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NVG meeting, 26 November 2010, Soesterberg

r.B > C. Kin selection theory OK! Tom Wenseleers, Dept. Biology, K.U.Leuven e-mail: tom.wenseleers@bio.kuleuven.be. NVG meeting, 26 November 2010, Soesterberg. Inclusive fitness theory.

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NVG meeting, 26 November 2010, Soesterberg

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  1. r.B > C Kin selection theory OK!Tom Wenseleers, Dept. Biology, K.U.Leuvene-mail: tom.wenseleers@bio.kuleuven.be NVG meeting, 26 November 2010, Soesterberg

  2. Inclusive fitness theory • If youwant to know whether a trait willspread or not you also have to takeintoaccount the effects on relatives • Idea of kinselection or inclusive fitness theory(W.D. Hamilton 1964): helping relatives canbefavouredevenat a cost to oneself when b.r > c • This inequality is known as the relative inclusive fitness effect. It is the partial effect of the actor’s trait on the actor’s own direct fitness (-c) plus the partial effect of the actor’s trait on the fitness of relatives (b), weighted by relatedness (r). • Puts the individual actor at the center of the analysis, and allows one to predict behaviour on the basis of which strategy maximises the individual’s expected inclusive fitness W.D. Hamilton (1964) The genetical evolution of social behaviour. Pt I & II. J. Theor. Biol. 7: 1-52. Cited nearly 7,000 times.

  3. Kin selection theory: its rise and fall??? Wilson Social Research 2005 Edward O. Wilson: tries to denounce kin selection and reinstate group selection as the appropriate framework to study social evolution Wilson & Hölldobler PNAS 2005

  4. Ed Wilson: the rise and fall of the prophet of sociobiology??? Foster, Wenseleers & Ratnieks Trends in Ecol. Evol. 2006

  5. ...but it didn’t help... Wilson & Wilson New Scientist 2007 Wilson & Wilson Q. Rev. Biol. 2007 Wilson & Wilson Amer. Scientist 2007 Wilson BioScience 2007

  6. Some silly quotes "It is often said in research reports on social insects that some particular set of empirical data is “consistent with kin selection theory.” But the same can be said of almost any other imaginable result, and the particular connection of data to the theory remains unclear. Hence, kin selection theory is not wrong. It is instead constructed to arrive at almost any imaginable result, and as a result is largely empty of content. Its abstract parameters can be jury-rigged to fit any set of empirical data, but not built to predict them in any detail, nor have they been able to guide research in profitable new directions." "the theory has contributed little or nothing not already understood from field and experimental studies“ (E.O. Wilson BioScience 2008)

  7. The love-hate relationship of Ed Wilson with Hamilton’s rule Wilson (1975) Sociobiology: The New Synthesis: discusses Hamilton’s rule as a special case of group selection and mentions that “Hamilton’s viewpoint is unstructured. The con-vential parameters of population genetics, allele frequencies, mutation rates, epistasis, migration, group size, and so forth, are mostly omitted from the equations. As a result, Hamilton’s mode of reasoning can be only loosely coupled with the remainder of genetic theory, and the number of predictions it can make is unnecessarily limited.” Hölldobler & Wilson (1990) The Ants, p. 182: better treatment of inclusive fitness theory and mentions that “Hamilton’s rule is robust as a theoretical prediction” Hölldobler & Wilson (2009) The Superorganism: authors criticize kin selection theory in one place, support it in others, at one stage admit that kin and group selection are simply alternative bookkeeping methods to measure gene frequency change, but elsewhere maintain that they are not

  8. Also back at Harvard... Martin Nowak: found 5 supposedly fundamental rules for the evolution of cooperation

  9. ...criticized by others Laurent Lehmann: not a fundamental classification scheme – all the rules ultimately reduce to Hamilton’s rule Ohtsuki et al. (2006): “Natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. ... We note the beautiful similarity of our finding with Hamilton’s rule...” Lehmann et al. (2007): it is Hamilton’s rule!!!

