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Fluctuation in Population Dynamics

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Stochastic Methods in Biology

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 70))

Abstract

A dynamics for a large population of randomly mating individuals is formulated as a Markov process on a large product space which involves a pairwise interaction between components. Each individual in the population possesses a character (the state of individual). An individual undergoes Markovian change of its character during its life time. Two individuals may make random mating after which they die, leaving two children with new characters. Each individual is a unique member of a lineage at each time. We are interested in the number of lineages which, comprise individuals possessing the character xi at time ti for i = 1,…,m, where xl,…,xm and tl,…,tm are given in advance. If the initial distribution is i.i.d. and the size n of the population is very large, the proportion of this number to n is approximately computed by means of a joint distribution of a nonlinear Markov process (for a single individual in a infinite population). We shall study the law of the error in this approximation and establish a limit theorem about it.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Nara Joshi Daigaku, Nara 630, Japan

    Kōhei Uchiyama

Authors
  1. Kōhei Uchiyama
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Editor information

Editors and Affiliations

  1. National Institute of Genetics, Yata 1, 111 Mishima, Shizuoka-ken, 411, Japan

    Motoo Kimura

  2. Center for Stochastic Processes, Department of Statistics, University of North Carolina, 27514, Chapel Hill, NC, USA

    Gopinath Kallianpur

  3. Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan

    Takeyuki Hida

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© 1987 Springer-Verlag Berlin Heidelberg

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Uchiyama, K. (1987). Fluctuation in Population Dynamics. In: Kimura, M., Kallianpur, G., Hida, T. (eds) Stochastic Methods in Biology. Lecture Notes in Biomathematics, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46599-4_18

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  • DOI: https://doi.org/10.1007/978-3-642-46599-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17648-0

  • Online ISBN: 978-3-642-46599-4

  • eBook Packages: Springer Book Archive

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