Genetic variation

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Genetic variation is the difference in DNA among individuals [1] or the differences between populations among the same species. [2] The multiple sources of genetic variation include mutation and genetic recombination. [3] Mutations are the ultimate sources of genetic variation, but other mechanisms, such as genetic drift, contribute to it, as well. [2]

Contents

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Darwin's finches or Galapagos finches Darwin's finches.jpeg
Darwin's finches or Galapagos finches
Parents have similar gene coding in this specific situation where they reproduce and variation in the offspring is seen. Offspring containing the variation also reproduce and passes down traits to their offspring. Genetic Variation and Inheritance.svg
Parents have similar gene coding in this specific situation where they reproduce and variation in the offspring is seen. Offspring containing the variation also reproduce and passes down traits to their offspring.

Among individuals within a population

Genetic variation can be identified at many levels. Identifying genetic variation is possible from observations of phenotypic variation in either quantitative traits (traits that vary continuously and are coded for by many genes (e.g., leg length in dogs)) or discrete traits (traits that fall into discrete categories and are coded for by one or a few genes (e.g., white, pink, or red petal color in certain flowers)).[ citation needed ]

Genetic variation can also be identified by examining variation at the level of enzymes using the process of protein electrophoresis. [5] Polymorphic genes have more than one allele at each locus. Half of the genes that code for enzymes in insects and plants may be polymorphic, whereas polymorphisms are less common among vertebrates.[ citation needed ]

Ultimately, genetic variation is caused by variation in the order of bases in the nucleotides in genes. New technology now allows scientists to directly sequence DNA, which has identified even more genetic variation than was previously detected by protein electrophoresis. Examination of DNA has shown genetic variation in both coding regions and in the noncoding intron region of genes.[ citation needed ]

Genetic variation will result in phenotypic variation if variation in the order of nucleotides in the DNA sequence results in a difference in the order of amino acids in proteins coded by that DNA sequence, and if the resultant differences in amino-acid sequence influence the shape, and thus the function of the enzyme. [6]

Between populations

Differences between populations resulting from geographic separation is known as geographic variation. Natural selection, genetic drift, and gene flow can all contribute to geographic variation. [7]

Measurement

Genetic variation within a population is commonly measured as the percentage of polymorphic gene loci or the percentage of gene loci in heterozygous individuals. The results can be very useful in understanding the process of adaption to the environment of each individual in the population. [8]

Sources

A range of variability in the mussel Donax variabilis Coquina variation3.jpg
A range of variability in the mussel Donax variabilis

Random mutations are the ultimate source of genetic variation. Mutations are likely to be rare, and most mutations are neutral or deleterious, but in some instances, the new alleles can be favored by natural selection. Polyploidy is an example of chromosomal mutation. Polyploidy is a condition wherein organisms have three or more sets of genetic variation (3n or more).

Crossing over (genetic recombination) and random segregation during meiosis can result in the production of new alleles or new combinations of alleles. Furthermore, random fertilization also contributes to variation. Variation and recombination can be facilitated by transposable genetic elements, endogenous retroviruses, LINEs, SINEs, etc.[ citation needed ] For a given genome of a multicellular organism, genetic variation may be acquired in somatic cells or inherited through the germline.

Forms

Genetic variation can be divided into different forms according to the size and type of genomic variation underpinning genetic change. Small-scale sequence variation (<1 kilobase, kb) includes base-pair substitution and indels. [9] Large-scale structural variation (>1 kb) can be either copy number variation (loss or gain), or chromosomal rearrangement (translocation, inversion, or Segmental acquired uniparental disomy). [9] Genetic variation and recombination by transposable elements and endogenous retroviruses sometimes is supplemented by a variety of persistent viruses and their defectives which generate genetic novelty in host genomes. Numerical variation in whole chromosomes or genomes can be either polyploidy or aneuploidy.

Maintenance in populations

A variety of factors maintain genetic variation in populations. Potentially harmful recessive alleles can be hidden from selection in the heterozygous individuals in populations of diploid organisms (recessive alleles are only expressed in the less common homozygous individuals). Natural selection can also maintain genetic variation in balanced polymorphisms. Balanced polymorphisms may occur when heterozygotes are favored or when selection is frequency dependent.

