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Multi Locus Allele Clusters
Lewontin argued that because the overwhelming majority of human genetic variation (85%) is between individuals within the same population, and about 6–10% is between populations within the same continent, racial classification can only account for between 5–10% of human variation, and is therefore of virtually no genetic or taxonomic significance. This implies that any two humans from the same group are almost as different as any two humans from different groups.
Edwards argued that while Lewontin's statements on variability are correct when examining the frequency of individual loci between individuals, the probability of misclassification rapidly approaches 0% when one takes into account more loci. This happens because differences at different loci are correlated across populations — the alleles that are more frequent in a population at one locus and those that are more frequent in thatpopulation at another locus are correlated when we consider the two populations simultaneously. In Edwards' words, "most of the information that distinguishes populations is hidden in the correlation structure of the data." These correlations can be extracted using commonly-used ordination and cluster analysis techniques. As Edwards showed, even if the probability of misclassifying an individual based on a single locus is as high as 30% (as Lewontin reported in 1972), the misclassification probability based on 10 loci can drop to just a few percent.
Neven Sesardic has pointed out that, unbeknownst to Edwards, Jeffry B. Mitton already made the same argument about Lewontin's claim in two articles published in The American Naturalist in the late 1970s.
Genetic clusters and the fallacy
Studies of human genetic clustering have shown the possibility of categorisation of humans using correlations between alleles from multiple loci. For instance, a 2001 paper by Wilson et al. reported that an analysis of 39 microsatellite loci divided their sample of 354 individuals into four natural clusters, which broadly correspond to four geographical areas (Western Eurasia, Sub-Saharan Africa, China, and New Guinea) .
On the other hand the results obtained by clustering analyses are dependent on several criteria:
- The clusters produced are relative clusters and not absolute clusters; each cluster is the product of comparisons between sets of data derived for the study, results are therefore highly influenced by sampling strategies, different sampling strategies will produce different clusters. (Edwards, 2003)
- The geographic distribution of the populations sampled; because human genetic diversity is marked by isolation by distance, populations from geographically distant regions will form much more discrete clusters than those from geographically close regions. 
- The number of genes used. The more genes used in a study the greater the resolution produced, and therefore the greater number of clusters that will be identified.
Whether or not Lewontin's Fallacy is a fallacy depends on how one defines the concept of "difference" between two genomes. Talking of two genomes being "more similar" or "less similar" implies the existence of a metric. The most naive metric, and the one used implicitly by Lewontin, is that of simply counting the number SNPs. Edwards's criticism of Lewontin amounts to the statement that it is a "fallacy" to use this naive metric, because some SNPs may be in a meaningful way more significant to other SNPs.
If differences are considered to exist when individuals can be accurately classified according using a single randomly chosen trait, then Lewontin's results imply that human races are not distinct in this sense. If, on the other hand, "real differences" are considered to exist when individuals can be accurately classified using a number of traits, then accurate and meaningful classification of human groups is possible. The ability to accurately classify groups using multiple loci is, of course, not simply a property of populations from different continents — any two populations can have their individuals accurately classified in this manner, if enough loci are used.
Conversely, in the paper "Genetic similarities within and between human populations" Witherspoon et al. (2007) show that even when individuals can be reliably assigned to specific population groups, it is still possible for two randomly chosen individuals from different populations/clusters to be more similar to each other than to a randomly chosen member of their own cluster. This is because multi locus clustering relies on population level similarities, rather than individual similarities, so that each individual is classified according to their similarity to the typical genotype for any given population. The paper claims that this masks a great deal of genetic similarity between individuals belonging to different clusters. Or in other words, two individuals from different clusters can be more similar to each other than to a member of their own cluster, while still both being more similar to the typical genotype of their own cluster than to the typical genotype of a different cluster. When differences between individual pairs of people are tested, Witherspoon et al. found that the answer to the question "How often is a pair of individuals from one population genetically more dissimilar than two individuals chosen from two different populations?" is not adequately addressed by multi locus clustering analyses. They found that even for just three population groups separated by large geographic ranges (European, African and East Asian) the inclusion of many thousands of loci is required before the answer can become "never". On the other hand, the accurate classification of the global population must include more closely related and admixed populations, which will increase this above zero, so they state "In a similar vein, Romualdi et al. (2002) and Serre and Paabo (2004) have suggested that highly accurate classification of individuals from continuously sampled (and therefore closely related) populations may be impossible". Witherspoon et al. conclude "The fact that, given enough genetic data, individuals can be correctly assigned to their populations of origin is compatible with the observation that most human genetic variation is found within populations, not between them. It is also compatible with our ﬁnding that, even when the most distinct populations are considered and hundreds of loci are used, individuals are frequently more similar to members of other populations than to members of their own population"
- Race and genetics
- Human genetic clustering
- Y-DNA haplogroups by ethnic groups
- Population groups in biomedicine
- ^ Made in The apportionment of human diversity (1972) and again in the 1974 book The Genetic Basis of Evolutionary Change.
- ^ Sesardic, Neven: Race: A Social Destruction of a Biological Concept, Biology and Philosophy (2010, forthcoming). The said articles are: Mitton JB (1977) Genetic differentiation of races of man as judged by single-locus and multilocus analyses. Am Nat 111:203–212, andMitton JB (1978) Measurement of differentiation: reply to Lewontin, Powell, and Taylor. Am Nat 112:1142–1144
- ^ Population genetic structure of variable drug response — Nature Genetics
- ^ * Kittles and Weiss (2003) RACE, ANCESTRY, AND GENES: Implications for Deﬁning Disease Risk Annu. Rev. Genomics Hum. Genet. 4:33–67 doi:10.1146/annurev.genom.4.070802.110356
- ^ Tang H, Quertermous T, Rodriguez B, et al. (February 2005). [Expression error: Missing operand for > "Genetic structure, self-identified race/ethnicity, and confounding in case-control association studies"]. American Journal of Human Genetics 76 (2): 268–75. doi:10.1086/427888. PMID 15625622.
- ^ Chakraborty, R. (1982). [Expression error: Missing operand for > "Allocation versus variation: The issue of genetic differences between human racial groups."]. American Naturalist 120: 403–404. doi:10.1086/283998.
- ^ * Witherspoon DJ, Wooding S, Rogers AR, Marchani EE, Watkins WS, Batzer MA, Jorde LB. (2007) Genetic similarities within and between human populations. Genetics. 176(1):351–9. Full Text
- Human Genetic Diversity: Lewontin's Fallacy, published in BioEssays Volume 25, Issue 8, Date: August 2003, Pages: 798–801
- Human Genetic Diversity: Lewontin's Fallacy, published in BioEssays Volume 25, Issue 8.
- Population genetic structure of variable drug response, published in Nature Genetics 29, 265 (2001).
- Categorization of humans in biomedical research: genes, race and disease, published in Genome Biology 3, 7 (2002).