On the banks of the Kinta River, at the furthest navigable point inland from Peninsular Malaysia’s western coast, stands the former mining town of Ipoh. Behind the bustling Chinese shophouses, white colonial town hall and railway station lies a backdrop of some seventy limestone hills, clad in forest. As visitors climb steps to the Buddhist temples perched in these green humps, or descend into the caves beneath them, they are surrounded by biological treasures, including some of the world’s smallest and strangest shells.
Karst limestone formations, like the ones in Ipoh, can be seen throughout South-east Asia, from northern Vietnam through Cambodia and Thailand to the Philippines and Indonesia; they rise from the sea as idyllic islands, and poke through rainforest canopies. The limestones were formed millions of years ago by the remains of ancient sea creatures, including corals and shells. Since then, their calcium carbonate skeletons have been uplifted, then eroded by wind and rain into jagged silhouettes with giant caves inside them and underground rivers running through them.
A riot of unusual wildlife lives in these limestone landscapes. Bumblebee Bats, the world’s smallest mammals, flit through the caves; blind fish crawl from subterranean ponds and out onto rocks; beetles and millipedes prosper in huge piles of bat dung; and out on the rugged hilltops roam troops of leaf monkeys, including such incredibly rare species as the Delacour’s Langur with its striking black and white fur (the Vietnamese name for it, vooc mong trang, means ‘the langur with white trousers’). The chalky soils are also a haven for molluscs that find a plentiful supply of the principal raw material to make their shells.
A single Malaysian limestone hill can be home to between 40 and 60 species of tiny microsnails, each one a millimetre tall, and all of them with highly ornate shells. Of those, two or three species could be unique to that individual hill. As well as snails, there are heaps of other endemic species here, ones that are found nowhere else on the planet: geckos, crickets, orchids, begonias and spiders. Just like oceanic islands, the limestone outcrops are isolated dots of habitat where evolution dances to a different beat, generating new and peculiar species.
When biologist Reuben Clements went snail-hunting in the hills of Ipoh, he discovered a shell like no other. To find it, all he had to do was take a few scoops of soil, place them in a bucket of water and wait for the empty shells to rise to the surface (for a long time only recently dead specimens were found, and no living snails). Seen under a microscope, these tiny shells reveal their curious physique. They look like the corrugated pipe of a vacuum cleaner that’s been left tangled on the floor, with the end flared out like a tiny trumpet. These shells twist and turn, this way and that, as if they can’t decide which way to grow.
A few years later, Clements’ colleague Thor-Seng Liew finally tracked down live specimens of this tiny snail and set about studying them for his Ph.D, devising a theory to explain their bizarre coiling shapes. Liew suggested that the snails are doing their best to avoid getting eaten by predatory slugs. Retreating into their shells, the snails force their attackers to reach into an empty, bendy tube while their prospective dinner cowers at the end. The slugs’ proboscis simply can’t reach into such a deep and convoluted recess.
Meanwhile, Clements and other limestone enthusiasts have been campaigning to protect the remarkable but often overlooked places these snails come from. Being useless for agriculture or development, limestone hills were left more or less alone for a long time, but now cement companies are getting in on the act, razing them to the ground for the limestone inside. These are imperilled arks of biodiversity that few people have heard of. Year on year, hundreds of species are going extinct, most of them before they are discovered, when the hills they once lived on are taken away.
Compared to Clements and Liew’s bizarre find in the Malaysian hills, most shells are far less erratic in the way they grow, and indeed they are often quite predictable. For centuries, many great minds have contemplated the elegant sculptures and patterning of shells and wondered what might govern their construction. They have hunted for clues to explain the amazing realities and tempting possibilities of shells; they have probed ideas of what makes a shell work and which shapes may ultimately never show up; and they imagined that if they could find ways of drawing shells, if they could mimic what nature has been doing for eons, it would not only bring them closer to understanding how molluscs make their intricate homes, but they might also catch a glimpse of the origins of beauty itself. What many generations of mathematicians, artists, biologists and palaeontologists have found is unexpected and elegant: to construct an elaborate seashell – and decorate it – requires only a handful of rules.
Of all shell shapes, one of the simplest and most pleasing is the spiral of the chambered nautilus. The internal twist of these ocean-wanderers is revealed when their empty shells are sliced in two, from top to bottom. Trace the outer edge of a nautilus shell and you’ll see that it spins inwards in a very particular way. This graceful curve was among the first shapes in nature to be granted its own mathematical formula.
In the seventeenth century, French philosopher René Descartes composed a simple piece of mathematics for drawing a shape called the logarithmic spiral. Unlike an Archimedean spiral, which has whorls that are always spaced the same width apart, like a coiled snake, the gaps between successive whorls on a logarithmic spiral get increasingly wide. Logarithmic spirals flare open as they get bigger, just like a nautilus shell.
A chambered nautilus shell cut in two, revealing its logarithmic spiral.
It was the cleric and mathematician Reverend Henry Moseley who, in 1838, first pointed out that many coiled shells are versions of the logarithmic spiral. Take a photograph of a nautilus shell cut in two, overlay the outline of a logarithmic spiral and, given the right dimensions, it should be a good fit.
These expanding spirals pop up all over the natural world; you can spot them in patterns of seeds in a sunflower, in spiralling galaxies, in the bands of rain and thunderstorms that swirl around the eye of a tropical cyclone, and in the path taken by a doomed moth as it flies mesmerised towards a candle. All these spirals are subtly different; what unites them is the fact that they all get bigger at a constant rate. In other words, the gaps between successive coils get wider by the same amount each time the spiral makes a complete turn around its central point. This means that no matter how big the spiral becomes, its overall shape doesn’t change – and that is one of the key rules for making a seashell.
