how to count complicated food webs such as the one that comes up when you type in how many chains are in this web? also the title of it...

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Since this is not my area of expertise, I searched Google under the key words "count complicated food webs" to get these possible sources:

https://www.google.com/search?client=safari&rls=en&q=count+complicated+food+webs&ie=UTF-8&oe=UTF-8

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.

http://www.hackcollege.com/blog/2011/11/23/infographic-get-more-out-of-google.html