Title: The Strategic Reference Gene: an organismal theory of inclusive fitness

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1 Title: The Strategic Reference Gene: an organismal theory of inclusive fitness Authors: Lutz Fromhage 1 *, Michael D Jennions 2 Affiliations: 1 Department of Biological and Environmental Science, University of Jyvaskyla, P.O. Box 35, Jyvaskyla, Finland 2 Evolution & Ecology, Research School of Biology, Australian National University, Canberra ACT 2601, Australia *Correspondence to: lutz.fromhage@jyu.fi Abstract: How to define and use the concept of inclusive fitness is a contentious topic in evolutionary theory. Inclusive fitness can be used to calculate selection on a focal gene, but it is also applied to whole organisms, which are predicted to appear designed as if to maximise their inclusive fitness. Here we argue that the latter usage is justified under far broader conditions than previously shown, but only if inclusive fitness is appropriately redefined. Specifically, organisms should maximise the sum of their offspring (including any accrued due to behaviour of relatives), plus any effects on their relatives offspring production, weighted by relatedness. In contrast, most theoreticians have argued that a focal individual s inclusive fitness should exclude any offspring accrued due to the behaviour of relatives. One Sentence summary: We redefine the quantity which organisms should be adapted to maximise. Main Text: What, if anything, are organisms shaped by evolution adapted to achieve (1 3)? To answer this question, consider that natural selection is roughly analogous to trial-and-error learning: mutations create gene variants which affect the phenotypes of organisms expressing them; variants then spread if their causal effects on the world, mediated by phenotype, aid their propagation (4). Accordingly, any naturally selected trait can be said to have evolved because genes contributing to the trait in past generations were more successful than their alternatives at leaving copies in the present. But this raises a question: what kinds of phenotypes should a gene contribute towards to aid its propagation?(3) Hamilton distinguished two causal pathways by which a gene, expressed in a given organism, can aid its propagation: by enhancing the organism s own reproduction (direct fitness), and by causing the organism to enhance the reproduction of others that carry the gene s identical copies (indirect fitness) (5, 6). To capture this insight, he defined inclusive fitness (!" #$%&'()* ) as a combined measure of direct and indirect fitness components. The indirect component is weighted by coefficients of relatedness between the focal organism and the recipients of its social acts. Crucially, the direct component has to be stripped of all components which can be considered as due to the individual s social environment (5). This stripping procedure serves to isolate the gene s causal effects when expressed in the focal organism from any correlated changes that arise because an individual tends to find its own phenotype mirrored by its relatives who also express the gene. We label this tendency the mirror effect. It is important to note that the mirror effect does not apply to all genes (Fig. 1). For example, a gene with a low probability of being expressed in any given individual or situation (i.e. low penetrance) will tend not to be simultaneously expressed in both the actor and the recipient during a social interaction even if both parties possess the gene. Likewise, if the expression of a behaviour is conditional on an

2 asymmetry between social partners (e.g. in size, residency, caste, or any arbitrary convention), the underlying gene is also exempt from the mirror effect (7). Instead of being a mere technicality that needs accounting for, the mirror effect can sometimes affect the direction of selection by biasing the flow of social benefits towards particular genotypes in non-additive interactions (Fig. 2). Hamilton showed that!" #$%&'()* works as a genetic accounting tool to predict when a focal gene is positively selected, which occurs when an individual expressing it enjoys increased inclusive fitness. He inferred from this that, as a long-term outcome of successive genes being selected in this way,!" #$%&'()* is also a phenotypic maximand, i.e. a quantity which organisms shaped by natural selection should be adapted to maximise (2). The phenotypic maximand concept is useful for studying adaptation because it suggests that organismal design can be understood in terms of its causal effects on gene propagation. Specifically, it predicts that an organism s (naturally selected) traits should tend to be shaped so as to cause a higher expected value of the maximand than feasible alternative traits. This implies that, to be a candidate for the role of phenotypic maximand,!" #$%&'()* must refer to a measurable property of an individual organism, reflecting the entire organism s causal effects on gene propagation, and using a concept of relatedness that applies to whole organisms rather than to particular genes only. By contrast, most inclusive fitness models explicitly consider causal effects of particular genes only, predicting that a gene will only spread by selection if it satisfies Hamilton s rule +,. > 0 (where r is relatedness,. and, are changes caused to the reproduction of self and other, and the left-hand-side is jointly called the gene s inclusive fitness effect (5, 8)). This gene-centred view calls for a gene-specific ( genic ) definition of relatedness (9) which unlike pedigree relatedness between organisms accounts for the fact that genetic similarity between self and other for a focal gene can be influenced by processes that do not apply equally to all genes (e.g. non-random assortment of organisms carrying the gene). Similarly, if the magnitude of b is conditional on the recipient s genotype at the focal locus (Fig 2), pedigree relatedness does not correctly capture the resultant effect on the focal gene s propagation. Gene-centred reasoning undermines the idea that individual organisms have a coherent evolutionary interest, in the sense that each of their numerous genes is best propagated by the same phenotype. Some theorists have therefore concluded that inclusive fitness is not a meaningful property of an organism (10 13), which precludes it being a phenotypic maximand (but see (2, 8)). A second problem with!" #$%&'()*, if treated as a property of an organism, is the assumption that effects due to the social environment are independent of the focal organism s phenotype (i.e., fitness effects are strictly additive). In nature, fitness effects often depend on the phenotypes of all parties involved (14, 15). In particular, the magnitude of fitness effects due to the social environment usually depends on the focal individual s phenotype. For example, individuals vary in their efficiency in converting help from others into offspring. In such cases, the effects due to the social environment cannot readily be discarded ( stripped away ) on the grounds that they are not caused by the focal individual (14, 15). Non-additive interactions between actors and recipients can still be analysed with inclusive fitness methods by assuming that genes are of small effect size, which renders gene effects approximately additive (16, 17). However, additivity at the gene level does not justify the stripping of effects at the organism level as is required to measure a focal organism s!" #$%&'()*. To quote Grafen (8): the question of how to define inclusive fitness in the absence of additivity has not been settled, and so fundamental theory on the non-additive case can hardly yet begin. Here we argue that neither of these apparent limitations prevents the use of inclusive fitness as a phenotypic maximand. These problems can be overcome if we use a suitably modified definition of inclusive fitness. The outline of our argument is as follows. Our starting point is the observation that genes with different expression patterns (e.g. high versus low penetrance) can simultaneously be selected for despite having opposite phenotypic effects (Fig. 2, Supplementary Material 1). To 2

