Rock-paper-scissors tournaments explain ecological diversity

Mar 14, 2011

According to classical ecology, when two species compete for the same resource, eventually the more successful species will win out while the other will go extinct. But that rule cannot explain systems such as the Amazon, where thousands of tree species occupy similar ecological niches.

The childhood game of rock-paper-scissors provides one solution to this puzzle, report researchers at the University of Chicago and the University of California, Santa Barbara in . A designed around the game's dynamics produced the potential for limitless biodiversity, and suggested some surprising new ecological rules.

"If you have two competitors and one is better, eventually one of the two will be driven extinct," said co-author Stefano Allesina, PhD, assistant professor of ecology and at the University of Chicago. "But if you have three or more competitors and you use this rock-paper-scissor model, you can prove that many of these species can co-exist forever."

The rock-paper-scissors rules are an example of an "intransitive" competition, where the participants cannot be simply ordered from best to worst. When placed in pairs, winners and losers emerge: rock beats scissors, paper beats rock, and scissors beat paper. But when all three strategies compete, an impasse is reached where no one element is the undisputed winner.

In nature, this kind of rock-paper-scissors relationship has been observed for three-species groups of bacteria and . But scientists had not yet studied how more complex intransitive relationships with more than three players – think rock-paper-scissors-dynamite, and beyond – could model the more complex ecosystems.

"No one had pushed it to the limit and said, instead of three species, what happens if you have 4,000? Nobody knew how," Allesina said. "What we were able to do is build the mathematical framework in which you can find out what will happen with any number of species."

Allesina and co-author Jonathan Levine, PhD, professor of , evolution & marine biology at UCSB, combined the advanced mathematics of game theory, graph theory, and dynamical systems to simulate the outcome when different numbers of species compete for various amounts of "limiting factors" with variable success. An example, Allesina said, is a group of competing for multiple resources such as nitrogen, phosphorus, light, and water.

When more limiting factors are added to the model, the amount of biodiversity quickly increases as a "tournament" of rock-paper-scissors matches develops between species, eliminating some weak players but maintaining a stable balance between multiple survivors.

"What we put together shows that when you allow species to compete for multiple resources, and allow different resources to determine which species win, you end up with a complex tournament that allows numerous species to coexist because of the multiple rock-paper-scissors games embedded within," Levine said.

In some models, where each species' advantage in one limiting factor is coupled to a disadvantage on another, a mere two limiting factors is capable of producing maximal – which stabilizes at half the number of species originally put into the model, no matter how large.

"It basically says there's no saturation," Allesina said. "If you have this tradeoff and have two factors, you can have infinite species. With simple rules, you can create remarkable diversity."

The model also produced a strange result: when the limiting factors are uniformly distributed, the total number of species that survive is always an odd number. Adjusting the model's parameters to more closely model the uneven distribution of resources in nature removed this intriguing quirk.

Allesina and Levine tested the realism of their model by successfully reverse-engineering a network of species relationships from field data on populations of tropical forest trees and marine invertebrates. Next, they will test whether the model can successfully predict the population dynamics of an ecosystem. Recently, Allesina was awarded a $450,000 grant by the James S. McDonnell Foundation to conduct experiments on bacterial populations that test the rock-paper-scissors dynamics in real time.

In the meantime, the rock-paper-scissors model proposes new ideas about the stability of ecosystems – or the dramatic consequences when only one species in the system is removed.

"The fact that many species co-exist could depend on the rare species, which are more likely to go extinct by themselves. If they are closing the loop, then they really have a key role, because they are the only ones keeping the system from collapsing," Allesina said.

"If you're playing rock-paper-scissors and you lose rock, you're going to end up with only scissors in the system," Levine said. "In a more complex system, there's an immediate cascade that extends to a very large number of species."

Explore further: Game theory analysis shows how evolution favors cooperation's collapse

More information: The paper, "Competitive network theory of species diversity," was published online by the Proceedings of the National Academy of Sciences on March 14, 2011.

Provided by University of Chicago Medical Center

4.8 /5 (6 votes)

