Exegeses on maximum genetic differentiation

Mathematical constraints on FST: multiallelic markers in arbitrarily many populations

Interpretations of values of the FST measure of genetic differentiation rely on an understanding of its mathematical constraints. Previously, it has been shown that FST values computed from a biallelic locus in a set of multiple populations and FST values computed from a multiallelic locus in a pair of populations are mathematically constrained as a function of the frequency of the allele that is most frequent across populations. We generalize from these cases to report here the mathematical constraint on FST given the frequency M of the most frequent allele at a multiallelic locus in a set of multiple populations. Using coalescent simulations of an island model of migration with an infinitely-many-alleles mutation model, we argue that the joint distribution of FST and M helps in disentangling the separate influences of mutation and migration on FST. Finally, we show that our results explain a puzzling pattern of microsatellite differentiation: the lower FST in an interspecific comparison between humans and chimpanzees than in the comparison of chimpanzee populations. We discuss the implications of our results for the use of FST. This article is part of the theme issue 'Celebrating 50 years since Lewontin's apportionment of human diversity'.

Highly polymorphic mitochondrial DNA and deceiving haplotypic differentiation: implications for assessing population genetic differentiation and connectivity

Background

Hyperdiverse mtDNA with more than 5% of variable synonymous nucleotide sites can lead to erroneous interpretations of population genetic differentiation patterns and parameters (φ_ST, D_EST). We illustrate this by using hyperdiverse mtDNA markers to infer population genetic differentiation and connectivity in Melarhaphe neritoides, a NE Atlantic (NEA) gastropod with a high dispersal potential. We also provide a recent literature example of how mtDNA hyperdiversity may have misguided the interpretation of genetic connectivity in the crab Opecarcinus hypostegus.

Results

mtDNA variation surveyed throughout the NEA showed that nearly all M. neritoides specimens had haplotypes private to populations, suggesting at first glance a lack of gene flow and thus a strong population genetic differentiation. Yet, the bush-like haplotype network, though visually misleading, showed no signs of phylogeographic or other haplotype structuring. Coalescent-based gene flow estimates were high throughout the NEA, irrespective of whether or not mtDNA hyperdiversity was reduced by removing hypervariable sites.

Conclusions

Melarhaphe neritoides seems to be panmictic over the entire NEA, which is consistent with its long-lived pelagic larval stage. With hyperdiverse mtDNA, the apparent lack of shared haplotypes among populations does not necessarily reflect a lack of gene flow and/or population genetic differentiation by fixation of alternative haplotypes (D_EST ≈ 1 does not a fortiori imply φ_ST ≈ 1), but may be due to (1) a too low sampling effort to detect shared haplotypes and/or (2) a very high mutation rate that may conceal the signal of gene flow. Hyperdiverse mtDNA can be used to assess connectivity by coalescent-based methods. Yet, the combined use of φ_ST and D_EST can provide a reasonable inference of connectivity patterns from hyperdiverse mtDNA, too.

Mathematical Constraints on FST: Biallelic Markers in Arbitrarily Many Populations

[Formula: see text] is one of the most widely used statistics in population genetics. Recent mathematical studies have identified constraints that challenge interpretations of [Formula: see text] as a measure with potential to range from 0 for genetically similar populations to 1 for divergent populations. We generalize results obtained for population pairs to arbitrarily many populations, characterizing the mathematical relationship between [Formula: see text] the frequency M of the more frequent allele at a polymorphic biallelic marker, and the number of subpopulations K We show that for fixed K, [Formula: see text] has a peculiar constraint as a function of M, with a maximum of 1 only if [Formula: see text] for integers i with [Formula: see text] For fixed M, as K grows large, the range of [Formula: see text] becomes the closed or half-open unit interval. For fixed K, however, some [Formula: see text] always exists at which the upper bound on [Formula: see text] lies below [Formula: see text] We use coalescent simulations to show that under weak migration, [Formula: see text] depends strongly on M when K is small, but not when K is large. Finally, examining data on human genetic variation, we use our results to explain the generally smaller [Formula: see text] values between pairs of continents relative to global [Formula: see text] values. We discuss implications for the interpretation and use of [Formula: see text].

BRIP1 coding variants are associated with a high risk of hepatocellular carcinoma occurrence in patients with HCV- or HBV-related liver disease

The molecular mechanisms of hepatocellular carcinoma (HCC) carcinogenesis are still not fully understood. DNA repair defects may influence HCC risk. The aim of the study was to look for potential genetic variants of DNA repair genes associated with HCC risk among patients with alcohol- or viral-induced liver disease. We performed four case-control studies on 2,006 European- (Derivation#1 and #2 studies) and African-ancestry (Validation#1 and #2 studies) patients originating from several cohorts in order to assess the association between genetic variants on DNA repair genes and HCC risk using a custom array encompassing 94 genes. In the Derivation#1 study, the BRIP1 locus reached array-wide significance (Chi-squared SV-Perm, P=5.00×10^-4) among the 253 haplotype blocks tested for their association with HCC risk, in patients with viral cirrhosis but not among those with alcoholic cirrhosis. The BRIP1 haplotype block included three exonic variants (rs4986763, rs4986764, rs4986765). The BRIP1 'AAA' haplotype was significantly associated with an increased HCC risk [odds ratio (OR), 2.01 (1.19-3.39); false discovery rate (FDR)-P=1.31×10^-2]. In the Derivation#2 study, results were confirmed for the BRIP1 'GGG' haplotype [OR, 0.53 (0.36-0.79); FDR-P=3.90×10^-3]. In both Validation#1 and #2 studies, BRIP1 'AAA' haplotype was significantly associated with an increased risk of HCC [OR, 1.71 (1.09-2.68); FDR-P=7.30×10^-2; and OR, 6.45 (4.17-9.99); FDR-P=2.33×10^-19, respectively]. Association between the BRIP1 locus and HCC risk suggests that impaired DNA mismatch repair might play a role in liver carcinogenesis, among patients with HCV- or HBV-related liver disease.

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

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/(I(2)-1)). These results extend our understanding of the behavior of FST in relation to other population-genetic statistics.

Evolution in subdivided plant populations: concepts, recent advances and future directions

Research into the evolution of subdivided plant populations has long involved the study of phenotypic variation across plant geographic ranges and the genetic details underlying that variation. Genetic polymorphism at different marker loci has also allowed us to infer the long- and short-term histories of gene flow within and among populations, including range expansions and colonization-extinction dynamics. However, the advent of affordable genome-wide sequences for large numbers of individuals is opening up new possibilities for the study of subdivided populations. In this review, we consider what the new tools and technologies may allow us to do. In particular, we encourage researchers to look beyond the description of variation and to use genomic tools to address new hypotheses, or old ones afresh. Because subdivided plant populations are complex structures, we caution researchers away from adopting simplistic interpretations of their data, and to consider the patterns they observe in terms of the population genetic processes that have given rise to them; here, the genealogical framework of the coalescent will continue to be conceptually and analytically useful.