Table 1 The arsenal of parameters for population genetics/genomics analyses: measures of nucleotide diversity, LD, and tests of selection
Measure/testDescriptionReferences
Nucleotide diversity measures (uni-dimensional measures)
S, sNumber of segregating sites (per DNA sequence or per site, respectively)Nei (1987)
H, ηMinimum number of mutations (per DNA sequence or per site, respectively)Tajima (1996)
kAverage number of nucleotide differences (per DNA sequence) between any two sequencesTajima (1983)
πNucleotide diversity: average number of nucleotide differences per site between any two sequencesJukes and Cantor (1969); Nei and Gojobori (1986); Nei (1987)
θ, θWNucleotide polymorphism: proportion of nucleotide sites that are expected to be polymorphic in any suitable sampleWatterson (1975); Tajima (1993, 1996)
SFSSite/allele frequency spectrum: distribution of allele frequencies at a given set of loci in a population or sampleRonen et al. (2013)
LD (multi-dimensional association among variable sites) and recombination
DCoefficient of LD whose range depends of the allele frequenciesLewontin and Kojima (1960)
DNormalized D, independent of allele frequenciesLewontin (1964)
R, R2Statistical correlation between pairs of sitesHill and Robertson (1968)
ZnSAverage of R2 over all pairwise comparisonsKelly (1997)
ZA/ZZZA is the average of R2 only between adjacent polymorphic sites. ZZ is ZA minus ZnS, which is an estimate of the recombination parameter rRozas et al. (2001)
Four-gamete testMeasure of historical recombination under the infinite-sites modelHudson and Kaplan (1985)
ρPopulation-scaled recombination rate ρ = 4Ner [computed, e.g., by LDhat (Auton and McVean 2007) and LDhelmet (Chan et al. 2012)]Hudson (1987)
Selection tests based on the allele frequency spectrum and/or levels of variability
Tajima’s DNumber of nucleotide polymorphisms with the mean pairwise difference between sequencesTajima (1989)
Fu and Li’s D, D*Number of derived nucleotide variants observed only once in a sample with the total number of derived nucleotide variantsFu and Li (1993)
Fu and Li’s F, F*Number of derived nucleotide variants observed only once in a sample with the mean pairwise difference between sequencesFu and Li (1993)
Fay and Wu’s HNumber of derived nucleotide variants at low and high frequencies with the number of variants at intermediate frequenciesFay and Wu (2000)
Zeng’s E, θL, DHDifference between θL and θW: the first is sensitive to changes in high-frequency variants. DH is a joint test including Tajima’s D and Fay and Wu’s HZeng et al. (2006)
Achaz’s YUnified framework for θ estimators on the basis of the allele frequency spectrumAchaz (2009)
Fu’s FSTest based on the allele frequency spectrumFu (1997)
Ramos-Onsins’ and Rozas’ R2, R3, R4, R2E, R3E, R4ETests based on the difference between the number of singleton mutations and the average number of nucleotide differencesRamos-Onsins and Rozas (2002)
CL, CLRGenome scan for candidate regions of selective sweeps based on aberrant allele frequency spectrumNielsen et al. (2005)
Selection tests based on comparisons of polymorphism and/or divergence between different classes of mutation
dN/dS, Ka/KsRatio of nonsynonymous to synonymous nucleotide divergence/polymorphism (ω)Li et al. (1985); Nei and Gojobori (1986)
HKADegree of polymorphism within and between species at two or more lociHudson et al. (1987)
MKRatios of synonymous and nonsynonymous nucleotide divergence and polymorphismMcDonald and Kreitman (1991)
Estimators derived from extensions of the MK test or the DFE
NINeutrality index that summarizes the four values in an MK test table as a ratio of ratiosRand and Kann (1996)
DoSDirection of selection: difference between the proportion of nonsynonymous divergence and nonsynonymous polymorphismStoletzki and Eyre-Walker (2011)
αProportion of substitutions that are adaptiveCharlesworth (1994); Smith and Eyre-Walker (2002)
