Cases. In: Kurzhanski, A.B., Sigmund, K. (eds) Dynamical Systems. Lecture Notes in Economics and Mathematical Systems, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00748-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-00748-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17698-5

  • Online ISBN: 978-3-662-00748-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics