Hardy-Weinberg Law

Genetic epidemiology aims to understand how genetic variation contributes to disease risk. To best characterize risk relationships, one must first understand how the exposure of interest is distributed within and across populations, before attempting to relate [Page 452]exposure distributions to disease distribution. For genetic exposure, this involves understanding how genetic variation arises in populations and how it is maintained within and across populations over time. The Hardy-Weinberg law describes a state of equilibrium in allele frequencies at a particular genetic locus over generations that are randomly mating. This law also describes a relationship between the allele frequencies and genotype frequencies within a population as a result of random mating.

Variation at a genetic locus can be described by noting the different ‘spellings,’ called ‘alleles,’ that exist at the same location among chromosomes in a population. For example, the sequence at a particular site may be ATCCinsomeandATTC in others, which would be referred to as two alleles ‘C’ or ‘T.’ When such diversity exists, the location is considered to be ‘polymorphic.’ Because humans are ‘diploid,’ each person carries two copies of the genome, one from their father and one from their mother. So at any polymorphic location, each person carries two alleles, one from each parent. The particular combination of the two alleles carried by a single individual is referred to as a ‘genotype.’ Following the example above, there are three possible genotypes for the C/T polymorphism with two possible alleles: CC, CT, TT. The Hardy-Weinberg law characterizes the relationship between alleles and genotypes in a population due to random mating and the equilibrium state of allele frequencies from generation to generation. It is thus often also referred to as HardyWeinberg equilibrium (HWE).

Traditionally, the frequency of the first allele is denoted as p and the alternative allele frequency as q. These are the proportions of that particular allele among all chromosomes in the population (e.g., among 2 × N, where N is the number of people), and p + q = 1. Under an assumption of random mating in a sexually reproducing diploid population with no other population genetic forces such as mutation, natural selection, migration, or drift, it can be shown that the expected genotype frequencies are a specific function of the allele frequencies p2,2pq, and q2 (see Table 1) and that these values, p and q, will remain constant over generations. Proof of this result was reported by three separate papers in the early 1900s, by Castle (1903), Hardy (1908), and Weinberg (1908). As an example, suppose a population of 10,000 people contained a genetic polymorphism with alleles C and T, where 11,000 of the 20,000 genomes in that population contained a C allele (p=11 000/20,000=0.55; q=0 45). The Hardy-Weinberg law, which assumesrandom mating, would expect the genotype frequenciesin the population to be CC genotype=p2=0.552=0.3025, or 3,025 people with CC; CT=2pq=2×0.55×0.45=0.495, or 4,950 people with CT; andTT=q 2=0 452=0 2025 or 2,025 people with TT. These genotype proportions based on allele frequencies are often referred to as Hardy-Weinberg proportions.

One can measure the amount of departure from Hardy-Weinberg expectations by comparing the observed genotype frequencies in a sample to those expected under HWE based on the allele frequencies for that sample. This value is considered the Hardy-Weinberg disequilibrium coefficient: DHW = observed genotype frequency expected genotype frequency. For example, if among 1,000 people, 350 were CC, 400 were CT, and 250 were TT, one could calculate the allele frequencies as p = (2×350+400)/2,000=0.55 and q=0 45. The expected genotype frequenciesunder HWE would be E(CC)=p2=0.552=0.3025;E(CT)=2pq=2×0.55×0.45=0.495; E(TT)=q2=0.452=0.2025. The DHW=observed-expected=0.350–0.3025=0.0475. This could also be calculated using the other homozygous genotype: DHW =0.250–0.2025=0.0475. One could test the statistical signif-icance of this by testing the hypothesis that DHW=0versus the alternative DHW 6 1/4 0 usingaz

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