Evolving Slower Gets You The Bigger Piece Of The Pie

Mutualistic interactions, in which species provide services to one another, are abundant in nature. Examples are everywhere: from the mitochondria, once free-living bacteria that provide energy from burning sugars with oxygen to every cell in our body, to fungi that enable plants to take up nitrogen from the soil, to ants interacting with caterpillars providing them with protection for food. When such an interaction occurs, who will benefit most? Will the ant benefit most by providing very little protection for a lot of food, or will the caterpillar benefit most by providing very little food for a lot of protection?

Michael Lachmann from the Max Planck Institute for Mathematics in the Sciences in Leipzig and Carl Bergstrom from the University of Washington examined this question by using mathematical analysis. One can abstract the behavior of each species as being "generous" and giving much of the benefit to the other species, or being "selfish" and asking for most of the benefit for itself. In a mutualistic interaction, the two species benefit most from coordinating - when one is "generous" and the other "selfish". Benefits to each are less than optimal in other cases - when both are selfish, or both generous.

When the population of one species is all generous, and of the other all selfish, no evolutionary changes can occur, since no species can benefit from changing its behavior. When pairings of selfish-selfish or generous-generous occur in some cases, then evolutionary change might happen. If there are many pairings of the type generous-generous, the faster evolving species will quickly evolve to be selfish, and thus the population will evolve to benefit the fast evolver. If, on the other hand, there are mostly pairings of the type selfish-selfish, the faster evolving species will quickly evolve to become generous (since the generous-selfish is better than selfish-selfish) and thus the population will evolve to benefit the slow evolver.

This is the first surprising result. In interactions that require coordination of strategies, it is not necessarily an advantage to evolve fast. In many cases, the slow evolver will gain the upper hand. However, an additional twist provides an advantage for the slow evolver: each species grows best when it is selfish and the other generous, and thus one might expect most individuals in a species to come from areas which are predominantly selfish. This would mean that there is a bias towards selfish-selfish pairing, and those favor the slow evolver. Thus, in some evolutionary scenarios it takes all the evolving one can do just to stay in the same place, as the Lewis Carroll's red queen would say, and in other scenarios it pays to take one step at a time as the red king would do, and wait patiently for the other player to make the big move.

"The model is also important for evolutionary economics. It is linked to a result known in economics: when bargaining it is sometimes better to have "one's hands tied". The model applies to cases in which individuals/companies interact, and have several possible stable outcomes - agreements, or simply stable interactions", says Michael Lachmann.

The study of evolution and learning in biological systems is part of the key research area of "Dynamics of Complex Systems" at the Max Planck Institute for Mathematics in the Sciences. Other areas of research in the institute include: the dynamics of neural networks, information processing, learning in cognitive systems, questions of synchronization and time delays in complex networks, analysis of genetic networks, mathematical models of chemotaxis, and the study of tumor growth.