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# Population genetics

Population genetics is the study of the allele frequency distribution and change under the influence of the four evolutionary forces: natural selection, genetic drift, mutation and gene flow. It also takes account of population subdivision and population structure in space. As such, it attempts to explain such phenomena as adaptation and speciation. Population genetics was a vital ingredient in the modern evolutionary synthesis, its primary founders were Sewall Wright, J. B. S. Haldane and R. A. Fisher, who also laid the foundations for the related discipline of quantitative genetics.

## Scope and theoretical considerations

Perhaps the most significant "formal" achievement of the modern evolutionary synthesis has been the framework of mathematical population genetics. Indeed some authors (Beatty 1986) would argue that it does define the core of the modern synthesis.

Lewontin (1974) outlined the theoretical task for population genetics. He imagined two spaces: a "genotypic space" and a "phenotypic space". The challenge of a complete theory of population genetics is to provide a set of laws that predictably map a population of genotypes (G1) to a phenotype space (P1), where selection takes place, and another set of laws that map the resulting population (P2) back to genotype space (G2) where Mendelian genetics can predict the next generation of genotypes, thus completing the cycle. Even leaving aside for the moment the non-Mendelian aspects revealed by molecular genetics, this is clearly a gargantuan task. Visualizing this transformation schematically:

$G_1 \rightarrow^{T_1}P_1 \rightarrow^{T_2}P_2 \rightarrow^{T_3}G_2 \rightarrow^{T_4}G_1' \rightarrow \cdots$

(adapted from Lewontin 1974, p. 12).

T1 represents the genetic and epigenetic laws, the aspects of functional biology, or development, that transform a genotype into phenotype. We will refer to this as the "genotype-phenotype map". T2 is the transformation due to natural selection, T3 are epigenetic relations that predict genotypes based on the selected phenotypes and finally T4 the rules of Mendelian genetics.

In practice, there are two bodies of evolutionary theory that exist in parallel, traditional population genetics operating in the genotype space and the biometric theory used in plant and animal breeding, operating in phenotype space. The missing part is the mapping between the genotype and phenotype space. This leads to a "sleight of hand" (as Lewontin terms it) whereby variables in the equations of one domain, are considered parameters or constants, where, in a full-treatment they would be transformed themselves by the evolutionary process and are in reality functions of the state variables in the other domain. The "sleight of hand" is assuming that we know this mapping. Proceeding as if we do understand it is enough to analyze many cases of interest. For example, if the phenotype is almost one-to-one with genotype (sickle-cell disease) or the time-scale is sufficiently short, the "constants" can be treated as such; however, there are many situations where it is inaccurate.

## Population geneticists

The three founders of population genetics were the Britons R.A. Fisher and J.B.S. Haldane and the American Sewall Wright. Fisher and Wright had some fundamental disagreements and a controversy about the relative roles of selection and drift continued for much of the century between the Americans and the British. The Frenchman Gustave Malécot was also important early in the development of the discipline. John Maynard Smith was Haldane's pupil, whilst W.D. Hamilton was heavily influenced by the writings of Fisher. The American George R. Price worked with both Hamilton and Maynard Smith. On the American side, Richard Lewontin and the Japanese Motoo Kimura were heavily influenced by Wright.

## References

• J. Beatty. "The synthesis and the synthetic theory" in Integrating Scientific Disciplines, edited by W. Bechtel and Nijhoff. Dordrecht, 1986.
• Luigi Luca Cavalli-Sforza. Genes, Peoples, and Languages. North Point Press, 2000.
• Luigi Luca Cavalli-Sforza et al. The History and Geography of Human Genes. Princeton University Press, 1994.
• James F. Crow and Motoo Kimura. Introduction to Population Genetics Theory. Harper & Row, 1972.
• Warren J Ewens. Mathematical Population Genetics. Springer-Verlag New York, Inc., 2004. ISBN 0-387-20191-2
• John H. Gillespie Population Genetics: A Concise Guide, Johns Hopkins Press, 1998. ISBN 0-8018-5755-4.
• Richard Halliburton. Introduction to Population Genetics. Prentice Hall, 2004
• Daniel Hartl. Primer of Population Genetics, 3rd edition. Sinauer, 2000. ISBN 0-87893-304-2
• Daniel Hartl and Andrew Clark. Principles of Population Genetics, 3rd edition. Sinauer, 1997. ISBN 0-87893-306-9.
• Richard C. Lewontin. The Genetic Basis of Evolutionary Change. Columbia University Press, 1974.
• William B. Provine. The Origins of Theoretical Population Genetics. University of Chicago Press. 1971. ISBN 0-226-68464-4.
• Spencer Wells. The Journey of Man. Random House, 2002.
• Spencer Wells. Deep Ancestry: Inside the Genographic Project. National Geographic Society, 2006.

Cheung, KH; Osier MV, Kidd JR, Pakstis AJ, Miller PL, Kidd KK (2000). "ALFRED: an allele frequency database for diverse populations and DNA polymorphisms". Nucleic Acids Research 28 (1): 361-3.

• History of population genetics
• National Geographic: Atlas of the Human Journey (Haplogroup-based human migration maps)
• Monash Virtual Laboratory - Simulations of habitat fragmentation and population genetics online at Monash University's Virtual Laboratory.

Nordic and Celtic DNA Project - (Saami & Iberian).

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