The Evolution of Altruism: The Sober/Wilson Model* Peter Gildenhuys †‡ Inwhatfollows,IcritiquetheinterpretationthatSoberandWilsonofferoftheirgroup selectionmodelinUntoOthers.SoberandWilsonmistakenlyclaimthattheirmodel operates as an example of Simpson’s paradox and defend an interpretation of their modelaccordingtowhichgroupsareoperateduponbynaturalselection.Intheplace of their interpretation, I offer one that parallels the mathematical calculationofthe model’soutcomeanddoesnotdependonthepostulationofaforceofgroupselection oravalueforgroupfitness. 1.Introduction.InUntoOthers:TheEvolutionandPsychologyofUnselfish Behavior(1998),ElliotSoberandDavidSloanWilsonmakesomeconsid- erableheadwayinexplainingtheevolutionofaltruisticbehaviorthrough the development of a model that specifies circumstances in which there canbeselectionforaltruism.Whilethisadvanceissignificant,Soberand Wilson’sdefinitionsbothofa“biologicalgroup”andof“altruism”remain inadequate.IwillpointouttheseflawsasIgoalong,butmymaincritical focus will be on Sober and Wilson’s interpretation of the mathematical model they putforward to explaintheevolutionofaltruism.Novalueis given for “group fitness” in the mathematical representation of their model, which leaves their explanation of the evolution of altruism by groupselectionquestionable.IwanttocontestSoberandWilson’sinter- pretationofthemathematicalmodeltheypresentintheirtextbypresent- ing an alternative causal analysis of what is going on when altruism evolves in the circumstances hypothesized by Sober and Wilson. First, I *ReceivedDecember2001;revisedAugust2002. †To contactthe author, please writetoPeterGildenhuys,DepartmentofHistoryand PhilosophyofScience,1017CL,UniversityofPittsburgh,Pittsburgh,PA15260;e-mail: [email protected]. ‡Thanks to David Hull and two anonymous referees for their helpful commentson earlierdraftsofthispaper. PhilosophyofScience,70(January2003)pp.27–48.0031-8248/2003/7001-0004$10.00 Copyright2003bythePhilosophyofScienceAssociation.Allrightsreserved. 27 28   lay out thegeneralmodel ofgroupselectionfromUntoOthers,andthen IcriticizeSoberandWilson’sinterpretationofhowitworks.Next,Ipres- ent my own version of the situation described by Sober and Wilson. Fi- nally, I will argue that there is a case for group selection here, or rather selection operating between individual populations, but there is no case forgroupselectionoccurringbetweenthesubgroupsonwhichSoberand Wilsonfocus. 2. The General Model of Group Selection. Sober and Wilson eschew the simple model of altruism according to which altruism is sustained in a populationbecauseeveryoneisanaltruist.Insuchasituation,reciprocity isguaranteedstraightforwardlyamongaltruists;noonebutaltruistsbene- fits from altruism. But such models suffer from a couple of familiar ob- jections.First,theydonotexplaintheevolutionofaltruism,onlyitsper- petuation. Second, were a selfish alternative allele to arise within a population,itwouldeliminatethealtruisticallelebytakingadvantageof thealtruisticbehaviorofotherswithoutitselfpayingthecostsofaltruistic behavior. The Sober and Wilson model is more complex than the simple model andworksthisway:Apopulationoforganisms,onlysomeofwhichcarry genes that code for altruism, is split into subgroups in which interaction among organisms takes place, sometimes for only a small portion of the developmentoforganisms,sometimesformultiplegenerations.Afterthis, theorganismscongregateintoaglobalpopulationbeforeoncemorebeing distributed into new subgroups with a different assortment of members. The cycle continues, with new subgroups formed at every cycle. For al- truism to evolve within the population, everything depends on the char- acterofthesubgroupsformedwithinit.Itisonlywhenthesubgroupsare uneven in terms of their proportion of altruists and nonaltruists that al- truistsstandafightingchance. The most basic version of the model, the one that Sober and Wilson