Lab 1: post-lab assignment - Population Genetics By Amina Nur and Timothea Muljadi

Part 1: Distribution of Genes in a Population

Ho: The distribution of genes in the bean population does not differ from the Mendelian ratios.

Ha: The distribution of genes in the bean population differ from the Mendelian ratios.

Prediction:

If the distribution of genes in a population does not differ from the Mendelian ratios, then out of 50 pairs of beans, the genotype distribution will be: 25% (12.5: 12/13 pairs) homozygous white (white/white), 25% (12.5: 13/12 pairs) homozygous speckled (speckled/speckled), and 50% (25 pairs) heterozygous (white/speckled).

Figure 1. Observed frequencies of the genotypes in the bean population compared to the Mendelian ratios.

Figure 2. Photo of the observed bean pairings from the gene pool.

Table 1. Chi-squared calculations for observed and expected distribution of genes in a population:

	Observed (O)	Expected (E)	O-E	(O-E)2	(O-E)2/E
Homozygous White	13	12.5	0.5	0.25	0.02
Homozygous Speckled	13	12.5	0.5	0.25	0.02
Heterozygous	24	25	-1	1	0.04
Total	50	50			0.08

Table 1. shows that chi-square =0.08 which is smaller than the critical value (5.99 )

Degrees of Freedom = 4-1 = 3 (critical value = 5.99)

Based on the results, the data does not support the hypothesis because the distribution of genes in the bean population follows the Mendelian ratios. The expected values are based on the Mendelian ratios calculated using the Punnett square, where out of 50 pairs of beans there will be 25% (12.5: 12/13 pairs) homozygous white (white/white), 25% (12.5: 12/13 pairs) homozygous speckled (speckled/speckled), and 50% (25 pairs) heterozygous (white/speckled). Figure 1 shows that the observed values are slightly different than the expected value. However, based on table 1, the chi-square is less than the critical value for degrees of freedom of 2 (0.08<5.99), meaning there is not a significant deviation from the expected genotype ratios. Therefore, we cannot reject the null hypothesis that the distribution of genes in the bean population follows the Mendelian ratios.

Part 2: Genetic Drift or Natural Selection

Ho: The allele frequencies of the bean population do not change over generations.

Ha: The allele frequencies of the bean population change over generations.

Prediction:

If the allele frequencies of the bean population change over generations, then the allele frequencies in the 10th generation will be the same as the 1st generation.

Figure 3. The number of allele frequency of four different types of beans after random selection over generations for population A (50 beans/ trail).

Figure 4. The number of allele frequency of four different types of beans after random selection over generations for population B (50 beans/ trail).

Table 2. Chi-squared calculations for observed and expected generations in population A.

	Observed (O)	Expected(E)	O-E	(O-E)2	(O-E)2/E
Red	21	13	8	64	4.92
Speckled	27	17	10	100	5.88
Black	2	11	-9	81	7.36
White	0	9	-9	81	9
Total	50	50			27.16

Table 2.shows that chi-square =27.16 which is bigger than the critical value (7.82 )

Degrees of Freedom = 4-1 = 3 (critical value = 7.82)

Figure 1. First and tenth generation in population A:

First Generation for population A: Expected      Tenth Generation for population A: Observed

                                 

Figure 5. Photo of the expected (first generation) and observed (tenth generation) of a populations of four different types of beans from population A. It demonstrates the sizes of beans in each allele.

Table 3. Chi-squared calculations for observed and expected generations in population B.

	Observed (O)	Expected(E)	O-E	(O-E)2	(O-E)2/E
Red	12	12	0	0	0
Speckled	38	8	30	900	112.5
Black	0	14	-14	196	14
White	0	16	-16	256	16
Total	50	50			142.5

Table 3. shows that chi-square =142.5 which is bigger than the critical value (7.82 )

Degrees of Freedom = 4-1 = 3 (critical value = 7.82)

Based on the results, the data supports the hypothesis because the allele frequencies in the bean population change over generations. Figure 3 and 4 show that the allele frequencies of the 10th generation is different than the 1st generation for both populations. Chi-square is greater than the critical value for degrees of freedom of 3 (Population A: 27.16>7.82, and Population B: 142.5>7.82), meaning there is a significant change in alleles in both population A and B.

Natural selection is the evolutionary process demonstrated in this exercise instead of the genetic drift. As shown in figure 5, the red and speckled beans are relatively larger in size compared to black and white beans. Their larger size contributed to higher chance on being selected to survive to the next generation because they are the easiest to pick. The number of white and black beans decrease significantly in both populations due to their smaller size that makes them sink to the bottom of the gene pool, thus results in fewer chances to be picked. Genetic drift occurs by chance, and it is not related to the fitness of alleles. Therefore, we reject the null hypothesis because natural selection is occurring in the population, which makes the allele frequencies change over generations. The allele frequencies of the 10th generation differ so greatly from the 1st generation that it is very unlikely to have occurred by chance alone.