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Upper bounds on FST in terms of the frequency of the most frequent allele and total homozygosity: The case of a specified number of alleles

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  • Edge, Michael D.
  • Rosenberg, Noah A.

Abstract

FST is one of the most frequently-used indices of genetic differentiation among groups. Though FST takes values between 0 and 1, authors going back to Wright have noted that under many circumstances, FST is constrained to be less than 1. Recently, we showed that at a genetic locus with an unspecified number of alleles, FST for two subpopulations is strictly bounded from above by functions of both the frequency of the most frequent allele (M) and the homozygosity of the total population (HT). In the two-subpopulation case, FST can equal one only when the frequency of the most frequent allele and the total homozygosity are 1/2. Here, we extend this work by deriving strict bounds on FST for two subpopulations when the number of alleles at the locus is specified to be I. We show that restricting to I alleles produces the same upper bound on FST over much of the allowable domain for M and HT, and we derive more restrictive bounds in the windows M∈[1/I,1/(I−1)) and HT∈[1/I,I/(I2−1)). These results extend our understanding of the behavior of FST in relation to other population-genetic statistics.

Suggested Citation

  • Edge, Michael D. & Rosenberg, Noah A., 2014. "Upper bounds on FST in terms of the frequency of the most frequent allele and total homozygosity: The case of a specified number of alleles," Theoretical Population Biology, Elsevier, vol. 97(C), pages 20-34.
    • Handle: RePEc:eee:thpobi:v:97:y:2014:i:c:p:20-34
    DOI: 10.1016/j.tpb.2014.08.001
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    References listed on IDEAS

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    1. VanLiere, Jenna M. & Rosenberg, Noah A., 2008. "Mathematical properties of the r2 measure of linkage disequilibrium," Theoretical Population Biology, Elsevier, vol. 74(1), pages 130-137.
    2. Alcala, Nicolas & Goudet, Jérôme & Vuilleumier, Séverine, 2014. "On the transition of genetic differentiation from isolation to panmixia: What we can learn from GST and D," Theoretical Population Biology, Elsevier, vol. 93(C), pages 75-84.
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    Cited by:

    1. Alejandro Ochoa & John D Storey, 2021. "Estimating FST and kinship for arbitrary population structures," PLOS Genetics, Public Library of Science, vol. 17(1), pages 1-36, January.
    2. Garud, Nandita R. & Rosenberg, Noah A., 2015. "Enhancing the mathematical properties of new haplotype homozygosity statistics for the detection of selective sweeps," Theoretical Population Biology, Elsevier, vol. 102(C), pages 94-101.

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