The way molluscs make shells is reminiscent of the ancient practice of coiling pottery. For thousands of years, people around the world have rolled strips of clay between their hands and coiled them into simple pots. In a similar way, a mollusc creates its shell as a hollow tube. The mantle (the fleshy cloak that spreads across a mollusc’s body) lays down new shell only at this open end, known as the aperture. It does so by first secreting a scaffold of protein, which is then shored up with calcium carbonate in one of two varieties (and sometimes both): aragonite or calcite, the latter being a more stable form. The main building blocks for the shell are carbonate ions, consumed in the mollusc’s diet or absorbed from seawater, and squeezed into a small gap between the mantle and the growing edge of the shell. Finally a layer of nacre, or mother-of-pearl, is added on the inside, creating a smooth layer that protects the mollusc’s soft body. As this composite tube grows it becomes wider at the open end, transforming it into a cone. The mollusc scrolls this cone round and round, forming, in cross-section, a logarithmic spiral.
Before we go any further, I should point out that molluscs are not mathematicians. They aren’t aware of the arithmetical elegance of their homes. These patterns simply emerge from the way they grow. You could do the same thing with a tube of toothpaste, albeit a modified version in which the opening can be made wider as you go, so that it produces an expanding cone of minty freshness. Squeeze a coil of toothpaste onto a flat surface and you should see a seashell-like twist appear (our toothpaste coils are solid, unlike the molluscs’ hollow shells). Various different types of toothpaste shell will be made depending on how hard you squeeze and how quickly you move your hand away from the centre of coiling. You can make tightly coiled shapes or expansive ones that veer off and swiftly become enormous. However, keeping the toothpaste on a flat surface limits the types of shell you can make. As you’ve no doubt noticed, mollusc shells are not generally flat: most of them explore a third dimension.
‘The problem is one not of plane but of solid geometry,’ wrote Sir D’Arcy Wentworth Thompson in his classic On Growth and Form, as he began to grapple with the idea of three-dimensional seashells. While the First World War raged, the professor from St Andrew’s University in Scotland wrote more than a thousand pages packed with his ideas of how mathematics could explain shapes in nature, from horns and honeycombs, beaks and claws, to dolphins’ teeth and the shape of a splash. Thompson brought together many of his predecessors’ theories about the geometry of shells, including those of Sir Christopher Wren, who mused on their architectural beauty. Some earlier shell thinkers rejected the idea of logarithmic spirals, saying they were too simplistic, but Thompson underlined their importance and brought out lots of new examples of shells that were a good fit to this expanding curve. He then set out to find a way of drawing accurate three-dimensional model shells. His central idea was that coiled shells follow a set of rigid mathematical laws, which all stem from the fact that infant shells are simply smaller versions of their future, grown-up selves.
Molluscs only ever make a single shell, but it’s one they’ll never grow out of. Other creatures with hard exoskeletons tend to do things differently. Crabs, lobsters and all their crustacean relatives break out of their shells every now and then, cast them aside and grow a new version, one size bigger and sometimes in a wildly different shape from the one that came before. Turtles make their shells on the inside by modifying bones in their ribs and pelvis. By contrast, molluscs make their shells on the outside, and they hold on to them. They are among the few animals on the planet that wander around carrying with them the same body armour they had as babies; the pointy tip or innermost whorl is the mollusc’s juvenile shell. Day by day, the mollusc shell slowly expands, making room for the soft animal growing inside.
Thompson visualised the growth of a spiral shell as a two-dimensional shape spinning through three-dimensional space around a central axis; if you imagine poking a needle through a coiling seashell from the tip towards the open end, so that it rotates like a spinning top, then the needle takes the position of the axis. Our toothpaste shells stayed in the same flat plane and didn’t make much use of that axis. Now, imagine what happens if the toothpaste sets solid straight from the tube. You can drop the spiral downwards, along that vertical axis, and create a three-dimensional coiling shell.
Taking this idea (although using paper and pen rather than quick-setting toothpaste), Thompson devised a shell-making model based on four rules: first, the cross-section of the coil must stay the same shape, but grow bigger over time (in other words, slice across our expanding toothpaste cone at any point and you will see the same shape, in this case probably a circle); second, the shell’s curve expands from the centre at a fixed rate (making it logarithmic); third, the amount of overlap between successive whorls stays the same; finally, and most difficult to visualise (so don’t worry too much), the angle between the spinning whorls and the central axis also remains the same.
These four rules were all Thompson thought were needed to draw any version of a coiling seashell. But what would all those shells look like? That was the question asked by another scientist who, 40 years later, was inspired to customise Thompson’s model and use it to create a shell collection like no other.
The imaginary museum of all possible shells
Standing in the corner of a huge room, you see white walls stretching out in front of you and towering upwards, disappearing as if into the clouds. Suspended in the room’s cavernous space are what at first glance seem to be thousands of glass light bulbs. They dangle in neat rows and columns, beginning just above the floor and reaching up way above your head. Take a closer look and you’ll notice that they aren’t in fact light bulbs but intricate models of seashells.
Despite their glassy appearance, these shells are quite tough and you can push through them without breaking them. As you do you see that the shells differ subtly from one to the next. As you look upwards, the shells gradually become squatter and fatter. Walk forwards and the shells at eye-height flatten out until they are no longer coiled but more flattened, like clams. Stroll on through the museum of all possible shells and you’ll spot both familiar shells and some less familiar shapes.
The architect behind this imaginary museum is palaeontologist David Raup, from Johns Hopkins University in Maryland. In the 1960s he took Thompson’s shell-making model and made a series of adjustments, replacing the original rules with four of his own.
