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Inbreeding results in homozygosity.

I've come across this concept many times and there's a question that comes to my mind every time I read it.

Let us suppose the character we are trying to establish is dominant trait controlled by a biallelic gene and the two individuals (animals) we have selected to inbreed both have the genotypes Aa.

Aa x Aa = AA/ Aa/ aa in the ratio 1:2:1

So the possibility of having a homozygous dominant is 25% while that of heterozygous is 50%. As the breeder has no access to technologies and find out the genotype of the F1 individuals there's a possibility that he would choose two F1 individuals with Aa genotype once again (which has the highest possibility of occurrence). And the same is repeated , production of F2 offsprings with 50% possibility of heterozygous individuals.

Edit:

So getting a homozygous dominant individual is very less likely to happen.

My question, is inbreeding really efficient at producing homozygosity?

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  • $\begingroup$ Depends on the allele variants and their frequencies in the population. You can calculate the efficiency if you know these parameters. It also depends on the effects of the genotype on fitness. $\endgroup$ – WYSIWYG Dec 30 '16 at 7:34
  • $\begingroup$ I think this "problem" is somewhat contrived, as the modern breeder will have access to genetic technology, but even in "the old days", they would be selecting for a certain trait, whatever that may be. They then just take the offspring that exhibit that trait, backcross them, and so on and so on for as many generations as is needed (10 pops to mind for mouse knockouts/transgenics). $\endgroup$ – MattDMo Dec 31 '16 at 2:09
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And the same is repeated , production of F2 offsprings with 50% possibility of heterozygous individuals.

That's not correct.

Let's start with a population with 100% of heterozygotes:

100% Aa

And, just to create a highly exaggerated model, let's suppose that these individuals perform the most drastic case of inbreeding: self-fertilization. Inbreed occurs when an individual perform sexual reproduction with a closely related organism, and no one is more closely related to someone than himself!

After the first "inbreeding" generation, we'll have:

25% AA
50% Aa
25% aa

So, 50% of heterozygotes.

If this population inbreeds again, we'll have at the second generation:

37.5% AA
25% Aa
37.5% aa

So, 75% of homozygotes versus 25% of heterozygotes.

In the third generation:

43.75% AA
12.5% Aa
43.5% aa

And in the fourth generation:

46.875% AA
6.25% Aa
46.875% aa

Thus, in only 4 generations, we have 93.75% of homozygotes versus 6.25% of heterozygotes. Mathematically, the heterozygotes never disappear. Biologically, however, if a population shows self-fertilization, heterozygotes disappear in few generations.

Now, let's get out of this overly exaggerated example with self-fertilization and back to your question, where the organisms perform cross-fertilization:

The problem with your reasoning is that (correct me if I'm wrong) you're starting with a couple (Aa) and supposing that all their descendants will mate randomly. Of course, the allele frequencies will remain the same. But that's not inbreeding. By definition, inbreed is a non-random mating system. For a real inbreed to occur, the mating individuals should be more closely related than those drawn by chance from the population.

In conclusion, given enough time, inbreeding (and genetic drift as well) has the effect of eradicating heterozygotes from the population.

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