• range of environmental conditions tolerated
. . . can be broken into 2n+1 sub-ranges,
. . . where n = number of genes or chromosomes.

• with p = q:

 n = 1 .25 .50 .25 AA Aa aa
 n = 2 .0625 .2500 .3750 .2500 .0625 AAAA AAAa AAaa Aaaa aaaa
 n = 3 .015625 .093750 .234375 .312500 .234375 .093750 .015625 AAAAAA AAAAAa AAAAaa AAAaaa AAaaaa Aaaaaa aaaaaa

• However, if p is not equal to q:

 n = 1 p AA Aa aa q 0.1 0.01 0.18 0.81 0.9 0.2 0.04 0.32 0.64 0.8 0.3 0.09 0.42 0.49 0.7 0.4 0.16 0.48 0.36 0.6 0.5 0.25 0.50 0.25 0.5 0.6 0.36 0.48 0.16 0.4 0.7 0.49 0.42 0.09 0.3 0.8 0.64 0.32 0.04 0.2 0.9 0.81 0.18 0.01 0.1

• assumptions of the Hardy-Weinburg...
. . 1) mating is random,
. . 2) there is no selection,
. . 3) there is no mutation,
. . 4) there is no immigration nor emmigration, and
. . 5) the population is arbitrarily large (infinite)
• However, in the Real World, these five assumptions are not met;
. .. so the task becomes estimating which of the five
. . . has the most influence on the observed results.
. . 1) if mating is non-random,
. . . -is mathematically complex, or
. . . . requires simulation studies
. . 2) if there is selection,
. . . -multiply the Hardy-Weinburg values by fitness
. . . . {AA, Aa, aa} = {wAA*p2, wAa*2pq, waa*q2}
. . 3) if there is mutation,
. . . -is mathematically complex, or
. . . . requires simulation studies
. . 4) if there is immigration or emmigration, and
. . . -is mathematically complex, or
. . . . requires simulation studies
. . 5) if the population is small (finite)
. . . -requires simulation studies

• We do not currently have the mathematics necessary to solve these problems.