3 predict how these opposing forces play out over evolutionary time, we invoke the principle that traits should tend to be eliminated in the long run if they oppose the genome s majority interest. We then introduce the idea of an idealised reference gene as a tool to characterise the genome s majority interest. Finally, we identify our modified version of inclusive fitness as the quantity whose maximisation best serves this majority interest. To have biological meaning, a phenotypic maximand must tend to be approached through gene frequency changes under natural selection. But organisms are integrated units shaped by evolution at thousands of genetic loci over long timespans, so not every positively selected gene has to be a step in this direction. Once a focal gene has spread to propel a population along an evolutionary trajectory in phenotypic space, genetic variation at other loci takes over to determine how the trajectory continues. The focal gene s contribution could either be retained or eliminated. To acknowledge the latter possibility when studying long-term evolution, the commonly used guiding question: what kind of gene will be positively selected? should be complemented by adding, such that its phenotypic effect is not eliminated in the long run. To formalise this idea, we envisage organisms as vehicles (3) for gene propagation, defining an organism s vehicle quality as its general capacity to propagate its genes and their identical copies in a given social environment. To quantify vehicle quality, we envisage a hypothetical reference gene which is (i) present in the focal organism, (ii) rare in the population (iii) subject to Mendelian inheritance, and (iv) rarely or never expressed. These properties are chosen in part (i, ii) to make it easy to measure gene propagation (essentially, by counting copies), and in part (iii, iv) to exclude means of gene propagation that face counter-selection from other, unlinked genes in the population (Box 1). We measure an organism s vehicle quality in terms of how many reference gene copies can be causally attributed to the focal organism. These are the net number of additional copies that arise due to the focal organism s existence. Every sexually produced offspring of the focal organism counts for s copies, and every offspring produced by a relative of degree r counts for sr copies. Here s is the probability of transmitting a reference gene copy to a given offspring, which is given by the focal organism s consanguinity (18) with itself; in diploid, outbreeding populations, 1 = 0.5. And r is pedigree relatedness, i.e. the coefficient of relatedness (18) as it applies to weakly selected genes due to coancestry. This sums to 1 (+ 89 : ) copies, where 89 : is the net number of offspring produced (or not produced) by relatives of degree r (including all of the focal organism s own offspring, for which + = 1), because the focal organism exists. (To be exact, to quantify each reference gene copy s projected contribution to the future gene pool, each offspring should be weighted by V/l, where reproductive value V is the offspring s projected contribution to the future gene pool, and ploidy level l accounts for the fact that a diploid offspring s contribution is shared between two haploid genomes). An organism s vehicle quality is therefore maximised by expressing the phenotype that causes the greatest representation of the reference gene in future generations. This is the case when the organism maximises (+ 89 : ), which is the sum of its own offspring, plus the effects on its relatives number of offspring, weighted by relatedness. We call this Wilson s inclusive fitness,!" =&'>)*, based on a remark by Grafen (19) who called it a common misdefinition of inclusive fitness, given, for example, by Wilson (20). Unlike!" #$%&'()* there is no stripping of the social environment. Grafen argued that!" =&'>)* overestimates a helping gene s inclusive fitness effect because it counts the benefit of helping twice - both when giving and receiving help (19) (Fig. 1, Table S2). Here we argue, however, that this double accounting problem is not really a shortcoming of!" =&'>)*. Instead, it merely reflects the general difficulty of inferring a causal effect from correlational data. This difficulty can be avoided by measuring the effect of an appropriate (experimental) intervention: as explained in the legend to Fig. 1, the correct inclusive fitness effect is readily obtained as the gene s causal effect on a focal organism s!" =&'>)*, compared to the counterfactual where the gene is prevented from being expressed in this individual. 3

