Infinitesimal model

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Short description: Quantitative genetic model developed by Ronald Fisher in 1918

The infinitesimal model, also known as the polygenic model, is a widely used statistical model in quantitative genetics and in genome-wide association studies. 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.[1] 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".[2] 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.[3] The model served to reconcile Mendelian genetics with the continuous distribution of quantitative traits documented by Francis Galton.[4]

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.[5] Consequently, all decline in genetic variance is assumed to be due to genetic drift.[6] It also relies on the fact that there must be a large enough number of loci for the distribution of loci to be normal, an assumption which breaks down if a trait is influenced by a small number of loci. According to one research group, the model "…is obviously not an exact representation of the genome of any species," as humans do not have an infinite number of genes, "but is a useful assumption to make in genetic evaluation," such as "explaining the underlying variation of a trait."[7] Some phenotypes undergo evolutionary adaptation such that they involve a modest number of loci of large effect.[8] Complex traits, however, have been shown to be largely explained by additive effects, with dominance being of negligible importance, though dominance and epistasis are still relevant for rare Mendelian disorders.[improper synthesis?][9][10][11][12][13][14][15]


  1. 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. PMID 24161664. 
  2. 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. PMID 28622505. 
  3. 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. 
  4. Turelli, Michael (December 2017). "Commentary: Fisher's infinitesimal model: A story for the ages". Theoretical Population Biology 118: 46–49. doi:10.1016/j.tpb.2017.09.003. PMID 28987627. 
  5. Hill, William G (2014). "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. PMID 24395822. 
  6. Zhang, Xu-Sheng; Hill, William G (2005). "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. PMID 15677752. 
  7. 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. PMID 14736404. 
  8. Orr, H. Allen (December 1999). "The evolutionary genetics of adaptation: a simulation study". Genetics Research 74 (3): 207–214. doi:10.1017/S0016672399004164. PMID 10689798. 
  9. Hill, W.G.; Mäki-Tanila, A. (April 2015). "Expected influence of linkage disequilibrium on genetic variance caused by dominance and epistasis on quantitative traits". Journal of Animal Breeding and Genetics 132 (2): 176–186. doi:10.1111/jbg.12140. PMID 25823842. 
  10. Hivert, Valentin; Sidorenko, Julia; Rohart, Florian; Goddard, Michael E.; Yang, Jian; Wray, Naomi R.; Yengo, Loic; Visscher, Peter M. (May 2021). "Estimation of non-additive genetic variance in human complex traits from a large sample of unrelated individuals". The American Journal of Human Genetics 108 (5): 786–798. doi:10.1016/j.ajhg.2021.02.014. PMID 33811805. 
  11. Pazokitoroudi, Ali; Chiu, Alec M.; Burch, Kathryn S.; Pasaniuc, Bogdan; Sankararaman, Sriram (May 2021). "Quantifying the contribution of dominance deviation effects to complex trait variation in biobank-scale data". The American Journal of Human Genetics 108 (5): 799–808. doi:10.1016/j.ajhg.2021.03.018. PMID 33811807. 
  12. Okbay, Aysu; Wu, Yeda; Wang, Nancy; Jayashankar, Hariharan; Bennett, Michael; Nehzati, Seyed Moeen; Sidorenko, Julia; Kweon, Hyeokmoon et al. (April 2022). "Polygenic prediction of educational attainment within and between families from genome-wide association analyses in 3 million individuals". Nature Genetics 54 (4): 437–449. doi:10.1038/s41588-022-01016-z. PMID 35361970. 
  13. Hill, William G.; Goddard, Michael E.; Visscher, Peter M. (29 February 2008). "Data and Theory Point to Mainly Additive Genetic Variance for Complex Traits". PLOS Genetics 4 (2): e1000008. doi:10.1371/journal.pgen.1000008. PMID 18454194. 
  14. Crow, James F. (27 April 2010). "On epistasis: why it is unimportant in polygenic directional selection". Philosophical Transactions of the Royal Society B: Biological Sciences 365 (1544): 1241–1244. doi:10.1098/rstb.2009.0275. PMID 20308099. 
  15. Keightley, P D (April 1989). "Models of quantitative variation of flux in metabolic pathways". Genetics 121 (4): 869–876. doi:10.1093/genetics/121.4.869. PMID 2721937.