We present a simple framework that highlights the most fundamental requirement for the evolution of altruism: assortment between individuals carrying the cooperative genotype and the helping behaviours of others with which these individuals interact. We partition the fitness effects on individuals into those due to self and those due to the 'interaction environment', and show that it is the latter that is most fundamental to understanding the evolution of altruism. We illustrate that while kinship or genetic similarity among those interacting may generate a favourable structure of interaction environments, it is not a fundamental requirement for the evolution of altruism, and even suicidal aid can theoretically evolve without help ever being exchanged among genetically similar individuals. Using our simple framework, we also clarify a common confusion made in the literature between alternative fitness accounting methods (which may equally apply to the same biological circumstances) and unique causal mechanisms for creating the assortment necessary for altruism to be favoured by natural selection.

The longstanding debate about the importance of group (multilevel) selection suffers from a lack of formal models that describe explicit selection events at multiple levels. Here, we describe a general class of models for two-level evolutionary processes which include birth and death events at both levels. The models incorporate the state-dependent rates at which these events occur. The models come in two closely related forms: (1) a continuous-time Markov chain, and (2) a partial differential equation (PDE)derived from (1) by taking a limit. We argue that the mathematical structure of this PDE is the same for all models of two-level population processes, regardless of the kinds of events featured in the model. The mathematical structure of the PDE allows for a simple and unambiguous way to distinguish between individual-and group-level events in any two-level population model. This distinction, in turn, suggests a new and intuitively appealing way to define group selection in terms of the effects of group-level events. We illustrate our theory of group selection by applying it to models of the evolution of cooperation and the evolution of simple multicellular organisms, and then demonstrate that this kind of group selection is not mathematically equivalent to individual-level (kin) selection. K E Y W O R D S :Evolutionary dynamics, evolution of cooperation, evolution of multicellular organisms, multilevel selection.

Inclusive fitness and reciprocal altruism are widely thought to be distinct explanations for how altruism evolves. Here we show that they rely on the same underlying mechanism. We demonstrate this commonality by applying Hamilton's rule, normally associated with inclusive fitness, to two simple models of reciprocal altruism: one, an iterated prisoner's dilemma model with conditional behavior; the other, a mutualistic symbiosis model where two interacting species differ in conditional behaviors, fitness benefits, and costs. We employ Queller's generalization of Hamilton's rule because the traditional version of this rule does not apply when genotype and phenotype frequencies differ or when fitness effects are nonadditive, both of which are true in classic models of reciprocal altruism. Queller's equation is more general in that it applies to all situations covered by earlier versions of Hamilton's rule but also handles nonadditivity, conditional behavior, and lack of genetic similarity between altruists and recipients. Our results suggest changes to standard interpretations of Hamilton's rule that focus on kinship and indirect fitness. Despite being more than 20 years old, Queller's generalization of Hamilton's rule is not sufficiently appreciated, especially its implications for the unification of the theories of inclusive fitness and reciprocal altruism.

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If one defines altruism strictly at the population level such that carriers of the altruistic genotype are required to experience, on average, a net fitness cost relative to average population members, then altruism can never evolve. This is simply because a genetically encoded trait can only increase in a population (relative to alternative traits) if the mean fitness of individuals carrying this genotype is higher than the population average fitness. This is true whether the genotype of interest encodes a self-serving behaviour such as enhanced predator avoidance, or an altruistic behaviour in which the actor enhances the fitness of those it interacts with more than its own. The paradox in the evolution of altruism is that carriers that are, on average, at a local disadvantage (i.e. compared to those they interact with) can still have higher fitness than the population average and hence can increase overall.The most fundamental explanation for how altruism (defined by local interactions) increases in a population requires that there be assortment in the population such that the benefit from others falls sufficiently often to carriers (and at the same time nonaltruists are stuck interacting more with each other). Nonadditivity if present can play a similar role: when collective cooperation yields synergistic benefits (positive nonadditivity) altruistic behaviour can evolve even in the absence of positive assortment, and when there are diminishing returns for cooperation (negative nonadditivity) the evolution of altruism is hindered (Queller, 1985;Hauert et al., 2006).In their target article Lehmann & Keller (2006) use a form of Hamilton's rule (1964, 1975) to classify different mechanisms by which helping behaviours can evolve. However, the version they develop tends to obscure the fundamental roles that assortment and nonadditivity play. Their framework also confuses local and population-wide definitions of altruism in making distinctions between nonrelatives and relatives, and what they label as mere 'cooperation' vs. true 'altruism'. We argue that a previous generalization of Hamilton's rule developed by Queller (1985) makes clear the roles played by assortment and nonadditivity and therefore serves as a better starting point for classifying various proposed models and mechanism of how altruistic traits can evolve. Queller's generalization of Hamilton's ruleHamilton's rule predicts that the genotype frequency for an altruistic trait will increase in the next generation if the inequality rB > C is satisfied. Here C represents the fitness cost paid by an average individual for exhibiting the helping behaviour, B is the average benefit provided by this help, and r, while originally thought of narrowly as a measure of relatedness between helpers and recipients, can more generally be thought of as a measure of assortment between individuals with the helping genotype on the one hand, and the helping phenotypes (behaviours) of others with which helpers interact (Queller, 1985) on the other hand. Queller's r term, ...