4 Based on our definition of vehicle quality and!" =&'>)* we advance a heuristic argument about evolutionary dynamics, and a deductive argument about stability to infer the likely outcome of long-term natural selection on organisms. Consider a positively selected focal gene (of any effect size) that happens to increase vehicle quality through an initially inefficient mechanism, as is likely for novel traits. Other genes elsewhere in the genome that increase vehicle quality by enhancing that efficiency are thereby also selected for. In this way, traits that increase vehicle quality have the potential to evolve through complementary, cumulative contributions from unlinked genes. This potential is crucial because many genes (not necessarily all of whom will have small effects) are usually needed to produce finely adapted and/or complex traits, given the improbability of such traits arising in a single mutational step. Conversely, if a focal gene promotes development of a trait that reduces vehicle quality while facilitating the gene s own propagation (i.e., it is a rogue gene; Box 1), the trait faces counter-selection from elsewhere in the genome. The likely success of the rest of the genome in countering the effect of a rogue gene is aided by the architectural principle that complex structures are more easily destroyed than built. Taken together, these twin considerations suggest that vehicle quality will increase in the long run, even if rogue genes temporarily reverse the trend. This echoes the classic metaphor of organisms being controlled by a parliament of genes (21) that enforces its majority interest by suppressing dissent. In this context, it is relevant that our concept of relatedness is based solely on genetic similarity through coancestry; because this is the source of genetic similarity that, together with Mendelian inheritance, promotes wide agreement across the genome as to what traits best serve each constituent gene s propagation (2, 9). We next turn to an argument about evolutionary stability. Because a rare gene with low penetrance meets the definition of a reference gene, and a reference gene is selected for if it increases!" =&'>)*, only a population whose members already maximise!" =&'>)* (within some readily accessible range of phenotypic possibilities) leaves no scope for invasion of such genes. This implies that the maximisation of!" =&'>)* is necessary for evolutionary stability under far broader conditions than previously reported (22): it merely requires that mutations can arise with any degree of penetrance (i.e. including those with low penetrance, so without mirror effect). In particular, these broader conditions include non-additive fitness effects, and mutations of arbitrary step size. Earlier work (23, 24) that rejected the principle of!" =&'>)* being maximised by organisms made the biologically unrealistic assumption that genes without mirror effect do not exist (Supplementary Material 1). This assumption imposes an artificial genetic constraint because rare mutant genes cannot change the phenotype of the individual they are in without immediately facing a correlated change in its relatives. This constraint inadvertently limits the extent to which organisms can exhibit the optimal phenotype in a given social environment, potentially allowing selection for traits that reduce!" =&'>)* (based on mirror effect outlaw genes; Box 1, Fig. 2). Without this constraint, however, if we allow for multi-locus evolution involving genes with any degree of penetrance and conditionality, such traits will tend to be eliminated by counter-selection, and disappear from populations that exhibit long-term phenotypic stability (25). Although!" #$%&'()* is the conventional way that theoreticians define inclusive fitness, it only works as a phenotypic maximand when the number of offspring which the social environment causes an individual to produce is unaffected by any aspect of the focal individual s phenotype that could be selected for (i.e. when fitness effects are additive). These offspring can then be safely ignored ( stripped out ) because they are beyond the focal individual s control. However, when fitness effects are not additive, or when other individuals respond to the focal individual s phenotype, then the focal individual directly affects the benefits it receives from others. This makes it inappropriate to strip out their effect. Creel s paradox(12) neatly exemplifies the problem this 4

5 creates when trying to account for obviously adaptive traits:!" #$%&'()* implies it is better to be a helper than a breeder (Figure 3; Supplementary Material 3). To try to rescue!" #$%&'()* as a phenotypic maximand, some authors (2, 26) have invoked a general form of Hamilton s rule (HRG) in which costs and benefits are defined as partial regression coefficients (27 29). These are fitted to a population to force agreement between the statements: the gene is positively selected and the gene satisfies Hamilton s rule. This approach ensures that HRG works as an accounting tool for any positively selected gene (including the rogue genes highlighted in Box 1), but it does not resolve how the opposing effects of rogue and other genes on phenotypes play out over longer evolutionary time. As such, HRG is agnostic about organismal design. (See also Supplementary Material 4). Of the two competing versions of inclusive fitness we have discussed, only!" =&'>)* consistently answers the question that drives the empirical research of many evolutionary biologists: what are organisms adapted to achieve? Perhaps surprisingly, this actually increases the usefulness of Hamilton s rule, which now states that, for given effects? on the reproduction of self and other, a behaviour is adaptive (i.e. increases!" =&'>)* ) if it satisfies +@? > 0. The novelty here is that the effects B and C encompass all causal consequences of an organism performing (rather than a focal gene encoding) a behaviour - including any non-additive components that are mediated by the behaviour of others (Supplementary Material 3). This leaves us with two equivalent metaphors for long-term phenotypic evolution. We can think of reference genes strategically trying to maximise their propagation, which is a subtly modified version of the gene s eye view (3). Or we can think of organisms evolving to maximise their vehicle quality. Both views take into account that organisms are integrated systems whose development is shaped by many genes, and, as such, are not bound to perpetually retain traits that face counter-selection from the majority of the genome. Disregarding traits anticipated to face counter-selection imposed by other genes is not a new approach to the study of phenotypic evolution. For example, most evolutionary models already disregard Mendelian outlaw genes (Box 1), despite their high potential to be selected for in the short term. Here we argue that other types of rogue genes should likewise be disregarded in models of phenotypic evolution. Most notably, we include in this category the previously unrecognised class of mirror effect outlaw genes (Box 1), which have generated misleading results in models that failed to include realistic coevolutionary interactions between different types of genes (Fig. 2; Supplementary Material 1). Our main result will probably confirm what many readers have long intuitively thought that organisms appear to be designed to maximise the weighted offspring count that is defined by!" =&'>)*. This view has, however, lacked formal justification. Indeed, this view stands in contradiction to the prevailing orthodoxy in social evolution theory, where!" #$%&'()* is always used. The prevalence of this intuitive view is seen in the persistent tendency to define inclusive fitness as!" =&'>)* in teaching materials and other non-mathematical texts (20, 21, 30). If our present argument is essentially correct, we face the unusual situation that orthodoxy should change to match the textbooks, rather than the other way round. References and Notes: 1. C. Darwin, On the origin of species by means of natural selection. (John Murray, London., 1859). 2. S. A. West, A. Gardner, Adaptation and Inclusive Fitness. Curr. Biol. 23, R577 R584 (2013). 3. R. Dawkins, The Selfish Gene (Oxford Univ. Press, Oxford, UK, 1976). 4. S. A. Frank, G. A. Fox, in The Theory of Evolution, S. M. Scheiner, D. P. Mindell, Eds. (University of Chicago Press, Chicago, 2017), pp W. D. Hamilton, Genetical evolution of social behaviour I. J. Theor. Biol. 7, 1 16 (1964). 6. S. A. Frank, Natural selection. VII. History and interpretation of kin selection theory. J. Evol. Biol. 26, (2013). 7. G. A. Parker, Hamilton s rule and conditionality. Ethol. Ecol. Evol. 1, (1989). 5

