The evolutionary dynamics of spite in finite populations

Spite, the shady relative of altruism, involves paying a fitness cost to inflict a cost on some recipient. Here, we investigate a density dependent dynamic model for the evolution of spite in populations of changing size. We extend the model by introducing a dynamic carrying capacity. Our analysis shows that it is possible for unconditionally spiteful behavior to evolve without population structure in any finite population. In some circumstances spiteful behavior can contribute to its own stability by limiting population growth. We use the model to show that there are differences between spite and altruism, and to refine Hamilton's original argument about the insignificance of spite in the wild. We also discuss the importance of fixing the measure of fitness to classify behaviors as selfish or spiteful.