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Central limit theorems of pedigrees

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Summary

Two multivariate central limit theorems are proved for polygenic trait values over a pedigree or collection of pedigrees. These theorems presuppose Hardy-Weinberg and linkage equilibrium for all loci, absence of assortative mating and epistasis, and a small variance for each locus compared to the total variance over many loci. To prevent clustering of loci, an upper bound is also imposed on the number of loci per chromosome. In the case of zero dominance variance for each locus, arbitrary inbreeding is allowed. Otherwise inbreeding is not permitted. Further technical conditions are spelled out in the text.

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Authors and Affiliations

  1. Department of Biomathematics, University of California, 90024, Los Angeles, California, USA

    Kenneth Lange

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  1. Kenneth Lange
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Additional information

This research was supported by the University of California at Los Angeles, NIH Division of Facilities and Resources Grant RR-3, and National Foundation March of Dimes Grant 6-55.

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Lange, K. Central limit theorems of pedigrees. J. Math. Biology 6, 59–66 (1978). https://doi.org/10.1007/BF02478517

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  • DOI: https://doi.org/10.1007/BF02478517

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