6 8. A. Grafen, Optimization of inclusive fitness. J. Theor. Biol. 238, (2006). 9. A. Grafen, A geometric view of relatedness. Oxford Surv. Evol. Biol. 2, (1985). 10. R. Dawkins, The extended phenotype (Oxford University Press, Oxford, UK, 1982). 11. E. Akcay, J. Van Cleve, There is no fitness but fitness, and the lineage is its bearer. Philos. Trans. R. Soc. B Biol. Sci. 371, (2016). 12. D. C. Queller, The measurement and meaning of inclusive fitness. Anim. Behav. 51, (1996). 13. A. Grafen, in Behavioural ecology: an evolutionary approach (1984), pp B. Allen, M. A. Nowak, There is no inclusive fitness at the level of the individual. Curr. Opin. Behav. Sci. 12, (2016). 15. H. P. De Vladar, E. Szathmáry, Beyond Hamilton s rule. Science (80-. ). 356, (2017). 16. P. D. Taylor, S. A. Frank, How to make a kin selection model. J. Theor. Biol. 180, (1996). 17. P. D. Taylor, G. Wild, a Gardner, Direct fitness or inclusive fitness: how shall we model kin selection? J. Evol. Biol. 20, (2007). 18. M. Bulmer, Theoretical evolutionary ecology (Sinauer Associates, Sunderland, MA, 1994). 19. A. Grafen, How Not To Measure Inclusive Fitness. Nature. 298, (1982). 20. E. O. Wilson, Sociobiology (Harvard Univ. Press, Massachusetts, 1975). 21. E. G. Leigh, How does selection reconcile individual advantage with the good of the group? Proc Natl Acad Sci U S A. 74, (1977). 22. L. Lehmann, I. Alger, J. W. Weibull, Does evolution lead to maximizing behavior? Evolution (N. Y). 69, (2015). 23. A. Grafen, The hawk-dove game played between relatives. Anim. Behav. 27, (1979). 24. S. Okasha, J. Martens, Hamilton s rule, inclusive fitness maximization, and the goal of individual behaviour in symmetric two-player games. J. Evol. Biol. 29, (2016). 25. P. Hammerstein, Darwinian adaptation, population genetics and the streetcar theory of evolution. J. Math. Biol. 34, (1996). 26. P. Abbot et al., Inclusive fitness theory and eusociality. Nature. 471, E1 E4 (2011). 27. D. C. Queller, A general model for kin selection. Evolution (N. Y). 46, (1992). 28. A. Gardner, S. A. West, G. Wild, The genetical theory of kin selection. J. Evol. Biol. 24, (2011). 29. A. Gardner, The purpose of adaptation. Interface Focus. 7, (2017). 30. J. Alcock, Animal behavior: an evolutionary approach (Sinauer Associates, Cambridge, MA., 2005). 31. M. van Veelen, B. Allen, M. Hoffman, B. Simon, C. Veller, Hamilton s rule. J. Theor. Biol. 414, (2017). 32. J. Pearl, Causality: Models, Reasoning, and Inference (Cambridge Univ. Press, New York, ed. 2, 2009). 33. A. Gardner, S. A. West, Greenbeards. Evolution (N. Y). 64, (2010). 34. R. D. Alexander, G. Borgia, Group Selection, Altruism, and the Levels of Organization of Life. Annu. Rev. Ecol. Syst. 9, (1978). 35. D. C. Queller, Kin selection and frequency dependence: a game theoretic approach. Biol. J. Linn. Soc. 23, (1984). 36. W. G. S. Hines, J. M. Smith, Games between relatives. J. Theor. Biol. 79, (1979). 37. S. A. West, C. El Mouden, A. Gardner, Sixteen common misconceptions about the evolution of cooperation in humans. Evol. Hum. Behav. 32, (2011). 38. W. D. Hamilton, Genetical evolution of social behaviour II. J. Theor. Biol. 7, (1964). 39. R. Dawkins, Replicator Selection and the Extended Phenotype. Z. Tierpsychol. 47, (1978). 40. M. A. Nowak, C. E. Tarnita, E. O. Wilson, The evolution of eusociality. Nature. 466, (2010). 41. J. Starrfelt, H. Kokko, Bet-hedging-a triple trade-off between means, variances and correlations. Biol. Rev. 87, (2012). 42. P. Kennedy, A. D. Higginson, A. N. Radford, S. Sumner, Altruism in a volatile world. Nature. 555, (2018). 43. A. Grafen, Formal Darwinism, the individual-as-maximizing-agent analogy and bet-hedging. Proc. R. Soc. B Biol. Sci. 266, (1999). 44. A. I. Houston, J. M. McNamara, Models of adaptive behaviour. An approach based on state. (Cambridge Univ. Press, Cambridge, 1999). 45. P. D. Taylor, Altruism in viscous populations - an inclusive fitness model. Evol. Ecol. 7653, (1992). 46. D. S. Wilson, G. B. Pollock, L. A. Dugatkin, Can altruism evolve in purely viscous populations? Evol. Ecol. 6, (1992). 47. J. Maynard Smith, Optimization theory in evolution. Annu. Rev. Ecol. Syst. 9, (1978). 48. J. M. McNamara, A. I. Houston, J. N. Webb, Dynamic kin selection. Proc. R. Soc. B-Biological Sci. 258, (1994). Acknowledgements: We thank Piret Avila, Jaakko Toivonen, Jono Henshaw, and Jussi Lehtonen for discussions and comments on the manuscript; Tom Wenseleers, Zoltan Barta, Jutta Schneider, Mikael Puurtinen, Jannis Liedtke and Sara Calhim for comments on the manuscript; and Erol Akcay and Jeremy van Cleve for helpful criticism. Funding: Academy of Finland (LF; grant ) and the Australian Research Council (MDJ). Author contributions: LF had the idea and wrote the first draft. MDJ contributed through discussion of ideas and writing. Competing interests: We declare no competing interests. Data and materials availability: Code will be made available in an appropriate depository. 6

