Altruism and genetic relatedness. Buss Ed. Hoboken: Wiley. Google Scholar. Clutton-Brock, T. Breeding together: Kin selection and mutualism in cooperative vertebrates. Science, , 69— Dawkins, R. The extended phenotype. Oxford: Freeman. Dickinson, J. Fitness consequences of helping. Dickinson Eds. New York: Cambridge University Press. Griffin, A. Kin selection: Fact and fiction. Hamilton, W. The genetical evolution of social behavior, I and II.
Journal of Theoretical Biology, 7 , 1— West, S. Evolutionary explanations for cooperation. Current Biology, 17 16 , R—R Zahavi, A. Oxford: Oxford University Press.
We would also like to know whether different loci in the organism have their critical r pushed to the same extent or even in the same direction. This is why it is important that no one who offers alternatives offers a useful interpretive principle, or explains how far the existing principle is really compromised.
Even if we stopped using inclusive fitness to construct models, we would struggle to continue our empirical work. The reason is straightforward: when you stop using inclusive fitness, you start needing to know genetics Grafen More generally, we can regress the average adult offspring number on i the number of actions taken and ii the number of actions received. Thus even without knowing genotypes, we can apply inclusive fitness.
For NMF the situation is more complicated, and we need to know genotypes. This is because an actor will rarely be a recipient, and so the actors do worse, even though the trait may be favoured by acting on relatives.
We would need to know genotypes to add them to the actors, and to show that possessing the tendency to act was beneficial. To recover a maximisation principle in the field, then, we need genotypes.
At this point, one familiar with modelling may be confused, as models of NMF include relatednesses, and a mathematically equivalent NMF version of Hamilton's rule can be extracted. However, in the field, relatednesses are not needed for NMF — a simple count of mean offspring number already includes this information. However, knowing who to count requires knowing genotypes. Specifically, to average over bearers of the allele in question, we need to know the genotypes of the individuals we study usually impractical and the genetics of the trait in question which we rarely do in practice.
On the other hand, inclusive fitness offers the biologist a measure of phenotype that predicts evolutionary change. Fortunately, the phenotypic gambit, of assuming we do not need to know the genetic architecture of a trait, has proved remarkably successful Grafen ; West and Gardner ; Davies et al. It is also worth noting that the NMF approach does not involve identifying the fitness consequences of a social action.
Rather, we need to know only the genotype and the number of offspring. To study social behavior, we should investigate how the actions of one individual affect the number of offspring of another — that is what social behavior is.
Alternatives to inclusive fitness, such as NMF, do not offer the empirical utility of inclusive fitness. Inclusive fitness offers practical advantages to the modeler. Some authors Nowak et al. This approach is good at predicting gene frequency change in mathematical models.
However, it requires generating a custom model for each new biological scenario. Inclusive fitness is a single framework that works across systems, independent of many though of course not all details.
Hamilton's original model is surprisingly general, allowing both the theoretician and the empiricist to apply the ideas to systems with arbitrary numbers of interactions and many different kinds of individuals. This degree of generality and unity is a rare and sought after gift in the sciences. Of course, there will always be limitations to validity, and the more these are understood the better.
Recent critiques of inclusive fitness e. Before we proceed to discussing practicalities for behavioral ecologists, a simple model will help illustrate some of the above points. It is often pointed out that NMF and inclusive fitness calculations are mathematically equivalent, but what is less often clearly articulated is how they become distinct in practice. Here, a model makes the distinction clear, and shows how conditional behavior brings to light the difficulties of applying NMF.
All behavior is conditional, and models incorporating conditionality are important for understanding one of the advantages of inclusive fitness.
We assume an altruist suffers a cost of c and gives b to each other group member. Hamilton identified two measures of fitness for predicting gene frequency change. NMF is simply a measure of mean offspring number, which sums an individual's fitness in the absence of social interactions and the effects of all individuals in the population on that individual. Inclusive fitness IF sums baseline asocial fitness, and the effect the actor has on all individuals, including itself, weighted by relatedness.
When we substitute as indicated for n A and n B we obtain. The sum of these terms is the diluting factor of Hamilton , and its presence in a model is a sign that NMF rather than IF is used. For example, the important work of Rousset on the evolution of social behavior in structured populations employs NMF. However, in a conditional model, the difference remains very clear when altruists are rare.
