I’d be curious to see how this framework changes as we relax the individual simplifying assumptions. aa being lethal was an interesting example - I assume that there is some time it takes in that case for aa to become very rare, but that that doesn’t happen in a single period? Or does the theorem still hold (in that the ratio of Aa to AA is the long run ratio after just one generation).
Also would be curious about the dynamics - what if there is a period where aa is beneficial, and another then Aa/AA is beneficial (captured by some probability of reproducing that is period dependent. How does the population evolve over time.
Finally, curious what happens when the random matching is dropped!
The combination aa can only occur in a cross between Aa and Aa - which gives aa, Aa and AA in the ratio of 1:2:1. If aa is lethal, it just changes the viable genotypes of offspring from an Aa Aa cross. If on the other hand aa is not lethal but is associated with some disease, then the analysis is more complex. I will post a chapter on selection soon which should answer some of these questions.
For your second question, if there is a period when aa is beneficial and then some other genotype becomes beneficial, there is an example of this in sickle cell anemia, which is caused by a mutation (say aa) in both copies of the gene producing hemoglobin, the protein in red blood cells that carries oxygen. People with this disease are less fit than the other genotypes Aa and AA. However, in regions where Malaria is prevalent, this mutation has a protective benefit and the frequency of people with the aa genotype increases - but once that pressure is relieved - say by the use of mosquito nets or spraying, then the aa reverts back to low frequency.
Your last question was about dropping random matching. The only reason to do this is to make the analysis simple. It is of course unrealistic and does not happen in nature. The analysis then becomes quite complex. What happens then is that populations segregate by phenotype - skin or hair color, height etc. Sometimes there is also non random matching based on external issues. For example, people;e with dark skin can avoid diseases such as skin cancer - so they are at a selective advantage in equatorial regions. On the other hand, people in northern climates have a lighter skin because of the need to absorb more vitamin D (and avoid diseases like rickets etc). Again, this is an issue of selection - which I will discuss in a subsequent post.
I’d be curious to see how this framework changes as we relax the individual simplifying assumptions. aa being lethal was an interesting example - I assume that there is some time it takes in that case for aa to become very rare, but that that doesn’t happen in a single period? Or does the theorem still hold (in that the ratio of Aa to AA is the long run ratio after just one generation).
Also would be curious about the dynamics - what if there is a period where aa is beneficial, and another then Aa/AA is beneficial (captured by some probability of reproducing that is period dependent. How does the population evolve over time.
Finally, curious what happens when the random matching is dropped!
The combination aa can only occur in a cross between Aa and Aa - which gives aa, Aa and AA in the ratio of 1:2:1. If aa is lethal, it just changes the viable genotypes of offspring from an Aa Aa cross. If on the other hand aa is not lethal but is associated with some disease, then the analysis is more complex. I will post a chapter on selection soon which should answer some of these questions.
For your second question, if there is a period when aa is beneficial and then some other genotype becomes beneficial, there is an example of this in sickle cell anemia, which is caused by a mutation (say aa) in both copies of the gene producing hemoglobin, the protein in red blood cells that carries oxygen. People with this disease are less fit than the other genotypes Aa and AA. However, in regions where Malaria is prevalent, this mutation has a protective benefit and the frequency of people with the aa genotype increases - but once that pressure is relieved - say by the use of mosquito nets or spraying, then the aa reverts back to low frequency.
Your last question was about dropping random matching. The only reason to do this is to make the analysis simple. It is of course unrealistic and does not happen in nature. The analysis then becomes quite complex. What happens then is that populations segregate by phenotype - skin or hair color, height etc. Sometimes there is also non random matching based on external issues. For example, people;e with dark skin can avoid diseases such as skin cancer - so they are at a selective advantage in equatorial regions. On the other hand, people in northern climates have a lighter skin because of the need to absorb more vitamin D (and avoid diseases like rickets etc). Again, this is an issue of selection - which I will discuss in a subsequent post.