It is easier to see what is going on if you make yourself a square, called a Punnet square. What you do is write the individual genes symbol down along one side and the other parent's genes across the top. For each block in the square you write the gene contribution from the left edge and the gene contribution from the top in the block. For Helterskelter's example you have an "N" in one spot down the left and an "a" in the other. Across the top you have an "N" and and "a" again. When you fill in the 4 blocks in your square you end up with the top left block having "NN" the top right has "Na". In the second row, the first block gets an "a" from the left and an "N" from the top so it is "Na" the bottom right block gets an "a" from both parents so it is "aa". The percentages come out the way helterskelter said because you assume that all combinations are equally likely so the single block with "NN" in it is 25%, the single block with "aa" in it is another 25% and the third combination is in 2 different blocks so that makes 50% when you add those 2 blocks together. When you have a particular fish that you then want to breed with the "aa", you know exactly what to expect if all gene probabilities are equal. That means if you build the Punnet square for helterskelter's second example of breeding the "aa" to the F1 "Na", you have 2 blocks that come out "aa" and the other 2 come out "Na". If you want to see the result of breeding the NN to an F1 that is Na, you just set up the square and find out that you will get 50% NN and 50% Na. The trouble with this last one is you won't know which fish are which. That is why you always try to do your breeding with the known recessive being expressed in the fry. In that situation you know what you are working with.
Now the fun part, let's make believe you don't know what the combination is for a particular fish because you bought it at the pet shop and it came with no genetic pedigree. It could be NN or it could be Na since they look exactly alike. If you want to find the ones that are pure NN, you breed them with a known aa. If you get about half that look like an aa, a recessive, you know the parent that you bred is a Na. If all of the fry look like a type N, the parent you bred is an NN because you are seeing nothing but the N type which means the fry were all Na. Now you know the genetic makeup of the parent fish by probing with the "aa" parent. If you were trying to establish a line that never reverted to the recessive trait, you breed only the parents that test out as pure NN. That way none of the fry that you are breeding for your line are carrying the "a". It can shorten the cycle of establishing a line quite a bit if you know what you are working with and this is a way to probe the parents if you are trying to breed a dominant gene.
I need a calculator!.... (but, I believe you).... Thank the both of you.... I will try to comprehend......
