Population Genomics Tools for Implicit Pangenomes

Software required: agc, impg, odgi, povu

Dataset info

Nucleotide diversity

Sample-level unbiased estimator of average pairwise nucleotide diversity, with corrections for finite sample size wiki:

$$\hat{\pi} = \frac{n}{n-1} \sum_{ij} x_i x_j \pi_{ij} = \frac{n}{n-1} \sum_{i=2}^n \sum_{j=1}^{i-1} 2 x_i x_j \pi_{ij}$$

Nei, M.; Li, W.-H. (1979). "Mathematical Model for Studying Genetic Variation in Terms of Restriction Endonucleases". Proceedings of the National Academy of Sciences. 76 (10): 5269–5273. doi:10.1073/pnas.76.10.5269. PMC 413122. PMID 291943.

How to evaluate pi?

Hudson's Fst

Measure of genetic differentiation between populations, comparing average diversity within and between them wiki:

$$F_{ST} = \frac{\pi_{between} - \pi_{within}}{\pi_{between}}$$

Hudson, R. R.; Slatkin, M.; Maddison, W. P. (1992). "Estimation of levels of gene flow from DNA sequence data." Genetics. 132 (2): 583–589.

How to evaluate Fst?

Tajima's D

Test statistic comparing two estimates of genetic variation: the average pairwise nucleotide diversity (π) and the number of segregating sites (S). It detects departures from the neutral mutation–drift equilibrium, such as population expansion, bottlenecks, or selection wiki:

$$D = \frac{\pi - S/a_1}{\sqrt{e_1 S + e_2 S (S - 1)}}$$

Interpretation:

• D ≈ 0 → Consistent with neutral evolution and constant population size.
• D < 0 → Excess of low-frequency polymorphisms, suggesting population expansion or purifying selection.
• D > 0 → Excess of intermediate-frequency polymorphisms, suggesting balancing selection or a recent population bottleneck.

Tajima, F. (1989). Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. Genetics, 123(3), 585–595. Link to article (Genetics, 1989)

How to evaluate Fst?

Example: positive selection at EDAR

The EDAR (chr2:109355029-109449802 on CHM13) 370A variant shows one of the strongest signals of positive selection in the human genome. This mutation arose ~10,740 years ago and swept to near-fixation in East Asian and Native American populations while remaining virtually absent in Africans. The variant shows extreme population differentiation (Fst = 0.760) and enhances NF-κB activation, affecting the development of hair, teeth, and sweat glands.

The specific functional variant under selection is EDAR V370A (rs3827760, chr2:108897145-108897145 on hg38, chr2:109357703-109357703 on CHM13). This is a valine to alanine substitution at position 370 of the EDAR protein. The variant is located within the death domain of EDAR.

Interval	hg38	CHM13
SNP Position	chr2:108897145-108897145	chr2:109357703-109357703
50 kb Interval	chr2:108872145-108922145	chr2:109332703-109382703
100 kb Interval	chr2:108847145-108947145	chr2:109307703-109407703
200 kb Interval	chr2:108797145-108997145	chr2:109257703-109457703

Bryk, J.; Hardouin, E.; Pugach, I.; Hughes, D.; Strotmann, R.; Stoneking, M.; Myles, S. (2008). "Positive Selection in East Asians for an EDAR Allele that Enhances NF-κB Activation". PLOS ONE. 3 (5): e2209. doi:10.1371/journal.pone.0002209. PMC 2374902. PMID 18493316.

Sabeti, P.C.; Varilly, P.; Fry, B.; Lohmueller, J.; Hostetter, E.; Cotsapas, C.; Xie, X.; Byrne, E.H.; McCarroll, S.A.; Gaudet, R.; Schaffner, S.F.; Lander, E.S.; The International HapMap Consortium (2007). "Genome-wide detection and characterization of positive selection in human populations". Nature. 449 (7164): 913–918. doi:10.1038/nature06250. PMC 2687721. PMID 17943131.

Example: positive selection at ACKR1

The Duffy antigen locus (ACKR1/DARC) exemplifies powerful natural selection through malaria resistance. The FYO allele, carrying a promoter mutation that blocks DARC expression on red blood cells, provides near-complete protection against Plasmodium vivax malaria. This variant underwent one of the strongest selective sweeps in humans (selection coefficient 0.043), rising from 0.1% frequency ~42,000 years ago to >99% in sub-Saharan Africa while remaining virtually absent elsewhere. Despite being a textbook case of positive selection, its evolution from standing variation rather than a new mutation causes it to be overlooked by standard selection scans.

Key SNP: rs2814778 (T-42C) defines the FY*O (also known as Duffy null) in the GATA-1 transcription factor binding site in the ACKR1 gene promoter region.

Interval	hg38	CHM13
SNP Position	chr1:159204893-159204893 (rs2814778)	chr1:158341919-158341919 (rs2814778)
50 kb Interval	chr1:159179893-159229893	chr1:158316925-158366917
100 kb Interval	chr1:159154893-159254893	chr1:158291925-158391926
200 kb Interval	chr1:159104893-159304893	chr1:158241938-158441927

McManus, K. F.; et al. (2017). "Population genetic analysis of the DARC locus (Duffy) reveals adaptation from standing variation associated with malaria resistance in humans." PLoS Genetics. 13 (3): e1006560. doi:10.1371/journal.pgen.1006560.

Voight, B. F.; Kudaravalli, S.; Wen, X.; Pritchard, J. K. (2006). "A map of recent positive selection in the human genome." PLoS Biology. 4 (3): e72. doi:10.1371/journal.pbio.0040072.