杏吧原创

Under the bed? Behind the cushions? In a forgotten pocket? Searching for lost keys usually feels like a random hunt 鈥� or so you might think. While frantically overturning household items might seem a pot-luck approach, it now appears that the apparently chaotic way we look for things could in fact reflect a method perfected by our hunter-gatherer ancestors over millennia of evolution.

Not only could this realisation shed new light on human migration patterns and the spread of disease, it might also suggest new ways of planning towns and searching for archaeological remains, and even help explain why shops that force you along a prescribed route can be so maddening (see 鈥淚kea rage鈥�).

Searching has always been crucial to human survival. Hunter-gatherers had to be good at searching to find food and water. What鈥檚 more, their movement had knock-on effects on many phenomena, such as the spread of populations, the advance of disease and the emergence of civilisations. So modelling the migration of ancient hunter-gatherer communities helps us understand all these things.

Traditionally, scientists have assumed that ancient peoples moved from place to place in a random way. They based their models on a description of random movement borrowed from physics, called Brownian motion, which can accurately describe many different diffusion situations, such as the movement of ink blotting through paper, smoke in the air or pollen grains floating on the surface of a pond.

In Brownian motion the probability of taking a step of a particular length follows what statisticians call a normal distribution, meaning that there is a higher probability that the particle will take short to medium length steps and a much lower probability that it will take very long steps. Although no one had proved that ancient tribes moved in this way, no one had disproved it either, and it was widely accepted. The same was assumed to hold for the way animals and insects forage for food.

However, in recent years several papers have appeared describing how many animals 鈥� including bumblebees, albatrosses, jackals, reindeer, spider monkeys and even zooplankton 鈥� don鈥檛 forage in a Brownian pattern at all (www.newscientist.com/article/dn7419). It turns out their movement matches a model mathematicians call a L茅vy flight, named after French mathematician Paul L茅vy. This describes a special kind of random motion comprised of short jumps that cluster in a small area interspersed with long leaps to a new area (see Diagram).

In a L茅vy flight, the probability of taking a step of a particular length follows a power law distribution, meaning that very short steps and very long steps are more likely than in Brownian motion, and medium length steps are less likely.

L茅vy flights are the optimum way of foraging for food in the natural world, says Bruce West, a physicist at the Army Research Office in North Carolina, who studies L茅vy flight patterns in the natural world. 鈥淎 L茅vy flight strategy means you avoid going back to the places that are depleted of resources.鈥�

Clifford Brown, an archaeologist from Florida Atlantic University at Boca Raton, noticed these revelations and wondered if they might apply to humans too. Brown has a long-standing interest in fractal patterns that occur in nature and had come across L茅vy flights before in connection with natural fractal phenomena. To discover whether L茅vy flights held for human migration, he decided to return to first principles and began searching for concrete data on human movement.

Stalking the evidence

No empirical data exists on the movement of ancient hunter-gatherer tribes, so Brown chose something nearly as good: a set of intimately detailed records of the movements of one of the world鈥檚 few remaining hunter-gatherer tribes, the Dobe Ju/鈥檋oansi Bushmen (also known as the !Kung). The Bushmen have inhabited the Dobe area of the Kalahari desert, straddling the border of Namibia and Botswana, for thousands of years. Although most have now resettled, up until the late 1960s they lived in the traditional way, supplying as much as 85 per cent of their diet from hunting and gathering.

In 1968 John Yellen, an anthropologist at the Smithsonian Institution in Washington DC, spent six months living with the Ju/鈥檋oansi, recording their lifestyle, how far they travelled and much time they spent in each place as they hunted and moved from camp to camp.

Brown used Yellen鈥檚 notes to piece together a map of how the Ju/鈥檋oansi had moved around. In just six months the tribe moved 37 times and set up 28 different camps. At first glance, the pattern of movements looked haphazard, with frantic searching for food and water in one area, followed by long treks to new places. But upon careful analysis Brown discovered a distinctive pattern behind their movement 鈥� sure enough, the probability distribution of the distance moved each time and the time spent in each camp fitted a L茅vy flight model almost perfectly. It looks like the Ju/鈥檋oansi moved in L茅vy steps because it brought some distinct advantage when searching for food, Brown says. So what might that be?

The Kalahari is a harsh environment where water and food are scarce. One of the most important food sources is the mongongo tree, whose nuts are a major source of nutrition. The trees tend to grow along the crests of ancient east-west sand-dunes, with water holes dotted about in between. Brown noticed the mongongo trees were distributed in tightly packed clusters separated by large areas devoid of the trees. The Ju/鈥檋oansi seem to have learned to move in a L茅vy flight pattern as a result of the distribution of this food resource, says Brown.

He also believes the Ju/鈥檋oansi were not the only people to have adopted L茅vy flights. 鈥淢any natural food resources are distributed in fractal patterns, such that exploiting them would tend to move people around in a L茅vy flight pattern,鈥� he says.

So if people moved in L茅vy flights when hunting and foraging, might they move in L茅vy flights when exploring? Brown thinks it certainly merits further investigation. Michael Rosenberg, a computational evolutionary biologist from Arizona State University in Tempe, agrees that it is time to rethink our old models of early human migration. 鈥淭his evidence provides us with justification to try L茅vy flight models,鈥� he says.

