Googling for Extinction – Popular Algorithm Finds Food Webs' Critical Species

In the science of ecology, a network of inter-dependent, predator-prey relationships is known as a “food web”. For ecologists, one of the most crucial problems to solve is identifying the consequences (to the web, or ecosystem) when one species goes extinct. What’s more, certain species seem to be more critical in keeping these webs functioning; when they go extinct, they cause one or more co-extinctions. But due to these complexities, determining which species in a given web is the most critical (most likely to cause a cascade of extinctions) is very difficult.

And, it’s not like you can just “Google it”…Well, it is actually. More precisely, you’ll want to use Google’s Page Rank algorithm — after you’ve tweaked it a bit — as discovered by ecologists  Stefano Allesina and Mercedes Pascual.

Two ecologist discover that by adapting Google’s Page Rank algorithm they were able to “reverse engineer” the collapse of food webs, and thus determining which species in a given web are most critical to the web’s existence.

Publishing their results in the journal PLoS Computational Biology*, ecologists Stefano Allesina and Mercedes Pascua reveal their successful application of a modified “eigenvector” (a type of ranking algorithm) in determining which species’s extinction was most likely to cause the most number of co-extinctions, and thus critically damaging, or even collapsing, the entire food web.

The extinction area is the area described by the area below the curves.
(above) The area can take values from 1/2 (no secondary extinctions in response to the removal of species) to 1.0 (all species go extinct after the first removal). The x axis represents the fraction of species removed in the numerical experiment, while the y axis is the fraction of species that are extinct as the result of these removals. The example uses the St. Mark’s food web and the D (red) and EIG (blue) algorithm.

Their modified algorithm (based on what Google uses to rank web pages), termed the EIG algorithm, permitted the researchers to order species according to their importance for co-extinctions, providing “the sequence of losses that result in the fastest collapse of the network.”

There are many models used to predict food web and ecosystem interactions and extinctions, but this new approach identifies the subset of co-extinctions that is common to “all possible models”, that is, those extinctions that will happen, with certainty, given the loss of a prey species of any given predator species.

Modification of food webs from ecological considerations to satisfy the two constraints required for application of the EIG algorithm
(above) A special node is added to the food web by connecting this “root” to the primary producers. Every species in turn connects to the root to represent the buildup of detritus (dashed line). (Right) The analysis can be improved by removing the “redundant” connections that do not contribute to robustness (dashed, in red).

Further, while their model is also based upon network structure, it is more accurate in identifying extinction sequences than previous models wherein species importance was based upon “hubs”, or the number of connections.  They also found that their algorithm out-performed a genetic algorithm (also adapted for ecological analysis) capable of processing millions of sequences.

While there are many links in a food web, not all such links contribute to the robustness of that web. The adapted EIG algorithm simply finds the most efficient route to system collapse.  Concluding their findings, the scientists assert: “The algorithm works in this sense better than all the others previously proposed and lays the foundation for a complete analysis of extinction risk in ecosystems.

This modified algorithm will become an increasingly important tool in the years ahead as scientists and environmental policy experts seek to identify areas of greatest concern for funding of research and ecological preservation and restoration.

* ‘Googling Food Webs: Can an Eigenvector Measure Species’ Importance for Coextinctions?’, Stefano Allesina1, Mercedes Pascual, PLoS Computational Biology, Sept. 4, 2009

Top diagram: Diagram showing aquatic and terrestrial food webs; Creative Commons CC0 waiver.

Middle chart: Allesina, Pascual – under a Creative Commons Attribution License.

Bottom chart: Allesina, Pascual, under a Creative Commons Attribution License.

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