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.