The Mathematics of Altruism

For decades, biologists have debated whether individuals sacrifice themselves to save those who share their genes or in effect to benefit the whole group. University of Vermont researcher Charles Goodnight has shown through mathematical models that the two views of altruism, kin selection versus group selection, are in fact equivalent behaviors.

The research sheds new light on fundamental issues in evolutionary theory.

For kin selection to be important, the related individuals must be in groups that preferentially help each other. For group selection to operate, the members of a group must be closer to each other than to other groups. The two ideas are so close they actually can be converted to each other mathematically. This understanding has been stated in technical research articles for more than 30 years, but the broader scientific community hasn't often recognized it.

To this day, biologists debate about how altruistic behaviors evolve and persist. The classic example: bees that lay down their lives to defend the hive. On one side of the debate are those who argue in favor of kin selection, in which individuals are altruistic to those who share their genes. In defending the hive, a self-sacrificing bee increases the chances that the genes she shares with her sisters will be passed down. On the other side are those who argue in favor of group selection, (or, in its modern form, "multilevel" selection), in which altruism arises from being part of a group. The self-sacrificing behavior of the bee persists and spreads across generations because the whole hive, a group, competes more successfully, leaving more offspring than others.

Through sophisticated mathematical modeling, researchers have shown that the debate should no longer be about individual versus multilevel selection, but about how strong is each level of selection.