Interesting question, Thom! As a tree on an island grows, it adds mass to the island (at least momentarily), because plants build themselves out of CO₂ (from the atmosphere), sunlight, and water. When they die they decompose and contribute to the soil of the island, so in theory the island should be getting slightly "bigger" with each decomposing palm tree. At the same time, various forces act to make the island smaller. For example, the rocks and soil of the island are broken down slowly by weathering, and transported to the ocean by wind, rain water, or wave action, making the island smaller.

Unless some vigorous process (beyond the growth of coconut palms) is acting to actively build islands up (for example, volcanic activity, or the growth of coral reefs), they get smaller over geologic time (10s of thousands to millions of years).

A good example of this is the Hawaiian Islands, which were all once roughly the size of the modern "Big Island." The Big Island is where volcanic activity is happening today, so that island is still growing. As it grows, however, the movement of Earth's tectonic plates is simultaneously slowly shifting the Big Island northwest, ultimately cutting it off from its magma supply deep in the mantle. At that point, the Big Island will cease growing, start eroding away, and get smaller with time. Indeed the oldest Hawaiian Islands (those furthest to the NW) are also the oldest. There are even older former Hawaiian "islands," but they're now below sea level, so we call them sea mounts (the Emperor Sea Mount Chain, if you want to check out a map).

So no, I don't think its possible to make an island bigger simply by growing a bunch of plants, especially given that sea level is rising.

Thanks for a stimulating question!

Interesting question. One of the critical things that happen over time on an island is the development of soil, but that takes a REALLY long time. Soil is made of organic material (dead stuff) and minerals (tiny bits of rock). Weathering helps to break down rock. The organic material depends on both growth of plants, and breakdown of material by microbes. Growth and breakdown both happen faster if there is plenty of moisture and the temperature is warm. Even under the best of conditions, only about 1 mm of soil (the thickness of a dime) will form in a year. Some soil can also be carried in by the wind and water, but it can be carried away as well. Soil is critical for plant life (and the animals that depend on the plants), but it doesn't really influence the size of the island.

The size of the island is really determined more by geologic forces. I'm not a geologist, but I can tell you that many islands are formed by volcanoes. Islands also erode away due to wind and water erosion. Changes in sea level also make islands bigger or smaller.

What sorts of changes do you think would happen on an island that started with just coconut trees? What species would be likely to arrive? What would determine whether those species were able to survive on the island?

Typically, if an island is in the ocean, then it is shrinking, not growing, because wave action will erode the island away. Plants will slow the erosion down, but will not stop it.

If an island is in an environment where sediment is being deposited, such as in a lagoon behind barrier islands, then it can grow and plants can help it grow by providing a substrate for sand to collect. It would depend on the character of the vegetation, the amount of vegetation (just saying "coconut trees" isn't enough - how many coconut trees, and which of the many species of coconut trees?) and other conditions, so I can't answer specifically what would happen over the numbers of years that you quote.

The answer is mostly 'No'. Most islands seem to form from volcanoes, though I guess islands will form when sea levels fall in shallow waters, or when river deltas form. In those non-volcano cases, I think the movements of water and of silt in the river will do much more than plant growth to build - or destroy - the islands. But islands with plants on them will hold together better when water is 'trying' to wash them away, and islands with plants on them will be better at helping silt stay on the edges of the island. Thanks for your question!