Lab #1: Population Genetics by Jason Hall and Severin Robins

Part A: Distribution of Genes in a Population

Hypothesis:

H0: The null hypothesis was that there would be 12.5 homozygous brown, 12.5 homozygous white, and 25 heterozygotes.

Prediction: Our Prediction is that the distribution of alleles will fall out of Mendelian genetics.

Results:

Chi-Squared:

Table 1:

Category	Observed (O)	Expected (E)	((O-E)2)/E
Homo Brown	12	12.5	0.02
Homo White	12	12.5	0.02
Heterozygous	26	25	0.04

Chi-Squared (Χ2) = 0.08

The Table, shown above (Table 1), displays the number of allele pairs expected after 50 pairs, what was actually observed, and how closely our results matched that of the null hypothesis.

Hardy Weinberg:

*For the purpose of the equation, it is assumed that being Brown is the dominant trait.

Brown: 38                                                                                   q=0.49                                                             

White: 12                                                                        p=0.51                                                 

1250=0.24                                                              q2=0.24                                     

0.24=0.49                                                               p2=0.26

1-0.49=0.51

0.512=0.26                                                                              

0.26+(20.510.49)+0.24=1

500.26=13                                                           Homo Brown= 13

500.24=12                                                                     Homo White= 12

50(20.490.51)=25                                                  Heterozygous= 25

Figure 1:

Figure 1 shows how closely related the observed results are to the expected results.

Conclusion:

We have concluded the null hypothesis was supported but our prediction was refuted
by this experiment, based on the results of the both the Chi-squared and Hardy Weinberg
equation. The results of the Chi-squared were 0.02+0.02+0.04=0.08,
which is well below the threshold of our designated deviation of 5.99,
meaning that the null hypothesis was supported and our prediction was refuted as the
chi-squared would need to be above 5.99 to be supported. Our results were also very
near Hardy Weinberg equilibrium and to the Mendelian ratio of 12.5 Homozygous Brown,
12.5 Homozygous White, and 25 Heterozygous. Both of these situations would only happen
if the null hypothesis were supported and our prediction refuted.

Part B: Genetic Drift

Hypothesis:

H0: The null hypothesis is that there will be no significant change in allele frequency
after 10 generation.

Prediction: Our prediction is that there will be a significant change in allele frequencies,
possibly losing some altogether or coming close.

Results:

Table 2:

Bead Color	Observed (Gen 10)	Expected (Gen 1)	((O-E)2)/E
Blue	29	16	10.563
Red	5	14	5.786
White	2	10	6.400
Clear	14	10	1.600

Chi-Squared (Χ2) = 24.349

The Table, shown above (Table 2), displays the number of beads (alleles) for the first generation, that would be the expected value and the number of alleles in the last, or tenth generation, this is our observed value.

Figure 2:

The graph which you see above (Figure 2) clearly shows the ten generations and how it deviates from the expected, or null hypothesis. The blue beads have shown a steady increase, minus the fourth generation, while white has shown a steady decrease from generation 1 to generation 10.

Conclusion:

The results from our data over the course of 10 generations in response to bead
(allele) frequency we have concluded that based on our chi-squared value of 24.349
falls out of the accepted range to confirm our null hypothesis and therefore we must
NOT accept our null, this, in turn, does confirm our prediction.
In Figure 2 under the ((O-E)2)/E column you can see the individual values that we
added up to our chi-squared value. 10.563+5.786+6.400+1.600 = 24.349 and
our accepted range is anything under 7.82 so the null hypothesis is NOT accepted.
This is also clearly shown in the Blue and the White bead colors. Blue grew by almost
twice the amount and white shrank by five times as much as the expected.