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| The '''infinite alleles model''' is a mathematical model for calculating genetic [[mutation]]s. The Japanese geneticist [[Motoo Kimura]] and American geneticist [[James F. Crow]] (1964) introduced the ''infinite [[allele]]s model'', an attempt to determine for a finite [[Ploidy#Diploid|diploid]] population what proportion of [[Locus (genetics)|loci]] would be [[homozygous]]. This was, in part, motivated by assertions by other geneticists that more than 50 percent of ''[[Drosophila melanogaster|Drosophila]]'' loci were [[heterozygous]], a claim they initially doubted. In order to answer this question they assumed first, that there were a large enough number of alleles so that any [[mutation]] would lead to a different allele (that is the probability of back mutation to the original allele would be low enough to be negligible); and second, that the mutations would result in a number of different outcomes from neutral to [[Wiktionary:deleterious|deleterious]].
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| They determined that in the neutral case, the probability that an individual would be homozygous, ''F'', was:
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| :<math>F = {1 \over 4 N_e u + 1}</math>
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| where ''u'' is the mutation rate, and ''N''<sub>e</sub> is the [[effective population size]]. The effective number of alleles ''n'' maintained in a population is defined as the inverse of the homozygosity, that is | |
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| :<math>n = {1 \over F} = 4N_e u + 1</math>
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| which is a lower bound for the actual number of alleles in the population.
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| If the effective population is large, then a large number of alleles can be maintained. However, this result only holds for the ''neutral'' case, and is not necessarily true for the case when some alleles are subject to [[selection]], i.e. more or less [[fitness (biology)|fit]] than others, for example when the fittest genotype is a heterozygote (a situation often referred to as [[overdominance]] or [[heterosis]]).
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| In the case of overdominance, because [[Mendelian inheritance|Mendel's second law]] (the law of segregation) necessarily results in the production of homozygotes (which are by definition in this case, less fit), this means that population will always harbor a number of less fit individuals, which leads to a decrease in the average fitness of the population. This is sometimes referred to as ''[[genetic load]]'', in this case it is a special kind of load known as ''segregational load''. Crow and Kimura showed that at [[Genetic equilibrium|equilibrium]] conditions, for a given strength of selection (''s''), that there would be an upper limit to the number of fitter alleles (polymorphisms) that a population could harbor for a particular locus. Beyond this number of alleles, the selective advantage of presence of those alleles in heterozygous genotypes would be cancelled out by continual generation of less fit homozygous genotypes.
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| These results became important in the formation of the [[Neutral theory of molecular evolution|neutral theory]], because neutral (or nearly neutral) alleles create no such segregational load, and allow for the accumulation of a great deal of polymorphism. When [[Richard Lewontin]] and [[J.L. Hubby|J. Hubby]] published their groundbreaking results in 1966 which showed high levels of genetic variation in Drosophila via protein [[electrophoresis]], the theoretical results from the infinite alleles model were used by Kimura and others to support the idea that this variation would have to be neutral (or result in excess segregational load).
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| ==References==
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| {{reflist}}
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| *{{cite journal|author=[[Motoo Kimura|Kimura, M.]] and [[James F. Crow|Crow, J]] | year=1964 |title=The Number of Alleles that Can Be Maintained in a Finite Population | journal=[[Genetics (journal)|Genetics]] |volume=49| pages=725–738 | pmid=14156929|pmc=1210609}}
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| *{{cite journal|author=[[Richard Lewontin|Lewontin, R.C.]] and Hubby, J.L. |year=1966 |title=A Molecular approach to the study of genic heterozygosity in natural populations. II. Amount of variation and degree of heterozygosity in natural populations of ''Drosophila pseudoobscura'' | journal=[[Genetics (journal)|Genetics]] |volume=54| pages=595–609}}
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| ==See also==
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| *[[Infinite sites model]]
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| [[Category:Evolutionary biology]]
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| [[Category:Population genetics]]
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| [[Category:Mathematical and theoretical biology]]
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I would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my full title. Playing badminton is a factor that he is totally addicted to. Alaska is where I've always been living. Invoicing is what I do.
Also visit my webpage ... tarot card readings (relevant internet page)