Martin Zwick

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Systems Science


Systems Science

Physical Description

1 online resource (208 p.)


Altruism, Prisoner's dilemma game, Game theory; Group selection, Games of strategy (Mathematics)




In evolutionary theory the existence of self-sacrificing cooperative traits poses a problem that has engendered decades of debate. The principal theories of the evolution of altruism are inclusive fitness, reciprocal altruism, and multilevel selection. To provide a framework for the unification o f these apparently disparate theories, this dissertation identifies two fundamental conditions required for the evolution of altruism: 1) non-zero-sum fitness benefits for cooperation and 2) positive assortment among altruistic behaviors. I demonstrate the underlying similarities in these three theories in the following two ways. First, I show that the game-theoretic model of the prisoner’s dilemm a (PD) is inherent to all three theories. While the PD has been used extensively to model reciprocal altruism, I demonstrate that the n-player PD captures fundamental aspects o f multilevel selection and inclusive fitness in that NPD model parameters relate simply to Simpson’s paradox, the Price covariance equation, and Hamilton’s rule. The tension between hierarchical levels that defines a PD reflects the tension between Abstract levels o f selection that is explicit in multilevel selection theory, and im plicit in the other two theories. Second, Ham ilton’s rule from inclusive fitness theory applies to the other theories. As mentioned, I demonstrate that this rule relates to multilevel selection via the NPD. I also show that Queller’s generalization of Hamilton’s rule applies to the conditional strategies of reciprocal altmism. This challenges the selfish-gene viewpoint by highlighting the fact that it is the phenotypes o f others, not their genotypes, that is critical to the evolution o f altruism. I integrate the PD and H am ilton’s rule as follows: the evolution o f altruism in general involves PD situations in which Hamilton’s rule specifies the necessary relationship between 1) the degree of non-zero-sumness within the PD and 2) the degree of positive assortment among altruistic behaviors. Additional contributions of this research include a demonstration that randomly formed associations can provide the necessary positive assortment for strong altruism to evolve, the development of a new selection decomposition that is symmetrical to the Price equation, and a game-theoretic analysis showing the essential similarity of weak and strong altruism under selection.


A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Systems Science.

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