Sources and simplifications

Every reference cited on this site, and every place a figure idealizes the real system.

References§

1. Hardy, G. H. (1908). Mendelian proportions in a mixed population. Science 28(706): 49–50. doi:10.1126/science.28.706.49. primary (Hardy–Weinberg)
2. Edwards, A. W. F. (2008). G. H. Hardy (1908) and Hardy–Weinberg equilibrium. Genetics 179(3): 1143–1150. doi:10.1534/genetics.104.92940. scholarship History of Hardy's letter: Yule's question at Punnett's 1908 lecture, Punnett taking it to Hardy; Weinberg's paper read 13 January 1908. (Hardy–Weinberg)
3. Crow, James F. (1999). Hardy, Weinberg and language impediments. Genetics 152(3): 821–825. doi:10.1093/genetics/152.3.821. scholarship (Hardy–Weinberg)
4. Graffelman, Jan (2015). Exploring diallelic genetic markers: the HardyWeinberg package (includes the Mourant et al. 1976 MN data set). Journal of Statistical Software 64(3). doi:10.18637/jss.v064.i03. dataset MN blood-group counts for 216 populations, from Mourant, Kopeć and Domaniewska-Sobczak (1976), The Distribution of the Human Blood Groups and Other Polymorphisms, 2nd ed., Oxford University Press, Table 2.5. (Hardy–Weinberg)
5. Coop, Graham (2020). Population and Quantitative Genetics (open textbook, version of October 2021). University of California, Davis (CC BY 3.0). textbook Ch. 2 (Hardy–Weinberg, F), ch. 4 (drift, heterozygosity, fixation), ch. 5 (population structure, island model), ch. 10–12 (selection, selection and drift). (Hardy–Weinberg)
6. Wigginton, Janis E.; Cutler, David J.; Abecasis, Gonçalo R. (2005). A note on exact tests of Hardy–Weinberg equilibrium. American Journal of Human Genetics 76(5): 887–893. doi:10.1086/429864. primary (Hardy–Weinberg)
7. Wahlund, Sten (1928). Zusammensetzung von Populationen und Korrelationserscheinungen vom Standpunkt der Vererbungslehre aus betrachtet. Hereditas 11: 65–106. doi:10.1111/j.1601-5223.1928.tb02483.x. primary (Hardy–Weinberg)
8. Cook, L. M.; Grant, B. S.; Saccheri, I. J.; Mallet, J. (2012). Selective bird predation on the peppered moth: the last experiment of Michael Majerus. Biology Letters 8(4): 609–612. doi:10.1098/rsbl.2011.1136. primary (Natural selection)
9. van't Hof, A. E.; Campagne, P.; Rigden, D. J.; et al. (2016). The industrial melanism mutation in British peppered moths is a transposable element. Nature 534: 102–105. doi:10.1038/nature17951. primary (Natural selection)
10. Saccheri, I. J.; Rousset, F.; Watts, P. C.; Brakefield, P. M.; Cook, L. M. (2008). Selection and gene flow on a diminishing cline of melanic peppered moths. PNAS 105(42): 16212–16217. doi:10.1073/pnas.0803785105. primary (Natural selection)
11. Bersaglieri, T.; Sabeti, P. C.; Patterson, N.; et al. (2004). Genetic signatures of strong recent positive selection at the lactase gene. American Journal of Human Genetics 74(6): 1111–1120. doi:10.1086/421051. primary (Natural selection)
12. Enattah, N. S.; Sahi, T.; Savilahti, E.; Terwilliger, J. D.; Peltonen, L.; Järvelä, I. (2002). Identification of a variant associated with adult-type hypolactasia. Nature Genetics 30(2): 233–237. doi:10.1038/ng826. primary (Natural selection)
13. Allison, A. C. (1954). Protection afforded by sickle-cell trait against subtertian malarial infection. British Medical Journal 1(4857): 290–294. doi:10.1136/bmj.1.4857.290. primary (Natural selection)
14. Piel, F. B.; Patil, A. P.; Howes, R. E.; et al. (2010). Global distribution of the sickle cell gene and geographical confirmation of the malaria hypothesis. Nature Communications 1: 104. doi:10.1038/ncomms1104. primary (Natural selection)
15. Wright, Sewall (1931). Evolution in Mendelian populations. Genetics 16(2): 97–159. doi:10.1093/genetics/16.2.97. primary (Genetic drift)
16. Kimura, Motoo; Ohta, Tomoko (1969). The average number of generations until fixation of a mutant gene in a finite population. Genetics 61(3): 763–771. doi:10.1093/genetics/61.3.763. primary (Genetic drift)
17. Buri, Peter (1956). Gene frequency in small populations of mutant Drosophila. Evolution 10(4): 367–402. doi:10.2307/2406998. primary (Genetic drift)
18. Laruson, Áki J.; Reed, Floyd A. (2021). popgenr: Population genetics in R (data set 'fly': Buri's bw75 counts). CRAN, version 0.2. dataset (Genetic drift)
19. Kimura, Motoo (1968). Evolutionary rate at the molecular level. Nature 217: 624–626. doi:10.1038/217624a0. primary (Genetic drift)
20. MedlinePlus Genetics, US National Library of Medicine (2026). Ellis-van Creveld syndrome (Genetics condition summary). National Institutes of Health. institutional (Founders and bottlenecks)
21. McKusick, V. A.; Egeland, J. A.; Eldridge, R.; Krusen, D. E. (1964). Dwarfism in the Amish. I. The Ellis–van Creveld syndrome. Bulletin of the Johns Hopkins Hospital 115: 306–336 (PMID 14217223). primary The primary description of EvC in the Lancaster County Amish (part I of the series; part II, on cartilage–hair hypoplasia, is Bull Johns Hopkins Hosp 116:231, 1965). Verifier (2026-11-08): only the bibliographic record is readable (no abstract or full text online); cited only for the 1964 description and the series, not for frequency or distribution. (Founders and bottlenecks)
22. Ridanpää, M.; Jain, P.; McKusick, V. A.; Francomano, C. A.; Kaitila, I. (2003). The major mutation in the RMRP gene causing CHH among the Amish is the same as that found in most Finnish cases. American Journal of Medical Genetics C 121C(1): 81–83. doi:10.1002/ajmg.c.20006. primary (Founders and bottlenecks)
23. Sundin, O. H.; Yang, J.-M.; Li, Y.; et al. (2000). Genetic basis of total colourblindness among the Pingelapese islanders. Nature Genetics 25(3): 289–293. doi:10.1038/77162. primary (Founders and bottlenecks)
24. Morton, N. E.; Lew, R.; Hussels, I. E.; Little, G. F. (1972). Pingelap and Mokil atolls: historical genetics. American Journal of Human Genetics 24(3): 277–289. primary Scanned article; the builder opened only the PMC record. The verifier should check the typhoon date and survivor count in the scan. (Founders and bottlenecks)
25. Winick, J. D.; Blundell, M. L.; Galke, B. L.; Salam, A. A.; Leal, S. M.; Karayiorgou, M. (1999). Homozygosity mapping of the achromatopsia locus in the Pingelapese. American Journal of Human Genetics 64(6): 1679–1685. doi:10.1086/302423. primary Abstract: high frequency 'most likely resulted from a sharp reduction in population in the late 18th century, in the aftermath of a typhoon and subsequent geographic and cultural isolation.' (Founders and bottlenecks)
26. Hoelzel, A. R.; Gkafas, G. A.; Kang, H.; et al. (2024). Genomics of post-bottleneck recovery in the northern elephant seal. Nature Ecology & Evolution 8: 686–694. doi:10.1038/s41559-024-02337-4. primary (Founders and bottlenecks)
27. Mills, L. Scott; Allendorf, Fred W. (1996). The one-migrant-per-generation rule in conservation and management. Conservation Biology 10(6): 1509–1518. doi:10.1046/j.1523-1739.1996.10061509.x. primary (Gene flow)
28. Bürger, Reinhard (2014). A survey of migration–selection models in population genetics. Discrete and Continuous Dynamical Systems – Series B 19(4): 883–959. doi:10.3934/dcdsb.2014.19.883. review Sec. 4.4, the continent–island model: equilibria (eq. 4.42) and swamping thresholds (Theorem 4.11, eq. 4.44), after Haldane (1930) and Nagylaki (1992, ch. 6.1). Added by the verifier, 2026-11-08. (Gene flow)
29. King, Richard B.; Lawson, Robin (1995). Color-pattern variation in Lake Erie water snakes: the role of gene flow. Evolution 49(5): 885–896. doi:10.1111/j.1558-5646.1995.tb02324.x. primary (Gene flow)
30. Haldane, J. B. S. (1927). A mathematical theory of natural and artificial selection, Part V: selection and mutation. Proceedings of the Cambridge Philosophical Society 23(7): 838–844. doi:10.1017/S0305004100015644. primary (Selection vs drift)
31. Kimura, Motoo (1962). On the probability of fixation of mutant genes in a population. Genetics 47(6): 713–719. doi:10.1093/genetics/47.6.713. primary (Selection vs drift)
32. Ohta, Tomoko (1973). Slightly deleterious mutant substitutions in evolution. Nature 246: 96–98. doi:10.1038/246096a0. primary (Selection vs drift)