concentrateuponintheirexposition,presentsalargepopulationsplitinto two subgroups, the members of which interact in some fashion relevant tothefitnessofeachindividual.1Whenthelargegroupdivides,twosub- groups that are disproportionate in their constitution are formed: one subgroup contains 80 percent altruists and 20 percent nonaltruists, the othercontains80percentnonaltruistsand20percentaltruists.Thealtru- ists acquire an evolutionary edge because, by and large, they help other altruists whilethe majority of nonaltruistsaresegregatedintoadifferent subgroup.Ofcourse,thenonaltruistsdocapitalizeonthealtruismoftheir 1.Twosubgroups,ratherthanthreeormore,areeasiertodealwithmathematically, butnothingdependsonthenumberofsubgroupsformedoutoftheglobalpopulation.   : ⁄  29 fellows,buttoofewofthemturnupinthesamegroupasthemajorityof altruists, so they profit less than do other altruists from the altruism of their conspecifics. Because most of the altruists are in a group together with only a few nonaltruists, on average the altruists with their altruistic genesfinishaheadbyco-operatingwithoneanother. As the number of altruists within the global population grows, it be- comesmorebeneficialforthenonaltruiststofreeload,soaltruismcannot take over a population. Instead, a polymorphism evolves, kept stable by frequency-dependent selection. The more altruists there are, the more it paystobeselfish.Thefeweraltruiststhereare,themoreitpaystobean altruist, though it is worth remarking that altruists will gain ground againstnonaltruistsbeginningataverylowpopulationdensityonlywhen such pioneer altruists somehow manage to end up in the same subgroup so as to take advantage of each other’s altruism. Early on, Sober and Wilson offer a hypothetical scenario involving the infamous D. dendriti- cum “brain-worm” parasite that shows how altruism could evolve intoa stable polymorphism with selfishness beginning from a single mutant al- truistic parasite. Sober and Wilson discuss the formation of biased sub- groupsmoregenerallylateronintheirwork,somethingIgettobelow. Here are the numbers that Sober and Wilson lay out for the simplest versionoftheirgroupselectionmodel(1998,25): Group1 Group2 n 100 100 p 0.2 0.8 Wa 10(cid:1)1(cid:2)5(19)/99(cid:3)9.96 10(cid:1)1(cid:2)5(79)/99(cid:3)12.99 Ws 10(cid:2)5(20)/99(cid:3)11.01 10(cid:2)5(80)/99(cid:3)14.04 n(cid:4) 1080 1320 p(cid:4) 0.184 0.787 GlobalPopulation 100(cid:2)100(cid:3)200 N [0.2(100)(cid:2)0.8(100)]/200(cid:3)0.5 P N(cid:4) 1080(cid:2)1320(cid:3)2400 P(cid:4) [0.184(1080)(cid:2)0.787(1320)]/2400(cid:3)0.516 n(cid:3)numberoforganismsinasubgroup p(cid:3)proportionofsubgroupmembersthatarealtruistic Wa(cid:3)averagefitnessofaltruists Ws(cid:3)averagefitnessofnonaltruists 30   n(cid:4)(cid:3)numberoforganismsafterinteractionwithinsubgroups p(cid:4)(cid:3)proportionofsubgroupmembersthatarealtruisticaftersubgroup interaction N(cid:3)numberoforganismsintheglobalpopulation P(cid:3)proportionoftheglobalpopulationthatisaltruistic N(cid:4)(cid:3)numberoforganismsintheglobalpopulationaftersubgroupin- teraction P(cid:4)(cid:3)proportionoftheglobalpopulationthatisaltruistic IhavedescribedSoberandWilson’smodelasoneinwhichaltruismis sustainedbyaspecificsortofgroupstructureallowingaltruisticgenesto causethereplicationofaltruisticgenesinotherorganismsthroughaltru- isticbehavior.Theimportanceofthepossibilityofaltruisticgenescausing their replication inthis manner is whatexplainstherequirementthatthe subgroupsvaryintheirproportionofaltruists.Altruistsmustbegrouped together such that more altruists benefit from altruistic deeds than do nonaltruists. ThisisnothowSoberandWilsonunderstandtheirmodel.Theyclaim that two sorts of forces are at work in the above scenario, the force of organismic(theysay“individual”)selectionandtheforceofgroupselec- tion.Theforceofgroupselectionpromotesaltruismwithinthesubgroups, while the force of organismic selection promotes selfishness. When con- sidering the evolution of altruism, Sober and Wilson taketheseforcesto actinoppositiontooneanother: Between-group selection favors the evolution of altruism; within- group selection favors the evolution of selfishness. These two pro- cessesopposeeachother.Ifaltruismmanagestoevolve,thisindicates thatthegroup-selectionprocesshasbeenstrongenoughtooverwhelm theforcepushingintheoppositedirection.