7 Supplementary Materials: 1) Mirror effect outlaw genes 2) Individual based simulations 3) Maximisation of IFWilson vs. IFHamilton 4) Maximisation of IFWilson vs. neighbour-modulated fitness 5) Questions and answers 7

8 Figure 1. Performance of inclusive fitness measures as an accounting tool for genes without or with mirror effect. Big circles represent adults; the shaded one is the focal actor. Small circles represent offspring produced without help from the social environment. Crossed-out small circles represent offspring not produced as a result of a costly helping act. Small squares represent offspring produced through helping. The shading of small squares represents such offsprings pedigree relatedness to the focal individual, relative to its own offspring. Black arrows represent helping acts performed by the focal individual, pointing to the resultant offspring produced by the non-focal individual. Dashed arrows represent helping acts received by the focal individual from its social environment. We compare!" #$%&'()* with!" =&'>)*, which differs from!" #$%&'()* in that none of the focal individual s offspring are stripped away. A) In a population where by default each individual produces two offspring without giving or receiving help (baseline = 2), a mutant gene without mirror effect causes the focal individual to help a relative, yielding an indirect fitness benefit rb, at cost c. Because the focal individual s behaviour is not mirrored by its relative, we have!" #$%&'()* =!" =&'>)* =,A1BCD9B + +,., and the gene is positively selected if!" >,A1BCD9B (i.e. rb - c > 0). Thus, both!" #$%&'()* and!" =&'>)* work as an accounting tool. B) Similar to A, but with mirror effect: here the mutant gene which causes the focal individual to help is also expressed in any relatives that carry its identical copies. As a result, the focal individual produces F, additional offspring, where F = F[+, I] is the probability of receiving help, which is a function of relatedness r and the gene s frequency, p. This situation yields!" #$%&'()* =,A1BCD9B + +,. (not including the F, offspring produced due to the social environment) and!" =&'>)* =,A1BCD9B + +,. + F,. Now!" #$%&'()* >,A1BCD9B still correctly predicts selection on the focal gene because it isolates the gene s causal effects from the correlational component F, that would arise even if the gene in the focal organism were not expressed (provided fitness effects are additive (31)).!" =&'>)* >,A1BCD9B does not correctly predict selection because the term F, includes a benefit (in the focal individual) whose cost (in another individual) is unaccounted for (19). However, rather than being a shortcoming of!" =&'>)*, this merely reflects the general difficulty of inferring a causal effect from correlational data. The standard scientific way to avoid this problem is through experimental intervention, which can be simulated theoretically with the do operator used in causal modelling (32). Namely, let!"k =&'>)* = L!" =&'>)* MNO(PB9B 9OR BSI+B11BN)T =,A1BCD9B + F, be the focal individual s counterfactual value of!" =&'>)* that would arise if the gene were experimentally prevented from being expressed in the focal individual. Then the focal gene s causal effect on the focal organism s!" =&'>)* is positive if!" =&'>)*!"K =&'>)* = +,. > 0, which recovers the correct inclusive fitness effect. Thus, the focal gene is selected for if expressing it (causally) increases the focal organism s!" =&'>)*. 8

9 Figure 2. Example of how the mirror effect, in combination with non-additive interactions between individuals, can generate selection for a trait that reduces vehicle quality. Consider a population where relatives interact (e.g., pedigree relatedness r = 0.5), and where unilateral help (A) is highly efficient (e.g., b = 10, c = 1) whereas mutual help (B) is completely inefficient due to strong interference between matching phenotypes (symbolised by lightning bolt; d = -10 in the notation of Supplementary Material 1). In this situation, helping cannot evolve based on a gene with full penetrance, because benefits accrue exclusively to individuals who lack the gene in question. Thus, when a full-penetrance helping gene (which is subject to the mirror effect) is introduced at low frequency into the population, its allele (which can be considered a full-penetrance, non-helping gene) will quickly spread back to fixation. This occurs even though, at the phenotypic level, the average individual could increase its vehicle quality by unilaterally helping to reap the indirect benefits shown in A. In other words, even though defection to non-helping reduces vehicle quality, it spreads to fixation based on a mirror effect outlaw gene (Box 1) - leading to an equilibrium where organisms appear not to maximise vehicle quality (hence IFWilson). Crucially, however, this equilibrium is only stable under the unrealistic assumption that genes without mirror effect do not exist (Supplementary Material 1). If they exist (e.g. as modifier genes at other loci), they generate selection for helping due to the indirect benefits shown in A. Put another way, the above equilibrium without helping is an artefact of the unrealistic assumption, albeit commonly made in population genetics models, that a phenotype of interest can only arise through a single mutation, rather than through the cumulative contributions of genes with various levels of effect size, penetrance, and conditional expression. 9

