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I've read super-earths might become archipelago planets. Picture shallow seas, under a thick atmosphere that alternates between muggy and clammy. Because a bigger share of the surface would be continental shelf, there would be more room for kelp forests and other habitats propicious to photosynthesizers, who get more light in shallower waters; so would it follow that an archipelago planet would have very oxygen-rich air and big arthropods to go with it?

EDIT: Presume there could be mats of green sulphur bacteria or some other kind of photosynthetic anaerobes covering those big, sunny, shallow shelves, and that my arthropods would be about like Earth's dead eurypterids. To be clear on intent: Would an archipelago planet get to some sort of "Cambrian phase" earlier in it's history than Earth, and would my pseudo-Cambrian animals be better off with having dry land spread out more instead of closely packed together like Earth's used to be.

Thank you by your answers so far.

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    $\begingroup$ Most oxygen on Earth is made by phytoplankton... And phytoplankton, quite obviously, is plankton, small organisms living in large bodies of water, not anchored to any substrate. $\endgroup$ – AlexP Jul 5 at 6:17
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    $\begingroup$ @AlexP Phytoplankton still require nutrients that are typically sourced from solid substrates, though. Coastal areas and shallows support much more life for that reason than open deep ocean, where the concentration of dissolved nutrients is low, limiting phytoplankton growth. $\endgroup$ – Logan R. Kearsley Jul 5 at 15:37
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No

There are a lot of issues with that assumption, but I'll go through it all as concisely as I can.

Oxygen isn't the only limiting factor to arthropod size
Arthropods are exoskeletal by definition. Ultimately, that means that they are an organic creature inside a hard shell, more or less. By comparison to endoskeletal creatures, that means that their outer carapaces have a limit on how hard and strong they can be as they scale up which is less of a limitation on a creature with a skeleton on the inside. If you're dealing with a 'super-earth' that implies higher gravity, meaning arthropods (especially on land) won't be able to grow beyond a certain size as their carapaces would collapse, or their internal organs would put too much pressure on each other lying in a pile inside said carapace; take your pick.

It's volume of oxygen that counts, not percentage.
A planet with a thicker atmosphere doesn't need as high a percentage of oxygen to support earth based life because the amount of oxygen we breathe (and that we need in each breath) is determined by Partial Pressure, which is a fancy way of saying a set amount of oxygen, regardless of the ambient pressure. The Apollo missions flew with pure oxygen environments because they were only pressurised to less than a third of sea level pressure. Conversely, deep sea divers use much thinner mixes of oxygen (filling the gap with an inert gas like Argon) because at pressure, they're breathing in so much larger a volume of air with every breath. So yes, you need a LOT of oxygen (in terms of volume) to support large arthropods, but don't think of that as a percentage as such, and in an environment with a denser atmosphere the pressure on the carapaces might become the limiting factor rather than oxygen (see above).

Your plants must be in place for millions of years prior to animals.
Your planet still needs a Great Oxygen Event in some form to release the molecular oxygen and put it into the atmosphere. Planets are highly unlikely to start off with such an atmosphere because oxygen reacts with so many other elements. That's what makes it so useful as an oxidiser. So, you need a constant endothermic reaction like photosynthesis going for millions of years before animals even come onto the scene, just to supply the oxygen needs they'll have. By the time your planet is ready for animals, it's probably not an archipelago anymore. Just saying.

This is all based on our current model of life
For all we know, on some of these worlds you could have photosynthesizing animals. Arthropods could have lungs, too. They may not have, but could have a form of gills that extract the CO2 out of the atmosphere instead, harnessing sunlight to form their own oxygen. They could have a combination of exoskeletal and endoskeletal body structures that allow them to grow bigger because of a segmented carapace and their growth model could be adding new segments as they grow. That's the thing about evolution; we really don't know what life would look like on another planet because we don't know the starting structures and we don't know the pressures in the environment that force it to evolve in order to survive.

Put simply, the existence of archipelagos and photosynthesizing plants don't in any way increase the chances of large arthropods on your planet, although there is the chance that they make the environment favourable for them to evolve. But, evolution and planetary ecology is an immensely complex and fragile interaction of billions of factors and as such, it would be wrong to say that the one follows the other as a general rule as defined in your question. It's not to say that you're wrong; merely that the process is almost infinitely more complex than that.

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    $\begingroup$ Arthropods also have the problem of regularly moulting their whole carapace. Effectively they throw away their skeleton and, until the new one hardens, there is nothing to support their internal organs. I'm guessing there's a body size point where - as an example - the weight of the liver bruises or crushes the kidney underneath it. They can return to water to moult and that might help (supports body weight, but can't go too deep or squished by water pressure). Arthropods as big as a bear need a place as big as a bear's hibernation den to hide in to moult, or something will eat them! $\endgroup$ – DrBob Jul 5 at 8:42

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