Group Selection  Simulator

For the last two decades, biologist David Sloan Wilson has been engaged in a sustained reassessment of group selection theory in evolutionary biology and ecology. Group selection theory centers on the claim that selection in structured populations can result in the stabilization of group level adaptations - traits that are good for the group even though they put individuals carrying those traits at a competitive disadvantage within the group. It is thought that group selection is the key to understanding the evolution of altruism, morality, and cooperation. For the last five years or so, Wilson has been joined by philosopher Elliott Sober in this enterprise. The result of this collaboration is a (highly recommended) new book: Unto Others: the evolution and psychology of unselfish behavior.

Simpson's Paradox: Part of Sober and Wilson's argument is that the standard ways of explaining the evolution of unselfish behavior, which include "kin selection", "reciprocal altruism", and non-random interaction patterns, are in fact kinds of group selection, in that the stabilization of self-sacrificing behavior patterns in these models depends critically on group structure. To this collection of standard models, they propose an additional mechanism by which self-sacrificing behavior can stabilize.

The paradigm for understanding the evolution of altruism is a game called the Prisoner's Dilemma. Each time two individuals interact, each "player" has the choice of either cooperating or defecting. How well each player does depends on what both players do. Typical payoffs are given in the following matrix. In the long run everyone does better if everyone cooperates. In the short run, however, defectors do better, no matter which move their opponents make.

Evolutionary models interpret the payoffs as darwinian finess, or competitive growth rates. In populations where cooperators and defectors interact at random, defection always displaces cooperation within a local population (or group). This is true even in a structured population where individuals only play against members of their own group. In any group which has a mix of cooperators and defectors, the percentage of cooperators decreases. In groups that aren't mixed, there is no change in percentages. So it seems, at first glance, as though group structure by itself isn't enough to stabilize cooperatvie behavior.

Simpson's paradox consists of the following observation: even though a trait is decreasing in percentage in every group, this doesn't mean that it is decreasing overall.   The reason that this is possible is because group sizes change, and groups with lots of cooperators grow faster than groups of mostly defectors. Suppose we start with two populations with 100 indifividuals each, the first consisting of 10% cooperators and the second consisting of 90% cooperators. Using the growth rates in the table above, for the first generation we get:

So even though the percentage of cooperators decreases in both groups, the percentage   of cooperators increases in the overall population. Of course this effect can't be maintained, since defectors will end up taking over every population, and the percentage of cooperators in the total population will drop.

Sober and Wilson propose, however, that if groups break up and reform at the right rate, then the "Simpson's paradox effect" can be sustained. One way that this could happen would be if cooperators tended to find each other to form new groups. S&W argue, however, that even in the absence of such selective assortment mechanisms, cooperation can stabilize. The trick is that when groups reform at random, they do not all resemble the overall population in their proportions of cooperators. Some will accidentally end up with more cooperators, others with fewer. And those groups with more cooperators will grow faster than those without. So the proposal is that sampling error in group composition can be enough to sustain cooperation in structured populations. We configured the EAME agent-and-patch simulator to explore this proposal.

The Isolation Game Start Simulator

• On a 12x12 grid, agents breed and play prisoner's dilemma. The trick is that they are locked into a cell on the grid with other agents and their offspring for the "isolation cycle", then they are allowed to move for the "movement cycle". Note that we start out with four individuals who get to feed, breed, and move freely for the first hundered cycles. This gets a nice random distribution of cooperators and defectors.
• Group selection theory claims that under these conditions cooperation can stabilize. The simulator demonstrates that this can happen. Without isolation, however, the demise of cooperators is inevitable.  Start Simulator without Isolation Cycle
• The mechanism that is supposed to operate is that described by "Simpson's Paradox". Seems that just because defection increases in relative frequency in every group, this doesn't mean that defection must increase globally. The trick is that groups that start with more cooperators grow more quickly, and if groups break up at just the right time and reform in ways that get different ratios of cooperators in different groups, then the paradoxical growth of cooperation can continue.
• COLORS: White bars for cooperators, black bars for defectors.
• THE DIE-OFF: turns out that the if population density gets too high then reforming groups tend not to diverge much from the general population in their proportions of cooperators and defectors. So I've engineered a major killing off of agents in the middle of each movement cycle. This is rather severe. Three out of four patches have their members all killed. (Every second row and every second column.) Question: if this is what is necessary in order for group selection to work, how realistic an assumption is it? Start Simulator without Die-Off
• The initial settings are such that paradoxical growth is frequently sustained. Part of the reason is that intial group size after die offs and the movement cycle is quite small. (There are 144 patches and usually less than 200 agents surviving the die-off.) In fact, lots of groups start out with just one member! If the isolation cycle is longer, then there will be more individuals before and after the die-off. Start simulator with isolation cycle of 300

• Play with the settings and see what you think! If you hit "interactive simulators" and then "code list" in the left frame, there are instructions for customizing the available parameter settings.
• More information on the Agent-and-Patch Simulator