10 Figure 3. Creel s paradox, modified after ref. (12): in an obligate cooperative breeding system where reproduction requires exactly one breeder and one helper, the focal individual has a choice between becoming the breeder (A) or the helper (B), while the non-focal individual (based on some asymmetry) must take the remaining role. Since offspring produced due to the social environment are excluded from!" #$%&'()*, the focal individual has lower!" #$%&'()* in A than B (0 versus 2r), despite transmitting more genes by becoming the breeder. Thus,!" #$%&'()* predicts wrongly that the focal individual should prefer to become the helper. In other words, it gives the wrong answer as to which behaviour should evolve (ref. (12); Supplementary Material 3). By contrast, the focal individual s!" =&'>)* is higher in A than B (2 versus 2+), predicting correctly that the focal individual should prefer to become the breeder. 10

11 Box 1: Rogue genes that can generate selection for traits that reduce vehicle quality Greenbeard genes can spread by causing their bearer to (i) exhibit an observable cue (e.g. a green beard), (ii) recognise this cue in others, and (iii) behave altruistically towards others bearing the cue (3, 10). However, even if a greenbeard gene can arise and spread, the maintenance of its phenotypic traits relies on the genetic constraint that the cue (which enhances vehicle quality) cannot be expressed without the altruistic behaviour (which reduces vehicle quality). In the long run, there will be selection for modifier genes that suppress the altruistic behaviour, but not the cue (33). Mendelian outlaw genes spread at the expense of unlinked genes in the same organism by violating the laws of Mendelian inheritance. For example, a meiotic drive gene that ends up in more than half of an organism s zygotes may spread despite reducing the organism s total number of successful zygotes. Such genes select for unlinked modifier genes that partly or completely neutralise the outlaw gene s phenotypic effect (34). Mirror effect outlaw (MEO) genes, by our definition, reduce vehicle quality but still spread via the mirror effect. This requires non-additive fitness effects with interference between similar phenotypes (e.g. mutual help is less efficient than unilateral help), such that one s relatives correlated response is a disincentive against expressing a trait (Fig. 2). In the long run, however, MEO genes should not prevent organisms from maximising vehicle quality, because equilibria established by MEO genes under the unrealistic assumption that genes without mirror effect do not exist are unstable when this assumption is relaxed (Supplementary Material 1). MEO genes merit inclusion here, not because there is empirical evidence for them (indeed, we are unaware of attempts to look for them), but because many theoretical models (22 24, 31) have unwittingly made assumptions under which MEO genes are expected to occur. This has prompted conclusions which, at face value, appear to contradict our result that evolution leads to the maximisation of!" =&'>)*. 11

12 Supplementary Material 1: Mirror effect outlaw genes We have defined mirror effect outlaw (MEO) genes as genes which reduce the vehicle quality of the individuals expressing them, but which still spread via the mirror effect. This definition implies that MEO genes have phenotypic effects that are subject to counter-selection at other loci. In particular, it follows from our definition of vehicle quality that an unlinked modifier gene leaves more copies in the next generation if it slightly reduces the MEO gene s probability of being expressed. This follows because the modifier gene resembles a reference gene in being rarely expressed (only in rare instances where its small effect on the MEO gene is realised), implying that fewer copies of it are produced if the focal organism s vehicle quality is reduced. The above argument suggests that, if MEO genes exist, they are unlikely to contribute to organismal design in the long run. It leaves open, however, under what circumstances MEO genes can exist, and how their potential existence has influenced earlier findings (23, 24) that selection does not lead to maximisation of!" =&'>)*. Here we use a model to address these points and argue that MEO genes pose no impediment to!" =&'>)* being a phenotypic maximand. First, we characterise the conditions under which there is selection for behaviours encoded by genes with mirror effect. Next, we characterise the conditions under which there is selection for behaviours encoded by genes without mirror effect. Then, we compare the two sets of conditions to identify conditions where selection acting on genes with or without mirror effect favours opposite phenotypes. These are the conditions where MEO genes can occur. Finally, we show that equilibria established by MEO genes (at which!" =&'>)* is not maximised) are not stable against invasion by mutant genes without mirror effect, whereas the corresponding equilibria established by genes without mirror effect (at which!" =&'>)* is maximised) are stable against mutant genes both with and without mirror effect. Consider a haploid species (for simplicity) with the following life cycle: individuals interact for one round of a pairwise game, played between relatives of pedigree relatedness r. For example, everyone interacts once with a full sibling (+ = 0.5), or everyone interacts once with a half-sibling (+ = 0.25), or everyone interacts once with either a clone (with probability r) or with an unrelated individual. The essential point is that a rare gene, if present in a focal individual, occurs in its social partner with probability r due to coancestry. After this pairwise interaction, individuals disperse randomly, mate, and reproduce. There are two behavioural options: cooperate (denoted + ) or defect (denoted - ). If a focal individual cooperates, it pays cost c to provide to its relative either benefit b (if the relative defects) or, + N (if the relative cooperates). If the focal individual defects, it pays no cost nor does it provide a benefit. If there is synergy (N > 0), mutual cooperation is more efficient than unilateral cooperation. If there is interference (N < 0), unilateral cooperation is more efficient than mutual cooperation. If fitness effects are additive (N = 0), mutual and unilateral cooperation are equally efficient. focal actor non-focal actor b + d - c - c - b 0 The focal individual s resultant payoffs, as listed in the matrix above, are changes in reproductive success: i.e., offspring produced (or not produced) as a result of the interaction, as compared to some baseline number. Genes with mirror effect Consider a gene which always causes its carriers to cooperate, whereas its allele always causes its carriers to defect. In a population where relatives interact, this type of gene expression creates a mirror effect, i.e. a tendency of individuals to interact disproportionally with their own type. 12