(1998,33) The“force”ofgroupselectionactsinoppositiontothe“force”oforgan- ismicselectioninjustthesamewaythatNewtonianforcescanopposeone another. The analogy made by Sober and Wilson (1998, 33) is withindi- vidualspushinguponabilliardballindifferentdirections.Altruismpro- motes the “group fitness” of the subgroups, causing them to grow larger attheexpenseoftheorganismicfitnessoftheirmembers,whileselfishness promotes organismic fitness, the reproduction of organisms within the subgroup, at the expense of the fitness of the subgroup. When theforces of group selection for altruism and the force of organismic selection for selfishnesscancelout,thestablepolymorphismisreached. Sober and Wilson’s understanding of their own model suffers from a seriousdrawback.Despitetheirrepeateduseof“groupfitness”todescribe what is going on in their model, there is no value in their mathematical   : ⁄  31 analysisfortheterm.Instead,thefitnesscalculationsaredoneentirelyin terms of thefitness ofdifferenttrait groups withineachsubgroup.These traitgroupsarethepopulationofaltruistsinsubgroupone,thepopulation of nonaltruists in subgroup one, the group of altruists in subgroup two, andthegroupofnonaltruistsinsubgrouptwo. To show that “group fitness” is never used inSober and Wilson’scal- culations,and thatthey are madeinstead using fitnessvaluesascribedto traitgroups,let’swalkthroughSoberandWilson’scalculations.Theav- erage fitnesses for the four trait groups (group 1 altruists, group 1 non- altruists,group2altruists,group2nonaltruists)appearinlinesthreeand four. These are calculated by giving everyone a base fitness value of ten units,subtractingthecostofaltruism,ifperformed,andaddingthebene- fits of altruism received. How much fitness is gained by the members of each subgroup from others’ altruistic actions is directly proportional to theconstitutionofthesubgroup.Morealtruistsinasubgroupmeansmore benefitforeveryoneinthesubgroup. The next number to appear in Sober and Wilson’s mathematical for- mulation is n(cid:4), reflecting the new size of the subgroups. This figure is generated (1998, 20–21) for each subgroup by multiplying the average fitnessesofthealtruistsbytheirfrequencywithinthepopulation,perform- ingthesameoperationonthenonaltruists,addingtheproductstogether, and multiplying the sum by the number ofindividualsineachsubgroup: n(cid:4)(cid:3)n[pWa(cid:2)(1-p-Ws)].Noticehowthenewsizeofthesubgroupmust becalculatedbyaddingthegrowthofeachofitstraitgroups,thealtruists andthenonaltruists,separately.Thesymbolp(cid:4)representsthepercentage ofaltruistswithinthesubgroupafterinteractionamongitsmembers.This value is generated by multiplying the original number of altruists within the subgroup (np) by their average fitness and dividing this figure by the totalnumberofmembersofthesubgroupafterinteraction. At this point, Sober and Wilson have values for the average fitness of altruistsandnonaltruistswithineachsubgroup,theproportionofaltruists in each subgroup, and the size of each subgroup. In the last two lines of their mathematical analysis, they use these values to generate a value for thesizeofthecombinedgroupthroughsimpleaddition,aswellasavalue fortheproportionoftheglobalpopulationthatisaltruistic.Nowheredoes any value for “group fitness” fit into the mathematical representation. Rather,suchavaluecanatbestbeabstractedbycomparingthegrowthof thegroupwithahighproportionofaltruists(grouptwo)withtheonethat hasalowproportionofaltruists(groupone).Thegroupwithmorealtruists growslargerandhenceis“morefit”(SoberandWilson1998,26). Sober and