First, Raup defined the rate at which a shell flares outwards. This is the whorl expansion rate, or ‘W’: tightly coiled shells have lower W values compared to more flared, open shells. Clams and other bivalves have such high W values that they flare right open before having a chance to do much coiling. They may not look it but, in essence, bivalve shells are still spirals.
W: Whorl expansion rate (becoming more clam-like).
Next comes ‘T’, a factor that determines how tall the shell will be (the T in fact stands for Translation, meaning how much the growing spiral travels along its central axis, but it could just as easily mean Tall). In shells with a tall spire, the coil creeps downwards along the axis as it spins round and round. The further it creeps, the taller the shell spire and the greater the value of T.
Raup kept one of Thompson’s rules. He admitted that in the real world, the cross-section of a shell’s growing cone can change, but to keep things simple Raup fixed his shape and made it a circle. He allowed the circle to get bigger as a shell grows but it always stayed the same shape.
T: Translation rate (getting taller).
D: Distance from axis (becoming more wormy).
The final part of Raup’s model is the distance ‘D’ from the whorls to the axis. Adjusting the value of D can produce thin, wormy shells with big gaps between whorls, or chubbier shapes in which the whorls touch or even squash into each other.
Armed with his new idea for plotting shell shapes, Raup did something unusual for a palaeontologist at the time: he used a computer. He bought himself time at the helm of the fastest one available. The enormous mainframe IBM 7090 was a state-of-the-art scientific computer that was intended for the design of missiles, nuclear reactors and supersonic aircraft, but for a short time Raup channelled its power into making shells. He plugged in a few combinations of values for T, W and D and programmed the computer to draw the corresponding shells on a Calcomp x-y plotter. The computer’s output was a series of dots outlining several shells in cross-section, which were then interpreted into three dimensions by an artist. These drawings appeared in Raup’s 1962 paper in the journal Science. To make more of these scatter plots would have taken way too long and been too expensive on computer time. Raup knew that the available technology was limiting his work.
His next step was to team up with an electrical engineer, Arnold Michelson, and together they tried a more affordable set-up, the PACE TR-10 analogue computer (which despite its gargantuan size was one of the earliest desktop computers, although presumably only for a rather large desk). They plugged in a wide range of values for T, D and W from Raup’s shell model, hooked the computer up to an oscilloscope that traced the shapes of shells as fast-moving circles across the screen, then stood back and watched.
Unfolding before their eyes was a stunning collection of shells that looked like thousands of tiny X-rays. Among the PACE TR-10 output were examples of just about every type of shell, from the nautilus through to all sorts of coiled snails and even flattened clams and scallops. Their findings were so stunning that one of their virtual shells made it to the front cover of Science. Raup and Michelson had shown that from a simple set of rules emerges the great complexity of real shells. And their imaginary shell collection contained plenty more besides. Once they had traced out the shapes of all these shells, Raup turned his attention to the next big question: which of these shells can be seen in the real world?
Back inside the virtual museum of glass seashells, we can now understand how things are arranged: along one wall the thin, wormy shells become chubbier, as values for D shift from zero to one; in another direction the shells become gradually taller, as the values for T start at zero and run along to four; and from ceiling to floor, shells have progressively higher W values, from one to a million, and snails morph into clams. The glass shells are versions of the output from Raup and Michelson’s PACE TR-10 computer program of all possible shells.
Now something changes in our museum. The main lights are dimmed and individual glass shells, here and there, begin to glow (funnily enough, like light bulbs). These are the models that closely resemble real shells, living or extinct. And as parts of the room light up, something becomes obvious: large regions of the museum remain in darkness.
I illuminated the real species among our glass shell models and Raup did a similar thing on paper. He plotted a graph with three axes (for D, T and W) and shaded in areas where real mollusc shells can be found, as well as the brachiopods, which are only distantly related to molluscs but even so make similar shells. Drawing in the boundaries of reality onto his imaginary shell museum, Raup immediately saw that only a small fraction of his theoretical shells have ever actually evolved. Substantial regions seem to be out of bounds. He theorised that some of the empty space in his museum was filled with ‘bad’ shells that, in reality, don’t work. Maybe they would be too heavy or too weak, or would leave their inhabitants in some way vulnerable to attack? There is an empty region filled with shells that suffer from what Raup referred to as the ‘problem of bivalveness’. Clams, mussels and scallops would be permanently clamped shut if their gentle whorls overlapped (the only option for opening up would be to build a new hinge on the outside and keep moving it as the mollusc grows bigger, and bivalves in the real world don’t do this).
Other parts of the museum were empty, Raup suggested, simply because the process of natural selection hasn’t got around to filling them yet. He thought that as soon as a situation arises in which those theoretical shells become useful and confer an advantage on their owners, then, sure enough, they will evolve. Other researchers disagree. They think the vacant spaces of the museum will never be filled, because the necessary genetic mutations to make those shells haven’t happened and maybe never will. Their view is that natural selection doesn’t have at its disposal all the genetic variation that is necessary to fill every part of the imaginary museum. Debates still rage over who is right.
Following on from Raup’s original concept, many other museums of possible creatures have been built (they are now known technically as theoretical morphospaces). There are museums for beetles, aquarium tanks for fish, sea urchins and phytoplankton, even a herbarium for plants and aviaries for birds and pterosaurs. Just like the shell museum, these rambling spaces are filled with both real and imaginary beasts, and they are encouraging biologists to think about which forms and shapes in nature are possible and popular, and which are impossible or for some other reason have never occurred or will never occur.
