The method Google uses to rank the importance of web pages can help identify the species whose extinction would most likely trigger an ecosystem’s collapse.
The same method Google uses to rank the importance of web pages can also help scientists identify the species whose extinction would most likely trigger an ecosystem’s collapse, according to new research by Howard Hughes Medical Institute (HHMI) scientists and their colleagues.
The scientists say their method provides a simple and elegant solution to ranking the importance of species in an ecosystem—from the species whose loss would cause the most damage to the one that would cause the least damage.
A species is important if important species rely on it for their survival.
Mercedes Pascual, an HHMI investigator at the University of Michigan, and Stefano Allesina at the University of Chicago published their work in the September 4, 2009, issue of PLoS Computational Biology.
In ecosystems, species are connected to each other in tangled networks of relationships known as food webs. Pascual, who is an expert in epidemiology and computational biology, studies the relationships and interdependence of species in these webs—or, as she puts it, “who eats whom.” To understand these relationships, she and her colleagues investigate the properties of both abstract and real-world networks. The work reported in the new paper emerged directly from a comparison of food webs to one of the most familiar real-world networks—the World Wide Web.
The idea for this strategy came to Allesina when he was working as a postdoctoral fellow in Pascual’s laboratory. One day, he read an article describing a key component of the algorithm that Google uses to rank the importance of web pages, which connect to one another through a network of hyperlinks. The algorithm is crucial to ensuring that top-ranked pages appear at the top of search results. Suddenly he realized that the same algorithm, which is known as PageRank, could be applied to food webs. “I saw that this would be perfect for what we were studying,” he says.
PageRank uses a circular approach to rank web pages. It rates a page as important if the page receives links from pages that also are rated as important. A clever application of linear algebra solves this circular problem by calculating what is called an eigenvector, which identifies the most important pages in the web.
In a food web, nutrients move from one species to another through feeding links. A species must receive enough food through these links if it is to survive. The analogy with PageRank, says Pascual, is that “a species is important if important species rely on it for their survival.”
But PageRank could not be applied directly to information about food webs without modification. Food webs lack the particular network structure that enables researchers to calculate an eigenvector—but Allesina solved that problem in two steps. All of the biomass in a food web originates from primary producers—like plants or bacteria—that draw matter and energy from the environment. Allesina gave the web the circular structure that it needed by creating an artificial species that links all of the organisms to the primary producers—representing the recycling of nutrients back into the food web after an organism dies. He also added a variable indicating at what rate members of the food web were eating one another. “What I liked about Stefano’s solution is that, to make this elegant algorithm work, he added something that made sense biologically,” Pascual says.
Previously, ecologists had developed other methods of assessing the importance of species in ecosystems. One method looks at the number of connections between a given species and other species. Species with a large number of connections are considered “keystones” or “hubs” in the network, with disproportionate influence on the health of an ecosystem. Another measure of species’ importance looks at their positions within networks. Species that mediate interactions between the densely connected center of a network and more peripheral species are assumed to be important.
Pascual and Allesina tested their algorithm against these other ways of measuring the importance of species, using both computer models and published data from 12 real ecosystems, such as the Chesapeake Bay and coral reefs. They also used a lengthy computational approach to estimate the best solution in both the model and real-world ecosystems. The new algorithm equaled or outperformed, often by substantial margins, all of the other methods. “We were a bit surprised when it did as well as a heavily computational approach,” says Pascual. “And the beauty of this algorithm is that you can get an answer in one computation.”
As an additional benefit, the algorithm automatically estimates the amount of biomass flowing through each species in a food web. Ecologists can use this information, along with the ranking of species’ importance, to “predict which species’ losses might cause the greatest damage to the integrity of an ecosystem,” Pascual says.
The algorithm considers only the presence or absence of links between species, not the way the abundance of species might change dynamically as ecosystems are disrupted, so Pascual cautions that the effects of ecosystem disruption may be even worse than the ones predicted. “Additional extinctions could result, on top of the ones considered here,” she says. For example, if the numbers of a species get too low, a predator species may not be able to find enough of its prey to eat.
Pascual and Allesina also note in their paper that PageRank can be used to analyze other biological networks, such as metabolic networks within cells or interactions of cells within organisms. The challenge will be to adapt the algorithm in each case to yield a solution, but “our work shows that this is doable if you think of biologically sensible ways to satisfy the algorithm’s requirements.”