Acta Applicandae Mathematicae

, Volume 148, Issue 1, pp 71–102

The Stochastic Encounter-Mating Model

Article

DOI: 10.1007/s10440-016-0079-9

Cite this article as:
Gün, O. & Yilmaz, A. Acta Appl Math (2017) 148: 71. doi:10.1007/s10440-016-0079-9
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Abstract

We propose a new model of permanent monogamous pair formation in zoological populations with multiple types of females and males. According to this model, animals randomly encounter members of the opposite sex at their so-called firing times to form temporary pairs which then become permanent if mating happens. Given the distributions of the firing times and the mating preferences upon encounter, we analyze the contingency table of permanent pair types in three cases: (i) definite mating upon encounter; (ii) Poisson firing times; and (iii) Bernoulli firing times. In the first case, the contingency table has a multiple hypergeometric distribution which implies panmixia. The other two cases generalize the encounter-mating models of Gimelfarb (Am. Nat. 131(6):865–884, 1988) who gives conditions that he conjectures to be sufficient for panmixia. We formulate adaptations of his conditions and prove that they not only characterize panmixia but also allow us to reduce the model to the first case by changing its underlying parameters. Finally, when there are only two types of females and males, we provide a full characterization of panmixia, homogamy and heterogamy.

Keywords

Population dynamics Pair formation Encounter-mating Assortative mating Random mating Panmixia Homogamy Heterogamy Monogamy Mating preferences Mating pattern Contingency table Multiple hypergeometric distribution Simple point process Poisson process Bernoulli process 

Mathematics Subject Classification (2000)

92D25 60J28 60G55 

Funding information

Funder NameGrant NumberFunding Note
EU Seventh Framework Programme
  • 322078

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Weierstrass InstituteBerlinGermany
  2. 2.Department of MathematicsKoç UniversityIstanbulTurkey

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