Throughout his papers, Raup was always careful to point out that his model isn’t perfect, and it doesn’t account for all the things we see in the real world. For one thing, he confessed to being overly simplistic about fixing the various shell dimensions throughout a mollusc’s lifespan; there are real shells that seem to shift the values of T, D and W over time, so they hop around the imaginary museum as they get older. And, as Clements and Liew found with their strange microsnails, there are some molluscs that break all the rules. One of the tiny snail species from the limestone hills of Malaysia makes a shell that spins around not just a single axis but four: the most of any known shell.
For the sake of simplicity, other features seen on many real shells are also omitted from the museum of all possible shells. For example, Raup left out the ornaments – spikes, knobbles, ribs and spines – that molluscs use to decorate their shells.
Why shape matters
Geerat ‘Gary’ Vermeij has probably spent more time than anyone else thinking about the shapes of seashells. Born and raised in the Netherlands, the first shells he encountered were what he describes as ‘drab chalky clams’ on windswept North Sea beaches. Then, in 1955, his family moved to Dover, New Jersey, where Vermeij experienced something of an epiphany. His fourth-grade teacher, Mrs Colberg, decorated the classroom windowsills with dozens of shells she had gathered during holidays to southern Florida’s tropical shores. They were nothing like the shells Vermeij had got to know in Europe, being elegantly sculpted and covered in prickles and bumps. Her cowrie and olive shells were so shiny he was sure someone had varnished them. When a classmate brought shells from the Philippines to ‘show and tell’, Vermeij saw these were even more exotic and enthralling. He resolved to begin collecting his own shells and to find out as much as he could about them.
A decade or so later, Vermeij graduated with a Ph.D from Yale University, and since the 1980s has been Professor of Paleoecology at the University of California, Davis. It became his lifelong passion to understand how and why shells grow in so many different forms throughout space and time. He has travelled the world exploring the coasts and seashells of nearly every continent, and published more than a hundred scientific papers and four books about shells and evolution. And, since the age of three, Gary Vermeij has been blind.
Using his finely tuned sense of touch, Vermeij studies shells by turning them over and over in his hands, feeling their intricate shape and noticing details that other people miss. In his book A Natural History of Shells, he writes about how his hands have allowed him to explore the way shells from different places vary in appearance: the geography of shape.
He describes how the shells he finds on tropical shores are radically different from those on Dutch beaches. For starters, they are much more carefully made. Individuals from the same species of tropical mollusc will make shells that are identical copies of each other. They stick closely to a set of hidden rules, imposed perhaps by the presence of so many predators and competitors. Slightly wonky shells just won’t cut it in the race for survival in these crowded, species-rich waters; they might not be strong enough, or well protected enough from attack. In cooler and deeper waters, where life in many ways is more relaxed and less extreme, molluscs can get away with being less finicky about their shells. On the whole, away from the tropics, molluscs are built relatively sloppily.
Vermeij also writes in his book about another key moment in his life, when a big idea hit him. He spent the summer of 1970 in the western Pacific Ocean, on the island of Guam, on a field trip with his friend Lucius G. Eldredge. On one particular day they were searching for shells in the falling tide at Togcha Bay on the windy side of the island when Eldredge (known as Lu) handed Vermeij the shell of a Money Cowrie with its top sliced clean off. Lu made an offhand remark that he often saw crabs cutting open cowries in his aquarium tanks.
Until then, Vermeij hadn’t paid much attention to the fact that he often found masses of broken shell pieces on tropical beaches and he suddenly got to thinking about predation. He realised that tropical seashells have a really hard time with so many predators trying their best to crack, smash, peel open and drill into them. He began to wonder how their shells have evolved to ward off these attacks, and soon realised there are many reasons why shape matters.
An obvious way a mollusc can avoid getting eaten is by making a very big, thick shell, but that comes at the cost of having to make and then drag around a massive, heavy lump. A more economical way to make a shell more difficult to handle and swallow is to give it a covering of spines and bumps. Realising this, Vermeij finally understood why Mrs Colberg’s Floridian shells, and so many other tropical species, have fancy ornaments. In the crowded tropics, molluscs are doing their best to survive. As they grow, they can add embellishments to their shells; prongs can be added at regular intervals, or they can form a dense tangle like the quills of a porcupine. Spondylus, for example, the thorny oysters, are industrious spine-makers, expertly producing new ones and fixing any that have broken at a rate of a few millimetres every day.
Vermeij also figured that the pleats and corrugations on many tropical shells are a cost-effective way of creating a strong body armour that’s difficult to break into while keeping the weight down. Thickening and flaring out the aperture of shells is another way of deterring predators, as in the Malaysian microsnails with their trumpet-shaped mouths.
Shape can also help shells to hide. Sleekly shaped molluscs can slip silently through the water without sending out telltale ripples that predators detect; being more hydrodynamic also allows for a quicker getaway. We can surmise that parts of Raup’s imaginary museum may remain empty of real shells simply because they are not streamlined enough.
For shells that live in sandy, muddy places, shape can mean the difference between resting on top and sinking in. Epifaunal species are ones that have adapted to a life of lying on the surface of the seabed; their shells are often wide and flat, acting like snow shoes. They include species like the Big Ear Radix, a gastropod that lives in lakes across Europe; throughout their lives they continually expand a winglike flap on their shells that prevents them from sinking into silty mud. Another strategy used by epifaunal species is what Vermeij describes as the ‘iceberg habit’. Instead of lying on the surface they allow themselves to sink in slightly so that most, but not all, of the shell is submerged. Scallops commonly have a curved lower shell that sticks a short way into the mud.
Shape also matters for infaunal species, those that spend their lives burrowed down into mud and sand. Among the sea snails and bivalves there are champion diggers that use their feet as spades to bury themselves completely in under a second. Some have tiny ratchets on their shells to prevent them slipping backwards, and others have smooth whorls to make sure sand and mud don’t stick to them and increase the load.
