Multilevel and kin selection in a connected world.

Wild et al. argue that the evolution of reduced virulence can be understood from the perspective of inclusive fitness, obviating the need to evoke group selection as a contributing causal factor. Although they acknowledge the mathematical equivalence of the inclusive fitness and multilevel selection approaches, they conclude that reduced virulence can be viewed entirely as an individual-level adaptation by the parasite. Here we show that their model is a well-known special case of the more general theory of multilevel selection, and that the cause of reduced virulence resides in the opposition of two processes: within-group and among-group selection. This distinction is important in light of the current controversy among evolutionary biologists in which some continue to affirm that natural selection centres only and always at the level of the individual organism or gene, despite mathematical demonstrations that evolutionary dynamics must be described by selection at various levels in the hierarchy of biological organization.

Hamilton's rule in multi-level selection models.

Hamilton's rule is regarded as a useful tool in the understanding of social evolution, but it relies on restrictive, overly simple assumptions. Here we model more realistic situations, in which the traditional Hamilton's rule generally fails to predict the direction of selection. We offer modifications that allow accurate predictions, but also show that these Hamilton's rule type inequalities do not predict long-term outcomes. To illustrate these issues we propose a two-level selection model for the evolution of cooperation. The model describes the dynamics of a population of groups of cooperators and defectors of various sizes and compositions and contains birth-death processes at both the individual level and the group level. We derive Hamilton-like inequalities that accurately predict short-term evolutionary change, but do not reliably predict long-term evolutionary dynamics. Over evolutionary time, cooperators and defectors can repeatedly change roles as the favored type, because the amount of assortment between cooperators changes in complicated ways due to both individual-level and group-level processes. The equation that governs the dynamics of cooperator/defector assortment is a certain partial differential equation, which can be solved numerically, but whose behaviour cannot be predicted by Hamilton's rules, because Hamilton's rules only contain first-derivative information. In addition, Hamilton's rules are sensitive to demographic fitness effects such as local crowding, and hence models that assume constant group sizes are not equivalent to models like ours that relax that assumption. In the long-run, the group distribution typically reaches an equilibrium, in which case Hamilton's rules necessarily become equalities.

A simple and general explanation for the evolution of altruism.

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.

Unifying the theories of inclusive fitness and reciprocal altruism.

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.

The kin composition of social groups: trading group size for degree of altruism.

Why some social systems form groups composed of kin, while others do not, has gone largely untreated in the literature. Using an individual-based simulation model, we explore the demographic consequences of making kinship a criterion in group formation. We find that systems where social groups consist of one-generation breeding associations may face a serious trade-off between degree of altruism and group size that is largely mediated by their kin composition. On the one hand, restricting groups to close kin allows the evolution of highly altruistic behaviors but may limit group size to suboptimal levels, the more severely so the smaller the intrinsic fecundity of the species and the stricter the kin admission rule. Group size requirements, on the other hand, can be met by admitting nonkin into groups, but not without limiting the degree of altruism that can evolve. As a solution to this conundrum, we show that if helping roles within groups are assigned through a lottery rather than being genetically determined, maximum degrees of altruism can evolve in groups of nonrelatives of any size. Such a "lottery" mechanism may explain reproductive and helping patterns in organisms as varied as the cellular slime molds, pleometrotic ants, and Galapagos hawks.

Towards a general theory of group 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.

Spatio-temporal differentiation and sociality in spiders.

Species that differ in their social system, and thus in traits such as group size and dispersal timing, may differ in their use of resources along spatial, temporal, or dietary dimensions. The role of sociality in creating differences in habitat use is best explored by studying closely related species or socially polymorphic species that differ in their social system, but share a common environment. Here we investigate whether five sympatric Anelosimus spider species that range from nearly solitary to highly social differ in their use of space and in their phenology as a function of their social system. By studying these species in Serra do Japi, Brazil, we find that the more social species, which form larger, longer-lived colonies, tend to live inside the forest, where sturdier, longer lasting vegetation is likely to offer better support for their nests. The less social species, which form single-family groups, in contrast, tend to occur on the forest edge where the vegetation is less robust. Within these two microhabitats, species with longer-lived colonies tend to occupy the potentially more stable positions closer to the core of the plants, while those with smaller and shorter-lived colonies build their nests towards the branch tips. The species further separate in their use of common habitat due to differences in the timing of their reproductive season. These patterns of habitat use suggest that the degree of sociality can enable otherwise similar species to differ from one another in ways that may facilitate their co-occurrence in a shared environment, a possibility that deserves further consideration.

The evolution of altruism: game theory in multilevel selection and inclusive fitness.

Although the prisoner's dilemma (PD) has been used extensively to study reciprocal altruism, here we show that the n-player prisoner's dilemma (NPD) is also central to two other prominent theories of the evolution of altruism: inclusive fitness and multilevel selection. An NPD model captures the essential factors for the evolution of altruism directly in its parameters and integrates important aspects of these two theories such as Hamilton's rule, Simpson's paradox, and the Price covariance equation. The model also suggests a simple interpretation of the Price selection decomposition and an alternative decomposition that is symmetrical and complementary to it. In some situations this alternative shows the temporal changes in within- and between-group selection more clearly than the Price equation. In addition, we provide a new perspective on strong vs. weak altruism by identifying their different underlying game structures (based on absolute fitness) and showing how their evolutionary dynamics are nevertheless similar under selection (based on relative fitness). In contrast to conventional wisdom, the model shows that both strong and weak altruism can evolve in periodically formed random groups of non-conditional strategies if groups are multigenerational. An integrative approach based on the NPD helps unify different perspectives on the evolution of altruism.

Strong altruism can evolve in randomly formed groups.

Although the conditions under which altruistic behaviors evolve continue to be vigorously debated, there is general agreement that altruistic traits involving an absolute cost to altruists (strong altruism) cannot evolve when populations are structured with randomly formed groups. This conclusion implies that the evolution of such traits depends upon special environmental conditions or additional organismic capabilities that enable altruists to interact with each other more than would be expected with random grouping. Here we show, using both analytic and simulation results, that the positive assortment necessary for strong altruism to evolve does not require these additional mechanisms, but merely that randomly formed groups exist for more than one generation. Conditions favoring the selection of altruists, which are absent when random groups initially form, can naturally arise even after a single generation within groups-and even as the proportion of altruists simultaneously decreases. The gains made by altruists in a second generation within groups can more than compensate for the losses suffered in the first and in this way altruism can ratchet up to high levels. This is true even if altruism is initially rare, migration between groups allowed, homogeneous altruist groups prohibited, population growth restricted, or kin selection precluded. Until now random group formation models have neglected the significance of multigenerational groups-even though such groups are a central feature of classic "haystack" models of the evolution of altruism. We also explore the important role that stochasticity (effectively absent in the original infinite models) plays in the evolution of altruism. The fact that strong altruism can increase when groups are periodically and randomly formed suggests that altruism may evolve more readily and in simpler organisms than is generally appreciated.