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Answer:
The flowering population is in Hardy Weinberg equilibrium.
Step by Step Explanation:
Total initial population size = 60
As both the populations are homozygous so the frequency of alleles will be,
P = 80/120= 0.66
q = 40/120= 0.33
The predicted frequencies for genotypes once the population has reached Hardy-Weinberg
p2 = 0.4356
2pq= 0.4356
q2 = 0.1089
The number of plants with each type of flower in a papulation of 420 is,
Homozygous dominant= 185
heterozygous= 185
Homozygous recessive= 50
Chi square analysis:
The observed values for red-flowered plants, pink-flowered plants, and white-flowered plants are not significantly different from the expected values predicted by Hardy Weinberg equilibrium.
Phenotype observed(o) expected (e) (o-e)2/e
Red 178 185 0.26
Pink 190 185 0.135
White 52 50 0.08
chi-square = 0.474
With 2 degree of freedom this chi-square gives a p value of 0.7 - 0.8, which is not significant.
Considering that the critical value is lower than the chi-square value, with a significance level of 0.05 and 2 degrees of freedom, we can conclude that this population is not in Hardy-Weinberg equilibrium.
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Available data:
- original population, N = 60 individuals
- 40 red-flowered plants
- 20 white-flowered plants
after many generations
- 178 red-flowered plants ⇒ RR
- 190 pink-flowered plants ⇒ Rr
- 52 white-flowered plants ⇒ rr
- N = 178 + 190 + 52 = 420 plants
Hypothesis: The population is in H-W equilibrium
Let us firts get the genotypic frequencies in the original population.
F(RR) = p² = 40/60 = 0.667
F(rr) = q² = 20/60 = 0.333
Now, let us take the allelic frequencies, following H-W equilibrium.
To do it, we can use the recessive genotypic frequency, F(rr).
q² = 0.333
q = √0.333 = 0.577
Now, by clearing the following equation, we can get the dominant allelic frequency, p.
p + q = 1
p + 0.577 = 1
p = 1 - 0.577
p = 0.423
If this population is in H-W equilibrium, after many generations the genotypic frequencies should be as follow,
- p² = 0.423² = 0.179
- 2pq = 2x0.423x0.577 = 0.488
- q² = 0.333
Now, assuming that this population is in H-W equilibrium, the allelic and genotypic frequencies will remain equal generation after generation.
So, the expected numbers in a population of 420 individuals are,
- RR = 0.179 x 420 = 75.18
- Rr = 0.488 x 420 = 204.96
- rr = 0.333 x 420 = 139.86
Now, to get to know if the population is in hardy-weinberg equilibrium, we will use chi square. And to calculate it, we will use the following equation
X² = Σ(Obs-Exp)²/Exp
RR Rr rr
Observed 178 190 52
Expected 75.18 204.96 139.86
(Obs-Exp)²/Exp 140.62 1.092 55.193
X² = Σ(Obs-Exp)²/Exp = 140.62 + 1.092 + 55.193 ≅ 197
Now, we need to get the degrees of freedom.
Freedom degrees = n - 1 = 3 - 1 = 2
Now, using a Significance level of 5% = 0.05, and the degrees of freedom, we will look for the critical value.
Critical value = 5.991
Chi-square = 197
P₀.₀₅ < X²
5.991 < 197
The difference between the observed individuals and the expected individuals is statistically significant.
Not probably to have differe by random chances.
There is enough evidence to reject the null hypothesis.
The population is not in equilibrium H-W.
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