Basically there’s a “hot spot” in the Earth’s mantle that periodically shoots magma onto the surface. Wherever a plate of the crust moves over the hot spot, the ejecting magma creates a new island.

The hotspot gets weaker over time which is why the oldest islands in the chain are also the biggest (and usually the only ones that make it above the water surface)

other way around actually

Oh, so it starts with small blips and then it fucking goes?

It feels counterintuitive mainly because of how explosive volcanoes work (and how Hollywood and cartoons convinced the world that every volcano will explode AND throw lava around before slowly calming down.

Do you have a paper about this phenomenon or is it something that can be found in a textbook?

That’s not why hot spot island chains get smaller with age. The reason the older islands shrink is because erosion starts wearing them away as soon as plate tectonics carries them off the mantle plume they sit on top of. The mantle plume fuels them, without it the volcano becomes inactive. See for example the diagram below. It doesn’t have anything to do with how large or active the plume is. Those things keep running about as long as we are able to keep track of them, as far as I’m aware. It’s actually really easy to debunk, because hawaii, the only volcanically active Island in that figure OP posted, is also the biggest, and the youngest.

Also, this is completely besides the point, and it’s very much not yet certain, so take this with a grain of salt, but there’s some evidence that points to the birth of these mantle plumes actually being responsible for one of the most violent geological events in existence: Large igneous provinces. Which are best known as “that thing we thought for a while might’ve put an end to dinosaurs if it weren’t a meteorite” and also “that thing that was likely partly responsible for killing like 70-80% of life on earth that one time”

also, there’s also non-hotspot island chains, but I think this post has gone on for long enough without me discussing subduction-related shenanigans.