Advanced Hardy-Weinberg Problem Solving: Inbreeding
Hardy-Weinberg equilibrium is the state of a population that follows the following 5 conditions:
1. large population size
2. no immigration/emigration (no gene flow)
3. random mating
4. no natural selection
5. no mutation
Assuming that these conditions are true allows us to calculate allele and genotype frequencies across generations. Here are the basic equations for H-W:
Now that we have the basics out of the way, let's make it interesting.
Imagine that, instead of random mating, a population practices inbreeding (basically incest), preferentially mating with others who have similar characteristics and thus genotypes. This would reduce the number of heterozygotes because if people are exclusively mating with their own kind, then the lineages will be more "pure" with the same allele (and in the case of heterozygote inbreeding, some homozygous would be made as well; we'll see this later). To quantify the degree of inbreeding, we can calculate the inbreeding coefficient:
(E-O)/E
where E = expected number of heterozygotes (2pq)
and O = observed number of heterozygotes (should be smaller than E in cases of inbreeding)
To do H-W problems with inbreeding, we need to break up the cases of possible mating pairs, as traditional H-W equilibrium does not apply. Let's derive a formula for a situation where a population previously in H-W equilibrium decided to practice exclusive inbreeding for one generation. Let's call the alleles D and d.
Inbreeding, in this case, means that DD only mates with DD, Dd with Dd, and dd with dd. Here's what that looks like:
Let p = the frequency of allele D, and q = frequency of d. Let's add things up:
You can use these formulas for any problem with this scenario.
Here are some nice videos on this topic:
https://www.youtube.com/watch?v=BYvASyBIRuw - inbreeding coefficient calculation.
https://www.youtube.com/watch?v=8mZog-IQOqg - a problem using the formulas we derived.
Comment below / text me if you'd like me to continue the H-W series! I can write about how to do H-W problems with multiple alleles or sex-linked inheritance. Or lmk any other topics!
