Reading The Essential Talmud about ten years ago I vaguely recall the author stating that it was common for working class males to devote each day to one page of one a tractate from the commentaries on the oral law of the Jewish religion. As I am not religious, and look dimly on excessive orthopraxy, it struck me as a depressing thought.
But I am not entirely different. I often will relax at some point in the day and open up a random page of a population genetics textbook. Just as those Jewish men attempted to gain insight into the divine intent for how they should live their life, so with population genetics I am attempting to refine the theory which allows me to interpret the world around me.
It would probably help anyone who reads many of my posts as well, as it develops particular habits of mind. Though I often recommend Principles of Population Genetics, Elements of Evolutionary Genetics is also excellent. So in the future I’ll try to write up short insights which are pretty banal to most population geneticists, but which might be interesting to a motivated public, if my modest readership can be considered the “public.”
Page 100 has a section, “Selection in inbreeding populations.” The most important formal relationship on this page is:
Δq ≈ qs[h(1 –f) + f]
q = minor allele frequency on a biallelic locus, that is, the remainder from 1 – p
h = dominane coefficient , so that h = 0 means q is totally recessive and h = 0.5 means that the locus is additive in regards to allelic effect.
f = inbreeding coefficient, a basic measure of two alleles at the same locus sharing recent common ancestry (and therefore, rendering the genotype likely homozygous). From 0 to 1, with 1 meaning totally inbred and homozygous.
s = selection coefficient against the population mean fitness. Usually the value is near zero, though not exactly zero. A positive selection coefficient of 0.01 is considered very favorable for a new mutant.
What you see here is that in an instance where q is entirely recessive, inbreeding increases the selection on the locus. In a normal population with lots of random mating homozygous recessive genotypes are rare. When f ≈ 0 the change in the frequency of q is just a function of the selection coefficient and the dominance. As inbreeding increases, the importance of alleles (or lack thereof) in heterozygote genotypes decreases. For recessive traits inbreeding is another way to expose the novel alleles to selection.
This is one reason that unscrupulous breeders of animals sometimes utilize very close relatives in programs to change traits. The problem is that inbreeding has an effect across the whole genome, even if you are interested in particular loci. And that effect on the whole genome is often very bad, as lots of deleterious alleles with recessive expression are present in populations which are normally outbred. Of course in plants this also results in purging of genetic load, as alleles get flushed out of the system. Unfortunately for mammals, and complex metazoans in general, this doesn’t seem to work to well for out lineage. If it did work well zoological veterinarians, who I’ve talked to, would be a lot more hopeful about what they’re trying to do by mating near relations in the hopes that they can get a large enough population to maintain a viable breeding program.
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