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genetic drift (allele frequencies can change because of random chance). give mathematical explanation

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Genetic drift: In small populations, random events can cause allele frequency changes. Mathematically, it's modeled by the formula p' = (p + Qx)/2.

Consider a population of 100 diploid organisms, each with two alleles for a particular gene. Let's say the frequency of the allele A is 0.5, meaning that 50% of the alleles in the population are A and 50% are a.

When these organisms reproduce, they randomly pass on one of their two alleles to each of their offspring.

This means that there is a chance that the allele frequencies in the offspring population will be different from the allele frequencies in the parent population.

This is because some offspring may inherit two A alleles, while others may inherit two a alleles.

The amount of drift that occurs in a population is determined by the size of the population.

Genetic drift can have a significant impact on the evolution of a population.

If a rare allele is beneficial, genetic drift can help to increase its frequency in the population.

Conversely, if a rare allele is harmful, genetic drift can help to eliminate it from the population.

Here is the mathematical formula for genetic drift:

p' = (p + Qx)/2

where:

p' is the frequency of the allele A in the offspring population

p is the frequency of the allele A in the parent population

Q is the frequency of the allele a in the offspring population

x is a random number between 0 and 1

This formula can be used to calculate the probability of a particular allele frequency in the offspring population.

In the example above, the probability of the allele A frequency being 0.5 in the offspring population is 0.25.

This means that there is a 25% chance that the allele A frequency will remain the same after one generation of reproduction.

The probability of the allele A frequency being 0.4 or 0.6 is 0.375. This means that there is a 37.5% chance that the allele A frequency will change by 0.1 after one generation of reproduction.

The probability of the allele A frequency being less than 0.4 or greater than 0.6 is 0.125.

This means that there is a 12.5% chance that the allele A frequency will change by more than 0.1 after one generation of reproduction.

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