Neo Martinez' Home Page

The weakest link
by Arran Frood

Published in The New Scientist 18 Aug 2001
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Kill off one species and the whole ecosystem could collapse. To stop it happening you'll need to work out who eats who-and that's the hard part, says Arran Frood

SAVING the world used to be the job of superheroes. But now, with millions of plant and animal species facing extinction, it's down to us mere mortals. Where do we begin? We don't even know how many species are out there. And even if we did, the numbers are meaningless until we know how the different species interact.

Collecting all this detail is a Herculean task. Yet without the detail, how can we know which human activities are most likely to have apocalyptic consequences, let alone work out ways to avoid them?

What we need is a way to make predictions based on the information we already have. But the fledgling science of ecology has struggled to describe the natural world, let alone understand it. Like early astronomers, ecologists are faced with a unique system that doesn't lend itself to scientific methods such as experimentation, replication or manipulation. However, just as stargazers learnt to predict eclipses and alignments of planets, ecologists are now starting to build models that can explain patterns in nature and help predict how ecosystems will react to change.

One pioneer of this approach to understanding biocomplexity is Neo Martinez from San Francisco State University in California. He has made a career of studying food webs-in other words, who eats who within any ecosystem. Charles Darwin once described such webs as intractable "tangled banks". But Martinez is starting to trace the strands that tie the beautiful mess together. He has come up with a way to discover how the animals and plants in a given community interact, without resorting to exhaustive observation and sampling. His computer models open the door to a better understanding of how specific extinctions affect biodiversity as a whole.

Martinez's breakthrough came when he noticed curious patterns in the links between trophic species in food webs. When it comes to understanding natural relationships, trophic species-groups of organisms that share the same predators-are more relevant than biological species. They also make up a much larger fraction of the biodiversity under scrutiny. Working at Little Rock Lake in Wisconsin, home to a notoriously complex food web containing 92 such species, Martinez discovered that each species was either prey for or preyed upon by 10 per cent of all the other species. He describes this in terms of "connectance"-the fraction of predator links actually present out of all those possible within a food web.

What's more, this percentage of links between species-the connectance-did not change as Martinez added new species to build up a detailed picture of the system. "The constant-connectance hypothesis asserts that a particular balance of food-web complexity exists in nature," he says. "This balance is between everything eating everything and everything eating nothing." And his trawl of the literature confirmed the pattern in a variety of complex ecosystems, from deserts and islands to estuaries and lakes. Ten per cent wasn't a magic number, but whatever the connectance within a given ecosystem, it remained curiously constant no matter how many new species were added to the food web.

No single ecological or biological theory could predict or explain such a pattern. What was going on? Martinez suspected the answer lay in the way new links are created when a species enters the system, whether by migration or evolution. To investigate what happens when a new species lands in the web, he teamed up with Richard Williams from San Francisco State University's Romberg Tiburon Center for Environmental Studies. Their mathematical model started with the notion that complex food webs arise from a simple pecking order. Then they added two rules. First, that species higher up in a fixed pecking order tend to eat those lower down. And secondly, that if an organism eats two species in a web then it must also eat all the intervening species in the hierarchy. So, for example, a shark that preys on large fish such as tuna and small fish including mackerel will also eat cod and any other medium-sized fish.

By including just two parameters in the model-the number of species in a given web and the connectance between these-Martinez and Williams can accurately predict 12 ecological characteristics of that web. These include the length of food chains, the number of omnivores and cannibals, the distribution of specialists-those with a restricted diet-and generalists-those that eat whatever's going-and perhaps most importantly from a conservation viewpoint, the vulnerability of various groups of species.

When it comes to predicting the way complex natural communities interact, this model is far superior to any other. "It was surprising to me, and I think most people, that a model with such a simple conceptual basis would do such a good job of predicting the properties of observed feeding networks," says Williams.

And a model that shows what's already there has obvious potential to forecast what might be. In any community of organisms, each species fits into its own niche. The niche model devised by Martinez and Williams is novel because it successfully predicts the niche any species will adopt in terms of its "connectedness" to other organisms in the system.

Using the niche model you can build virtual versions of real food webs and then see what happens when you simulate speciation or extinctions. "We can play games in the computer and see if species at the bottom of the food web are more important to maintaining diversity than those at the top. We can play similar games comparing specialists and generalists," says Martinez. The niche model could also show how pollutants such as DDT and PCBs accumulate in food webs of different sizes and complexities.

Martinez's approach has been well received. "He has made a huge effort in exploring the regularities displayed by ecological interactions," says Ricard Sole from the Santa Fe Institute in New Mexico. "His model with Williams will be a classic reference in ecology." This could be the leap that ecology has been waiting for. But in some ways, Martinez's thinking is quite conservative because he has natural selection as the driving force behind ecological patterns. Other students of biocomplexity are much more radical. They talk about food webs in the language of the physical sciences, explaining the complexities of nature in terms of "emergent properties" rather than biological principles.