RNA viruses

A high mutation rate caused by the lack of a proofreading mechanism appears to be a major source of the genetic variation that contributes to RNA virus evolution. [10] Genetic recombination also has been shown to play a key role in generating the genetic variation that underlies RNA virus evolution. [10] Numerous RNA viruses are capable of genetic recombination when at least two viral genomes are present in the same host cell. [11] RNA recombination appears to be a major driving force in determining genome architecture and the course of viral evolution among Picornaviridae ((+)ssRNA) (e.g. poliovirus). [12] In the Retroviridae ((+)ssRNA)(e.g. HIV), damage in the RNA genome appears to be avoided during reverse transcription by strand switching, a form of genetic recombination. [13] [14] [15] Recombination also occurs in the Coronaviridae ((+)ssRNA) (e.g. SARS). [16] Recombination in RNA viruses appears to be an adaptation for coping with genome damage. [11] Recombination can occur infrequently between animal viruses of the same species but of divergent lineages. The resulting recombinant viruses may sometimes cause an outbreak of infection in humans. [16]

History of genetic variation

Evolutionary biologists are often concerned with genetic variation, a term which in modern times has come to refer to differences in DNA sequences among individuals. However, quantifying and understanding genetic variation has been a central aim of those interested in understanding the varied life on earth since long before the sequencing of the first full genome, and even before the discovery of DNA as the molecule responsible for heredity.

While today's definition of genetic variation relies on contemporary molecular genetics, the idea of heritable variation was of central importance to those interested in the substance and development of life even before the writings of Charles Darwin. The concept of heritable variation—the presence of innate differences between life forms that are passed from parents to offspring, especially within categories such as species—does not rely on modern ideas of genetics, which were unavailable to 18th- and 19th-century minds.

Pre-Darwinian concepts of heritable variation

In the mid-1700s, Pierre Louis Maupertuis, a French scholar now known primarily for his work in mathematics and physics, posited that while species have a true, original form, accidents during the development of nascent offspring could introduce variations that could accumulate over time. [17] In his 1750 Essaie de Cosmologie, he proposed that the species we see today are only a small fraction of the many variations produced by "a blind destiny", and that many of these variations did not "conform" to their needs, thus did not survive. [18] In fact, some historians even suggest that his ideas anticipated the laws of inheritance further developed by Gregor Mendel. [19]

Simultaneously, French philosopher Denis Diderot proposed a different framework for the generation of heritable variation. Diderot borrowed Maupertuis' idea that variation could be introduced during reproduction and the subsequent growth of offspring, [20] and thought that production of a "normal" organism was no more probable than production of a "monstrous" one. [21] However, Diderot also believed that matter itself had lifelike properties and could self-assemble into structures with the potential for life. [20] Diderot's ideas on biological transformation, introduced in his 1749 work Letter on the Blind, were thus focused on variability of spontaneously generated forms, not variability within existing species. [22]

Both Maupertuis and Diderot built on the ideas of Roman poet and philosopher Lucretius, who wrote in De rerum natura that all the universe was created by random chance, and only the beings that were not self-contradictory survived. [23] Maupertuis' work is distinguished from the work of both Lucretius and Diderot in his use of the concept of conformity in explaining differential survival of beings, a new idea among those who believed that life changed over time. [23]

Like Diderot, two other influential minds of the 18th century—Erasmus Darwin and Jean-Baptiste Lamarck—believed that only very simple organisms could be generated by spontaneous generation, so another mechanism was necessary to generate the great variability of complex life observed on earth. [17] Erasmus Darwin proposed that changes acquired during an animal's life could be passed to its offspring, and that these changes seemed to be produced by the animal's endeavors to meet its basic needs. [24] Similarly, Lamarck's theory of the variability among living things was rooted in patterns of use and disuse, which he believed led to heritable physiological changes. [17] Both Erasmus Darwin and Lamarck believed that variation, whether it arose during development or during the animal's life, was heritable, a key step in theories of change over time extending from individuals to populations.

