Counting Beads (Lab)

COUNTING BEADS:Heredity and Evolution

Table 1: Mating Genotypes of Genotypes of offspring parents RR Rr rr1 Rr Rr → 1 2 12 RR Rr → 2 2 impossible3 rr rr → impossible impossible 44 RR RR → 4 impossible impossible5 RR rr → impossible 4 impossible6 Rr rr → impossible 2 232 Rr rr → impossible 2 2 Total 34 68 26 The three column totals should always add up to 128. Why?

• For Experiment I (no selection): Since the total number of offspring is 128, divide each number by two in order to maintain the population size at 64. Otherwise, your population will grow exponentially! Write these numbers in the next empty row of the “genotype” columns of Table 2. Table 2: Allele frequency (no selection) Number of each genotype Frequency of Frequency of Generation allele R allele r RR Rr rr 0 (initial) 16 32 16 1 17 34 13 2 3 4 5

• From your spare beads, find those that represent the genotypes of the current generation (in this example, 17 RR, 34 Rr, and 13 rr). Put these 64 beads into the bag. Using Table 1, produce the next generation of offspring. Divide the total of each column by two, and transfer the results to the next empty row of the “genotype” columns of Table 2. Continue this procedure until you have the results for 5 generations. Table 2: Allele frequency (no selection) Number of each genotype Frequency of Frequency of Generation allele R allele r RR Rr rr 0 (initial) 16 32 16 1 17 34 13 2 14 35 15 3 16 32 16 4 15 31 18 5 16 33 15

You may calculate allele frequencies from genotype distribution asfollows: Genotypes in RR Rr rr population Number of each genotype in a 17 34 13 population of 64 Number of each allele 34 R 34 R + 34 r 26 r in the population Frequency of each 34 R + 34 R = 68 R 34 r + 26 r = 60 r allele in the 68/128 = 0.53 R 60/128 = 0.47 r population

Table 2: Allele frequency (no selection) Number of each genotype Frequency of Frequency ofGeneration allele R allele r RR Rr rr 0 (initial) 16 32 16 0.5 0.5 1 17 34 13 0.53 0.47 2 14 35 15 0.49 0.51 3 16 32 16 0.50 0.50 4 15 31 18 0.48 0.52 5 16 33 15 0.50 0.50

• For Experiment II (selection): The rr genotypes in each generation do not survive to reproduce, so you will begin with a bag that contains only 16 RR and 32 Rr. Therefore, there will be only 24 pairs of parents in the first round and, consequently, a total of only 96 offspring. In fact, N (the sum of the three column totals in Table 1) varies from generation to generation. If N is not 64, multiply each number by 64/N to maintain the population size at 64. If multiplication produces a decimal number, round off to make the sum of all genotypes equal to 64. Write the number of each genotype in the next empty row of the “genotype” columns of Table 3. 32 Rr rr → impossible 2 2 Total 31 44 21The sum of the three column totals equals “N” and varies from generation to generation.

• For example, let’s say the totals for the three columns of Table 1 after the first round are: 31 RR, 44 Rr, and 21 rr. Since N = 31 + 44 + 21 = 96, we will need to multiply each total by 2/3 (because 64/96 = 2/3). That gives us: 2/3  31= 21; 2/3  44 = 29; and 2/3  21 = 14. Table 3: Allele frequency (selection) Number of each genotype Frequency of Frequency of Generation allele R allele r RR Rr rr 0 (initial) 16 32 -0- 1 21 29 14 2 3 4 5

• From your spare beads, find those that represent only the genotypes RR and Rr of the current generation, since offspring with the genotype rr die before they are able to reproduce (in this example, 21 RR and 29 Rr). Put these beads into the bag. Using Table 1, produce the next generation of offspring. Multiply the total of each column by 64/N, and transfer the results to the next empty row of the “genotype” columns of Table 2. Continue this procedure until you have the results for 5 generations. Table 3: Allele frequency (selection) Number of each genotype Frequency of Frequency of Generation allele R allele r RR Rr rr 0 (initial) 16 32 -0- 1 21 29 14 2 30 24 10 3 36 21 17 4 41 17 6 5 48 12 4

As before, you may calculate allele frequencies from genotypedistribution as follows: Genotypes in RR Rr rr population Number of each genotype in a 21 29 14 population of 64 Number of each allele 42 R 29 R + 29 r 28 r in the population Frequency of each 42 R + 29 R = 71 R 29 r + 28 r = 57 r allele in the 71/128 = 0.55 R 57/128 = 0.45 r population

Table 3: Allele frequency (selection) Number of each genotype Frequency of Frequency ofGeneration allele R allele r RR Rr rr 0 (initial) 16 32 -0- 0.5 0.5 1 21 29 14 0.55 0.45 2 30 24 10 0.65 0.35 3 36 21 17 0.72 0.28 4 41 17 6 0.77 0.23 5 48 12 4 0.84 0.16

Plot changes in the frequency of allele r by generation. The following figure illustrates the results obtained in this example. Figure 1: Changes in frequency of allele r over time, with selection and without selection. 0.6 0.5Allele r frequency 0.4 0.3 non-selection 0.2 selection 0.1 0 0 1 2 3 4 5 6 Generations

Counting Beads (Lab)

by Professor Olsen @ Large

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