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2 Hardy-Weinberg Simulations Deme 1.0 is a Microsoft Excel spreadsheet available on the course website. The simplest case: large population (Drift OFF) no mutation (rates = 0) no migration (immigration = 0) random mating no selection (all fitnesses = 1) Frequency of A allele = p Frequency of B allele = q Since all 5 HWE conditions hold, the population is at HWE forever - allele frequencies stay the SAME in all generations Evolution 4-2

3 Uses of HWE (1): Human Genetic Traits Example: attached/detached earlobes (model for genetic disease) allele contribution to phenotype E unattached earlobe (dominant) p e attached earlobe (recessive) q EE Ee ee Phenotype unattached unattached attached Q: How many people in class are carriers for the attached allele? Assume that this trait is at HWE. Evolution 4-3

4 Bio 112: Hardy-Weinberg Equilibrium Examples General Info : the of each allele (R or r, for example) in the gene pool. The symbols p and q are used to represent these frequencies. frequencies: the of each genotype (RR, Rr, rr for example) in the population. These are always equal to the number of individuals with a particular genotype divided by the total population size. They are sometimes equal to p 2, 2pq, and q 2 - only when the population is at HWE. For a particular pair of allele frequencies (p = 0.2 and q = 0.8 for example), there are many possible sets of genotype frequencies that have the same allele frequencies (actually, infinitely many). This is illustrated by the 4 example populations below; all 4 of these populations have the same allele frequencies. However, given a pair of allele frequencies, there is only one set of these genotype frequencies that are at HWE. This is illustrated by the last two populations shown below; in addition to having the same allele frequencies as the other populations, their genotype frequencies match the predictions of HWE - that the of RR = p 2 (0.04 in this example), the of RR = 2pq (0.32 in this example), and the of rr = q 2 (0.64 in this example). Population 1 # RR Rr rr totals Freq. of R = p = 40/200 = 0.2 Freq. of r = q = 160/200 = 0.8 frequencies Freq. of RR = 0, not 0.04 Freq. of Rr = 0.4, not 0.32 Freq. of rr = 0.6, not 0.64 NOT AT HWE Population 2 # RR Rr rr totals Freq. of R = p = 800/4000 = 0.2 Freq. of r = q = 3200/4000 = 0.8 frequencies Freq. of RR = 0.2, not 0.04 Freq. of Rr = 0.0, not 0.32 Freq. of rr = 0.8, not 0.64 NOT AT HWE Evolution 4-4

5 Population 3 # RR Rr rr totals Freq. of R = p = 40/200 = 0.2 Freq. of r = q = 160/200 = 0.8 frequencies Freq. of RR = 0.04 Freq. of Rr = 0.32 Freq. of rr = 0.64 AT HWE Population 4 # RR Rr rr totals Freq. of R = p = 120/600 = 0.2 Freq. of r = q = 480/600 = 0.8 frequencies Freq. of RR = 0.04 Freq. of Rr = 0.32 Freq. of rr = 0.64 AT HWE Evolution 4-5

6 Evolution 4-6

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