Hardy-Weinberg

The Hardy-Weinberg equation describes a single gene with two alleles.  For example the gene for colour has two alleles: B = black and b = white.  The probability of gametes meeting is traditionally worked out using a grid, sometimes called a punnet square.  the possible combinations are shown below.

The punnet square assumes that the sperm are produced by one heterozygous (Bb) male and that sperm produced are 50% "B" and 50% "b".  A similar assumption is made for the female. 

Suppose we are dealing with fish which spawn as a group.  Sperm and eggs from many individuals would be mixing. Obviously the punnet square as shown is useless but we can modify it.  We can  use the same punnet squares but work out the % of gametes which are "B" or "b".  We don't actually use percentages but use fractions instead.  These are usually converted to decimals:  ³/₁₀ becomes 0.3,  ⁵/₁₀ becomes 0.5 etc...

If the fraction of  "B" alleles is 0.7, then the "b" alleles will be 0.3.  If we put this into our punnet square.  The chances of a "b" gamete meeting another "b" gamete are slight.  In the punnet square the "bb" genotype will form 0.09 of the new generation (⁹/₁₀₀).

This has given rise to the formula based on the frequency of the alleles B (p) and b (q).  The letter p is used to represent the dominant allele and q the recessive.  Since all the fractions add up to the whole population i.e. 1

p² + 2pq  + q²  = 1