ArticleJournal of mathematical biology2018
Bounding measures of genetic similarity and diversity using majorization.
Article in Journal of mathematical biology, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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8 citing papers in PubMed.
- Reflections on the Human Genome Diversity Project: a conversation with Marcus W. Feldman, Henry T. Greely, and Mary-Claire King.Genetics · 2026Article
- Using mathematical constraints to explain narrow ranges for allele-sharing dissimilarities.Theoretical population biology · 2025Article
- Mathematical bounds on rTheoretical population biology · 2025Article
- Mathematical bounds onbioRxiv : the preprint server for biology · 2024Article
- Article
- Mathematical constraints on a family of biodiversity measures via connections with Rényi entropy.Bio Systems · 2024Article
- Mathematical bounds on Shannon entropy given the abundance of the ith most abundant taxon.Journal of mathematical biology · 2023Article
- Measures of care fragmentation: Mathematical insights from population genetics.Health services research · 2020Article
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2 authors.
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Abstract
The homozygosity and the frequency of the most frequent allele at a polymorphic genetic locus have a close mathematical relationship, so that each quantity places a tight constraint on the other. We use the theory of majorization to provide a simplified derivation of the bounds on homozygosity J in terms of the frequency M of the most frequent allele. The method not only enables simpler derivations of known bounds on J in terms of M, it also produces analogous bounds on entropy statistics for genetic diversity and on homozygosity-like statistics that range in their emphasis on the most frequent allele in relation to other alleles. We illustrate the constraints on the statistics using data from human populations. The approach suggests the potential of the majorization method as a tool for deriving inequalities that characterize mathematical relationships between statistics in population genetics.
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