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Why would a cyclops, that is to say, a sizeable(bear-elephant sized), land vertebrate creature with only one eye, evolve as opposed to the same creature with two eyes?

That is to say, is there any reason why this organism would either be better off with only one eye or why two eyes wouldn't benefit it?

Is there some other reason why an organism like this would evolve rather than one with binocular vision and depth perception?

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You can do depth perception with just one eye - octopuses do it. Yes they have 2 eyes, but they point in opposite directions, so the images from them don't overlap.

So the octopus uses one eye to look at prey, and bobs up and down (on a tiny scale), capturing the image from the top of the bob and one from the bottom of the bob. Those 2 images are then processed into a 3D image to give accurate range information for a pounce.

There's a technical name for this, but I'm utterly blanking on it. Will edit when I remember.

I'm guessing from the fact it is really rare that doing the 'traditional' two eye way is more efficient. Certainly two eyes gives you two different methods of depth perception:

  1. 3D stereoscopy where you make one image from input from 2 eyes. This is what humans use for hand to eye coordination. It is very heavy on processing power.
  2. Optic flow. You measure how fast things flick out of the corner of your eyes when you are moving. This is what humans use to avoid bumping into trees when walking through a forest or avoid crashing into other cars when driving at 90mph on the motorway. It is cheap on processing power, but unreliable in poor light conditions, which is one reason why the motorway crash rate goes up in foggy weather!

Anyone know if optic flow is inhibited or less efficient with only one eye?

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In vertebrates, cyclopia is caused by a trisomy. In humans for example it is the 13, sometimes the 4. I have seen it in cats also, and one case has been reported in sharks.

Do not google for it if you are sensitive to images of deformed, stillborn babies.

Also, for those who don't know what trisomy means: it's when you have one extra copy of a chromosome.

Now let's supoose that, due to chance, a mutation happens where some specimens have not trisomy, but tetrasomy, and they somehow survive and breed.

Supoose that a gene, or set of genes, in the affected chromosome significantly increases survivability, and having multiple copies helps even further. Natural selection would favor the tetrasomic and they would eventually give rise to a new species.

If this set of genes gives more chances of survival and breeding than having two eyes instead of one, then having only one eye is just a small price to pay.

Such tetrasomy may also explain the cyclops' great size and strength. Perhaps in their environment those were the factors that helped them survive.

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    $\begingroup$ This is an unstable solution though; given enough time to evolve they would find the genetic combination that allows for both the advantages given by the extra chromosome and the stereoscopc vision. $\endgroup$
    – Annonymus
    Commented Jul 23, 2016 at 19:42
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If for some reason a creature didn't need depth perception, or had some other means of perceiving depth then a cyclops doesn't seem impossible. If a large creature from the ocean transitioned to being a land creature and was able to continue using either echolocation (not too likely) or electroreception then a cyclops wouldn't be to far outside the realm of possibility. Another possibility is that the creature doesn't need sight, if it was more of an earthworm, or a mole like species and had only a single eye and has recently moved above ground. Yet another way this could have evolved is if the creature were largely stationary, depth perception wouldn't be as important to such a species of beings.

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