Now, we amend our model so that in each group one individual is selected at random to be the potential altruist, and a random other individual is selected to be the potential recipient. One interesting question is which of these quantities is likely to be observable in the absence of genetic information, if all we can observe are the actions, and the offspring numbers of the individuals.
We assume that by direct sequencing or pedigree information or demographic modeling we can estimate r. However, owing to ignorance of p , we cannot estimate most of the NMF values. A second point is that it is not true that selection favors altruism if the NMF of realized altruists is greater than the average NMF.
Thus the correct mathematical statement that NMF predicts gene frequency changes applies in the theoretical situation that we know the genotypes of all the individuals, but not in the common empirical situation where we can observe only the actions. In a more realistic situation, in which altruism opportunities arise randomly across the groups, and in which the chance of taking up an opportunity is genetically multifactorial, the simplicity of the inclusive fitness approach remains, while the NMF approach becomes more and more enmired.
The theoretical and usual empirical situations are thus very distinct, and these differences need to be respected. This simple model illustrates that even if NMF works better in a wider range of theoretical scenarios, as has been pointed out for decades Hamilton ; Grafen ; Lehmann et al.
We now turn to the question of what behavioral ecologists can make of these challenges. The previous discussion suggests that, while offspring number is useful for predicting gene frequency change in mathematical models, for those interested in social behavior and design, it is not a viable option.
Offspring number, being outside the control of the individual, cannot be an individual level design principle. Further, measuring predictions using NMF usually requires knowing the relationship between genotype and phenotype, and being able to measure genotypes, something that is for now impractical in the field and usually the laboratory, too.
How should whole organism biologists proceed, then, if they were to aim to work without using the concept of inclusive fitness? We see three options. The limitations of inclusive fitness have led some authors to call for abandoning an individual level design principle altogether Nowak et al.
However, none of these authors provide i an alternative explanation for design, ii a consistent, unified way to generate predictions, or iii an adaptive principle that can be tested in the field and the laboratory. Instead, they offer no design principle, and suggest making custom models for each new situation, usually using metrics that will be impractical to measure empirically, such as genotypes and the relationship between genotype and phenotype.
It is therefore unsurprising that inclusive fitness has a huge empirical literature and the alternatives essentially none Krebs and Davies , ; Charnov ; Krebs and Davies ; West ; Westneat and Fox ; Davies et al.
This strengthens Birch's resolution that inclusive fitness offers a useful organizing framework, and goes further in highlighting its practical and empirical utility Birch a , b.
While the alternative approaches are useful for theoretical models of gene frequency change, when it comes to social behavior, we see exquisite design, which demands explanation. Further, theories must make predictions that can be tested on real organisms. To be clear, we mean that hypotheses about social behavior are tested using the working hypothesis that inclusive fitness is maximized: we do not mean that it is usually possible to test whether inclusive fitness is in fact maximized.
That would require the same kind of genetic information that we argue is currently vanishingly rare and likely to remain rare. For students of social behavior, abandoning the design approach is not a viable option. Fortunately, the design approach has been spectacularly successful. A more detailed discussion of the utility of adaptationism can be found elsewhere Welch ; Gardner Another option is to rewrite Hamilton's rule so that it makes correct predictions.
Hamilton's rule is an inclusive fitness tool used for predicting the direction of selection. As we have said, inclusive fitness is undefined to the extent that fitness effects are strictly nonadditive. Some authors have pointed out that one option is to redefine components of Hamilton's rule to make it fully general, even allowing for nonadditive interactions Queller , ; Gardner et al. In the standard approach, b and c are effects on offspring number, and r is a measure of genetic similarity between two individuals.
If we replace these values with regressions on fitness, we recover a fully general Hamilton's rule, which does not require additivity and always correctly predicts the direction of evolutionary change Queller ; Gardner et al. Depending on the causal breakdown we desire, nonadditive effects can be incorporated into their own term Queller , , or, alternatively, we can leave the fitness effects b and c unchanged, but replace r with a higher order relatedness coefficient, for example one that captures the relatedness between a focal individual and a pair of recipients Taylor , Both of these are very valuable theoretical advances, showing the complete generality of Hamilton's rule when parameters are chosen correctly.
However, as various authors have pointed out Birch and Okasha ; Birch ; Taylor , ; Allen and Nowak ; Okasha and Martens a , the cost of this generality is a loss in simple interpretation of the terms.