Burrowing shells face the additional problem of being unearthed. If you’ve ever stood barefoot in lapping waves on a sandy beach, you may have noticed the sand being scoured from around your toes. When waves and currents flow around a solid object they stir sand grains into suspension and whisk them off elsewhere. To overcome this, burrowing shells evolved spines and ribs that trap sand particles and stabilise the sediments around them. A group of typical diggers are tower shells, which look like little unicorn horns; their sculpted whorls help to hold them in place in their sandy, muddy homes and reduce the chances of being swept away.
Back inside Raup’s imaginary museum of all shells, there is another perplexing detail that needs explaining: all the coiling shells twirl in the same direction. Suspended from their wires, the glass models have their tips pointing downwards and their apertures all open to the right. Or, seen from the top, they coil in a clockwise direction. Raup could easily have filled his museum with shells that twist the other way, or perhaps made two giant rooms that were mirror images of each other. But he didn’t, and for good reason.
Take a look at any real, spiralling shell and see which way it turns. Go and find that seashell sitting on a bookcase, or pick up a snail from your garden or local park; your shell almost certainly coils to the right. There is a smattering of species that always coil to the left, and occasionally sinistral oddities will occur in a right-coiling species, but currently the natural world favours righties over lefties. More than nine out of ten coiled shells today are dextral (curiously, a similar proportion of people are right-handed).
Shell collectors go crazy for rare sinistral specimens, so much so that over the years clandestine trades have prospered in fake lefties. Some are right-coiling shells that have undergone a bizarre molluscan version of plastic surgery, with some bits cut off and others glued back on; X-rays show their insides are in fact dextral. There are also true left-coiling shells that masquerade as something more special. Around the world, Hindus and Buddhists are summoned to prayer by the call of sacred conch-shell trumpets, known as shankh in Sanskrit. These are made from a large species of Indian Ocean gastropod, known in English as a chank shell, which normally coils to the right. Rare left-coiling specimens are highly revered, and are referred to variously as dakshinavarti shankh or sri lakshmi shankh. Their anticlockwise whorls are said to mirror the passage of the stars and sun across the heavens, and the curly hair and twisting bellybutton of the Buddha. Unscrupulous shell-traders make counterfeit sri lakshmi shankh shells from a different species, the Lightning Whelk, which lives in the Gulf of Mexico and normally coils to the left.
A famous left-handed shell was drawn by Rembrandt. He portrayed a Marbled Cone Snail which, like most of the poisonous cone snails, naturally coils to the right. Art historians speculate that Rembrandt hadn’t made a mistake, as many early shell illustrators did. Failing to appreciate the significance of coiling direction, artists would commonly etch what they saw into metal plates; their shells would then become reversed as mirror images in the printing process. In Rembrandt’s case, though, it’s thought he reversed his shell on purpose, for aesthetic reasons: he just felt it looked better that way. Pleasingly, other artists who copied Rembrandt’s cone did so directly and faithfully, without thinking to reverse the etching, so these printed shells were restored to their rightful place as right-coilers.
The abundance of right-coiling shells in the natural world, and lack of left-coilers, comes down to one simple but inescapable truth: if right- and left-coiling snails try to mate, their genitals don’t match. Not only are shells coiled one way or another but the rest of the snail’s body is also asymmetrical. Female snails have a genital pore offset to one side into which a male will inject sperm through his penis. Most gastropods in the oceans have separate sexes – they are shes and hes; land snails are commonly hermaphrodites, each one with both bits of equipment, but they will pair up and take turns being male and female. Face-to-face is a popular position for snail sex, and for this to work it’s crucial for the female pore and male penis to overlap: this only happens if both snails coil in the same direction (a little like when you go to shake someone’s hand – it only works if you both offer the same hand). The shells and bodies of left- and right-coiling species are mirror images of each other. Even the corkscrew-shaped penis of the Asian Trampsnail twists the other way in lefties, and the choreography of their circular mating dances is reversed. In a tryst between right- and left-coiling snails, everyone is confused, and everything is in the wrong place.
To gauge just how much of a problem coiling direction is in mating molluscs, researchers place pairs of mismatched snails together in cosy containers. Roman Snails, known and eaten in France as escargots (and highly protected in England), are often used in these sorts of sex studies because most of them are right-coiling, but once in a while a lefty shows up. No matter how much the left-right partners are feeling in the mood, the slurp of a baby snail’s feet never issues from the mating cubicles.
An alternative mating tactic adopted by some snails is for one to clamber up from behind on the shell of the other. Similar snail-in-a-box studies show that shell climbers have more success in crossing the left-right divide than face-to-facers, but things are still rather awkward. Far fewer offspring will result from a right-left union than from snails paired up with same-shelled partners.
All of this means that for sinistral snails in a mostly dextral world, life can be lonely. It’s not that right-coiling shells are inherently any better than their left-coiling brethren, it’s really just a matter of chance. Whichever form is less abundant within a species will be less likely to find a matching mate and therefore not as successful at passing on its genes; this pushes a population towards one dominant coiling direction. It just happens that at the moment right-handed shells are most abundant and get the best chances to mate. But that hasn’t always been the case, and the fossil record shows that fashions can change, although exactly why this happens remains a mystery. In The Natural History of Shells, Vermeij describes the eight or nine ancient groups of cephalopods that, through time, evolved right- and left-coiling shells, with no particular inclination towards twisting one way or the other.