  10. The latest in the series... Martin Nowak, Corina Tarnita, Ed Wilson: IF theory is limited in scope and traditional population genetics and game theory are better frameworks to study social evolution The New York Times: “The scientists argue that studies on animals since Dr. Hamilton’s day have failed to support it.The scientists write that a close look at the underlying math reveals that Dr. Hamilton’s theory is superfluous. It’s precisely like an ancient epicycle in the solar system, said Martin Nowak. The world is much simpler without it.”Others disagree: “This paper, far from showing shortcomings in inclusive fitness theory, shows the shortcomings of the authors”, said Francis Ratnieks of the University of Sussex.

  11. ...others also joined in... “Rather than saying the paper is wrong, it would be more fruitful if critics also went back to basics: state model assumptions, derive predictions, test empirically. Such a return to rigour would help the field advance to the next level.” Arne Traulsen: Hamilton’s rule cannot do evolutionary dynamics and requires weak selection Matthijs van Veelen: statistical derivations of Hamilton’s rule based on the Price equation are no good

  12. wΔz (2007) A series of deaths have started occurring in New York; Some are being found mutilated while others have an equation wΔz = Cov (w,z) carved onto their skin. As police investigate they discover each victim was forced to choose between sacrificing their own life or a loved ones' life. Before long it becomes clear that this perpetrator has suffered just such a similar fate...so now is coping by seeking a way of solving this philosophical enigma. Can Captain Maclean and his officers such as Eddie Argo and his new partner Helen Westcott stop this suspect, because he will not until he gets to the end of this equation. Rated R for strong brutal violence including a rape, gruesome images and pervasive language.

  13. Claim (1) standard natural selection is better than IF theory Abbot et al. (2010) Nature, in press : “Is there a sharp distinction between IF theory and ‘standard natural selection theory’? No. Natural selection explains the appearance of design in the living world, and IF theory explains what this design is for. Specifically, natural selection leads organisms to become adapted as if they were trying to maximize their IF. IF theory is based on population genetics, and is used to make falsifiable predictions about how natural selection shapes phenotypes, and so it is not surprising that it generates identical predictions to those obtained using other methods.” The power of IF theory is that it led to an increadibly powerfulstrategic way of thinking about animal behaviour.

  14. Claim (2) IF theory has many limitations • Nowak et al.(2010): IF theory • requires weak selection (gradual evolution) • cannot deal with synergistic, nonadditivefitness effects • can only deal with pairwise interactions • cannot take into account details of genetic inheritance (e.g. arbitrary dominance) • Each of these claims is manifestly wrong! Corina Tarnita, from http://smartbabesaresexy.blogspot.com/

  15. Where does the confusion come from? • Original version of IF theory (the “gradient” version) was indeed derived in the limit of weak selection • Hamilton (1964) was actually explicit about this: “Considering that, the present use of the coefficients of reIationships is only valid when selection is slow” • The “gradient” version of IF theory was further extended in the ESS IF maximisation methods of Peter Taylor & Steve Frank (1996) and the IF methods of FrançoisRousset (2004), it is also this version that is used by NWT • But there is also a more general, statistical version of IF theory, first derived from the Price equation by Hamilton (1970), which also works under strong selection

  16. Gradient version of IF theory • Simplest gradient version of Hamilton’s rule: • w = fitness of actor, w’ = fitness of recipientg = breeding value for actor’s level of cooperation • E.g. with additive fitness effects :w = 1-C.g + B.g’, w’=1-C.g’ + B.g→ increase in level of cooperation when -C + B.r > 0 • E.g. with nonadditive fitness effects:w = 1-C.g + B.g’ + D.g.g’, w’=1-C.g’ + B.g + D.g.g’ → increase in level of cooperation when (-C+D.g) + (B+D.g).r > 0ESS level of cooperation g*=(C-B.r)/(D(1+r)) relatedness -c b Frank 1997, Wenseleers et al. 2010

