American Palaeontologist Stephen Gould. Wally McNamee/CORBIS/Corbis via Getty Images

In 1972 the eminent palaeontologist Stephen Jay Gould and his colleague Niles Eldredge proposed an idea about the way evolution worked and, in so doing, sparked a fight of almighty proportions.

New modelling revealed by Michael Landis and Joshua Schraiber of Temple University in Pennsylvania, US, however, adds considerable extra weight to their case.

Gould and Eldredge sought to explain so-called gaps in the palaeontological record – missing fossils assumed to represent transitional phases between ancient species and the modern ones into which they evolved – by suggesting they were an illusion.

Evolution, they proposed, wasn’t a gradual process, marked by the slow accumulation of new characteristics. Rather, they said, “the history of evolution is not one of stately unfolding, but a story of homeostatic equilibria, disturbed only ‘rarely’ … by rapid and episodic events of speciation.”

Two important principles underpinned their explanation, which they dubbed the theory of punctuated equilibria.

The first was that once a species evolved, it tended to stay pretty much the same from thereon in until extinction ended its run. The second was that when part of a species became isolated from the rest and thus fell under new selection pressure, if it was going to evolve into something new it would do so very quickly (at least, on a geological scale).

“If new species arise very rapidly in small, peripherally isolated local populations,” the pair wrote, “then the great expectation of insensibly graded fossil sequences is a chimera.”

The theory was roundly attacked by some other prominent voices in the field. In his book, The Blind Watchmaker, Richard Dawkins said punctuated equilibrium was an idea that “does not deserve a particularly large measure of publicity”.

Philosopher Daniel Dennett, in his book Darwin’s Dangerous Idea, also slammed Gould – who responded by calling him “Dawkins’ lapdog”. Dennett shot back that in doing so Gould was “turn[ing] up the volume of his vituperation.”

Gould died in 2002, Dennett is now 75, and the debate is still a long way from settled.

However, Landis and Schraiber, publishing on the preprint site bioRxiv, push the argument back in favour of speciation as a comparatively rapid, rather than gradual, process.

The title of their paper serves also as its bold conclusion: Punctuated evolution shaped modern vertebrate diversity.

The pair constructed a mathematical model based on random probability distribution and fed in datasets derived from the morphological characteristics of about 50 clades (genetically-related groups of animals) covering mammals, birds, reptiles, fish and amphibians.

The results fitted best within a framework of punctuated development, with long periods of stasis – averaging around 10 million years – between “jump processes” of “pulsed evolution” lasting as little as 100 generations.

All of the data used concerned modern species. Landis and Schraiber suggest that future work integrating their work with the paleontological evolutionary research kick-started by Gould and Eldredge will throw up more detailed evidence about how rapid spurts of evolution and speciation are related.

The reactions of professors Dawkins and Dennett remain unknown, but might be memorable.