Let's start with the second question: "When did the sole fish start having eyes on the same side of its head"? There's two ways to go about this question: "When do baby sole fish start migrating one of its eyes to the other side of the head?" and

"Sole" refers to many different flatfish. In fact, the word sole comes from the Latin word for sandal, solea, referring to how flat they are! However, even though we usually see them as these flat things with eyes on one side of their head, sole fish don't start that way. When they hatch as young fish, called larvae, they look like normal (transparent) fish, with their eyes on each side of their body as they swim around. They start metamorphosing at around one to two weeks old, their skulls twisting and moving around so that one eye (and their inner ear) migrates from one side of their head to the other.[1] The now eye-less side turns pale, while the double-eyed side becomes colored like the ocean floor. They also stop swimming freely in the water and settle down to live as a bottom-dweller for the rest of its life.[2]

Now if we talk about them as a species instead of as individual fish, Matt Friedman from the University of Chicago (now at the University of Michigan) noted that there are transitional fossils from the Eocene epoch, 56 to 33.9 million years ago. Transitional fossils are fossilized remains that have traits common to both an ancestral group and its descendant groups. In this case, the transitional fossils of Heteronectes and Amphistium were fossils of fish that were strongly asymmetrical, but had not yet migrated both eyes over to the same side, almost like incomplete flatfish.[3]

In 2016, scientists from the University of Oxford and Yale University estimated that the weird asymmetry in flatfish evolved over a period of 2.97 million years, an astoundingly short period of time! For reference, human evolution took, almost twice as long, approximately 6 million years![4] They compared DNA datasets and fossil records to estimate when flatfish and other fish started to become genetically and physically dissimilar.[5] Other scientists expected evolution to take a much longer time because changing skulls and methods of movement is pretty extreme. So this finding is still being debated and, depending on who you're talking to, a hot take.

So now that we've answered that, we'll go back to the first question: "Why does the sole fish go flat on the sand instead of moving?" There's a number of reasons for that, chief of which is that they're excellent ambush predators. Flatfish have a camouflaged side that is patterned like the ocean floor that hides them from both prey and predators. They like to bury themselves under the sand to help hide better. Also, the less movement, the better they are at hiding, just like humans playing hide-and-seek.[6] That's not to say soles stay still all the time! There are studies that track how environmental changes like temperature, light, and salinity (how salty the water is) will cause flatfish to swim to different areas than they normally live in. They have also observed several species that spend considerable amounts of time swimming around, usually at night, although they don't give reasons why.[7]

Sources:
[1]Jabr, Ferris. “The Improbable—but True—Evolutionary Tale of Flatfishes.” PBS , Public Broadcasting Service, 7 May 2014, www.pbs.org/wgbh/nova/article/flatfish-evolution/ . ↩︎ [2]Seligson, Sherri. “Migrating Eyes and the Fascinating World of Flatfish Design.” Sherri Seligson , Sherri Seligson, 21 Feb. 2017, www.sherriseligson.com/blog/migrating-eyes-fascinating-world-flatfish-design . ↩︎ [3]Friedman, Matt. “The Evolutionary Origin of Flatfish Asymmetry.” Nature , vol. 454, no. 7201, 2008, pp. 209–212., doi:10.1038/nature07108. ↩︎ [4]“The Smithsonian Institution's Human Origins Program.” Introduction to Human Evolution | The Smithsonian Institution's Human Origins Program , Smithsonian National Museum of History, 27 Oct. 2020, humanorigins.si.edu/education/introduction-human-evolution. ↩︎ [5]Harrington, Richard C., et al. “Phylogenomic Analysis of Carangimorph Fishes Reveals Flatfish Asymmetry Arose in a Blink of the Evolutionary Eye.” BMC Evolutionary Biology , vol. 16, no. 1, 2016, doi:10.1186/s12862-016-0786-x. ↩︎ [6]neptune3. “Why Are Flounders Flat? Because It Works.” Poseidon's Web , 27 June 2020, poseidonsweb.com/why-are-flounders-flat/. ↩︎ [7]Gibson, R.n. “Behaviour and the Distribution of Flatfishes.” Journal of Sea Research , vol. 37, no. 3-4, 1997, pp. 241–256., doi:10.1016/s1385-1101(97)00019-1. ↩︎

Flatfish like sole escape predators by hiding on the sea floor. It is very difficult to see them as they stay still, and even cover themselves with sand. The ancestors of flatfish had bodies shaped like most other fish. A random mutation caused a change in the development of the fish that made it flatter. Flatter fish had an advantage over other individuals and left more offspring. It may have taken a more than one mutation to arrive at the the body form we see today. Each mutation is random. Natural selection--better-adapted fish leaving more offspring--is non-random.

You can watch how a flatfish can develop a regular body shape from hatching until maturity at this site.

Which do you think came first, the flat body or hiding in the sand?

Sole are part of an order of fish called Pleuronectiformes, which contains most flatfish. Flatfish all or nearly all have their eyes on the same side of their heads and swim along the seafloor. The earliest member of this order of fish lived about 50 million years ago, and was partially, but not completely, like modern flatfish in this regard.

I can think of a good reason for not moving: Predators would have a hard time seeing you. Also this: the fish can lie motionless for hours, waiting for a tasty morsel to swim by.

Here's when the eyes move: Flatfishes are born with one eye on each side of their head, but undergo larval metamorphosis where one eye migrates to the other side of the fish's head late in larval development, producing asymmetrical juvenile fishes. By the time the skull is fully ossified, the eyes are permanently fixed in place.

It makes sense that fish didn't survive and reproduce well when their eyes had only partly moved. But there are no known transitional fossils with only partially displaced eyes that would link these asymmetrical flatfishes with their symmetrically shaped relatives. This lack of transitional fossils has been the source of tremendous scientific controversy regarding whether this asymmetry evolved gradually or through a sudden evolutionary leap that produced "hopeful monsters," as originally described by geneticist Robert Goldschmidt in the 1930s.

They become sand-colored on sandy bottoms and patchy stone-colored on pebbly bottoms.