Population dynamic models leading to logarithmic and Yule distribution

János Izsák, L. Szeidl

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Abstract

A significant field of species abundance distribution (SAD) has a population dynamical character, in which it is supposed that the stochastic speciation process and the evolution of different species are determined by the same linear birth and death process. The distributions of the number of individuals after the speciation tend to a discrete limit distribution depending on some condition if the observation time increases. In the earlier publications, in general, the speciation process was supposed to be a homogeneous Poisson process. In a more realistic case, if the speciation process is inhomogeneous Poisson, the investigation of the model is obviously more difficult. In this paper we deal with the models, in which the birth and death intensities are identical, the speciation rate is bounded, locally integrable and has asymptotically power type behaviour. Limit parameters for these models, depending on the speciation rate, are proportional to a logarithmic or (exactly or asymptotically) Yule distribution. In connection with the sample statistics some results are derived in general and also in special cases (logarithmic and Yule distribution), which are related to the random choice of a species or an individual from the whole population of the system.

Original languageEnglish
Pages (from-to)149-162
Number of pages14
JournalActa Polytechnica Hungarica
Volume15
Issue number1
DOIs
Publication statusPublished - Jan 1 2018

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Keywords

  • Kendall process
  • Logarithmic distribution
  • Poisson process
  • Population dynamic model
  • Species abundance distribution
  • Yule distribution

ASJC Scopus subject areas

  • Engineering(all)

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