Sole is one such thinker. Working with Jose Montoya of the Complex Systems Research group at the Polytechnic University of Catalonia, Barcelona, he claims to have found the "small worlds" phenomenon in food webs. Small worlds are big news among mathematicians and modellers trying to understand all sorts of complex networks from the Internet to the nervous system of worms. This is the science behind the folklore that there are no more than six degrees of separation between any two people, and that Kevin Bacon can be linked to any other movie actor in just a few moves (New Scientist, 4 December 1999, p 24).

In essence, a small world is any network containing many nodes that have a few links, together with a few nodes-or hubs-with many links. This arrangement, known as a power law distribution, greatly reduces the number of steps needed to link any two nodes compared with a completely regular network. The distribution of species in food webs fit the pattern, say Sole and Montoya, because most species are connected to a small proportion of others, while a few hub species have many connections. These "keystone species" have long been recognised by some ecologists as the linchpins of ecosystems, essential to the stability of the community.

Seeing food webs in this way has advantages, because networks exhibiting small-world phenomena show predictable responses to change. "The very topology of these networks plays a crucial role in how these systems behave," says Albert-László Barabási of the University of Notre Dame, Indiana. "Finding that food webs follow a power law distribution, just like we see for the cell, and the Internet, suggests that nature displays a high degree of
economy when it spins its various networks-it uses the same blueprint for most of them."

BarabÁsi's own work reveals that such complex systems have emergent properties-they are more than the sum of their parts, having properties that emerge from the network as a whole. He has found, for example, that the Internet is inherently stable and well protected against random removal of sites, because most have very few links, and only a concentrated attack could remove the rarer hubs and bring down a large part of the structure. "We have shown that these networks are highly robust against random node removal but fragile against concentrated attacks," says Barabási.

In a new study, Sole and Montoya found that food webs can tolerate random removal of species, but that directed removal of keystone species could bring about the collapse of the entire ecosystem. "Our analysis shows that removal of around 5 to 10 per cent, a small fraction of highly connected species, can lead to ecosystem collapse," says Sole.

The implications for conservation are obvious. A high level of close interconnection between organisms in a shared ecosystem means that biodiversity loss and species invasions may affect many more species than we had anticipated. "It might be the case that some human-driven perturbations could target some of the highly connected species, and thus eventually promote a cascade of extinctions through the system," says Sole. "If true, then current estimates of biodiversity loss might be much lower than we expected."

But can such a theoretical approach really help at ground level? Stuart Pimm, an ecologist and complexity theorist at the University of Tennessee in Knoxville believes it can. "Finding these broad-scale patterns is a fascinating insight into the way nature works, helping us to rethink old ideas," he says. Pimm says that modelling extinctions has revealed some original insights.
"Extinctions are caused by habitat destruction, introductions of new species and hunting. Secondary extinctions-when a species goes extinct because of the removal of a closely connected neighbour-are the last part of the deadly quartet." And, says Pimm, the modelling reveals that secondary extinctions are much more important than ecologists suspected.

In the real world, this means that many more species might need to be protected. On a positive note, small-worlds modelling could help ecologists identify those organisms whose continued existence is crucial to entire ecosystems. That way, conservationists have their best chance of preventing the runaway collapse of ecosystems through secondary extinctions. But we are running out of time. "The speed of species loss is, sadly, very fast," says Sole. "Many species with low populations are simply going down slowly but inevitably to their extinction."

Barabási is more optimistic. He believes that in the next few decades, biocomplexity will take centre stage. "We will learn more and more about the structure, origin and evolution of these systems," he says. "Eventually, we all hope that this will culminate in large-scale modelling, allowing us to develop the same mathematically rigorous framework for living systems that was so successful in the physical sciences."

A theory of everything?

"In the early nineties, there was great excitement about the possibility of formulating a general theory of complex systems," says Ricard Sole from the Santa Fe Institute in New Mexico. But there were some major gaps in the overall picture. Improvements in biocomplexity and network thinking have helped fill these. "A new wave of theoretical results is changing many of our previous ideas now, and the possibility of formulating a general theory of complexity seems much more feasible."

The discovery that real ecological networks share common traits with some other systems, both biological and technological, has important implications. It suggests that patterns in nature are not derived from biological processes alone. Distributions of species, the World Wide Web and metabolic networks all seem to show robust self-organisational phenomena. It is the global features of such webs that matter, not the individual characteristics of the units that make them up.

But while it is tempting to describe all systems along similar lines, the details in each discipline matter. And, Sole cautions, although many complex networks share common patterns, it is still unclear if, and how, similar dynamics shape their order and evolution. As a result, using complexity theory to come up with practical solutions such as conservation policy is still a daunting challenge.