Infinitesimal model

The infinitesimal model, also known as the polygenic model,[1] is a widely used statistical model in quantitative genetics. Originally developed in 1918 by Ronald Fisher, it is based on the idea that variation in a quantitative trait is influenced by an infinitely large number of genes, each of which makes an infinitely small (infinitesimal) contribution to the phenotype, as well as by environmental factors.[2] In "The Correlation between Relatives on the Supposition of Mendelian Inheritance", the original 1918 paper introducing the model, Fisher showed that if a trait is polygenic, "then the random sampling of alleles at each gene produces a continuous, normally distributed phenotype in the population".[3] However, the model does not necessarily imply that the trait must be normally distributed, only that its genetic component will be so around the average of that of the individual's parents.[4] The model served to reconcile Mendelian genetics with the continuous distribution of quantitative traits documented by Francis Galton.[5]

The model allows genetic variance to be assumed to remain constant even when natural selection is occurring, because each locus makes an infinitesimal contribution to the variance.[6] Consequently, all decline in genetic variance is assumed to be due to genetic drift.[7] It also relies on the assumption of normal distributions, an assumption which breaks down if a trait is influenced by a finite number of loci. According to one research group, the model "...is obviously not an exact representation of the genome of any species, but is a useful assumption to make in genetic evaluation."[8] Similarly, the model's assumption of infinitely many genes each with an infinitely small effect on the phenotype has been described as "practical but biologically unrealistic",[9] and the genetic basis of evolutionary adaptation, contrary to the prediction of the model, often involves a modest number of loci of large effect.[10]

References
  1. Xu, Shizhong; Wang, Zhiquan; Hu, Zhiqiu (2012-07-18). "An Infinitesimal Model for Quantitative Trait Genomic Value Prediction". PLOS ONE. 7 (7): e41336. doi:10.1371/journal.pone.0041336. ISSN 1932-6203. PMC 3399838. PMID 22815992.
  2. Nelson, Ronald M.; Pettersson, Mats E.; Carlborg, Örjan (December 2013). "A century after Fisher: time for a new paradigm in quantitative genetics". Trends in Genetics. 29 (12): 669–676. doi:10.1016/j.tig.2013.09.006. ISSN 0168-9525. PMID 24161664.
  3. Boyle, Evan A.; Li, Yang I.; Pritchard, Jonathan K. (June 2017). "An Expanded View of Complex Traits: From Polygenic to Omnigenic". Cell. 169 (7): 1177–1186. doi:10.1016/j.cell.2017.05.038. ISSN 0092-8674. PMC 5536862. PMID 28622505.
  4. Barton, N.H.; Etheridge, A.M.; Véber, A. (December 2017). "The infinitesimal model: Definition, derivation, and implications". Theoretical Population Biology. 118: 50–73. doi:10.1016/j.tpb.2017.06.001. PMID 28709925.
  5. Turelli, Michael (2017-12-01). "Commentary: Fisher's infinitesimal model: A story for the ages". Theoretical Population Biology. 118: 46–49. doi:10.1016/j.tpb.2017.09.003. ISSN 0040-5809. PMID 28987627.
  6. Hill, William G. (2014-01-01). "Applications of Population Genetics to Animal Breeding, from Wright, Fisher and Lush to Genomic Prediction". Genetics. 196 (1): 1–16. doi:10.1534/genetics.112.147850. ISSN 1943-2631. PMC 3872177. PMID 24395822.
  7. Hill, William G.; Zhang, Xu-Sheng (2005-01-01). "Predictions of Patterns of Response to Artificial Selection in Lines Derived From Natural Populations". Genetics. 169 (1): 411–425. doi:10.1534/genetics.104.032573. ISSN 1943-2631. PMC 1448869. PMID 15677752.
  8. Martinez, Victor; Bünger, Lutz; Hill, William G. (2000-01-15). "Analysis of response to 20 generations of selection for body composition in mice: fit to infinitesimal model assumptions". Genetics Selection Evolution. 32 (1): 3–21. doi:10.1186/1297-9686-32-1-3. ISSN 1297-9686. PMC 2706859. PMID 14736404.
  9. Hill, William G. (12 January 2010). "Understanding and using quantitative genetic variation". Philosophical Transactions of the Royal Society B: Biological Sciences. 365 (1537): 73–85. doi:10.1098/rstb.2009.0203. PMC 2842708. PMID 20008387.
  10. Orr, H. Allen (December 1999). "The evolutionary genetics of adaptation: a simulation study". Genetics Research. 74 (3): 207–214. doi:10.1017/S0016672399004164. ISSN 1469-5073. PMID 10689798.
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