Abstract
We present a new model of evolutionary dynamics in one-dimensional space. Individuals are arranged on a cycle. When a new offspring is born, another individual dies and the rest shift around the cycle to make room. This rule, which is inspired by spatial evolution in somatic tissue and microbial colonies, has the remarkable property that, in the limit of large population size, evolution acts to maximize the payoff of the whole population. Therefore, social dilemmas, in which some individuals benefit at the expense of others, are resolved. We demonstrate this principle for both discrete and continuous games. We also discuss extensions of our model to other one-dimensional spatial configurations. We conclude that shift dynamics in one dimension is an unusually strong promoter of cooperative behavior.
| Original language | English |
|---|---|
| Pages (from-to) | 28-39 |
| Number of pages | 12 |
| Journal | Journal of Theoretical Biology |
| Volume | 311 |
| DOIs | |
| State | Published - Oct 21 2012 |
| Externally published | Yes |
Funding
We thank Jeff Gore for conversations that inspired this work. We also thank Kyle A. Ward, José Reyes, and Anna S. Roth for their work on higher-dimensional analogues of the shift model. B.A. is supported by the Foundational Questions in Evolutionary Biology initiative of the John Templeton Foundation.
Keywords
- Adaptive dynamics
- Cooperation
- Evolutionary game theory
- Evolutionary graph theory
- Fixation probability