CancerEvo is a research group led by David Basanta

We are mathematical modellers who work with biologists and clinicians

We try to understand

  • the ecology of tumors

  • the evolutionary dynamics of cancer progression

  • resistance to treatment

Based at the Moffitt Cancer Center, Florida

Nowak: Five rules for the evolution of cooperation

Five rules for the evolution of cooperation

Martin Nowak

Science Magazine, December 2006

I am discussing with some people in Dundee and Vanderbilt about how to study cancer progression in terms of evolution of cooperation (as hinted by Axelrod et al.). One of the leading researchers in the field of biomathematics and game theory is Harvard’s Martin Nowak, In this paper he discusses five potential mechanisms of cooperation that could appear through Darwinian evolution.

Kin selection refers to the cooperation between individuals that are genetically related. It is easy to see how an individual will sacrifice something in order to help another individual as long as the relationship between what is sacrificed and the level of relatedness crosses a given threshold.

Direct reciprocity is also quite clear: if from our mutual cooperation we both get something more than what we put then it is viable. To explain its emergence Axelrod performed an study a couple of decades ago in which he found that of all competing strategies, the most successful one was Tit for tat. A player following this strategy will cooperate unless the other player does not. If the non cooperating player starts cooperating at some point then tit for tat will resume cooperation. In circumstances in which a level of noise might affect the perception of cooperation (if, for instance, one player thinks that the other one is not willing to cooperate when in fact he or she is) then a better strategy would be win-stay, lose-shift in which the player will keep a strategy for as long as it reports a benefit and will switch to the alternative one (be it cooperate or not) otherwise.

Indirect reciprocity on the other hand is less clear and is based on the idea of reputation. If individuals with a reputation for cooperation can be perceived by other participants and these participants are more likely to cooperative with individuals with a good reputation then cooperation could evolve even when the individuals in the population do not interact repeatedly. Problem with indirect reciprocity is that, depending on reputation requires skills normally not found in animals outside our own species.

Network reciprocity falls in the easily understandable category. Most game theoretical studies assume a well mixed population. That is not realistic and spatial models (like those based on Cellular Automata) and graph models (known as network models among physicists) make it easier to study cooperation when the individuals are more likely to interact with a subset of the population. It is known that in many cases, cooperation is more likely to emerge in spatial than in non spatial models. From the mathematical point of view though, these systems are easy to simulate in a computer than to analyse formally.

Group selection is a controversial type of selection in which selection does work not only at the level of the individuals but also at the level of the species to which these individuals belong. According to this line of thought although cooperation might not benefit cooperative individuals (whose efforts could be misused by freeriders), species in which cooperation emerges are more likely to stick around that species with exclusively selfish behaviour.


Friday 18 January 2008

Rafe Furst

I’m really glad to see someone addressing the role of cooperation in cancer. Nowak’s work on the dynamic of cooperation (and its importance) is seminal. I believe his 5 rules are missing an important factor for cancer progression though, namely disruptive cooperation. Simply put, by disrupting existing cooperation amongst normal cells, cancerous cells can be thought of as cooperating with one another.

Cooperation is also a key to understanding emergence, it being one of the mechanisms for the emergence of new levels of organization (another being autocatalysis). Cancer is interesting in that it is an emergent system/agent, like all biological forms, but it is “special” in the sense that it is a sort of photo negative of existing biological complexity. Cancer is an unwinding of emergent complexity that appears to be emergent itself when set against the backdrop of the positively accrued complexity born out of cooperation between cells.

David Basanta

Thanks for your comment, that is an interesting observation. I agree that tumour cells are basically cells that stop cooperating with the society of cells as a whole and that in some cases (although I am not sure if that is a sizable number of cases) they cooperate with a subset of themselves.

About disruptive cooperation, I am not sure that this type of cooperation could not be considered as a composite of the others?

BTW… nice blog!

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