  17. Gradient version of IF theory • Can deal with nonadditive fitness interactions since weak selection linearises all nonlinearities + extensions for dominance • Can easily be extended to interactions between > 2 individuals by adding more terms for additional relatives that are affected • Realistic model for continuous traits, probabilistically expressed traits or discrete traits with strong selective effect that are only rarely expressed (low penetrance) • Weak selection is usually realistic since distribution of fitness effects of new mutations usually follows an exponential distribution (most mutants only deviate slightly from wild type) • Also good (1st order) approximation for when selection is strong • IF theory provides an easier, more powerful & general method for finding ESS’s than traditional population genetic theory

  18. Gradient version of IF theory W.D. Hamilton (1995): “...my confidence that I had proved maximisation of inclusive fitness, with or without multiple alleles under weak selection was important to me. I was and still am a Darwinian gradualist for most of the issues of evolutionary change. Most change comes, I believe, through selected alleles that make small modifications to existing struc-ture and behaviour. If one could understand just this case in social situ-ations, who cared much what might happen in the rare cases where the gene changes were great and happened not be disastrous? Whether under social or classical selection, defeat and disappearance would, as always, be the usual outcome for genes that cause large changes.I think that a lot of the  objection to so-called 'reductionism' and 'bean-bag reasoning' directed at Neodarwinist theory comes from people, who, whether through inscrutable private agendas or ignorance, are not gradualists, being instead inhabitants of some imagined world of super-fast progress.Big changes, strong interlocus interactions, hopeful monsters, mutations so abundant and so hopeful that several may be under selection at one time -- these have to be the stuff of their dreams if their criticisms are to make sense. ...”

  19. The Price equation • Hamilton (1970) also derived a more general version ofhis rule based on a population genetic theoremknownas the Price equation (also see Queller 1992, Frank 1997, Gardner et al. 2007, Wenseleers et al. 2010) • Trait (e.g. gene for altruism) willspread in a population when • Covariance between relative fitness and individualallele frequency (or breeding value) + mean fitness-weighted change across inheritance paths (transmission biases, e.g. due to meiotic drive or biased mutation) • Notransmission biases → George Price

  20. Statistical version of Hamilton’s rule • The expected neighbour-modulated fitness of a random individual can be written in an additive way as • β‘s: average effect of being more cooperative than average and of interacting with an individual that is more cooperative than average, defined in terms of partial least-square regressions • (neighbour-modulated fitness condition) • This is identical to the inclusive fitness condition since normally

  21. Statistical version of Hamilton’s rule • That the expected neighbour-modulated fitness is written in an additive way doesn’t mean that fitness has to be frequency independent and that you can’t have synergy, since the costs & benefits can be a function of the behaviour of the other individual(s) • E.g. with discrete strategies (X=Y=0: defect, X=Y=1: cooperate)Gardner et al. (2007) and Wenseleers et al. (2010): under haploidy average costs & benefits can be calculated using least-square regression calculus as

  22. Statistical version of Hamilton’s rule • Cooperation spreads when –c + b.r > 0 i.e. when –C + B.r + D.(r+(1-r).p) > 0, pure ESS p*=(C-(B+D)r)/(D(1-r)) • The Price equation and Hamilton’s rule are dynamically sufficient and can do evolutionary dynamics provided that explicit model assumptions are made, e.g. about the fitness function and how genotypes form, etc... • Costs, benefits & relatedness may change from generation to generation but split in direct & indirect fitness effects always possible • E.g. in the absence of relatedness, cost=-C+p.DNo surprise that cost of cooperating is frequency dependent!! • If you work with breeding values the approach also works for arbitrary dominance