They can no longer be understood as simple effects on offspring number, we no longer have a simple interpretation of social behavior, and, without knowing genetics, the parameters are no longer easily measurable in the field and in the laboratory. Recently some authors Nowak et al. Indeed, critics of the general form of Hamilton's rule have not offered an alternative that rivals the empirical utility of standard Hamilton's rule.
The regression approach is a powerful conceptual advance Rousset , but not empirically useful in the usual situation that the genetics of the individuals studied are unknown.
A final option, then, is to use additive inclusive fitness as an approximation, and remain alert to when this approximation will fail and by how much. Grafen has a list of reasons why additivity is probably nonproblematic in practice. This resolution has been discussed by a number of authors in specific cases, and here we argue for it being a potentially general solution Queller ; Grafen ; Birch a.
Nonadditivity creates a problem for inclusive fitness in that fitness effects and therefore, changes in gene frequency are no longer wholly attributable to a focal genotype. For example, consider a simple two player game with discrete strategies, where each player can choose to play either Cooperate to give b at cost c or Defect, and where when two cooperators interact they receive an added effect, d.
A cooperator will have many occasions on which she encounters another cooperator, and how likely these occasions are depends on the degree of relatedness, or assortation, in the population r. If we imagine a mutant in the population that played Cooperate instead of Defect, increasing r increases the likelihood that its partner's strategy will also be Cooperate, and inclusive fitness fails to take this alteration in the partner's behavior into account.
In other words, it plays Cooperate instead of Defect on one occasion out of many, and the probability that it is the same occasion its related partner also plays Cooperate instead of Defect because of the mutant strategy—it may often play Cooperate in absolute terms is very low Grafen In this case, the only way r impacts the direction of selection is through an actor's vested interest in its social partners. When this type of variability is high, r also determines assortation of strategies, which inclusive fitness does not capture.
Fortunately, a low genetic component of variability will be the norm for populations near equilibria, where it is usually reasonable to suppose we study organisms Fisher ; Grafen , a point endorsed by Birch a , b.
Thus, for traits of interest to behavioral ecologists, inclusive fitness should often make the correct predictions even under nonadditivity. Our point here is to explain the kinds of biological scenarios that deliver this mathematical convenience, extending brief verbal arguments by Grafen and Queller In a companion paper Levin and Grafen, Submitted , we formalize this otherwise verbal argument and discuss two recent papers that look for inclusive fitness maximization but fail to find it Lehmann et al.
Levin and Grafen Submitted show that probabilistic mixing of phenotypes recovers inclusive fitness maximization. We also note that this type of probablistic mixing may also resolve some questions about how inclusive fitness moves from the level of the trait to the individual. Specifically, when individuals adopt different roles in an interaction, it is not always clear how to assign offspring number to the control of one actor, analogous to the challenges of assigning offspring number when there is synergy between traits.
In the absence of a formal analysis, we suspect that this type of nonadditivity will also be resolved by allowing probabilistic mixing. In the meantime, we are reassured that Grafen allowed different types of social actions, including unique roles, and still recovered inclusive fitness maximization.
The effect of conflict on inclusive fitness equilibria is interesting, but beyond the scope of this paper for an entry into that literature, see, e. Genetic conflict would indeed very likely require genetic genetic knowledge to investigate. Of course, effective nonadditivity may not always hold. Fortunately, theory tells us what to be on the lookout for. For example, recent environmental change may mean populations are not near equilibria, and therefore additive genetic variability may be high.
This is a caveat that applies to all evolutionary biologists, not just those studying social dilemmas. More specifically, we might suggest that students of social behavior be on the lookout for clear assortation of actions in nature.
As we have said, nonadditivity is problematic when there is strong assortation of actions, because inclusive fitness calculations do not take that additional effect of relatedness into account. This is something a field or laboratory worker can observe. For example, consider a population of birds in a wood. If relatives are not interacting, we would not expect strategies to be correlated.
The reason, as stated above, is that the chances of two interacting relatives expressing the deviant action on the same occasion are low. If we do observe clear assortation of deviant actions between partners in nature, it can be taken as a red flag that individuals may be engaged in a discrete game, and in this case, inclusive fitness may give the wrong answer if the payoffs are also strongly nonadditive.
This kind of discreteness might be most likely to arise in bacteria, because they are more likely to have single gene phenotypes. It may turn out that situations that generate problems for inclusive fitness are rare in nature. Either way, they do not require abandoning inclusive fitness. Instead, they serve as specific caveats for which to be on the lookout when conducting experiments.
