The concept of group heritability

This paper investigates the role of the concept of group heritability in group selection theory, in relation to the well-known distinction between type 1 and type 2 group selection (GS1 and GS2). I argue that group heritability is required for the operation of GS1 but not GS2, despite what a number of authors have claimed. I offer a numerical example of the evolution of altruism in a multi-group population which demonstrates that a group heritability coefficient of zero is perfectly compatible with the successful operation of group selection in the GS2 sense. A diagnosis of why group heritability has wrongly been regarded as necessary for GS2 is suggested.