• Johannes Müller
  • Christina Kuttler
Part of the Lecture Notes on Mathematical Modelling in the Life Sciences book series (LMML)


In the present chapter, we discuss two different approaches to model evolution. The first focuses on genes. The presence of different gene variations indicates different discrete levels of fitness, i.e., of reproductive success. We will look at this kind of models (Hardy-Weinberg, Wright model and Fisher-Wright-Haldane model) first. The second approach is not directly related to the genotype, but to the phenotype. The latter is assumed to vary continuously (e.g. as the average size of an individual of a species – this is a real value that may vary in principle continuously). Inspecting the performance of individuals with this phenotype, a certain kind of dynamics – adaptive dynamics – is developed that indicates how evolution will change the phenotype. In this way, phenotypes can be identified that are in particular effective. Adaptive dynamics claim that these are the phenotypes we observe.


Singular Point Gene Frequency Random Mating Rare Mutant Evolutionary Stable Strategy 
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  1. 22.
    Z.D. Blount, C.Z. Borland, R.E. Lenski, Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli. Proc. Natl. Acad. Sci. 105, 7899–7906 (2008)Google Scholar
  2. 44.
    O. Diekmann, A beginner’s guide to adaptive dynamics. Banach Cent. Publ. 63, 47–86 (2004)MathSciNetGoogle Scholar
  3. 52.
    E. Duarte, D. Clarke, A. Moya, E. Domingo, J. Holland, Rapid fitness losses in mammalian RNA virus clones due to muller’s ratchet. Proc. Natl. Acad. Sci. USA 89, 6015–6019 (1992)CrossRefGoogle Scholar
  4. 82.
    S. Geritz, E. Kisdi, G. Meszena, J. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12, 35–57 (1998)CrossRefGoogle Scholar
  5. 121.
    J. Hofbauer, K. Sigmund, Evolutionstheorie und Dynamische Systeme (Parrey Verlag, Berlin, 1984)Google Scholar
  6. 148.
    J. Kingman, The coalescent. Stoch. Proc. Appl. 13, 235–248 (1982)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 189.
    M. Nowak, Evolutionary dynamics. President and Fellow of Harvard College, 2006Google Scholar
  8. 199.
    O. Ramírez, E. Gómez-Díaz, I. Olalde, J.C. Illera, J.C. Rando, J. González-Solís, C. Lalueza-Fox, Population connectivity buffers genetic diversity loss in a seabird. Front. Zool. 10, 1–5 (2013)CrossRefGoogle Scholar
  9. 242.
    E. Yuste, S. Sánchez-Palomino, E. Domingo, C. López-Galíndez, Drastic fitness loss in human immunodeficiency virus type 1 upon serial bottleneck events. J. Virol. 73, 2745–2751 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Johannes Müller
    • 1
  • Christina Kuttler
    • 1
  1. 1.Centre for Mathematical SciencesTechnical University MunichGarchingGermany

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