Wilson call group selection “the mechanism that we have proposedtoexplaintheevolutionofaltruism”(1998,31;myitalics),and also tell us that “if altruism manages to evolve, this indicates that the 32   group-selection process has been strong enough to overwhelm the force pushingintheotherdirection”(1998,33;myitalics).Theuseofmultiple terms to capture the role of group selection in the model, along with the aforementionedforceanalogy,alreadyindicatessomeconfusionoverpre- ciselywhatthisroleismeanttobe.Thedifficultieswiththeirinterpretation become clearer if the parallel they draw between classic formulations of thetheoryofnaturalselectionandtheirowninterpretationoftheirmodel areanalyzed. InapurportedanalogywithstandardformulationsofDarwiniannat- ural selection, Sober and Wilson list the conditions that are necessary to bring about an increase the number of altruists in the global population in their model. Three of the conditions are that there be multiple sub- groups,thatthesethatvaryintheirproportionofaltruists,andthatthey periodicallysubdivideintointeractingsubgroupsbeforereassemblinginto aglobalpopulation(SoberandWilson1998,26).Thefirsttwoconditions correspond to the conditions in the standard formulation of natural se- lectioninwhichtheremustbemultipleindividualsthatvaryintheirchar- acteristics, while the last condition is a special feature of their model. In an extension of the analogy, they also say that subgroups with more al- truistsmustbemorefitthansubgroupswithfeweraltruists,wherefitness isunderstoodastheproductionofmoreorganisms: Theremustbeadirectrelationshipbetweentheproportionofaltruists inthegroupandthegroup’soutput;groupswithmorealtruistsmust be more fit (produce more individual offspring) than groupswithout altruists.(SoberandWilson1998,26) Asitstands,theformulationofthisconditionisinneedofrevision.Quite simply, the groups do not produce offspring, or at least if they did, they wouldproduceoffspringgroupsratherthanindividualorganisms.Butthe latter possibility is explicitly denied by Sober and Wilson: it is of crucial importancetotheoperationofthemodelthatthemembersofanyoneset of subgroups formed by periodic subdivision of the global population recombineafterinteractionintoaglobalpopulationfromwhichnewsub- groupsareformedwithadifferentassortmentofmembers.Thesubgroups inthemodeldonotautonomouslyorindependentlygoontoproducethe nextsetofsubgroups.Thus,theanalogywithDarwinianselectionismis- placed since, according to Darwin,individuals thatare morefit go on to produce other individuals that are more fit, while in Sober and Wilson’s model, individual subgroups that are more fit do not go on to produce individualsubgroupsthataremorefit. SoberandWilsonciteafinalconditionforthesuccessfuloperationof theirmodel:   : ⁄  33 To be sufficient, the differential fitness of groups (the force favoring thealtruists)mustbestrongenoughtocounterthedifferentialfitness ofindividualswithinthegroups(theforcefavoringtheselfishtypes). (1998,26) Hereconfusionhasreallysetin,foritis“fitness,”orrather“differential fitness,” both of organisms and of groups, that is acting as a force that affects the resultant distribution of altruists in the global population. If this last condition is understood as an oblique reference to the fact that, allthingsconsidered,themembersofthegroupwithmorealtruistsmust produce more offspring than do the members of the group with fewer altruists, then the condition is not tendentious or even interesting.How- ever, the claim that fitness is a causally relevant variable that determines how many altruists and nonaltruists end up in the global population is certainly wrongheaded, since thefitness ofthe organisms andthe groups is calculated in terms of the number of offspring actually produced, as explainedinthepriorconditioncitedabove.Asitstands,theconditionis a mere tautology: only if members of one subgroup actually go on to produce more offspring will they produce