Modified PageRank Helps Preserve Ecosystems
Ecosystems are huge networks of interconnecting parts, and it’s not always clear where efforts should be focused in order to preserve them. However, one researcher has come up with a plan: modify the powerful PageRank algorithm to find out which prey species are critical to the ecosystem’s success.
Conservational biologists have traditionally used an intensive algorithm to find the importance of prey species. To start it off, a prey species is taken out of the system, and the possible fitnesses of all the remaining species are calculated. The algorithm is run again on the most fit solutions, and this continues until a relatively stable ecosystem evolves. Although this approach is helpful in determining the magnitude of the effect of the removal of a prey species, it’s very time intensive for big food networks, which is why Allesina proposed a new solution involving PageRank.
Allesina’s solution uses the basic principle that if another animal eats you, then there is a pointer from that animal to you. The more pointers you have pointing at you, the more important you are as a prey species – just like how in our class a page had more importance if more pages pointed to it. Allesina also made sure to include one important detail to the network: detritus. In addition to the standard food web, he included a node for organisms that feed on droppings and carcasses. This ensured that the ecosystem networks didn’t have a collection of PageRank values in the upper level of the food webs (for example, the detritus would have a pointer to lions, and grass would have a pointer to detritus, therefore making the system less reducible). After the system is set up, the standard rules of PageRank apply: (1) For n organisms, give each organism a value of (1/n), (2) Each organism divides it’s current value by the number of outgoing pointers (what it eats), and then passes the divided value along the pointers, (3) Step 2 is repeated until every organism’s value remains constant after updates. The higher an organism’s final PageRank value, the more important it is to the ecosystem as a prey species.
Below are the first two updates of an over-simplified example:
The results of the PageRank formula are almost identical to results of the solution traditionally used by conservational biologists, proving that networks applications can be used across many different disciplines.
References:
http://www.nature.com/news/2008/080806/full/news.2008.1010.html