1984
DOI: 10.1002/bimj.4710260119
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Admissible Regions in a Simplex of Identity Coefficients

Abstract: Genealogical relationships between any number of individuals are characterized, from the genetic point of view, by the probabilitiea of ell poeeible gene identity states occuning at an autosomel IociiR. However, only a eubepece of the apace of all probabilities ie in fact accemible to any relationehip. B a d on a theorem of THOMPSON (1076). a characterization of the admissible region in the simplex of all condeneed identity coefficients of two non-inbred individuals is presented. Further s similar result in th… Show more

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Cited by 3 publications
(4 citation statements)
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“…We also showed that pedigrees with inbred founders are especially potent in constructibility problems for relatedness coefficients. Previous solutions by Karigl ( 1984 ) required combinations of several infinite pedigrees in order to produce a given set of IBD coefficients. In contrast, our Theorem 8 guarantees that a finite pedigree suffices if inbred founders are allowed.…”
Section: Discussionmentioning
confidence: 99%
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“…We also showed that pedigrees with inbred founders are especially potent in constructibility problems for relatedness coefficients. Previous solutions by Karigl ( 1984 ) required combinations of several infinite pedigrees in order to produce a given set of IBD coefficients. In contrast, our Theorem 8 guarantees that a finite pedigree suffices if inbred founders are allowed.…”
Section: Discussionmentioning
confidence: 99%
“…Karigl’s constructibility theorem for IBD coefficients can be stated, in our terminology, as follows (Karigl 1984 ):…”
Section: Constructibility Theoremsmentioning
confidence: 99%
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