A new model created by evolutionary mathematicians reveals that when cooperation between two species improves, the resulting beneficial behaviors can, surprisingly, become unequal. One species tends to gather all the benefits, while the other only consumes them.
Darwin was intrigued by the phenomenon of cooperation in nature, as it seemed to contradict natural selection and the idea that only the fittest survive. Over recent decades, evolutionary mathematicians have applied game theory to explain why mutual cooperation continues to exist despite natural selection favoring self-serving individuals.
Cooperation tends to thrive when it is inexpensive or when the advantages gained are significant. If cooperation becomes too costly, it tends to vanish—at least from a purely mathematical standpoint. However, intricate interdependent relationships, like those between pollinators and plants, demonstrate similar yet more complicated patterns.
New modeling published today in PNAS Nexus introduces a new element to this theory, suggesting that cooperative behavior between species may falter in contexts where, theoretically, it should actually thrive.
“As we enhanced the circumstances for cooperation in our model, we observed an expected increase in mutually beneficial behaviors in both species,” explains Dr. Christoph Hauert, a mathematician at the University of British Columbia focused on evolutionary dynamics.
“However, once the cooperation levels in our simulation approached 50 percent, a division occurred. More cooperators concentrated in one species while fewer appeared in the other, and this imbalance intensified as the cooperative conditions improved.”
Although the concept of ‘symmetry breaking of cooperation’ among two populations has been examined by mathematicians previously, this is the first model allowing individuals from each group to engage and collaborate in a more realistic manner.
Dr. Hauert and his associate Dr. György Szabó from the Hungarian Research Network utilized computational spatial models to position individuals from both species on distinct grids facing each other. This setup allows cooperators to form clusters and minimizes their chances of being taken advantage of by cheaters through enhanced interaction with fellow cooperators.
“Since we utilized symmetric interactions, cooperation levels remain the same in both populations,” states Dr. Hauert. “Though clusters can still form and safeguard cooperators, synchronization across grids becomes essential for interactions to occur.”
“This unusual symmetry breaking in cooperation resembles phase transitions seen in magnetic materials and underscores the effectiveness of methods developed in statistical and solid-state physics,” adds Dr. Szabó.
“Moreover, the model illuminates sharp increases in significant behavioral shifts that can greatly influence interactions within intricate living systems.”
The research received support from the National Science and Engineering Research Council of Canada.
Mutualisms: Cooperation Between Species
A model crafted by evolutionary mathematicians from Canada and Europe indicates that as cooperation becomes simpler, it may unexpectedly break down. Check out a simulation demonstrating the spatial interactions between cooperators and defectors in each species under various scenarios.