Simplifications§

• The figures assume a single gene with two alleles, discrete generations, and a gamete pool so large that sampling one generation from it adds no noise.
• These curves are deterministic: the population is infinite, fitnesses are constant, and generations are discrete and non-overlapping.
• The moth model treats one population with one generation per year, constant selection and no migration or drift.
• The sickle-cell figure uses one locus, constant fitnesses and fitness values chosen for illustration.
• The Wright–Fisher model assumes a constant number of individuals, non-overlapping generations, random union of gametes and every individual equally likely to reproduce.
• The fly figure compares the data with a Wright–Fisher population of Ne diploids, sampled exactly; for Ne ≠ 16 the model’s frequencies are spread over 2Ne + 1 values and rescaled to Buri’s 33 count classes.
• The founder figure draws founders independently from an infinitely large source population, and stops at the moment of founding.
• The bottleneck figure tracks independent neutral genes in a population that shrinks and recovers instantly, with Wright–Fisher sampling at the given sizes.
• The island figure uses equal islands of constant size, migrants drawn from the average of all islands, neutral genes and non-overlapping generations.
• The snake figure uses one locus with two alleles, constant selection and one-way migration from a mainland fixed for the banded allele.
• The figures use one locus, additive selection unless you switch dominance, constant N and s, and Kimura’s diffusion approximation alongside exact simulation.
• The practice problems assume one gene with two alleles and exact Hardy–Weinberg proportions, and the plate shows each population rounded to a dozen or twenty beetles.
• The figures use the Wright–Fisher model: constant size between events, non-overlapping generations, every individual equally likely to breed.
• The figures draw founders independently from an infinitely large source, and model the bottleneck as an instant crash and recovery of independent neutral genes.
• One gene with two alleles; non-overlapping generations; random mating; constant s and h; one-way migration from a source that does not change; effective size equal to census size.