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This is a question having to do with my generation ship story but more specifically, genetics, and even more specifically, genetic disease.

Here are the conditions as far as people with or without genetic disease go:

People with disease: sterilization + alternative ways to have children and absolutely no sex before sterilization

Carriers: warn that their children might need sterilizing

Not carriers: Absolutely nothing

Now I know these types of genetic diseases would be eliminated in 1 generation:

  • Y linked(Azoospermia for example)
  • X linked dominant(Such as Vitamin D resistant rickets)
  • Autosomal dominant(For example Huntington's disease)

A truly codominant genetic disease is impossible because you can't both have and not have the disease simultaneously. Instead it would be better to say it is incomplete dominant.

But with these conditions, is it possible for genetic disease to be totally eliminated after hundreds of generations(say 500 generations)? In other words is it possible for these types of disease to be eliminated:

  • Incomplete dominant(Alpha-1 antitrypsin deficiency as an example(but I found out this also falls under multiple alleles))
  • Autosomal recessive(sickle cell anemia for example)
  • X linked recessive(such as Hemophilia A)
  • Multiple alleles(Again A1AT deficiency is an example of this)

I found out that human population growth globally averages around 1.1% per year. And a reasonable number to have on a generation ship is 44,000 people. About 9% of them would be 65+, 65% between 15 and 64 with 20% of that being women of reproductive age, 50% being men of reproductive age, 15% post-menopausal women, and a small 5% being those that are still not in puberty, with the other 26% of the population being from 8 to 14, of which 75% are not in puberty yet and 25% are. Sex ratio is 1:1. This would mean a minimum of 815 babies born per year to compensate for 343 deaths per year. Or about 2.3 times as many babies born as deaths.

So given this and the genotype ratios for the possible punnet squares which I already wrote down, how would I figure out the probability that all genetic disease is eliminated after x generations?

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    $\begingroup$ It seems you are excluding spontaneous mutations which could lead to genetic diseases. Is that on purpose? $\endgroup$ – Arsak Apr 4 '18 at 6:04
  • $\begingroup$ To all the down voters, please leave a comment on how to improve the question. And please don't mix up the biological question "Is it possible?" with the ethical question "Should it be done?". Thank you. $\endgroup$ – Arsak Apr 4 '18 at 8:02
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    $\begingroup$ Please rephrase the question (title) to include the detail of being on a starship colony; or generally the fictional setting. The current question suggests you're asking about human genetic engineering. Clicking on that and not reading your question might be the reason for some of the unexplained downvotes. $\endgroup$ – Armatus Apr 4 '18 at 8:25
  • $\begingroup$ Or with slightly advanced technology you can simply edit the offsprings genome. $\endgroup$ – John Apr 4 '18 at 13:55
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Given your severe selection pressure against disease allele you have implemented, you can have the disease allele eliminated within 1 generation for dominant allele and 2 generations for recessive allele.

You could eliminate all those disease alleles while you were selecting the crew, prior to boarding your generational starship.

Your primary problem is spontaneous mutations. However if you are doing genetic test and this is a starship, you should have access to IVF technology. This will allow you to screen every embryo prior to implantation for genetic defects.

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Phenotype-level selection doesn't eradicate recessives

As long as you restrict yourself to purely phenotypic selection, you're extremely unlikely to eradicate recessive genetic diseases at your population size. That's the nature of recessive alleles - they persist in carriers that don't develop the phenotype. To eradicate this, you basically need the luck that in one generation, not a single child gets passed down a mutant allele from a heterozygous parent. The same goes for "incomplete dominant" (the appropriate term to use would be incompletely penetrant). X-linked recessive are more likely to be eradicated because you will never have male parents passing these on (males have only one X which means all recessive X-linked traits manifest in male phenotypes).

Predicted number of generations till eradication

As for the population statistics regarding your recessive eradication, it's not possible to predict after how many generations this will succeed. Depending on the initial prevalence, you will have an exponential decay due to your selection. At some point you will reach a near-zero level at which you won't be able to predict when that lucky moment will happen that no child receives a mutation. A small number of heterozygous individuals could produce a larger number of heterozygotes and infinitely cause low-level recurrence of the disease. At this point it's a computational rather than mathematical problem.

Practical genetics

A simple practical example is my experience with selecting the y allele out of a Drosophila population. y recessively causes yellow rather than brown body colour (basically a form of albinism). I've made a few attempts at selecting it out by discarding yellow-bodied flies, but there were always a few yellow-bodied individuals in the next generation. The only way I've succeeded in eradicating this is by doing crosses with a low parent number (~5 individuals) so that there is a reasonably high chance of picking parents without any mutant y allele.

Possibilities for eradicating alleles

The simplest solution to your problem is genetic screening at the embryonic level, which would allow theoretically to eliminate all pre-existing heritable genetic diseases in one generation. You would need continuous genetic screening to also keep de novo heritable mutations out. As for somatic genetic diseases (e.g. paroxysmal nocturnal haemoglobinuria), you will never eradicate those without targeted genetic engineering to make the problematic hotspots in the genome more damage-resistant.

Side note regarding multiple alleles: Multiple alleles don't require special consideration for your thinking because each allele can either be recessive or dominant to wildtype alleles in its phenotype. Also consider that "healthy" isn't an absolute standard. Genetically speaking, there is no "normal". Most (all?) genes have a range of alleles that persist in nature and cause nothing we would consider a disease or defect phenotype.

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