In the subsequent century, William Herschel's telescopic observations of diverse nebulae across the night sky suggested to him that different nebulae could each be in different stages in the process of condensation. This idea, which came to be known as the nebular hypothesis, suggested that natural processes could both create order out of matter and introduce variation, and that these processes could be observed over time. [17]  While it may seem to the modern reader that astronomical theories are irrelevant to theories of organic variation, these ideas became significantly conflated with ideas of biological transformation—what we now know as evolution—in the mid-19th century, laying important groundwork for the work of subsequent thinkers such as Charles Darwin. [25]

Darwin's concept of heritable variation

Charles Darwin's ideas of heritable variation were shaped by both his own scientific work and the ideas of his contemporaries and predecessors. [26] Darwin ascribed heritable variation to many factors, but particularly emphasized environmental forces acting on the body. His theory of inheritance was rooted in the (now disproven) idea of gemmules - small, hypothetical particles, which capture the essence of an organism and travel from all over the body to the reproductive organs, from which they are passed to offspring. [27] Darwin believed that the causal relationship between the environment and the body was so complex that the variation this relationship produced was inherently unpredictable. [28] However, like Lamarck, he acknowledged that variability could also be introduced by patterns of use and disuse of organs. [29] Darwin was fascinated by variation in both natural and domesticated populations, and his realization that individuals in a population exhibited seemingly purposeless variation was largely driven by his experiences working with animal breeders. [30] Darwin believed that species changed gradually, through the accumulation of small, continuous variations, a concept that would remain hotly contested into the 20th century. [31]

Post-Darwinian concepts of heritable variation

In the 20th century, a field that came to be known as population genetics developed. This field seeks to understand and quantify genetic variation. [31] The section below consists of a timeline of selected developments in population genetics, with a focus on methods for quantifying genetic variation.

See also

Related Research Articles

An allele, or allelomorph, is a variant of the sequence of nucleotides at a particular location, or locus, on a DNA molecule.

<span class="mw-page-title-main">Heredity</span> Passing of traits to offspring from the species parents or ancestor

Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic information of their parents. Through heredity, variations between individuals can accumulate and cause species to evolve by natural selection. The study of heredity in biology is genetics.

Microevolution is the change in allele frequencies that occurs over time within a population. This change is due to four different processes: mutation, selection, gene flow and genetic drift. This change happens over a relatively short amount of time compared to the changes termed macroevolution.

<span class="mw-page-title-main">Mutation</span> Alteration in the nucleotide sequence of a genome

In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mitosis, or meiosis or other types of damage to DNA, which then may undergo error-prone repair, cause an error during other forms of repair, or cause an error during replication. Mutations may also result from insertion or deletion of segments of DNA due to mobile genetic elements.

<span class="mw-page-title-main">Genetic recombination</span> Production of offspring with combinations of traits that differ from those found in either parent

Genetic recombination is the exchange of genetic material between different organisms which leads to production of offspring with combinations of traits that differ from those found in either parent. In eukaryotes, genetic recombination during meiosis can lead to a novel set of genetic information that can be further passed on from parents to offspring. Most recombination occurs naturally and can be classified into two types: (1) interchromosomal recombination, occurring through independent assortment of alleles whose loci are on different but homologous chromosomes ; & (2) intrachromosomal recombination, occurring through crossing over.

Population genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and population structure.

<span class="mw-page-title-main">Human variability</span> Range of possible values for any characteristic of human beings

Human variability, or human variation, is the range of possible values for any characteristic, physical or mental, of human beings.

<span class="mw-page-title-main">Genetic diversity</span> Total number of genetic characteristics in a species

Genetic diversity is the total number of genetic characteristics in the genetic makeup of a species, it ranges widely from the number of species to differences within species and can be attributed to the span of survival for a species. It is distinguished from genetic variability, which describes the tendency of genetic characteristics to vary.

<span class="mw-page-title-main">Evolution of sexual reproduction</span> How sexually reproducing multicellular organisms could have evolved from a common ancestor species

Sexual reproduction is an adaptive feature which is common to almost all multicellular organisms and various unicellular organisms. Currently, the adaptive advantage of sexual reproduction is widely regarded as a major unsolved problem in biology. As discussed below, one prominent theory is that sex evolved as an efficient mechanism for producing variation, and this had the advantage of enabling organisms to adapt to changing environments. Another prominent theory, also discussed below, is that a primary advantage of outcrossing sex is the masking of the expression of deleterious mutations. Additional theories concerning the adaptive advantage of sex are also discussed below. Sex does, however, come with a cost. In reproducing asexually, no time nor energy needs to be expended in choosing a mate and, if the environment has not changed, then there may be little reason for variation, as the organism may already be well-adapted. However, very few environments have not changed over the millions of years that reproduction has existed. Hence it is easy to imagine that being able to adapt to changing environment imparts a benefit. Sex also halves the amount of offspring a given population is able to produce. Sex, however, has evolved as the most prolific means of species branching into the tree of life. Diversification into the phylogenetic tree happens much more rapidly via sexual reproduction than it does by way of asexual reproduction.

