Movies S1 -- Response of a gravel island to a 2.5-m sea-level rise. Because the gravel is very permeable, waves that overwash the island very quickly seep into the gravel. This results in island retreat and the deposition of gravel very close to the ocean edge in the form of a narrow and high ridge. Movie S2 -- Response of a sand island to a 2.5-m sea-level rise. Because the sand is not very permeable, waves that overwash the island flow all the way to the back of the island, into the lagoon. This results in island retreat and the deposition of sand across the whole island, including into the lagoon, in the form of washovers. Movie S3 -- With a relatively modest storm wave height of 2 m only a small number of waves overwash the island and the average overwash discharge tends to be less than 20 liters per meter per second. This will result in sediment deposition around the crest and across the back of the island, enabling the island to keep up with rising sea level' Movie S4 -- With an extreme storm wave height of 4 m almost all waves overwash the island and even continue to travel into the lagoon. The average overwash discharge can be more than 100 liters per meter per second. This will result in removal of sediment from the entire island and will ultimately lead to the destruction and drowning of the island.