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GuruShabu
1 / 5 (5) Mar 14, 2011
As per my PhD studies I was always told to be as clear as possible about concepts, acronyms and ideas, of course. If one presents anything that thing has to be described in detail so everyone (even new to the subject) will know what you are talking about.
Now comes my point, quote:"rock-paper-scissors-dynamite" and then further on "rock-paper-scissors dynamics".
I don't know the meaning of those concepts but I am sure there is a mistake in, at least, one of them in spite of my ignorance on the subject.
My question is: What is rock-paper-scissors dynamics?
I won't go to the Internet to search for the concept as this should have been thoroughly explained in the paper.
Here it goes my complaint against these badly written articles.
paulthebassguy
3 / 5 (6) Mar 14, 2011
I understand that Scissors can beat Paper, and I get how Rock can beat Scissors, but there's no way Paper can beat Rock. Paper is supposed to magically wrap around Rock leaving it immobile? Why the hell can't paper do this to scissors? Screw scissors,why can't paper do this to people? Why aren't sheets of college ruled notebook paper constantly suffocating students as they attempt to take notes in class?I'll tell you why, because paper can't beat anybody, a rock would tear that up in 2 seconds. When I play rock/ paper/ scissors I always choose rock.Then when somebody claims to have beaten me with their paper I can punch them in the face with my already clenched fist and say, oh, I'm sorry I thought paper would protect you, idiot.
GuruShabu
1 / 5 (4) Mar 14, 2011
BTW adding before someone criticises me for being so "ignorant" about the game rock-paper-scissors". (Now, after reading the comment below mine I have an idea)
I have NEVER seen this game or anything whatsoever related to it, so the authors assume everybody knows what the game is but I have to warn him/her that the world is much bigger than the English culture.
Thus we are allowed not knowing something from their so familiar infancy.
SincerelyTwo
1 / 5 (1) Mar 14, 2011
GuruShabu;
The paper, "Competitive network theory of species diversity," was published online by the Proceedings of the National Academy of Sciences on March 14, 2011.

also, maybe you should be going to arxiv.org instead of physorg.com, perhaps you couldn't tell by the obvious nature of these articles that it's the intention of this website to share up-coming research in a more accessible way for general minds.

if you need any help trying to figure out anything else that's painfully obvious let me know! welcome to physorg and enjoy!
hush1
1 / 5 (1) Mar 15, 2011
The model also produced a strange result: when the limiting factors are uniformly distributed, the total number of species that survive is always an odd number.


You can easily imagine, the image posted at Wikipedia's Website of Alfred Habdank Skarbek Korzybski, smiling.

More so, if imagining Korzybski had not just read the above quote - but the entire article here and comments, as well.

The above quote simply reminded me of Korzybski's famous premise: "the map is not the territory".

Going off on a tangent, I honestly believe Korzybski's life's work originated from his fluency in four languages.
antialias
not rated yet Mar 15, 2011
Now comes my point, quote:"rock-paper-scissors-dynamite" and then further on "rock-paper-scissors dynamics".
I don't know the meaning of those concepts

There are extensions to the rock-paper-scissors game in which more symbols are used than the traditional three. Here is a balanced example of a variant using 25 symbols
w w w.umop.com/rps25.htm

ryggesogn2
1 / 5 (2) Mar 16, 2011
Sounds like the 'law' of comparative advantage.
http://www.flatwo...b-199670
GuruShabu
1.3 / 5 (3) Mar 16, 2011
Now comes my point, quote:"rock-paper-scissors-dynamite" and then further on "rock-paper-scissors dynamics".
I don't know the meaning of those concepts

There are extensions to the rock-paper-scissors game in which more symbols are used than the traditional three. Here is a balanced example of a variant using 25 symbols
w w w.umop.com/rps25.htm


Thank you, antialias!
My point was to complain on the paper quality.
I know I can find almost anything in the Internet but a paper should be self explanatory in all its points. If you need to go elsewhere to find a concept, an idea, even an acronym in the paper this shows the paper was not written properly.
But anyway, thanks for your kindness and help!
Cheers.
Ethelred
5 / 5 (3) Mar 17, 2011
ut a paper should be self explanatory in all its points
Not possible.

What is a POINT. Its a matter of context and in different languages different words could be used in each context.
What is a PAPER. Something to write on not what is written on it EXCEPT in the context of a science article.
What is ITS - Russian, for instance, doesn't have articles and Spanish doesn't have a neutral gender.

No individual can deal with all the ways thousands of people can fail to understand what they write.

Ethelred
hush1
1 / 5 (1) Apr 20, 2011
No individual can deal with all the ways thousands of people can fail to understand what they write.


Yes.
Two points that are worth thinking about here:

First, let's imagine languages that have no translations - let's say music is an example. Does "failure to understand" even make sense within this context? Someone might defend the stance that music has nothing to say. So there is nothing to understand.

Secondly, Marshall McLuhan - Canadian communications theorist Educator, Writer and Social Reformer, 1911-1980, had this to say:

"Say anything you want to say. Make sure you understand, yourself, that you know, what you said"

I assert no one considers the two points stated above.
And you point is well taken.

I believe, the more languages you speak, read and write, the less chance there is to state something no one will understand. And the greater the chance is, of reaching an understanding among the largest number of people. Music is such a 'language'.

cont...
hush1
1 / 5 (1) Apr 20, 2011
cont...
Math is not considered a 'language' by many people.
I believe there are many 'languages' in Nature we are not aware of - there is so much understanding just waiting for us...

to be understood.

@Ethelred:
Thanks for your thought provoking reflection and insight.

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