Discussion of “Googling Food Webs”: the use of PageRank like algorithms to analyze nutrient flow
A while ago our class discussed how PageRank is used by search engines to find reasonable answers to web-search queries. We discussed how PageRank “flows” down hyperlinks and eventually reaches an equilibrium, with pages that have greater “authority” receiving higher PageRank values than those of lesser “authority.” In a recent paper, two computational biologists, Stephano Allesina and Mercedes Pascual, applied an algorithm similar to Google’s PageRank to model nutrient flow in food webs (see PLoS Computational Biology’s September 2009 issue for the full article, entitled “Googling Food Webs: Can Eigenvector Measure Species’ Importance for Coextinction”). In their model, species took the place of webpages, and predator-prey relationships took the place of hyperlinks. Instead of PageRank, nutrients flowed down the network, and they hoped that those species with higher rates of nutrient flow would prove to be more important to the food web. Specifically, they wanted to know whether removing a species with a higher equilibrium nutrient flow rate would lead to greater rates of secondary extinction. They noted a couple key differences between their model and the standard PageRank model. Unlike in the PageRank model, the “authority” of a node was not determined by incoming links to that node, but rather by outgoing links – the more other species that a given species supports with the nutrients passing though it, the more important it is to the ecosystem. Another major difference between websites and food webs is that in food webs all nutrients originate in and are recycled to the external environment. They modeled this second difference by adding a “root” node which had directed edges pointing to all of the primary producers, and by adding directed edges pointing to the “root” node from every other node in the food web (see fig. 1).
fig. 1: 1a) Is a typical food web with trophic levels progressing from primary producers on bottom to secondary consumers on top. 1b) Is the same food web with a “root” node added representing the external environment, and dashed lines added to show recycling of nutrients back to the environment.
Allesina and Pascual ran a series of In-silico extinction experiments, comparing the PageRank-like algorithm to other algorithms, and discovered that the PageRank-like algorithm outperformed all the other algorithms, finding the species that, if removed, would lead to the most secondary extinctions eleven out of every twelve times. They also discovered that by removing redundant links in the food web they could make the PageRank-like algorithm find the most important species every time.
Simple graph-theory based algorithms such as PageRank are already immensely useful in finding the most important website out of many on the web. The use of such algorithms to find the most important species in an ecosystem may prove to be useful to government and other natural resource managers who must choose where to direct funding and man hours in protecting natural resources. The relatively simple PageRank algorithm has the added advantage of being entirely reliant on network structure, as opposed to actual flow from node to node. This means that natural resource managers do not need to do the difficult task of following nutrients through a food web, and instead need only to do the relatively easy task of finding out who eats whom.
One thing which has yet to be done, to my knowledge, with this PageRank-like algorithm is a field test. A removal experiment in a well controlled environment may help support, refine, or refute this simple model of ecosystem stability.