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 (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.Comment: 27 pages. We shortened the abstract, added Section 1.1 (Overview),
and updated reference