It is worth considering one more aspect of the failure of inclusive fitness. Take, for example, situations in which inclusive fitness would not hold, due to high additive genetic variability and strongly nonadditive fitness effects. Are these exceptional cases consistent, in the sense that they make some consistent prediction as to how we should expect organisms to look or behave?
Should they be more social than inclusive fitness predicts? Queller has suggested that in some cases, including simple two player games, the sign of the nonadditive component, d , contains some information about the direction selection will proceed in.
More generally, two questions are relevant to empirical biologists exploring this issue. Is there some design principle other than inclusive fitness, or is inclusive fitness the central target, with exceptional cases unpredictably moving organisms off the mark in varying directions? And if there is some other central target, does it differ from inclusive fitness in a way we could reliably measure? We surmise, in the absence of relevant work, that deviations depend on details of the genetics in an unilluminating way unless one happens to know the genetics , although of course we would be very interested in any theoretical argument that claims to show the contrary.
If we are interested in exact predictions of gene frequency change in mathematical models, offspring number is the measure of fitness we should use. However, if we are interested in social behavior and design, and in particular behavior and design in nature, we should use inclusive fitness under approximate additivity. It does have some limitations. But the alternatives are worse. And despite its limitations, inclusive fitness has many great conceptual and practical advantages for biologists.
Further, as we have argued here and illustrated elsewhere Levin and Grafen, Submitted , some of the theoretical limitations may disappear under biologically realistic scenarios. If inclusive fitness is applicable, then all biological principles of social behavior are equivalent to it. If inclusive fitness is not applicable, then we need to know genetics, and therefore, there can be no biological principle of social behavior. Thus, the significant questions are: how good an approximation is the inclusive fitness approach, and does it allow the subject of social biology to exist?
For the moment, it is consistent with what little we know that the approximation is reasonable, and the empirical successes of social biology back up this conclusion. Thus, the continuation of work with inclusive fitness is founded on a sophisticated notion of what assumptions are required for exactness of inclusive fitness, the consequences of likely deviations, and the assurance from empirical successes that the working hypothesis is by and large satisfactory. The cost of the nuance of this notion is that it is not easily captured in a fully general model.
But it is conceptually more suited to the various roles inclusive fitness plays within biology than the mathematically general models of population geneticists.
Not only is inclusive fitness a powerful organizing framework Birch a , b , but without it, we would have no useful theoretical approach for understanding social behavior in the laboratory, in the field, and in comparative work. National Center for Biotechnology Information , U.
Evolution; International Journal of Organic Evolution. Published online Apr Samuel R. Levin 1 and Alan Grafen 1 , 2. Author information Article notes Copyright and License information Disclaimer. Levin, Email: ku. Received Jul 23; Accepted Apr 2. Evolution published by Wiley Periodicals, Inc. This article has been cited by other articles in PMC. Inclusive Fitness under Additivity Hamilton observed that adult offspring number, a standard metric of fitness, is affected not just by the actions of an individual but by those of the individuals it interacts with.
The Challenge of Nonadditivity So far we have focused on inclusive fitness under additivity. Conditionality Before we proceed to discussing practicalities for behavioral ecologists, a simple model will help illustrate some of the above points. Practicalities for Behavioral Ecologists The previous discussion suggests that, while offspring number is useful for predicting gene frequency change in mathematical models, for those interested in social behavior and design, it is not a viable option.
Conclusion If we are interested in exact predictions of gene frequency change in mathematical models, offspring number is the measure of fitness we should use. Associate Editor: L. Chevin Handling Editor: M. Inclusive fitness theory and eusociality. Nature :E1. There is no fitness but fitness, and the lineage is its bearer. B Group selection and the hierarchical organization of life.
Inclusive fitness theory becomes an end in itself. BioScience 65 — Games among relatives revisited. There is no inclusive fitness at the level of the individual. Limitations of inclusive fitness. USA — Hamilton's rule and its discontents. The inclusive fitness controversy: finding a way forward. Open Sci. The philosophy of social evolution.
Oxford Univ. Press, Oxford, U. Kin selection and its critics. The validity and value of inclusive fitness theory. B Biol. Genes in conflict: the biology of selfish genetic elements. BelknapHarvard, Cambridge, MA. The theory of sex allocation. Princeton Univ. Press, Princeton, NJ. Cooperation facilitates the colonization of harsh environments.
Promiscuity and the evolutionary transition to complex societies. Nature The descent of man and selection in relation to sex. John Murray, London, U.
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