DFE-αFraction of adaptive nonsynonymous substitutions, robust to low recombinationEyre-Walker and Keightley (2009)
ωARate of adaptive evolution relative to the mutation rateCastellano et al. (2016); James et al. (2016)
Ka+Rate of adaptive amino acid substitution (Ka+ = αKa)Castellano et al. (2016)
Embedded Image Embedded Image Embedded Image Embedded Image Embedded ImageFractions of five different selection regimes derived from an extension of the MK test: Embedded Image fraction of new mutations that are strongly deleterious and do not segregate in the population; Embedded Image fraction of new mutations that are slightly deleterious and segregate at minor allele frequency (MAF) <5%; Embedded Image fraction of new mutations that are neutral, calculated after removing the excess of sites at MAF <5% due to slightly deleterious mutations; Embedded Image subset of Embedded Image corresponding to recently neutral sites; Embedded Image fraction of new mutations that are adaptive, calculated after removing slightly deleterious mutationsMackay et al. (2012)
LHRiProportion of adaptive substitutions lost due to HRiCastellano et al. (2016)
roptOptimal baseline recombination, above which the genome is free of the HRi and thus LHRi = 0Mackay et al. (2012); Castellano et al. (2016)
Selection tests based on LD
Hudson’s haplotype testDetection of derived and ancestral alleles on unusually long haplotypesHudson et al. (1994)
B/QBased on LD between adjacent pairs of segregating sites, under the coalescent model with recombinationWall (1999)
iHSIntegrated haplotype score, based on the frequency of alleles in regions of high LDVoight et al. (2006)
LRHLong-range haplotype test, based on the frequency of alleles in regions of long-range LDSabeti et al. (2002)
HSHaplosimilarity score: long-range haplotype similarityHanchard et al. (2006)
EHHExtended haplotype homozygosity: measurement of the decay of LD between loci with distanceSabeti et al. (2002)
LDDLD decay: expected decay of adjacent SNP LD at recently selected allelesWang et al. (2006)
SGSShared genomic segment analysis: detection of shared regions across individuals within populationsCai et al. (2011)
GIBDLDDetection of genomic loci with excess of identity-by-descent sharing in unrelated individuals as signature of recent selectionHan and Abney (2013)
XP-EHHLong-range haplotype method to detect recent selective sweepsSabeti et al. (2007)
H12, H2/H1Haplotype homozygosityGarud et al. (2015)
Population differentiation and associated selection tests
GSTAnalysis of gene diversity (heterozygosity) within and between subpopulationsNei (1973)
FSTAverage levels of gene flow based on allele frequencies, under the infinite-sites modelHudson et al. (1992b)
Bayesian FSTProbability that a locus is subject to selection based on locus-specific population differentiation, using a Bayesian methodFoll and Gaggiotti (2008)
GST, HST, KSTDifferent test statistics based on haplotype frequencies and/or the number of nucleotide differences between sequencesHudson et al. (1992a)
SnnGenetic differentiation of subpopulations based on haplotypic dataHudson (2000)
PhiSTCorrelation of haplotypic diversity at different levels of hierarchical subdivisionExcoffier et al. (1992)
Strobeck’s SMeasure of population structure based on the comparison of the observed number of alleles in a sample to that expected when θ is estimated from the average number of nucleotide differencesStrobeck (1987)
XP-CLRCross-population composite likelihood ratio test, based on allele frequency differentiation across populationsChen et al. (2010)
TLK, TF-LKOriginal Lewontin–Krakauer test (TLK) and an extension (TF-LK), aimed at detecting selection based on the variance of FST across lociLewontin and Krakauer (1973); Bonhomme et al. (2010)
LSBLLocus-specific branch length, based on pairwise FST distancesShriver et al. (2004)
hapFLKDetecting of selection based on differences in haplotype frequencies among populations with a hierarchical structureFariello et al. (2013)