Inclusive fitness in finite populations-effects of heterogeneity and synergy

Many-strategy games in groups with relatives and the evolution of coordinated cooperation

Humans often cooperate in groups with friends and family members with varying degrees of genetic relatedness. Past kin selection can also be relevant to interactions between strangers, explaining how the cooperation first arose in the ancestral population. However, modelling the effects of relatedness is difficult when the benefits of cooperation scale nonlinearly with the number of cooperators (e.g., economies of scale). Here, we present a direct fitness method for rigorously accounting for kin selection in n-player interactions with m discrete strategies, where a genetically homophilic group-formation model is used to calculate the necessary higher-order relatedness coefficients. Our approach allows us to properly account for non-additive fitness effects between relatives (synergy). Analytical expressions for dynamics are obtained, and they can be solved numerically for modestly sized groups and numbers of strategies. We illustrate with an example where group members can verbally agree (cheap talk) to contribute to a public good with a sigmoidal benefit function, and we find that such coordinated cooperation is favoured by kin selection. As interactions switched from family to strangers, in order for coordinated cooperation to persist and for the population to resist invasion by liars, either some level of homophily must be maintained or following through on the agreement must be in the self-interests of contributors. Our approach is useful for scenarios where fitness effects are non-additive and the strategies are best modelled in a discrete way, such as behaviours that require a cognitive 'leap' of insight into the situation (e.g., shared intentionality, punishment).

The evolution of signaling and monitoring in plant-fungal networks

Experiments have shown that when one plant is attacked by a pathogen or herbivore, this can lead to other plants connected to the same mycorrhizal network up-regulating their defense mechanisms. It has been hypothesized that this represents signaling, with attacked plants producing a signal to warn other plants of impending harm. We examined the evolutionary plausibility of this and other hypotheses theoretically. We found that the evolution of plant signaling about an attack requires restrictive conditions, and so will rarely be evolutionarily stable. The problem is that signaling about an attack provides a benefit to competing neighbors, even if they are kin, and so reduces the relative fitness of signaling plants. Indeed, selection is often more likely to push plant behavior in the opposite direction-with plants signaling dishonestly about an attack that has not occurred, or suppressing a cue that they have been attacked. Instead, we show that there are two viable alternatives that could explain the empirical data: 1) the process of being attacked leads to a cue (information about the attack) which is too costly for the attacked plant to fully suppress; 2) mycorrhizal fungi monitor their host plants, detect when they are attacked, and then the fungi signal this information to warn other plants in their network. Our results suggest the empirical work that would be required to distinguish between these possibilities.

A kin-selection model of fairness in heterogeneous populations

Humans and other primates exhibit pro-social preferences for fairness. These preferences are thought to be reinforced by strong reciprocity, a policy that rewards fair actors and punishes unfair ones. Theories of fairness based on strong reciprocity have been criticized for overlooking the importance of individual differences in socially heterogeneous populations. Here, we explore the evolution of fairness in a heterogeneous population. We analyse the Ultimatum Game in cases where players' roles in the game are determined by their status. Importantly, our model allows for non-random pairing of players, and so we also explore the role played by kin selection in shaping fairness. Our kin-selection model shows that, when individuals condition their behaviour on their role in the game, fairness can be understood as either altruistic or spiteful. Altruistic fairness directs resources from less valuable members of a genetic lineage to more valuable members of the same lineage, whereas spiteful fairness keeps resources away from the competitors of the actor's high-value relatives. When individuals express fairness unconditionally it can be understood as altruistic or selfish. When it is altruistic, unconditional fairness again serves to direct resources to high-value members of genetic lineages. When it is selfish, unconditional fairness simply improves an individual's own standing. Overall, we expand kin-selection based explanations for fairness to include motivations other than spite. We show, therefore, that one need not invoke strong reciprocity to explain the advantage of fairness in heterogeneous populations.

Extending the range of additivity in using inclusive fitness

Inclusive fitness is a concept widely utilized by social biologists as the quantity organisms appear designed to maximize. However, inclusive fitness theory has long been criticized on the (uncontested) grounds that other quantities, such as offspring number, predict gene frequency changes accurately in a wider range of mathematical models. Here, we articulate a set of modeling assumptions that extend the range of scenarios in which inclusive fitness can be applied. We reanalyze recent formal analyses that searched for, but did not find, inclusive fitness maximization. We show (a) that previous models have not used Hamilton's definition of inclusive fitness, (b) a reinterpretation of Hamilton's definition that makes it usable in this context, and (c) that under the assumption of probabilistic mixing of phenotypes, inclusive fitness is indeed maximized in these models. We also show how to understand mathematically, and at an individual level, the definition of inclusive fitness, in an explicit population genetic model in which exact additivity is not assumed. We hope that in articulating these modeling assumptions and providing formal support for inclusive fitness maximization, we help bridge the gap between empiricists and theoreticians, which in some ways has been widening, demonstrating to mathematicians why biologists are content to use inclusive fitness, and offering one way to utilize inclusive fitness in general models of social behavior.

Inclusive fitness is an indispensable approximation for understanding organismal design

For some decades most biologists interested in design have agreed that natural selection leads to organisms acting as if they are maximizing a quantity known as "inclusive fitness." This maximization principle has been criticized on the (uncontested) grounds that other quantities, such as offspring number, predict gene frequency changes accurately in a wider range of mathematical models. Here, we adopt a resolution offered by Birch, who accepts the technical difficulties of establishing inclusive fitness maximization in a fully general model, while concluding that inclusive fitness is still useful as an organizing framework. We set out in more detail why inclusive fitness is such a practical and powerful framework, and provide verbal and conceptual arguments for why social biology would be more or less impossible without it. We aim to help mathematicians understand why social biologists are content to use inclusive fitness despite its theoretical weaknesses. Here, we also offer biologists practical advice for avoiding potential pitfalls.