Evolvability is defined as the capacity of a system for adaptive evolution. Evolvability is the ability of a population of organisms to not merely generate genetic diversity, but to generate adaptive genetic diversity, and thereby evolve through natural selection.

A heterozygote advantage describes the case in which the heterozygous genotype has a higher relative fitness than either the homozygous dominant or homozygous recessive genotype. Loci exhibiting heterozygote advantage are a small minority of loci. The specific case of heterozygote advantage due to a single locus is known as overdominance. Overdominance is a rare condition in genetics where the phenotype of the heterozygote lies outside of the phenotypical range of both homozygote parents, and heterozygous individuals have a higher fitness than homozygous individuals.

Genetics, a discipline of biology, is the science of heredity and variation in living organisms.

Genetic association is when one or more genotypes within a population co-occur with a phenotypic trait more often than would be expected by chance occurrence.

Inbreeding depression is the reduced biological fitness which has the potential to result from inbreeding. Biological fitness refers to an organism's ability to survive and perpetuate its genetic material. Inbreeding depression is often the result of a population bottleneck. In general, the higher the genetic variation or gene pool within a breeding population, the less likely it is to suffer from inbreeding depression, though inbreeding and outbreeding depression can simultaneously occur.

Coalescent theory is a model of how alleles sampled from a population may have originated from a common ancestor. In the simplest case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure, meaning that each variant is equally likely to have been passed from one generation to the next. The model looks backward in time, merging alleles into a single ancestral copy according to a random process in coalescence events. Under this model, the expected time between successive coalescence events increases almost exponentially back in time. Variance in the model comes from both the random passing of alleles from one generation to the next, and the random occurrence of mutations in these alleles.

<span class="mw-page-title-main">Gene</span> Sequence of DNA or RNA that codes for an RNA or protein product

In biology, the word gene can have several different meanings. The Mendelian gene is a basic unit of heredity and the molecular gene is a sequence of nucleotides in DNA that is transcribed to produce a functional RNA. There are two types of molecular genes: protein-coding genes and non-coding genes.

In medical genetics, compound heterozygosity is the condition of having two or more heterogeneous recessive alleles at a particular locus that can cause genetic disease in a heterozygous state; that is, an organism is a compound heterozygote when it has two recessive alleles for the same gene, but with those two alleles being different from each other. Compound heterozygosity reflects the diversity of the mutation base for many autosomal recessive genetic disorders; mutations in most disease-causing genes have arisen many times. This means that many cases of disease arise in individuals who have two unrelated alleles, who technically are heterozygotes, but both the alleles are defective.

<span class="mw-page-title-main">Zygosity</span> Degree of similarity of the alleles in an organism

Zygosity is the degree to which both copies of a chromosome or gene have the same genetic sequence. In other words, it is the degree of similarity of the alleles in an organism.

RNA-based evolution is a theory that posits that RNA is not merely an intermediate between Watson and Crick model of the DNA molecule and proteins, but rather a far more dynamic and independent role-player in determining phenotype. By regulating the transcription in DNA sequences, the stability of RNA, and the capability of messenger RNA to be translated, RNA processing events allow for a diverse array of proteins to be synthesized from a single gene. Since RNA processing is heritable, it is subject to natural selection suggested by Darwin and contributes to the evolution and diversity of most eukaryotic organisms.

<span class="mw-page-title-main">Genetic variance</span> Biological concept

Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection. In his 1930 book The Genetical Theory of Natural Selection, Fisher postulates that the rate of change of biological fitness can be calculated by the genetic variance of the fitness itself. Fisher tried to give a statistical formula about how the change of fitness in a population can be attributed to changes in the allele frequency. Fisher made no restrictive assumptions in his formula concerning fitness parameters, mate choices or the number of alleles and loci involved.

