[Formula: see text] , Jost’s D, and [Formula: see text] are similarly constrained by allele frequencies: A mathematical, simulation, and empirical study
Statistics [Formula: see text] and Jost’s D have been proposed for replacing [Formula: see text] as measures of genetic differentiation. A principal argument in favour of these statistics is the independence of their maximal values with respect to the subpopulation heterozygosity H(S), a property no...
| Published in: | Molecular Ecology |
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| Main Authors: | , |
| Format: | Text |
| Language: | English |
| Published: |
2019
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| Subjects: | |
| Online Access: | http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6821915/ http://www.ncbi.nlm.nih.gov/pubmed/30589985 https://doi.org/10.1111/mec.15000 |
| Summary: | Statistics [Formula: see text] and Jost’s D have been proposed for replacing [Formula: see text] as measures of genetic differentiation. A principal argument in favour of these statistics is the independence of their maximal values with respect to the subpopulation heterozygosity H(S), a property not shared by [Formula: see text]. Nevertheless, it has been unclear if these alternative differentiation measures are constrained by other aspects of the allele frequencies. Here, for biallelic markers, we study the mathematical properties of the maximal values of [Formula: see text] and D, comparing them to those of [Formula: see text]. We show that [Formula: see text] and D exhibit the same peculiar frequency-dependence phenomena as [Formula: see text] , including a maximal value as a function of the frequency of the most frequent allele that lies well below one. Although the functions describing [Formula: see text] , D, and [Formula: see text] in terms of the frequency of the most frequent allele are different, the allele frequencies that maximize them are identical. Moreover, we show using coalescent simulations that when taking into account the specific maximal values of the three statistics, their behaviours become similar across a large range of migration rates. We use our results to explain two empirical patterns: the similar values of the three statistics among North American wolves, and the low D values compared to [Formula: see text] and [Formula: see text] in Atlantic salmon. The results suggest that the three statistics are often predictably similar, so that they can make quite similar contributions to data analysis. When they are not similar, the difference can be understood in relation to features of genetic diversity. |
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