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What is a genetic map function?

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Genetic Mapping and DNA Sequencing

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 81))

Abstract

We review the reasons that genetic map functions are studied and the way they are used. The connexions between chiasma point processes on four-stranded bivalents, crossover point processes on the single strand products of meiosis, multilocus recombination probabilities and map functions are discussed in detail, mainly, but not exclusively under the assumption of no chromatid interference. As a result of this discussion we obtain a number of inequalities constraining map functions which lead to both bound and smoothness constraints. We show that most of the functions proposed as map functions in the literature do in fact arise in association with a stationary renewal chiasma process, and we clarify the relation between their doing so, while failing to be multilocus feasible in the sense of Liberman & Karlin (1984). We emphasize the fact that map functions can in general neither define chiasma nor crossover processes nor multilocus recombination probabilities, nor can they fully reflect the nature of the interference present in a chiasma or crossover process. Our attempt to answer the question in the title of this paper is not wholly successful, but we present some simple necessary conditions which become sufficient when supplemented by two further simple conditions. The paper closes with the statement of several open problems.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, Berkeley, CA, 94720-3860, USA

    T. P. Speed

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  1. T. P. Speed
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Editors and Affiliations

  1. Department of Statistics, University of California at Berkeley, Evans Hall 367, Berkeley, CA, 94720-3860, USA

    Terry Speed

  2. Department of Mathematics and Molecular Biology, University of Southern California, 1042 W. 36th Place, DRB 155, Los Angeles, CA, 90089-1113, USA

    Michael S. Waterman

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© 1996 Springer Science+Business Media New York

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Speed, T.P. (1996). What is a genetic map function?. In: Speed, T., Waterman, M.S. (eds) Genetic Mapping and DNA Sequencing. The IMA Volumes in Mathematics and its Applications, vol 81. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0751-1_5

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  • DOI: https://doi.org/10.1007/978-1-4612-0751-1_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6890-1

  • Online ISBN: 978-1-4612-0751-1

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