References

  1. "What is genetic variation?". EMBL-EBI Train online. 2017-06-05. Retrieved 2019-04-03.
  2. 1 2 "Genetic Variation". Genome.gov. Retrieved 2020-09-28.
  3. Levinson, Gene (2020). Rethinking evolution: the revolution that's hiding in plain sight. World Scientific. ISBN   9781786347268.
  4. Darwin, 1845. Journal of researches into the natural history and geology of the countries visited during the voyage of H.M.S. Beagle round the world, under the Command of Capt. Fitz Roy, R.N. 2d edition.
  5. "What is gel electrophoresis?".
  6. Pavlopoulos, GA; Oulas, A; Iacucci, E; Sifrim, A; Moreau, Y; Schneider, R; Aerts, J; Iliopoulos, I (25 July 2013). "Unraveling genomic variation from next generation sequencing data". BioData Mining. 6 (1): 13. doi: 10.1186/1756-0381-6-13 . PMC   3726446 . PMID   23885890.
  7. Ann Clark, Mary; Douglas, Matthew; Choi, Jung (2018-03-28). Biology 2e. OpenStax. p. 476. ISBN   978-1-947172-52-4.
  8. "The Variety of Genes in the Gene Pool Can Be Quantified within a Population | Learn Science at Scitable". www.nature.com. Retrieved 2022-07-15.
  9. 1 2 Lars Feuk, Andrew R. Carson & Stephen W. Scherer (February 2006). "Structural variation in the human genome". Nature Reviews Genetics. 7 (2): 85–97. doi:10.1038/nrg1767. PMID   16418744. S2CID   17255998.
  10. 1 2 Carrasco-Hernandez, R.; Jácome, Rodrigo; López Vidal, Yolanda; Ponce De León, Samuel (2017). "Are RNA Viruses Candidate Agents for the Next Global Pandemic? A Review". Ilar Journal. 58 (3): 343–358. doi: 10.1093/ilar/ilx026 . PMC   7108571 . PMID   28985316.
  11. 1 2 Barr JN, Fearns R (June 2010). "How RNA viruses maintain their genome integrity". The Journal of General Virology. 91 (Pt 6): 1373–87. doi: 10.1099/vir.0.020818-0 . PMID   20335491.
  12. Muslin C, Mac Kain A, Bessaud M, Blondel B, Delpeyroux F (September 2019). "Recombination in Enteroviruses, a Multi-Step Modular Evolutionary Process". Viruses. 11 (9): 859. doi: 10.3390/v11090859 . PMC   6784155 . PMID   31540135.
  13. Hu WS, Temin HM (November 1990). "Retroviral recombination and reverse transcription". Science. 250 (4985): 1227–33. Bibcode:1990Sci...250.1227H. doi:10.1126/science.1700865. PMID   1700865.
  14. Rawson JM, Nikolaitchik OA, Keele BF, Pathak VK, Hu WS (November 2018). "Recombination is required for efficient HIV-1 replication and the maintenance of viral genome integrity". Nucleic Acids Research. 46 (20): 10535–45. doi: 10.1093/nar/gky910 . PMC   6237782 . PMID   30307534.
  15. Bernstein H, Bernstein C, Michod RE (January 2018). "Sex in microbial pathogens". Infection, Genetics and Evolution. 57: 8–25. doi: 10.1016/j.meegid.2017.10.024 . PMID   29111273.
  16. 1 2 Su S, Wong G, Shi W, Liu J, Lai AC, Zhou J, et al. (June 2016). "Epidemiology, Genetic Recombination, and Pathogenesis of Coronaviruses". Trends in Microbiology. 24 (6): 490–502. doi: 10.1016/j.tim.2016.03.003 . PMC   7125511 . PMID   27012512.
  17. 1 2 3 4 Bowler, Peter J. (1989). Evolution: the history of an idea (Rev. ed.). Berkeley: University of California Press. ISBN   0-520-06385-6. OCLC   17841313.
  18. Glass, Bentley (1947). "Maupertuis and the Beginnings of Genetics". The Quarterly Review of Biology. 22 (3): 196–210. doi:10.1086/395787. ISSN   0033-5770. PMID   20264553. S2CID   28185536.
  19. Sandler, Iris (1983). "Pierre Louis Moreau de Maupertuis: A precursor of Mendel?". Journal of the History of Biology. 16 (1): 102. doi:10.1007/bf00186677. ISSN   0022-5010. PMID   11611246. S2CID   26835071.