It is tempting to link the coiling of gastropod shells to the fact that when they are very young, their soft bodies also undergo a major twist. This process, torsion, is unique to the gastropods and involves all the major organs spinning around 180 degrees (clockwise in sinistral and anticlockwise in dextral shells). Among many things that move, the anus shifts to a new position above the mollusc’s head. Torsion is genetically determined, but a separate gene deals with shell coiling. It is an ancient gene, known as a nodal, that evolved long ago and today governs the asymmetry of many animals, including humans: we wear our hearts on the left thanks to the same gene that makes snails twist one way or the other.
Looking back into the fossil record, there are lineages of gastropods that over time have untwisted their shells, like limpets, until they look like conical Asian hats. In at least one group, molluscs have unwound their shells, then around 100 million years later, against all the odds, their descendants have coiled themselves back up again. These changes would have been driven by mutations in the coiling gene.
Given that a single mutation in an inherited nodal gene can switch a snail from being dextral to sinistral, all in one go, it raises the interesting possibility that a new species could instantly evolve. The mating struggles that take place between mismatched shells create exactly the kind of barrier that can subdivide populations and allow new species to split off, in this case leading to separate right- and left-coilers that can’t interbreed. And there are a few spots on the planet where having a rare sinistral shell can put a snail at a distinct advantage.
Satsuma snails live in the Ryukyu archipelago in southern Japan and a surprising number of them are left-coilers. It just so happens that these islands are also the realm of Iwasaki’s Snail-eating Snakes. A land-snail expert from Kyoto University, Masaki Hoso, studies these snails and has spent many hours watching what happens when a snake sneaks up on a target, sliding up silently and swiftly striking from behind. Because of the way their mouths are shaped, the snakes can grasp a shell with the upper jaw while plunging their teeth through the aperture and into the soft flesh inside – but only in right-coiling snails. When they try the same thing on left-coiling snails, the snake can’t get enough purchase and the shell pings off to safety. Snakes pose such a terrible threat for satsuma snails that when young dextral snails are attacked, they voluntarily amputate their feet (geckos do a similar thing, dropping their tails to confuse predators while they dash off and make their escape). Hoso has never spotted a sinistral satsuma resorting to such a risky escape strategy; they always hold on to their feet.
Mapping out the distribution of snails and snakes, Hoso found that left-coiling species of satsuma snails only occur in or near areas where there are also these fearsome reptilian predators. So it seems that avoiding the chomp of lopsided snake jaws gives the left-coiling snails the edge over right-coilers and as a consequence sinistral snails have flourished. Although it will probably be only a matter of time before the snakes likewise evolve to become left-handed.
When nature is allowed to play
The final flourish in the process of shell-making is where molluscs are at their most creative. As well as forming intricate shapes, shells are also decorated in elaborate patterns. There are few other animals that paint themselves in such a profusion of complex markings. With their spots, stripes, waves, zigzags and triangles you could perhaps assume molluscs are simply playing with their shells.
There are two strange things about the shell patterns. First, no one knows which pigments molluscs use to paint their shells. So far, only a broad group of organic molecules has been detected, including porphyrins and polyenes. The closest anyone has come to pinpointing an actual shell pigment is a carotenoid in the yellow rings of Money Cowries.
The second peculiar thing about seashell patterns is that often they go completely unseen. Many ornately painted bivalves and gastropods spend their lives hidden out of sight, burrowed in sand or mud. And there are some that grow a layer of protein (the periostracum) over the outside of their shell, often making them look like weedy rocks. What purpose, then, can there be for these shrouded shell patterns? Why should these highly decorated shells get all dressed up with nowhere to go?
For a long time, biologists assumed that shell patterns don’t really matter, one way or another. The assumption was that since their output is never seen, the processes that lay down intricate patterns in a snail’s shell had become unshackled from the strict forces of natural selection, and were essentially neutral – they had been left to wander around an art gallery of all possible patterns, without any rules telling them what they were allowed to do.
Exactly how and why such elaborate patterns evolve, with apparently no purpose, does seem at first to be a bizarre and inconvenient mystery, the sort of thing that creationists leap on as proof that it was God who made it so. But as scientists have unpicked the process that leads to these patterns, an explanation comes to light that makes sense without our having to wave a magic wand.
Shell patterns are so very diverse and complex that the idea of searching for a theory to explain how they’re all made seems foolhardy, to say the least. Undeterred, however, that’s exactly what some researchers have been trying to do for the last few decades. Just as mathematicians and palaeontologists have set out to describe shell shape, others have done the same for shell patterns.
Their general approach has been to think of these patterns as a form of space-time plot in two dimensions, rather like an inkjet printer. The printer nozzle squirts drops of ink onto a sheet of paper along a straight line and, likewise, the outer rim of a mollusc’s mantle secretes pigment into the growing edge of the shell. In both printing and shells, patterns are built up, line by line, as the paper passes through the printer or, much more slowly, as the shell is secreted. Running a finger from the top to the bottom of an inkjet-printed picture, or the pattern on a shell, you’re moving through time, from the part laid down first, and hence the oldest, down to the newest. For the printer, digital instructions come down a cable, or through the air, telling it which colours of ink to lay down and when. The question is, what form of instructions do molluscs have to guide them in laying down colours in their shells?
From the start, people tinkering with this question assumed that unlike a computerised printer, molluscs don’t carry an image of their complete patterns in their mind which they then break down and reconstruct line by line. Instead, the shell’s patterns could be assembled spontaneously at the mantle edge based on a series of relatively simple rules.
In the 1980s, Hans Meinhardt from the Max Planck Institute formulated a computer model that produced astonishing mimics of real shell patterns. Unlike David Raup, Meinhardt didn’t spend time thinking about all possible patterns, but was kept busy enough trying to recreate reality. He published a paper in 1987, followed by a book in 1995, The Algorithmic Beauty of Sea Shells, which comes with a CD of the MS-DOS program he developed so readers could have a go at decorating their own shells.
