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

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractA widespread claim in evolutionary theory is that every group selection model can be recast in terms of inclusive …tness. 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 …tness. The …rst is a limitation across models. We show that if inclusive …tness is to always give the correct prediction, the de…nition of relatedness needs to change, continuously, along with changes in the parameters of the model. This results in in…nitely many di¤erent de…nitions of relatedness -one for every parameter value -which strips relatedness of its meaning. The second limitation is across time. We show that one can …nd the trajectory for the group selection model by solving a partial di¤erential equation, and that it is mathematically impossible to do this using inclusive …tness. KeywordsGroup selection, inclusive …tness, kin selection, equivalence, social evolution. 1Group selection has always been a controversial issue. It is both advocated as an essential ingredient of human evolution (1-2), and described as a super ‡uous concept, that does not explain any phenomenon we do not already understand with other models (3-5). While there is disagreement concerning the relevance, both sides of the debate have come to agree that group selection models can always be reformulated in terms of inclusive …tness (6-13).The agreement on the equivalence still leaves room to disagree which one of the two is more valuable for understanding how group selection works. One position is that, since both are equivalent, there is no reason to look at group selection models other than through the lens of inclusive …tness (4, 7, 9,(11)(12)(13). Another position is that, even though the two are equivalent, there is value in the alternative way of looking at models, that stresses a balance of within-group selection and between-group selection (1, 2, 8, 10).Because the "mathematical equivalence" is such a central point of consensus, one would expect it to be a well-de…ned mathematical statement with a mathematical proof. There is, however, no such theorem in the literature (see also 6, 14). As a consequence it remains unclear what "mathematical equivalence" means here, and if the claim is correct. In this paper, we will present a class of group sele...

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“…2 is in line with standard de…nitions in the literature (12,13,(19)(20)(21); see also the Appendix).…”

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confidence: 75%

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

Veelen

Luo

Simon

2014

Journal of Theoretical Biology

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“…It is important to realise that this two-trait optimization approach is not at all at odds with this being a model with di erent levels of selection, when cooperation is concerned (see also Van Veelen, 2009 it looks at the e ect of an in-or decrease of the individual's own cooperative tendency on its own tness. As we will see below, it is an approximation; by taking derivatives for a monomorphic population, it ignores the possibility that this e ect may vary according to the composition of the rest of the group.…”

Section: Resultsmentioning

confidence: 99%

It takes grouping and cooperation to get sociality

Veelen

García

Avilés

2010

Journal of Theoretical Biology

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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 in uence selection for group size, and vice versa, it is worth studying how these traits coevolve. Using a generally applicable two-trait optimization approach, we provide analytical solutions for three speci c models. These solutions describe how cooperative associations of nonrelatives evolve, and predict how large and how cooperative they will be. The analytical solutions help understand how changes in parameter values, such as the group carrying capacity and the costs of cooperation, a ect group size and the level of cooperation in equilibrium. Although the analytical model makes a few simplifying assumptionspopulations are assumed to be monomorphic for grouping as well as for cooperative tendencies, and group size is assumed to be deterministic -simulations show that its predictions are matched quite closely by results for settings where these assumptions do not hold. 1A c c e p t e d m a n u s c r i p t

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“…However, knowing the coefficient of relatedness within groups (R) alone is not, in principle, enough to determine whether cooperation can increase because the fitness functions that we are considering are nonlinear functions of the frequency of cooperators in a group. To calculate the expected fitness of rare cooperators, the entire probability distribution of frequencies is required [13,14,19]. This distribution depends on the population structure.…”

Section: The Modelmentioning

confidence: 99%

A simple rule for the evolution of contingent cooperation in large groups

Schonmann

Boyd

2016

Phil. Trans. R. Soc. B

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One contribution of 18 to a theme issue 'The evolution of cooperation based on direct fitness benefits'. Humans cooperate in large groups of unrelated individuals, and many authors have argued that such cooperation is sustained by contingent reward and punishment. However, such sanctioning systems can also stabilize a wide range of behaviours, including mutually deleterious behaviours. Moreover, it is very likely that large-scale cooperation is derived in the human lineage. Thus, understanding the evolution of mutually beneficial cooperative behaviour requires knowledge of when strategies that support such behaviour can increase when rare. Here, we derive a simple formula that gives the relatedness necessary for contingent cooperation in n-person iterated games to increase when rare. This rule applies to a wide range of pay-off functions and assumes that the strategies supporting cooperation are based on the presence of a threshold fraction of cooperators. This rule suggests that modest levels of relatedness are sufficient for invasion by strategies that make cooperation contingent on previous cooperation by a small fraction of group members. In contrast, only high levels of relatedness allow the invasion by strategies that require near universal cooperation. In order to derive this formula, we introduce a novel methodology for studying evolution in group structured populations including local and global group-size regulation and fluctuations in group size.

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

Cited by 141 publications

References 32 publications

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

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

It takes grouping and cooperation to get sociality

A simple rule for the evolution of contingent cooperation in large groups

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