Xiphias

1. First generation. Let's say you have Mom ("M") with genes AA and Dad ("D") with genes aa. We're assuming that Dad is homozygous for the recessive "a", because otherwise we wouldn't know that he has the trait at all.

 

2. Second generation: children C1, C2, C3, C4. Each child inherits an A from M, and an a from D. Thus, all the children are Aa, and none show the recessive allele. The trait "skips" this generation.

 

3. Third generation: grandchildren GC1, GC2, etc. Each grandchild has a 50% chance of inheriting the a allele from its C1 parent. The chance of the grandchild inheriting another a from its other parent depends upon that other parent's genes. Suppose we take C1, who has Aa. C1 marries spouse S1. If S1 is AA, then C1's children (GC1, GC2, etc.) will inherit an A from S1, and either an A or an a from C1. Statistically, 50% of C1's children will be Aa, and the other 50% AA (statistically: of course, all of C1's children could be Aa, or all could be AA, or anything in between). If S1 is Aa, then each grandchild has a 50% chance of inheriting an a from S1, and a 50% chance of inheriting an a from C1, and thus a 25% chance of being aa and showing the recessive phenotype. If S1 shows the aa recessive phenotype, like grandpa, then the grandchildren will inherit an a from S1, and have a 50% chance of inheriting an a from C1: thus, the grandchildren would have a 50% chance of being aa, instead of the 25% chance when S1 is Aa.

 

If all the children in generation 3 are AA or Aa, the trait "skips" this generation as well. However, as long as some of the children are Aa, the trait is still carried.

 

4. Fourth and following generations. Assuming that there is no selection pressure against allele a, and that each generation has enough children, the recessive allele persists. It pops up (potentially) whenever another parent bearing the recessive allele marries into the family. From the third generation on (GCs), it is possible that none of the descendents carry the a allele. However, the a allele does not die out unless all of the children of a given generation are free of it.

OK, So, I'm trying to do some math here, but I keep confusing myself. Say I have 3 generations, and all generations exhibit dominant phenotypes. What I want to know is, if the all four grandparents are of the genotype Aa, what is the percent chance the grandchild will also be Aa?