Meinhardt’s idea was that there could be substances wafting through the mantle that trigger cells to produce pigment. It doesn’t so much matter what those substances actually are (they could be hormones or some other form of messenger molecule). What mattered to Meinhardt was their effects; imagine that instead of pumping out drops of coloured ink, a desktop printer produces colourless substances that react with the paper – and each other – in different ways, creating colours and patterns. One of these substances is an activator that switches on pigment production. The activator also triggers the production of more of itself as well as another substance that acts as an inhibitor. Meinhardt predicted that there are antagonistic waves of these activators and inhibitors, chasing each other across the mollusc’s mantle edge, stimulating colourful patterns as the shell grows.
At the heart of Meinhardt’s model are two differential equations that define how these activator and inhibitor molecules move and interact (and if you like numbers you can find them in his book). By tweaking those equations, he was able to simulate the basic patterns seen in real shells, including all manner of stripes, spots and zigzags.
Stripes parallel to the shell opening are made when pigment production is turned on and off periodically. At first all the pigment cells are stimulated to produce a line of colour, then they are switched off; keep repeating this and stripes unfurl on the growing shell. For bands in the other direction, perpendicular to the shell opening, some pigment cells are switched permanently on and others are permanently off. Meinhardt simulated both of these stripes by altering the relative speeds of the activators and inhibitors in his model.
Diagonal stripes are formed by a process similar to the movement of an epidemic through a human population. A cell loaded with activator can infect neighbouring cells, which after a delay then go on to infect the next-door cells, and so on. This triggers a travelling wave across the array of cells. Interesting things begin to happen when pairs of travelling waves collide. One possibility is they will mutually annihilate each other, drawing a ‘V’. Or one wave can annihilate the other, then carry on as a single stripe. Alternatively, they bounce off each other and continue in the opposite direction, drawing an ‘X’ (although the waves actually cancel each other out, then immediately reignite and continue on their way).
Some travelling waves veer off in different directions while keeping their tails in touch, until suddenly both waves stop in their tracks, creating empty triangles. Waves rushing at each other can also either speed up or slow down, producing spots and teardrops. More involved adjustments to Meinhardt’s basic equations lead to more complex patterns, including undulating waves, empty triangles on a dark background and fractal patterns of triangles within triangles, known as the Sierpinski Sieve. All of these shapes and patterns are seen on real shells.
There is, however, one major problem with Meinhardt’s ideas: there is no evidence to show that any of this actually happens in mollusc shells. No one has ever found a single diffusing substance, no activator or inhibitor, to prove that his ideas are correct. As Meinhardt himself admits in his book, ‘Theory can only provide a shopping list of possible mechanisms.’
At around the same time that Meinhardt first published his diffusion model, another research group wrote a paper with an alternative explanation for shell patterns. Bard Ermentrout from the University of Pittsburgh, along with his colleagues George Oster from University of California, Berkeley and John Campbell from UCLA, showed that similar patterns could be created not by unseen substances diffusing around the mantle but via the firing of nerves.
It was Campbell who, in 1982, suggested that the pigment-producing cells in the mollusc’s mantle might be stimulated by nerve impulses, just like secretory cells in other animals. The team’s model was in effect very similar to Meinhardt’s; both simulate a process known as Local Activation with Lateral Inhibition, or LALI. In the 1950s, the great mathematician Alan Turing showed how LALI could work with diffusing molecules, the concept on which Meinhardt based his models. A neural version of this was originally described back in 1865 by Ernst Mach, to explain the optical illusion now known as Mach bands. This occurs when a row of stripes in different shades of the same colour appears to curve inwards from a flat page. This happens because nerves in the back of the eye are activated by the edge of a stripe and will inhibit neighbouring nerves, accentuating the boundary between two stripes. And in a similar way to Meinhardt’s diffusing substances, nerve signals can also activate or inhibit the production of pigments and their effect can sweep along, creating travelling waves and various other intricate patterns. Ermentrout and the team implied a very different mechanism to the diffusion model, but made very similar patterns.
The neural and diffusion models had something else in common: Ermentrout, Oster and Campbell also had no proof that their model was correct. Back then no one knew whether nerves do in fact control pigment production in mollusc shells. ‘At the time there was no evidence for it, it was just a good idea,’ George Oster told me when we chatted on the phone about making shell patterns. After their original paper came out, it would be another 20 years before Ermentrout and Oster published again on shells. When they did, they came closer than anyone ever has to formulating a unified theory that explains not only how seashells get their patterns, but also why they do it.
Decoding the mollusc diaries
If you could listen in on a mollusc’s thoughts, the chances are you wouldn’t hear anything especially profound because, strictly speaking, they are brainless (unless you’re eavesdropping on one of the super-intelligent octopuses, the smartest of all invertebrates). Nevertheless, their simple nervous systems could be responsible for creating the complex decorations that seep across their shells as they grow. The latest computer models that reconstruct shell patterns involve an intriguing new idea: molluscs have the ability to read the patterns on their shells, like the pages of a diary. In this way, patterns become memories etched across their shells.
Shell-making is an expensive business, in terms of getting both raw materials to build them and the energy to lay down new shell. As such, molluscs don’t make their shells continually, but in bursts, when they can afford to. Because of the stop-start nature of shell-making, it’s vital that molluscs continue construction in the correct orientation, otherwise they’d be all over the place. In their most recent studies, Ermentrout and Oster put forward the idea that shell patterns are a way for molluscs to remind themselves where they left off. This allows them to line up their mantle and continue sculpting their shell in the right places, keeping their intricate shape on track. If this idea is right, then it could be that shell patterns are not quite so useless after all.
