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Geologist Bruce Saunders picks up the remains of a coiled mollusk.

His fossil-cluttered office at Bryn Mawr (Pa.) College, has many such mollusks, surfaces of which are etched with a wavy pattern as intricate as fine lace.

To Saunders, the natural artistry drawn on this 100 million-year-old fossil of a creature known as an ammonoid is a perfect example of a puzzle posed by Darwin’s theory of evolution: Why did simple creatures give rise to complex ones?

In the game of survival-of-the-fittest, bacteria and other simple-looking organisms would appear to be the big winners, coming through every major extinction and remaining the dominant form of life on the planet.

“We’ve always assumed — since Darwin — complexity and size tend to increase in time,” Saunders said. “In fact, there’s almost no evidence for this.”

Ammonoids turn out to make a good case study, because the complexity in their shells — which varied from postmodern minimalism to Victorian ornateness — is not hard to measure. And Saunders, considered a world expert on this family of creatures that goes back 395 million years, found a way to quantify the lines and squiggles.

Saunders found evidence that evolutionary pressure drove this particular creature toward ever fancier shells. His findings are in the current issue of the journal Science.

Saunders, 56, says his interest in ammonoids started around the fourth grade, when he found the fossil of a chambered nautilus in a flower bed.

Early in his career, he focused on the chambered nautilus, pursuing the modern ammonoids for 15 summers in the seas surrounding the South Pacific Island of Pilau.

In a leaky yellow boat nicknamed the Yellow Submarine, Saunders collected hundreds of specimens, scouring the seas to depths of 1,500 feet.

The nautilus, a deep-sea scavenger that gains buoyancy from its chambered shell, is the only surviving member of the ammonoid family. But ammonoids once filled the world’s seas. There were hundreds of species, some of them growing up to nine feet across.

As obscure as ammonoids may be as a subject of study, they turned out to make a good test animal for understanding the complexity problem.

Simple specimens such as the chambered nautilus have gently curved chamber walls. Complex ones have ruffled, wavy walls.

When another scientist, Harvard paleontologist Stephen Jay Gould ventured into the world of ammonoids, he concluded that the complicated ones came about through nothing more than the laws of probability. He argued that if you start with species that make the simplest possible shells, then new varieties are bound to look more complex.

In testing Gould’s conclusion that ammonoids get more complex merely by chance, Saunders invented his own method of measuring the complexity of the ammonoid suture patterns. His method combined measures of the length of the lines in the pattern and the number of hills, loops and valleys.

If the complex patterns were products of chance, he said, he would expect there to be as many species with simple shells as with complex ones. But if some force was driving the patterns toward complexity, then the simple ones would start to diminish over time.

Saunders used this and several other mathematical tests to trace complexity across 588 different ammonoid groups, or “genera,” which existed over a span of 140 million years.

Over that period, he found, the number of complex species blossomed while simple ones dwindled slightly — a sign that the complicated species had some advantage. But what?

At first, Saunders thought of corrugated cardboard and tin — and wondered whether the wavy patterns in the chamber walls could help the shells withstand the great pressures in deep water.

He asked Tom Daniel, an expert in biomechanics from the University of Washington. In fact, Daniel saw a disadvantage in the complicated patterns at crushing depths. “You don’t see many highly-ruffled submarines,” Daniel said.

But the corrugated-patterning might have brought strength against the bite of long-toothed marine dinosaurs that perhaps fed upon shallower-dwelling ammonoids. And that might explain why — in an apparent paradox — the only surviving member of this once diverse group is the simplest one: the deep-water chambered nautilus.

It could be, he speculated, that the wavy-shelled animals did better in shallower waters, where they needed to stand up to predators. The nautilus, on the other hand, took a different path — evading predators by staying in deep water, which suited its simple shell. And 65 million years ago, when an asteroid or other natural disaster altered the climate and wiped out the dinosaurs, only the deep-dwelling nautilus survived.