Understanding HWE: Observed vs Expected Frequencies
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When studying a population, the very first step is to record what we actually observe: the observed frequencies.
For example, in a village of 100 people (previous example), we studied eye color controlled by the gene Color B, which has two alleles: B and b.
After genotyping, we counted the genotypic numbers:
40 people with BB,
50 people with Bb,
10 people with bb.
These numbers are called the observed frequencies because they come directly from real data.
But, the Hardy–Weinberg principle asks a curious question: “If this population were in perfect equilibrium, what would we expect to see in next population?” To answer this, we need to calculate the expected frequencies.
Let's we understand this step by step:
Step 1: Formula to calculate observed allele frequencies.
The first step is to calculate the observed allele frequency, where we will use the formula of the Allele Frequency:
AF of p= 2 * (AA) + (Aa)/ 2N
AF of q= 2 * (aa) + (Aa)/ 2N
Where:
p = frequency of allele B
q = frequency of allele b
N = total number of individuals
Since each person carries two alleles, and in a population of 100 people, there are 200 alleles (2 * 100 = 200) in total.
Therefore, total allele is 200.
Step 2: Finding the Observed Allele frequencies.
Now let's put the values (observed genotypic numbers) into the formula:
Calculation of allele frequency of "B" allele (p):
p = 2 * (BB) + (Bb)/ 2(Total Number of Individual)
p = 2 * (40) + (50)/ 2(100)
p= 80+50/200
p = 130/200
p = 0.65
Now, repeat the step to calculate the frequency of "b" allele (q):
p = 2 * (bb) + (Bb)/ 2(Total Number of Individual)
p = 2 * (10) + (50)/ 2(100)
p= 20+50/200
p = 70/200
p = 0.35
So, the frequency of allele "B" is 0.65 and allele "b" is o.35.
Step 3: Predict genotype frequencies.
According to the Hardy–Weinberg formula:
p² + 2pq + q² = 1
Expected Genotypic Frequency of (BB):
p²=(0.65)² = (0.65 * 0.65) =0.4225
= 0.4225 * (total number of Individual)
= 0.4225 * 100 = 42 people
Expected Genotypic Frequency of (Bb):
2pq = (2 * 0.65 * 0.35) = 0.455
= 0.455 * 100 = 46 people
Expected Genotypic Frequency of (bb):
q²=(0.35)² = (0.35 * 0.35) = 0.1225
= 0.1225 * 100 =12 people
Step 4: Compare the observed and expected Frequency.
Our observed data was BB = 40, Bb = 50, and bb = 10,
while the expected values are BB' = 42, Bb' = 46, and bb' = 12.
The numbers are very close, which means our village is approximately in Hardy–Weinberg equilibrium.
Step 5: Conclude.
In simple words: Observed frequencies are what we actually see, expected frequencies are what the Hardy–Weinberg principle predicts. If the two match, the population is balanced; if not, something is disturbing the equilibrium.
That’s why the Hardy–Weinberg principle is often called the “baseline” or the “control experiment” of population genetics, as it gives us a standard to compare reality against.
Introduction to Statistical Test with HWE
Introduction to Statistical Test with HWE
(Chi-Square Test and the Null Model)
(Chi-Square Test and the Null Model)
To truly confirm whether there is an actual difference between the observed and expected frequencies in a population, we use a statistical test called the Chi-square (χ²) test. This test helps us determine if any differences are due to random chance or if some evolutionary force is acting on the population.
The Chi-square test calculates a value called the p-value, which tells us the probability that the observed differences happened by chance.
p < 0.05: The difference is statistically significant, meaning we have enough evidence to reject the null model (the population is not in equilibrium).
p ≥ 0.05: The difference is not statistically significant, meaning we do not have enough evidence to reject the null model (the population can be considered in equilibrium).
Think of it like a door to equilibrium:
p < 0.05: The door is closed; the population cannot stay in equilibrium.
p ≥ 0.05: The door is open; the population can remain in equilibrium.
No More Manual Math: Try Gene Risk Calculator
But calculating HWE manually takes time and effort. That’s why we created a tool called Generiskcalc, which gives you allele frequencies and Chi-square results in just one click!
With this calculator, we can:
Instantly check observed vs. expected frequencies.
Get the Chi-square value and p-value without long calculations.
Quickly decide whether your population is in Hardy–Weinberg equilibrium or not.
Save time and focus more on understanding concepts rather than getting stuck in math.
In short, the Gene Risk Calculator is like your personal assistant for population genetics — fast, accurate, and student-friendly.
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