Over the last few decades, evidence has been mounting to support the idea that shell-making in molluscs is under neural control. Electron microscopes reveal that mollusc mantles are filled with nerves. These connect back to paired clusters of densely tangled nerves, known as ganglia, that come as close as you will ever get to a general mollusc brain (the ganglia fuse to form a ring through which the oesophagus passes, which means that when a snail swallows, its food goes right through its mind). Nerves stimulate cells in the mantle to secrete new shell layers and, by controlling the amount and direction of material made, different shapes emerge. The mantle also has sensory nerves that seem capable of detecting existing patterns of pigment in the shell. It’s possible that each time a mollusc prepares to make more shell, it begins by licking its mantle over the edge of its shell to ‘taste’ the pattern already laid down. At the same time, nerves in the mantle could also be responsible for switching pigment production on and off.
Based on these ideas and using a revamped version of their 1980s equations, Ermentrout and Oster set out to build a new shell-making program, this time with the help of UC Berkeley grad student Alistair Boettiger. This model not only churned out complex two-dimensional patterns, but it wrapped them around three-dimensional models of shells. For the first time, a realistic mechanism had been formulated for growing shells and decorating them, using a single model.
Whether or not mollusc mantles can actually sense the colours on their shells remains unclear, and it’s a major challenge to study real shell-making because it happens so very slowly. A hint that this idea is right, though, comes from the way molluscs repair their shells. As Gary Vermeij knows only too well, in the real, dangerous world it’s easy for shells to get whacked, pinched by a crab claw or hurled against a rock. If they survive, molluscs will fix their shells and keep on growing. When a shell becomes damaged or part of it is chipped away, the pattern can get messed up with stripes knocked sideways or stopped in their tracks. But a short way down the line, the pattern usually recovers and continues as before. This suggests that molluscs can detect damage but take a little time to correct themselves. Boettiger’s computerised shells do exactly the same thing when inflicted with simulated injuries.
Chaos also features in this latest shell-making program – not that it is all a jumbled mess, but in the mathematical sense. Small changes in initial conditions produce different versions of the same pattern; a little bit of noise here and there makes a real difference. Ermentrout and Oster think this could be why shell patterns in nature can vary substantially between individuals of the same species. Rather than being identical, markings are commonly like human fingerprints, unique to each shell while still sharing similarities in overall pattern.
In 2012, Ermentrout and Oster used their neural model to look at how shell patterns evolve: if they could show that the way patterns change over time isn’t completely random, it would support their idea of patterns being useful to molluscs as a way to mark and read their shells. They gathered together a larger team of cell biologists and computer scientists, including Zhenqiang Gong from University of California, Berkeley, who constructed an even fancier computer programme, duplicating 19 species of cone snails that have complex patterns on their shells. The team mapped out a family tree based on the different shell patterns of living species, and used the model to reconstruct what the patterns would have looked like in ancestors further back in the cone snail lineage. They tracked how patterns may have changed over time, as species diverged and split apart. This suggested that some elements of the patterns remained relatively stable over long periods, while others have shifted quickly here and there.
To test the accuracy of their model, the team drew a second family tree, this time using DNA sequences from the cone snails. The match-up between the DNA and pattern-based family trees was striking, far closer than would be expected by chance alone.
All this backs up Ermentrout and Oster’s theory that shell patterns aren’t frivolous playthings but important registration markers for shell-making that have been subject to the forces of natural selection, and have evolved over time. It may not matter exactly what kind of patterns are made, as long as there is some way for a mollusc to figure out where to put its mantle before continuing to make more shell.
These latest models have undoubtedly taken us a major step closer to understanding how and why molluscs decorate their shells. At the same time, this area of research has cracked open a new window that could have a profound effect on broader reaches of science. The notion that molluscs may leave themselves messages across their shells, allowing them to track the past and make decisions about the future, could give neuroscientists vital clues about how more sophisticated nervous systems work. With this in mind, Ermentrout and Oster are moving on from gastropods and bivalves to work with brainier molluscs, the cephalopods, and in particular cuttlefish. At least that’s what the press release from their 2012 paper said. Both Ermentrout and Oster chuckle when I ask them about this. ‘We’ve talked about it a lot,’ Oster says. But the reality is that working with cuttlefish and the stunning patterns they display across their bodies is much more difficult than working with shells. Not only is funding for this sort of research hard to come by, but cuttlefish coloration is much more complex than shell-patterning. Ermentrout and Oster would have to turn their attention from patterns laid down over months to ones triggered in milliseconds. Cuttlefish (and octopuses too) are draped in a mantle that doesn’t secrete an external shell, but changes colour to camouflage them or to shout sexy messages to potential mates. These patterns are controlled by a similar network of nerves to those in shell-making molluscs, and, as George Oster points out, ‘there’s a lot of speculation, but nobody actually knows what the neural circuitry in cuttlefish skin is.’
Nevertheless, I get a strong sense that both of them would love to work with cuttlefish. ‘They can flash their colours like gang signs,’ Bard Ermentrout tells me. He spends each summer in Woods Hole on Cape Cod in Massachusetts, and clearly enjoys paying a visit to the Oceanography Institution to see the cuttlefish. ‘You’re not supposed to do this,’ he admits, ‘but if you put your hand in and touch them, the image of your finger remains on their skin for a few seconds. It’s really cool.’
If Ermentrout and Oster can find a way of working with cuttlefish, then perhaps by understanding how their networks of nerves create patterns of ‘thoughts’ across their skin, it could ultimately help reveal how human brains form memories, deep down where no one can see them.