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Why do geneticists usually need many pedigree charts to determine?

First, the more pedigrees you have, the more certain you are about the transmission (recessive, dominant, sex linked). In cases that 100% penetrant (ie if you have the disease allele, you get the disease) you wont need more than a few examples. Things get more interesting when the disease or trait is not 100% penetrant, have different multiple causing alleles for the same disease, there are errors in either phenotyping or genotyping. In these cases, we use statistical methods to infer the most likely inheiritance. Statistical methods need sufficient data to find a signal and the more pedigrees, the better. More importantly, we can combine information from different pedigrees that involve just trios (mom, dad, affected child), extended pedigrees (multiple generations) and any combination in between. They are more robust to noise and allow you to infer the loci that are likely to be associated with the trait or disease. Family inheirtance patterns depend on recombination events between loci. Because these do not happen often in humans, we need a lot of them to associate a region with a disease or trait. Pedigrees are very helpful but often difficult to collect especially in large numbers. GWAS methods are used because we can get large numbers of people but the power is much lower to detect association hence the need for very large numbers of individuals.

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