Already, other examples are emerging that support Brown鈥檚 observations. Marek Zvelebil, an archaeologist at the University of Sheffield in the UK, has analysed the advance of farming across Europe and noticed a pattern of motion that includes what he describes as 鈥渓eapfrogging鈥� from one region to another. This has led him to conclude that farming communities must have sent out pioneers to identify new areas to settle 鈥� rather than spreading out slowly from established territory as was previously assumed. He thinks a L茅vy flight might fit the spread of these peoples.

鈥淭he pot-luck approach to searching works amazingly well鈥�

Not everyone agrees that early farmers so closely match the hunter-gatherers, however. 鈥淔or hunter-gatherers it is not difficult to up sticks and move,鈥� says Graeme Ackland, a physicist at the University of Edinburgh, UK, who has been modelling the advance of farming populations. Ackland thinks it is unlikely these communities moved in the same way. His simulations used Brownian motion driven by population pressure to model how early agricultural peoples moved across Europe, and found they advanced at around 1 kilometre per year. Brown accepts that L茅vy flights may not be the answer to every kind of human movement. 鈥淚t may not apply if people have a different diet and distribution of resources,鈥� he concedes.

Puzzle solved?

All the same, L茅vy flights might explain one of the biggest migration puzzles of all time: how prehistoric native Americans settled the New World. Arriving over the Bering land bridge from Siberia to Alaska around 11,500 years ago, when sea levels were much lower, the so-called Clovis people radiated southwards, reaching the southern tip of South America in just 1000 years. They were a hunter-gatherer tribe living off mammoth and other game, which they hunted using distinctive fluted stone spear-points. No one has yet explained how and why these people travelled many thousands of kilometres in such a short time. 鈥淟茅vy flights give an explanation of how these people could have moved so fast,鈥� says Brown.

Meanwhile, Rosenberg thinks that the L茅vy flight model could even reveal the first steps of humankind. 鈥淚 think it would be interesting to see if it could help to explain some of the huge jumps that we see in the 鈥榦ut of Africa鈥� hypothesis of human evolution,鈥� he says.

And there are other conundrums that look like they might yield to a L茅vy flight explanation. For example, the spread of the hereditary disease sickle-cell anaemia through central Africa took just a few thousand years, much faster than the tens of thousands of years we would expect if it followed random Brownian motion. Sickle-cell anaemia is associated with the spread of malaria, which in turn is associated with the spread of farming. If sickle-cell anaemia spread fast, then both farming and malaria must have moved rapidly too. 鈥淟茅vy flight models could help us to describe this gene flow,鈥� says Henry Harpending, an anthropologist at the University of Utah in Salt Lake City who studies the migration of ancient African populations.

Could L茅vy flights still be influencing the way we live now? 鈥淚t鈥檚 certainly a possibility,鈥� says Brown. Others agree. Alan Penn, an architect from University College London, is applying this philosophy to the design of new towns and cities. Penn and his colleagues analysed the layout of city shops and showed that they tend to form a blotchy pattern resembling a L茅vy flight distribution. 鈥淪hops that are similar tend to group together. This means they compete, but they also attract the crowds,鈥� says Penn.

London is a perfect example of this. Tottenham Court Road is home to a cluster of electrical goods shops, Hatton Garden is the place for jewels, and Cork Street is where to go for fine art. In each of these areas there is a main street that acts like an artery carrying the flow of people, plus back streets where shoppers can poke around. On a smaller scale you can observe the same pattern in a market, with fruit and veg stalls in one corner, fish lining another alley and meat in yet another.

Penn created a computer model of a town into which he placed 鈥渁gents鈥� 鈥� representing people. The agents were programmed to search for goods by moving three steps at a time in a random direction within their field of view. If enough agents demanding a particular product congregated in one place, the computer would create a shop there selling what the agents wanted. Penn found that small clusters of similar shops would emerge over time. 鈥淚t seemed to help the agents be more efficient in finding the shops,鈥� he says. This implies that the layout of our towns and cities may well have been shaped by the search patterns we learned from our hunter-gatherer past.

Penn is now using his models to help urban planners rejuvenate ailing areas. One of his projects has been to help revitalise London鈥檚 South Bank cultural quarter, where he suggested introducing shortcuts between key locations and clustering sites of interest such as cafes, restaurants and books shops. Shops are easier to find if they are distributed in a pattern that mirrors the natural way we look for things, says Penn. He is also using these methods to help develop more pedestrian-friendly living areas in Milton Keynes, and other places in the south-east of England.

Brown plans to use his new understanding of L茅vy flights to help identify archaeologically interesting sites. 鈥淚n many parts of the world hunter-gatherers occupied the landscape for very long periods of time, but finding evidence of their campsites and movements is hard,鈥� he says. Conventional searches consist of choosing a region and then digging sample sites at equal intervals, which can be very expensive and time-consuming. Brown thinks that guiding the sampling according to a L茅vy flight pattern could cut costs and speed up search times. Ironically, the search patterns our long-lost ancestors bequeathed to us might be our best bet for rediscovering them.