The evolution of morality and the role of commitment.

A considerable share of the literature on the evolution of human cooperation considers the question why we have not evolved to play the Nash equilibrium in prisoners' dilemmas or public goods games. In order to understand human morality and pro-social behaviour, we suggest that it would actually be more informative to investigate why we have not evolved to play the subgame perfect Nash equilibrium in sequential games, such as the ultimatum game and the trust game. The 'rationally irrational' behaviour that can evolve in such games gives a much better match with actual human behaviour, including elements of morality such as honesty, responsibility and sincerity, as well as the more hostile aspects of human nature, such as anger and vengefulness.

The cancellation effect at the group level.

Group selection models combine selection pressure at the individual level with selection pressure at the group level. Cooperation can be costly for individuals, but beneficial for the group, and therefore, if individuals are sufficiently much assorted, and cooperators find themselves in groups with disproportionately many other cooperators, cooperation can evolve. The existing literature on group selection generally assumes that competition between groups takes place in a well-mixed population of groups, where any group competes with any other group equally intensely.

The group selection-inclusive fitness equivalence claim: not true and not relevant.

The debate on (cultural) group selection regularly suffers from an inclusive fitness overdose. The classical view is that all group selection is kin selection, and that Hamilton's rule works for all models. I claim that not all group selection is kin selection, and that Hamilton's rule does not always get the direction of selection right.

The problem with the Price equation.

In this paper, I will argue that the generality of the Price equation comes at a cost, and that is that the terms in it become meaningless. There are simple linear models that can be written in a Price equation-like form, and for those the terms in them have a meaningful interpretation. There are also models for which that is not the case, and in general, when no assumptions on the shape of the fitness function are made, and all possible models are allowed for, the regression coefficients in the Price equation do not allow for a meaningful interpretation.

Can Hamilton's rule be violated?

How generally Hamilton's rule holds is a much debated question. The answer to that question depends on how costs and benefits are defined. When using the regression method to define costs and benefits, there is no scope for violations of Hamilton's rule.

No Strategy Can Win in the Repeated Prisoner's Dilemma: Linking Game Theory and Computer Simulations.

Computer simulations are regularly used for studying the evolution of strategies in repeated games. These simulations rarely pay attention to game theoretical results that can illuminate the data analysis or the questions being asked. Results from evolutionary game theory imply that for every Nash equilibrium, there are sequences of mutants that would destabilize them.

Fisher's fundamental theorem of natural selection, dynamic sufficiency, and the necessity of higher moments.

The "average effects" of alleles in Fisher's Fundamental Theorem of Natural Selection are meant to capture what having an allele does to fitness. These average effects however are generally not constant, because the way they are determined implies that they may depend on the composition of the current population. This can easily be mistaken for dynamic insufficiency.

Hamilton's rule.

This paper reviews and addresses a variety of issues relating to inclusive fitness. The main question is: are there limits to the generality of inclusive fitness, and if so, what are the perimeters of the domain within which inclusive fitness works? This question is addressed using two well-known tools from evolutionary theory: the replicator dynamics, and adaptive dynamics. Both are combined with population structure.

A simple model of group selection that cannot be analyzed with inclusive fitness.

A widespread claim in evolutionary theory is that every group selection model can be recast in terms of inclusive fitness. Although there are interesting classes of group selection models for which this is possible, we show that it is not true in general. With a simple set of group selection models, we show two distinct limitations that prevent recasting in terms of inclusive fitness.

Evil green beards: Tag recognition can also be used to withhold cooperation in structured populations.

Natural selection works against cooperation unless a specific mechanism is at work. These mechanisms are typically studied in isolation. Here we look at the interaction between two such mechanisms: tag recognition and population structure.

Interpretations arising from Wrightian and Malthusian fitness under strong frequency dependent selection.

Fitness is the central concept in evolutionary theory. It measures a phenotype's ability to survive and reproduce. There are different ways to represent this measure: Malthusian fitness and Wrightian fitness.

Direct reciprocity in structured populations.

Reciprocity and repeated games have been at the center of attention when studying the evolution of human cooperation. Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Here we explore an open-ended, infinite strategy space, where every strategy that can be encoded by a finite state automaton is a possible mutant.

Multi-player games on the cycle.

In multi-player games n individuals interact in any one encounter and derive a payoff from that interaction. We assume that individuals adopt one of two strategies, and we consider symmetric games, which means the payoff depends only on the number of players using either strategy, but not on any particular configuration of the encounter. On the cycle we assume that any string of n neighbouring players interacts.

Group selection and inclusive fitness are not equivalent; the Price equation vs. models and statistics.

It is often suggested that any group selection model can be recast in terms of inclusive fitness. A standard reference to support that claim is "'Quantitative genetics, inclusive fitness, and group selection" by Queller (1992) in the American Naturalist 139 (3), 540-558. In that paper the Price equation is used for the derivation of this claim.

The replicator dynamics with n players and population structure.

The well-known replicator dynamics is usually applied to 2-player games and random matching. Here we allow for games with n players, and for population structures other than random matching. This more general application leads to a version of the replicator dynamics of which the standard 2-player, well-mixed version is a special case, and which allows us to explore the dynamic implications of population structure.

It takes grouping and cooperation to get sociality.

Cooperation and grouping are regularly studied as separate traits. The evolution of sociality however requires both that individuals get together in groups and that they cooperate within them. Because the level of cooperation can influence selection for group size, and vice versa, it is worth studying how these traits coevolve.

Group selection, kin selection, altruism and cooperation: when inclusive fitness is right and when it can be wrong.

Group selection theory has a history of controversy. After a period of being in disrepute, models of group selection have regained some ground, but not without a renewed debate over their importance as a theoretical tool. In this paper I offer a simple framework for models of the evolution of altruism and cooperation that allows us to see how and to what extent both a classification with and one without group selection terminology are insightful ways of looking at the same models.

In love and war: altruism, norm formation, and two different types of group selection.

We analyse simulations reported in "The co-evolution of individual behaviors and social institutions" by Bowles et al., 2003 in the Journal of Theoretical Biology 223, 135-147, and begin with distinguishing two types of group selection models. The literature does not provide different names for them, but they are shown to be fundamentally different and have quite different empirical implications.

Hamilton's missing link.

Hamilton's famous rule was presented in 1964 in a paper called "The genetical theory of social behaviour (I and II)", Journal of Theoretical Biology 7, 1-16, 17-32. The paper contains a mathematical genetical model from which the rule supposedly follows, but it does not provide a link between the paper's central result, which states that selection dynamics take the population to a state where mean inclusive fitness is maximized, and the rule, which states that selection will lead to maximization of individual inclusive fitness. This note provides a condition under which Hamilton's rule does follow from his central result.

Why kin and group selection models may not be enough to explain human other-regarding behaviour.

Models of kin or group selection usually feature only one possible fitness transfer. The phenotypes are either to make this transfer or not to make it and for any given fitness transfer, Hamilton's rule predicts which of the two phenotypes will spread. In this article we allow for the possibility that different individuals or different generations face similar, but not necessarily identical possibilities for fitness transfers.

On the use of the Price equation.

This paper distinguishes two categories of questions that the Price equation can help us answer. The two different types of questions require two different disciplines that are related, but nonetheless move in opposite directions. These disciplines are probability theory on the one hand and statistical inference on the other.