  20. 1 2 Gregory, Mary (2006-10-23). Diderot and the Metamorphosis of Species. Routledge. doi:10.4324/9780203943823. ISBN   978-1-135-91583-4.
  21. Hill, Emita (1968). "Materialism and Monsters in "Le Rêve de d'Alembert"". Diderot Studies. 10: 67–93. ISSN   0070-4806. JSTOR   40372379.
  22. Zirkle, Conway (1941). "Natural Selection before the "Origin of Species"". Proceedings of the American Philosophical Society. 84 (1): 71–123. ISSN   0003-049X. JSTOR   984852.
  23. 1 2 Gregory, Mary Efrosini (2008). Evolutionism in eighteenth-century French thought. New York: Peter Lang. ISBN   978-1-4331-0373-5. OCLC   235030545.
  24. Zirkle, Conway (1946). "The Early History of the Idea of the Inheritance of Acquired Characters and of Pangenesis". Transactions of the American Philosophical Society. 35 (2): 91–151. doi:10.2307/1005592. ISSN   0065-9746. JSTOR   1005592.
  25. Schweber, S.S. (1989). "John Herschel and Charles Darwin: A study in parallel lives". Journal of the History of Biology. 22 (1): 1–71. doi:10.1007/bf00209603. ISSN   0022-5010. S2CID   122572397.
  26. Egerton, Frank N. (1976). "Darwin's Early Reading of Lamarck". Isis. 67 (3): 452–456. doi:10.1086/351636. ISSN   0021-1753. JSTOR   230686. S2CID   144074540.
  27. Winther, Rasmus G. (2000). "Darwin on Variation and Heredity". Journal of the History of Biology. 33 (3): 425–455. doi:10.1023/A:1004834008068. ISSN   0022-5010. JSTOR   4331610. S2CID   55795712.
  28. Beatty, John (2006-12-01). "Chance Variation: Darwin on Orchids". Philosophy of Science. 73 (5): 629–641. doi:10.1086/518332. ISSN   0031-8248. S2CID   170396888.
  29. 1 2 Deichmann, Ute (2010). "Gemmules and Elements: On Darwin's and Mendel's Concepts and Methods in Heredity". Journal for General Philosophy of Science. 41 (1): 85–112. doi:10.1007/s10838-010-9122-0. ISSN   0925-4560. JSTOR   20722529. S2CID   42385140.
  30. Bowler, Peter J. (2009-01-09). "Darwin's Originality". Science. 323 (5911): 223–226. doi:10.1126/science.1160332. ISSN   0036-8075. PMID   19131623. S2CID   1170705.
  31. 1 2 Provine, William B. (2001). The origins of theoretical population genetics (2nd ed.). Chicago: University of Chicago Press. ISBN   0-226-68463-6. OCLC   46660910.
  32. "Heterozygosity". Oxford Bibliographies. Retrieved 2021-12-11.
  33. 1 2 Charlesworth, Brian; Edwards, Anthony W. F. (2018-07-26). "A century of variance". Significance. 15 (4): 20–25. doi: 10.1111/j.1740-9713.2018.01170.x . ISSN   1740-9705.
  34. Dietrich, Michael (2013-01-01). "R.A. Fisher and the Foundations of Statistical Biology". Outsider Scientists: Routes to Innovation in Biology.
  35. Rosenberg, Noah A. (2018). "Variance-Partitioning and Classification in Human Population Genetics". In Rasmus Grønfeldt Winther (ed.). Phylogenetic Inference, Selection Theory, and History of Science. Cambridge University Press. pp. 399–404. doi:10.1017/9781316276259.040. ISBN   9781316276259.
  36. Alcala, Nicolas; Rosenberg, Noah A (2017-07-01). "Mathematical Constraints on FST: Biallelic Markers in Arbitrarily Many Populations". Genetics. 206 (3): 1581–1600. doi: 10.1534/genetics.116.199141 . ISSN   1943-2631. PMC   5500152 . PMID   28476869.
  37. Excoffier, L.; Hofer, T.; Foll, M. (October 2009). "Detecting loci under selection in a hierarchically structured population". Heredity. 103 (4): 285–298. doi: 10.1038/hdy.2009.74 . ISSN   1365-2540. PMID   19623208.

Further reading