They can identiy rare alleles that are present in small numbers of families, usualy due to a founder mutation. Linkage is how you find an allele such as the mutations in BRCA1 associated with breast cancer. Association studies are used when you don't have pedigrees; here the statistical test is a logistic regression or a related test for trends. They work when the phenotype has much lower penetrance; they are in fact more powerful than linkage analysis in those cases, provided you have enough informative cases and matched controls.
Association studies are how you find common, low penetrance alleles such as the variations in FGFR2 that confer small increases in breast cancer susceptibility. In The Old Days, neither association tests nor linkage tests were "genome-wide"; there wasn't a technically feasable or affordable way to test the whole genome at once. Studies were often performed at various levels of resolution as the locus associated with the phenotype was refined. Studies were often performed with a small number of loci chosen because of prior knowledge or hunches.
Now the most common way to perform these studies in humans is to use SNP chips that measure hundreds of thousands of loci spread across the whole genome, thus the name GWAS. The reason you're testing "the whole genome" without sequencing the whole genome of each case and control is an important point that is a separate topic; if you don't yet know how this works, start with the concept of Linkage Disequilibrium. I haven't encountered the term GWLS myself, but I think it's safe to say that this is just a way to indicate that the whole genome was queried for linkage to a phenotype.
From here -. For organisms whose genomes are known, one might now try to exclude genes in the identified region whose function is known with some certainty not to be connected with the trait in question. If the genome is not available, it may be an option to sequence the identified region and determine the putative functions of genes by their similarity to genes with known function, usually in other genomes.
It is often not the actual gene underlying the phenotypic trait, but rather a region of DNA that is closely linked with the gene.
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