Generalizations of Hamilton's rule applied to non-additive public goods games with random group size

Marshall, James A. R.

doi:10.3389/fevo.2014.00040

Cited by 4 publications

(6 citation statements)

References 27 publications

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“…The benefits of cooperation to each cooperator surpasses the individual cost only when both cooperators end up in the same group. This is similar to what some describe as ‘synergistic effects’ [17,18,22]; although, we are considering these effects at the individual level instead of the group level. This ties into the earlier discussion on non-additivity.…”

Section: Methodssupporting

confidence: 63%

“…Non-additivity is often represented in terms of ‘synergistic’ benefits, though this ‘deviation from additivity’ produces the same benefit value each cooperator/cooperator interaction (e.g. Table 2 in [15]) [15–18,22]. By contrast, we will allow the benefits of cooperation to be a non-additive function of the number of cooperative interactions experienced, regardless of whether the recipient is an cooperator or not.…”

Section: Resultsmentioning

confidence: 99%

“…Some authors define relatedness in such a way that the fitness effects of an cooperative act are combined into the degree of cooperation expressed by an individual (or the genic value of an individual) [3,7,8,17,18,22]. In such models, any non-linearities in the benefits of cooperation (i.e.…”

Section: Resultsmentioning

confidence: 99%

“…Note that under this definition, P 1 may be zero (i.e. cooperators no more likely to interact with other cooperators than with non-cooperators), even when ″ r ″ ≠ 0 in models under which fitness effects are folded into the definitions of genic values [3,7,8,17,18,22]. Furthermore, when we make the model stochastic, we will show that individual behavior, fitness effects and clustering of individuals can have very different stochastic behavior.…”

Section: Resultsmentioning

confidence: 99%

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Stochasticity and non-additivity expose hidden evolutionary pathways to cooperation

Fumagalli

Rice

2019

PLoS ONE

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Cooperation is widespread across the tree of life, with examples ranging from vertebrates to lichens to multispecies biofilms. The initial evolution of such cooperation is likely to involve interactions that produce non-additive fitness effects among small groups of individuals in local populations. However, most models for the evolution of cooperation have focused on genealogically related individuals, assume that the factors influencing individual fitness are deterministic, that populations are very large, and that the benefits of cooperation increase linearly with the number of cooperative interactions. Here we show that stochasticity and non-additive interactions can facilitate the evolution of cooperation in small local groups. We derive a generalized model for the evolution of cooperation and show that if cooperation reduces the variance in individual fitness (separate from its effect on average fitness), this can aid in the evolution of cooperation through directional stochastic effects. In addition, we show that the potential for the evolution of cooperation is influenced by non-additivity in benefits with cooperation being more likely to evolve when the marginal benefit of a cooperative act increases with the number of such acts. Our model compliments traditional cooperation models (kin selection, reciprocal cooperation, green beard effect, etc.) and applies to a broad range of cooperative interactions seen in nature.

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Section: Methodssupporting

confidence: 63%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Stochasticity and non-additivity expose hidden evolutionary pathways to cooperation

Fumagalli

Rice

2019

PLoS ONE

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“…Any theoretical or empirical result that appears to violate Hamilton's rule can be reanalyzed using HRG to show that the outcome is "as predicted by Hamilton's rule." Indeed, this pattern has been repeated many times in the literature (7,14,28,(32)(33)(34)). It appears that there are no real or hypothetical data that the inclusive fitness community would accept as a violation of Hamilton's rule.…”

Section: Discussionmentioning

confidence: 76%

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Nowak

McAvoy

Allen

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Hamilton's rule asserts that a trait is favored by natural selection if the benefit to others, B, multiplied by relatedness, R, exceeds the cost to self, C. Specifically, Hamilton's rule states that the change in average trait value in a population is proportional to BR − C. This rule is commonly believed to be a natural law making important predictions in biology, and its influence has spread from evolutionary biology to other fields including the social sciences. Whereas many feel that Hamilton's rule provides valuable intuition, there is disagreement even among experts as to how the quantities B, R, and C should be defined for a given system. Here, we investigate a widely endorsed formulation of Hamilton's rule, which is said to be as general as natural selection itself. We show that, in this formulation, Hamilton's rule does not make predictions and cannot be tested empirically. It turns out that the parameters B and C depend on the change in average trait value and therefore cannot predict that change. In this formulation, which has been called "exact and general" by its proponents, Hamilton's rule can "predict" only the data that have already been given.amilton's rule is a widely known concept in evolutionary biology. It has become standard textbook knowledge and is encountered in undergraduate education. For many, Hamilton's rule expresses the intuition that cooperation evolves more easily when there are frequent interactions among relatives, because relatives are likely to share the cooperative trait. However, Hamilton's rule goes beyond this intuition by positing a quantitative condition, BR − C > 0, which is said to predict whether or not a trait will be selected. Specifically, it is claimed that the change in average trait value from one time point to the next is proportional to BR − C .We immediately encounter the question of how the "benefit," B , the "relatedness," R, and the "cost," C , are calculated for a given system. Surprisingly, there is no consensus about the correct method. A variety of derivations have been proposed over the years (1-10), which define B , R, and C in distinct (nonequivalent) ways. In the empirical literature, peer reviewers often disagree over which method should be used in a particular manuscript (11).A number of recent papers (7, 9, 10) have endorsed a particular formulation (4, 5) as the exact, general, and even "canonical" version of Hamilton's rule. This formulation, called "Hamilton's rule-general" (HRG) (12, 13), is claimed to be as general as natural selection itself (7,14). The derivation, which we recapitulate below, is simple and contains only a few steps.The mathematical investigation of HRG reveals three astonishing facts. First, HRG is logically incapable of making any prediction about any situation because the benefit, B , and the cost, C , cannot be known in advance. They depend on the data that are to be predicted. At the outset of an experiment, B and C are unknown, and so there is no way to say what Hamilton's rule would predict. Once the experiment is ...

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Relatedness and synergies of kind and scale in the evolution of helping

Peña,

Nöldeke,

Lehmann

2014

Preprint

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Relatedness and synergy affect the selection pressure on cooperation and altruism. Although early work investigated the effect of these factors independently of each other, recent efforts have been aimed at exploring their interplay. Here, we contribute to this ongoing synthesis in two distinct but complementary ways. First, we integrate models of n-player matrix games into the direct fitness approach of inclusive fitness theory, hence providing a framework to consider synergistic social interactions between relatives in family and spatially structured populations. Second, we illustrate the usefulness of this framework by delineating three distinct types of helping traits ("whole-group", "nonexpresser-only" and "expresser-only"), which are characterized by different synergies of kind (arising from differential fitness effects on individuals expressing or not expressing helping) and can be subjected to different synergies of scale (arising from economies or diseconomies of scale). We find that relatedness and synergies of kind and scale can interact to generate nontrivial evolutionary dynamics, such as cases of bistable coexistence featuring both a stable equilibrium with a positive level of helping and an unstable helping threshold. This broadens the qualitative effects of relatedness (or spatial structure) on the evolution of helping.

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Generalizations of Hamilton's rule applied to non-additive public goods games with random group size

Cited by 4 publications

References 27 publications

Stochasticity and non-additivity expose hidden evolutionary pathways to cooperation

Stochasticity and non-additivity expose hidden evolutionary pathways to cooperation

The general form of Hamilton’s rule makes no predictions and cannot be tested empirically

Relatedness and synergies of kind and scale in the evolution of helping

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