13 Specifically, let relatedness r cause phenotypic correlation X = + between social partners, such that the probability of facing a given phenotype is conditional on one s own phenotype as follows (35): cooperators face a cooperator with probability F Y = X + (1 X)I, while facing a defector with probability (1 F Y ). Here, R is the probability that a non-focal individual mirrors a focal individual s phenotype because their genes at the focal locus are identical by descent; and p, the frequency of cooperation in the population, corresponds to the probability that a focal cooperator faces a cooperator even when their genes at the focal locus are not identical by descent. Defectors face a cooperator with probability F Z = (1 X)I, while facing a defector with probability = (1 F Z ). This leads to expected payoffs [ Y = F Y (, + N.) + (1 F Y )(.) for cooperators and [ Z = F Z (,) for defectors. Since we are here concerned with genes that are always expressed, personal pay-offs of each phenotype are representative of the underlying genes transmission success. Hence we can use personal pay-offs of each phenotype to infer the direction of selection. If [ Y = [ Z, the focal gene for cooperation is selectively neutral. Solving for p, this occurs at equilibrium frequency I = ]Z:(^Y_) _(`Z:) (1). Likewise, the focal gene for cooperation is selected positively when [ Y > [ Z, and negatively when [ Y < [ Z. By substituting into these inequalities, we can characterise selection as follows. Given synergy (N > 0), cooperation is selected positively while I > I and negatively while I < I. This implies that, if p* is an internal equilibrium (i.e., in the range 0 < I < 1), it is unstable due to positive frequency-dependent selection. Given interference (N < 0), cooperation is selected positively while I < I and negatively while I > I. This implies that, if p* is an internal equilibrium, it is stable due to negative frequency-dependent selection. This is the equilibrium found in earlier studies (23, 24) where!" =&'>)* was not maximised. Genes without mirror effect In a population where interacting phenotypes tend to resemble each other due to the expression of genes with mirror effect (see above), consider selection at a second locus unlinked to the first. At this second (previously neutral) locus, a rare mutant gene variant arises that encodes defection without mirror effect (e.g., a reference gene), which transforms individuals that would otherwise have cooperated into defectors. If a focal individual expressing this defector gene faces a cooperator (as happens with probability F Y, since the focal individual would have cooperated but for the focal gene s effect), it obtains payoff b instead of, + N., amounting to net gain N +.. If the focal individual faces a defector (with probability 1 F Y ), it obtains payoff 0 instead of., amounting to net gain c. Thus, the focal gene s causal effect on the focal individual s expected change in direct fitness, as a result of defecting, is 8 _&:a]( = F Y ( N +.) + (1 F Y ).. Since a gene without mirror effect is not expressed by every individual that carries it, its transmission success cannot be inferred from exclusively considering the personal payoffs of each phenotype. Instead, the payoffs of individuals that carry the focal gene but do not express it must also be accounted for. We do this by considering indirect effects, mediated by the relative s payoff: if the relative is a cooperator, it obtains (due to the focal individual s change in behaviour). instead of, + N., amounting to net change, N. If the relative is a defector, it obtains 0 instead of,, amounting to net change,. Thus, the focal gene s causal effect on the focal individual s change in indirect fitness, as a result of defecting, is 8 &*_&:a]( = +[F Y (, N) + (1 F Y )(,)]. The focal gene encoding defection is selectively neutral if it has zero net effect on the number of copies transmitted to the next generation. This net effect includes all causal effects of the focal gene being expressed (compared to the counterfactual (32) of not being expressed) in the focal individual. Selective neutrality occurs when 8 _&:a]( + 8 &*_&:a]( = 0; i.e., when expressing the focal gene does not change the focal individual s vehicle quality. This occurs when I equals 13

