Note: If you understand up to Stage 1 of this post, you now understand how allele frequencies are determined in a population that has random mating and a few other biology related assumptions. The invisible “Players” choose which allele it is better to be, and they will settle onto an equilibrium as Manfred describes.
The above post contains everything you need to do some intro-level population genetics problems. If you learned something from the above most and would now like to test your shiny new genetics skills, here’s a problem set:
Suppose A and B are the only two alleles in a diploid genome, and AA has fitness 2, BB has fitness 1, and AB has fitness 3
Problem: What proportion of alleles are A? What proportion of alleles are B?
In practice for biologists, you’d be doing this problem backwards—looking at the percent of the population that expresses each phenotype, and using that to infer allele frequencies and relative fitness. If I tell you that 25% of a population has sickle cell, if you know that sickle cell disease comes from a homozygous recessive allele, and if you are willing to assume various things, that’s all you need to work backwards all the way to the payoff matrix.
In practice, of course, mating isn’t random. If AB is inferior to both AA and BB, then there is an incentive for A carriers to avoid B carriers and it is a trend towards speciation. If AB is superior to both AA and BB, there is an incentive for heterozygosity.) Also in practice, the allele frequencies are constantly shifting so you are following a moving target, and sometimes sampling is biased (for example, carriers of low fitness alleles die before you can measure them) etc.
Note: If you understand up to Stage 1 of this post, you now understand how allele frequencies are determined in a population that has random mating and a few other biology related assumptions. The invisible “Players” choose which allele it is better to be, and they will settle onto an equilibrium as Manfred describes.
The above post contains everything you need to do some intro-level population genetics problems. If you learned something from the above most and would now like to test your shiny new genetics skills, here’s a problem set:
Suppose A and B are the only two alleles in a diploid genome, and AA has fitness 2, BB has fitness 1, and AB has fitness 3
Problem: What proportion of alleles are A? What proportion of alleles are B?
Solution
Bonus question: What will the final distribution of AA, AB, and BB prototypes look like?
Solution
In practice for biologists, you’d be doing this problem backwards—looking at the percent of the population that expresses each phenotype, and using that to infer allele frequencies and relative fitness. If I tell you that 25% of a population has sickle cell, if you know that sickle cell disease comes from a homozygous recessive allele, and if you are willing to assume various things, that’s all you need to work backwards all the way to the payoff matrix.
In practice, of course, mating isn’t random. If AB is inferior to both AA and BB, then there is an incentive for A carriers to avoid B carriers and it is a trend towards speciation. If AB is superior to both AA and BB, there is an incentive for heterozygosity.) Also in practice, the allele frequencies are constantly shifting so you are following a moving target, and sometimes sampling is biased (for example, carriers of low fitness alleles die before you can measure them) etc.