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A Simple Model of Periodic Reproduction: Selection of Prime Periods

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Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 200))

Abstract

A discrete-time model of periodic reproduction with inter and intra-specific competition is proposed as a tool to investigate the selection of prime reproduction cycle lengths, observed in certain species of cicadas. An approximation for the average populations is proposed and analyzed for the case of 2 and 13 populations. Results indicate that prime periods are in advantage when compared with composite ones, suggesting that the prime periods displayed by cicada species in nature might arise by the process of natural selection of adaptive values (and not as a random result of evolutionary constraints).

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Author information

Authors and Affiliations

  1. Departamento de Matemática, UNEMAT, Sinop, MT, 78550-000, Brazil

    Raul Abreu de Assis

  2. Instituto de Ciências Naturais, Humanas e Sociais (ICNHS)—UFMT, Sinop, MT, 78557-257, Brazil

    Mazílio Coronel Malavazi

Authors
  1. Raul Abreu de Assis
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  2. Mazílio Coronel Malavazi
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Correspondence to Raul Abreu de Assis .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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de Assis, R.A., Malavazi, M.C. (2019). A Simple Model of Periodic Reproduction: Selection of Prime Periods. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_13

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  • DOI: https://doi.org/10.1007/978-3-030-12232-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12231-7

  • Online ISBN: 978-3-030-12232-4

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