14 I Z = ]Z:(^Y_Y:_) _(`Z: b ) (2). Likewise, when 8 _&:a]( + 8 &*_&:a]( > 0, the focal gene is selected positively because it causes more copies to be transmitted to the next generation (compared to the number transmitted in the absence of its phenotypic effect; i.e. compared to a neutral gene). And when 8 _&:a]( + 8 &*_&:a]( < 0, the focal gene is negatively selected for analogous reasons. By substituting into these inequalities, we can characterise selection as follows. Given synergy (N > 0), the focal gene is selected positively if I < I Z (i.e., the frequency of cooperators is sufficiently low) and negatively if I > I Z. Given interference (N < 0), the focal gene is selected positively if I > I Z (i.e., the frequency of cooperators is sufficiently high) and negatively if I < I Z. Conversely, now consider selection for a rare gene encoding cooperation without mirror effect, which transforms individuals that would otherwise have defected into cooperators. If a focal individual expressing this gene faces a cooperator (as happens with probability F Z, since the focal individual would have defected but for the focal gene s effect), it obtains payoff, + N. instead of b, amounting to net gain N.. If the focal individual faces a defector (with probability 1 F Z ), it obtains payoff. instead of 0, amounting to net gain.. Thus, the focal gene s causal effect on the focal individual s expected change in direct fitness, as a result of defecting, is 8 _&:a]( = F Z (N.) + (1 F Z ) (.). Now consider indirect effects, mediated by the relative s payoff: if the relative is a cooperator, it obtains (due to the focal individual s change in behaviour), + N. instead of., amounting to net gain, + N. If the relative is a defector, it obtains, instead of 0, amounting to net gain,. Thus, the focal gene s causal effect on the focal individual s change in indirect fitness, as a result of cooperating, is 8 &*_&:a]( = +[F Z (, + N) + (1 F Z )(,)]. The focal gene encoding cooperation is selectively neutral if has zero net effect on its number of copies transmitted to the next generation. This net effect includes all causal effects of the focal gene being expressed (compared to the counterfactual of not being expressed) in the focal individual. Selective neutrality occurs when 8 _&:a]( + 8 &*_&:a]( = 0. This occurs when I equals I Y = ]Z:^ _(`Z: b ) (3) Using the same logic as above, we can characterise selection as follows. Given synergy (N > 0), the focal gene is selected positively if I > I Y (i.e., the frequency of cooperators is sufficiently high) and negatively if I < I Y. Given interference (N < 0), the focal gene is selected positively if I < I Y (i.e., the frequency of cooperators is sufficiently low) and negatively if I > I Y. Mirror effect outlaw genes By our definition, a MEO gene spreads via the mirror effect despite (on average) reducing the vehicle quality of the individuals expressing it. This occurs when a trait is positively selected as described in Genes with mirror effect above, while the opposite trait is positively selected as described in Genes without mirror effect. The conditions for this to occur simultaneously can only be met when there is interference, N < 0 (Table S1). Then, a MEO gene for cooperation can spread at some I < I whenever pure defection is not an ESS. Likewise, a MEO gene for defection can spread at some I > I whenever pure cooperation is not an ESS. Intuitively, these findings can be explained as follows. Interference reduces the efficiency of cooperating with other cooperators. This creates conditions where switching to cooperation is worthwhile only if it can be done unilaterally, but not if it involves a correlated switch (due to the mirror effect) by the social partner. Likewise, there are conditions where switching to defection is worthwhile only if it can be done unilaterally, but not if the switch is mirrored by relatives. It is, perhaps, not obvious why MEO genes do not occur under synergy (N > 0), even though the mirror effect broadens the conditions under which a gene for cooperation can invade (from +, 14

15 . > 0 without mirror effect, to +,. + +N > 0 with mirror effect (24)). In the range where only the latter condition holds, the mirror effect evidently reverses the direction of selection, but it does so without reducing cooperators vehicle quality. Intuitively this can be explained as follows: the mirror effect elevates the (local) frequency of cooperators around any focal cooperator, up to the point where cooperation becomes optimal given positive frequency-dependent selection. Reciprocal invasion of genes with or without mirror effect What phenotypes will evolve in the long run, if predicted equilibria differ based on genes with or without mirror effect? This depends, in part, on whether each equilibrium can be invaded by genes of the other type. In what follows we assume N < 0, as required for stable mixed equilibria to exist. Because a gene for cooperation without mirror effect is selected for if I < I Y (see above), the equilibrium at I (with mirror effect) can be invaded by a gene for cooperation without mirror effect if I < I Y. This yields +,. + N(1 + +) < 0, which is the condition for pure cooperation not being an ESS (24). Thus, whenever pure cooperation is not an ESS, an equilibrium I based on the mirror effect can be invaded by a gene for cooperation without mirror effect. Similarly, the equilibrium at I can be invaded by a gene for defection without mirror effect if I > I Z. This yields +,. > 0, which is always true when I > 0 in the first place. Thus, any mixed equilibrium based on the mirror effect can be invaded by a gene for defection without mirror effect. Under the same parameter settings, two kinds of equilibrium can exist at which vehicle quality is maximised, such that mutant genes without mirror effect cannot invade. We do not model explicitly how these equilibria might be reached (but see Supplementary Material 2). Instead, we merely note that eventually one of them should be reached if phenotypic evolution follows the genome s majority interest towards increased vehicle quality. Symmetrical ESS If there exists no asymmetry (or negotiation) between interacting individuals on which gene expression could be conditional, then the mirror effect can still be avoided by genes having low penetrance (i.e., a low probability of being expressed in any given individual or situation). Successive invasions of such genes will tend to reduce the phenotypic correlation towards X = 0, so that F Y = F Z = I (i.e., the probability of facing a cooperator is independent of the focal individual s phenotype, and equals the frequency of cooperators in the population). Re-calculating either I Y or I Z with these settings yields the mixed ESS I = ]Z:^ as the value of p at which _(`Y:) further mutants without mirror effect cannot obtain a selective advantage by switching phenotypes one way or the other. This equilibrium may be approached in phenotypic space by the combined action of genes with and without mirror effect, where genes with successively weaker mirror effect are necessary to do the fine-tuning near the equilibrium (Supplementary Material 2). The average payoff in this population is [d = I [ Y + (1 I )[ Z, where [ Y = I (, + N.) + (1 I )(.) and [ Z = I (,) are the payoffs of cooperators and defectors, respectively. In this population, a mutant individual carrying a gene for cooperation with mirror effect obtains payoff [e Y = Ff Y (, + N.) + L1 Ff Y T(.), where Ff Y = + + (1 +)I. The resident population is stable against this mutant if [d > [e Y, which leads to +,. + N(1 + +) < 0 (4). This is the condition for pure cooperation not being an ESS, which is always satisfied when a mixed ESS exists. Similarly, a mutant individual carrying a gene for defection with mirror effect obtains payoff [e Z = Ff Z (,), where Ff Z = (1 +)I. The resident population is stable against this mutant if [d > [e Z, which leads to +,. > 0 (5). 15