A University of Leicester, UK, academic predicts rats will continue to grow and fill a "significant chunk" of Earth's emptying ecospace.
Dr Jan Zalasiewicz from the Department of Geology at Leicester suggests that people better get used to having rats around - and that their global influence is likely to grow in the future as larger mammals continue to become extinct.
Given enough time, rats could probably grow to be at least as large as the capybara, the world's largest rodent, that lives today - that can reach 80 kilos. If the ecospace was sufficiently empty, then they could get larger still, said the researcher.
"They are now on many, if not most, islands around the world - and once there, have proved extraordinarily hard to eradicate. They are often there for good, essentially. Once there, they have out-competed many native species and at times have driven them to extinction.
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Gigantism can occur in animals as they adapt to their environment and Zalasiewicz believes that rats will prove to be no exception to this timeless rule.
"Animals will evolve, over time, into whatever designs will enable them to survive and to produce offspring," he said.
"For instance, in the Cretaceous Period, when the dinosaurs lived, there were mammals - but these were very small, rat and mouse-sized, because dinosaurs occupied the larger ecological niches.
While looking to what may happen in the future, occurrences of gigantism in rodents in the past can show the scope for evolution - the largest extinct rodent discovered so far, named the Josephoartegasia monesi, was larger than a bull, and weighed over a ton, researchers said.
The variations in future rat sizes will not simply involve them blowing up to epic proportions, however.
Zalasiewicz suggests that there will be many types of evolutionary adaptations in rats over time.