# Hardy Weinberg Clarification

So I am taking an introductory Biology Course and I was recently introduced to the idea of Hardy Weinberg Equilibrium. I wanted to find out why exactly we calculate the frequencies of alleles in the next population using the law of multiplication.

For example,

In a hypothetical population of let's say 300 civets, 20% of the gene pool codes for blue eye color and the remaining 80% codes for black eye color. It is given that blue eye color is recessive.

300 civets = 600 alleles total
80% code for black eye color = 480 alleles
20% code for blue eye color = 120 alleles

When we calculate the frequencies of the next population we basically say what is the probability a given offspring will this pair of alleles. Following the example above, I would argue that the probability an offspring has two blue eye color alleles is (120/600) * (119/600). However, my textbook says that it is (120/600) * (120/600) = 0.04 but doesn't that assume replacement of alleles! My only rationale is that as the population tends towards infinity the difference becomes negligible.

Am I right?

• What do you mean by "replacement of alleles"? I posted an answer guessing what you meant. If I misunderstood could you elaborate on what you mean by it and why you think it is not possible? – BagiM Feb 23 '19 at 8:45

the population tends towards infinity

Well yes, Hardy–Weinberg principle is based on several assumptions one of them being "population size is very(infinitely) large". Another being "Mating is random".

However, even if the population is small your version of calculation does not make much sense biologically. If we talk about civets (gonochorists) the probability an offspring has two blue eye color alleles is (probability mother gives him blue eye allele copy)*(probability father gives him blue eye allele copy).

The two probabilities are not connected. What allele individual gets from mother has no influence over which allele they get from father. This is assured by "Mating is random" assumption.

To calculate the probability we should calculate:

(allele proportion in all possible mothers)*(allele proportion in all possible fathers)

In your example there is no information about sex of individuals, so the best approximation we have for allele proportion in females/males is the overall allele proportion in the whole population (20%) therefore the best calculation is 20%*20% = 0.04

but doesn't that assume replacement of alleles!

It seems you think that there is some rule that each parent allele copy is used only once in next generation. This is not true. Under random mating some parents can produce many children and some have none. Some allele copies get replicated several times some don't get replicated at all. In large populations the resulting random changes to allele frequency even out. In small populations allele frequency drifts.