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Since having (eg.) two arms is a result of evolution, how can we, considering modern technology, force embryos to grow another limb? Polymelia is known to me, but it is considered a birth defect. I know that evolution is only possible because of random mutation. I guess an alternative evolution needs parents to derive genes from.

Therefore my question would be:

Is it possible today, or would it be possible in the future to trigger growth of limbs by forced Mutation and if so, how many generations would it take to come to the point, where the third limb is as efficient as the other two?

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Is it possible today, or would it be possible in the future to trigger growth of limbs by forced Mutation?

Yes it is. Scientists are already able to trigger growth of ectopic eyes on fruit flies, therefore it is "just" a matter of introducing in the genome the triggering of the right genes at the right time for growing a third arm.

ectopic eyes

how many generations would it take to come to the point, where the third limb is as efficient as the other two?

That's not how evolution works. Bilateral symmetry (having two arms, two legs...) is part of the body plan of all vertebrates and dates back to the Cambrian explosion. If it has remained until today, it means it is pretty effective when compared to the alternatives.

As you state, polymelia is considered a defect because it is a deviation from the bilateral symmetry plan, and the only way to be transmitted to the offspring and be selected by natural selection would be that it gives a clear competitive advantage with respect to non mutated organisms.

Yes, nowadays a 3 armed man can be invited to talk shows and become a celebrity, maybe even find some willing mate for reproduction purposes. But if I look back at all the "freaks" who have reached their 15 minutes celebrities in the past, I don't see any of them having started a genealogy carrying on the same features which made them famous.

If you want your mutants to be successful, first find a clear case when they have a competitive advantage with respect to non mutants, then natural selection can kick in.

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I found an article discussing Polymelia in Angus calves. According to its author, current evidence points to Polymelia being genetically based (at least in calves.. not sure how this carries across to humans). That being said,

Although the current evidence suggests an underlying primary genetic basis to polymelia in these Angus calves, no clear pattern of inheritance has been identified to date.

Based off of that, I'd imagine using human selection (aka Eugenics) to try to promote the development of extra limbs would be difficult since we wouldn't be able to predict the pattern properly to choose whose genes to continue reproducing.

As far as technology is concerned, I'm not sure how feasible forced mutation would be (assuming what you mean by that is forcing genes to mutate to develop extra limbs). Genetic editing is apparently possible, but I doubt it's developed to the extent needed to code a new limb into someone's genetic code yet.

Someone else with more technical knowledge in the field of genetics could weigh in, but I've told you what I consider to be the answer based off of a few minutes of searching around online. Hope this helps.

Sources:

Angus calf Polymelia: http://www.flockandherd.net.au/cattle/reader/polymelia.html

Genetic editing feasibility: https://www.theguardian.com/science/2017/nov/15/scientists-make-first-ever-attempt-at-gene-editing-inside-the-body

EDIT: JUST SAW THAT BY TIME I'D POSTED THIS, ANOTHER USER HAD ANSWERED THE QUESTION IN MORE TECHNICAL DETAIL. I'D CONSIDER THEIR RESPONSE FIRST, OP.

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