  23. Parallels with an old controversy... • Late 1800's and early 1900's: debate between Mendelian geneticists (e.g. Bateson) and biometrical (i.e. statistical) geneticists (e.g. Pearson) • R.A. Fisher (1918): showed how to integrate bothapproaches by resort to least-square regressionmethods • Showed that one can define the average effect of an allele • Generalised Hamilton’s rule: defines costs & benefits in terms of the average effect of an allele (or strategy) on yourself and on your partners’ fitness using least-square regression calculus • Just as with the average effect, costs & benefits may then become “ecology-dependent”

  24. Claim (3) IF theory has little predictive power and empirical support Abbot et al. (2010) Nature

  25. Claim (3) IF theory has little predictive power and empirical support Abbot et al. (2010) Nature

  26. Successful predictions (1) caste determination Melipona stingless beesgreatly overproduce queens: ca. 10%-20% of all female larvae develop as queens, most are killed soon after eclosion Why? Mystery for >50 years. IF theory: becoming a queen with a probability of 14-20% is the individualIF optimum of developing larvae. z*=(1-Rf)/(1+Rm) Wenseleers et al. J. Evol. Biol. 2003; Ratnieks & Wenseleers Science 2006

  27. Successful predictions (2) policing A priori prediction: workers should be selected to prevent or ‘police’ each others’ reproduction particularly in species with multiple mated queens (Starr 1984, Ratnieks 1988)Ratnieks & Visscher Nature 1989: experimental confirmating of the occurrence of worker policing in the polyandrous honeybeeWenseleers & Ratnieks Am. Nat. 2006: meta-analysis of data from 100 species of ants, bees and wasps showing that worker policing occurs more frequently in species with multiple mated queens Starr 1984, Ratnieks Am. Nat. 1988, Ratnieks & Visscher Nature 1989; Wenseleers & Ratnieks Am. Nat. 2006

  28. Successful predictions (3) number of repr. workers A priori prediction: in colonies with a queen: when policing is more effective fewer workers should try to reproduce in the first place, in queenless colonies: species with low sister-sister relatedness shold have more reproductive workers (Wenseleers et al. 2004) IF optimum percentage of egg-laying workers derived in terms in parameters such as sister-sister relatedness, avg. colony size, policing effectiveness, queen fecundity, etc... Wenseleers & Ratnieks Nature 2006: both predictions empirically confirmed! Asian paper wasp 30 saxon wasp level of selfishness red wesp 10 tree wasp % of egg-laying workers Norwegian wesp median wesp 5 hornet German wasp common wasp honeybee 0 30 50 70 80 90 95 98 99 100 effectiveness of the policing Wenseleers et al. J. Evol. Biol. 2004, Wenseleers & Ratnieks Nature 2006, Ratnieks & Wenseleers TREE 2008

  29. Successful predictions (4) male parentage Stingless bee colonies: no variation in relatedness structure (single once-mated queen) but huge variation in % of males that are workers’ sons (0-95%).Why the variation?Inclusive fitness model: due to variation in the benefit of replacing an average queen-laid egg with a son caused by variation in the % of the queen’s eggs that are female, i.e. variation in costs & benefits.Cost in terms of reduced colony productivity calculated using a differential equation model.

  30. Thanks • T. Wenseleers, A. Gardner & K. R. Foster (2010) Social evolution theory: a review of methods and approaches. In: Social behaviour: genes, ecology and evolution (T. Szekely, A. J. Moore & J. Komdeur, eds). Cambridge University Press. • P. Abbot, ... , T. Wenseleers, S.A. West, ...., J.A. Zeh & A. Zink (2010) Inclusive fitness theory and eusociality. Nature, in press. • F.L.W. Ratnieks & T. Wenseleers (2008) Altruism in insect societies and beyond: voluntary or enforced? Trends in Ecology and Evolution 23: 45-52. • F.L.W. Ratnieks, K.R. Foster & T. Wenseleers (2006) Conflict resolution in insect societies. Annual Review of Entomology 51: 581-608. Kin selection theory OK!!!

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