more offspring. And it would be of no help for Sober and Wilson to claim that what matters is the expectedfitnessoftheorganismsorgroups,ratherthantheiractualfitness, since we would be left wondering why we should expect the results the model produces. Sober and Wilson have not offered us, in the form of a necessary condition, any explanation of why the model produces the re- sultsthatitdoes.Themodelisabstract,whatisexpectedtohappendoes happen. Other factors that could affect the actual reproduction of the organismsareruledoutofthepicturebytheauthors’explicitassumption ofgeneticdeterminism(SoberandWilson1998,22). WhatSoberandWilsonseemtobegettingatwiththeirlastnecessary condition for the evolution of altruism in their model is that the fitness losses accrued from altruists’ altruistic behavior must be somehow com- pensatedforbyafitnessbenefittothosesameorganisms.Groupselection is brought into play by Sober and Wilson to fulfill this role. Altruistic genes benefit the group and group selection favors groups that are more fit,soitisbybeinginthefaster-growinggroupthataltruistsgetcompen- sated for their altruism. But Sober and Wilson fail to provide any more determinatesenseofhowtheforceofgroupselectionoperates:Whatdoes it do that makes groups grow larger? Nor do Sober and Wilson provide anyexplanationofhowthealternativeforceofdifferential“groupfitness” isdetectedexceptthroughtheoutputofthemodelitself.Whileitisclear from the mathematics that one group does in fact grow larger than the other, and that this group is the one with more altruists in it, no expla- nation of how this happens is forthcoming. And, given the manner in 34   which the mathematical calculations are done, there is good reason to suspectthattheoutcomeofthemodelhasnothingtodowithgroupfitness atall.ItisworthstressingthatinSoberandWilson’smodelitisindividual organisms,notgroupsorpopulations,thatreproduceandperformaltru- isticacts.Sowhatweneedisanexplanationofhowaltruistsarecompen- satedadequatelyenoughfortheiraltruismthatappealstofactorsthatare causallyrelevanttothereproductionofindividualaltruists.Groupselec- tionasaforce,oramechanism,oraprocessaffectingorinvolvinggroups and group-level traits is not even a good candidate for fulfilling this ex- planatoryrolebecausethetraitinquestion,altruism,isatraitthatbelongs squarelytoorganismsratherthangroups. So, dispensing with the notion of “group fitness,” whichremainscon- spicuouslyabsentfromthemathematics,whatbecomesofSoberandWil- son’s interpretation of their model? Are there two distinct forces acting here, organismic selection and group selection, or group fitness and or- ganismicfitness,onefavoringtheevolutionofaltruismandtheotherpro- moting selfishness? No. Actually, the gene for altruism and the gene for selfishnesshavedifferenteffectsdependingontheenvironmentsinwhich thealtruisticandselfishorganismsfindthemselves.Whensurroundedby otheraltruists,altruismcausesthereproductionofaltruistsbyincreasing the fitness of other altruists who carry the same gene. Surrounded by nonaltruists,altruismiscostly,andcausesthespreadofselfishnesswithin the population. Each gene has distinct capacities to affect fitness whose operationsaredependentonthemake-upofthesurroundingsubgroup. 3.SoberandWilson’sModelExplained.Usingtheirmathematicalmodel, Iwilloffermyowndetailedexplanationoftheeffectsofaltruisticbehavior onthefitnessofeachaltruist.Altruisticdeedscanbothcauseanetincrease in the fitness of altruists or a net decrease in fitness, depending on the circumstancesinwhichtheyareperformed.Itisbecausebiasedsubgroups are formed in Sober and Wilson’s model that conditions are such that altruismisperpetuatedinthepopulation. SoberandWilsonintroducetheirmodelwithreferencetoapuzzlefor probabilistic theories of causality known as Simpson’s paradox. This is theproblemofspuriouscorrelation.Theclassicexampleofspuriouscor- relation comes from Cartwright (1979). It was thought for a while that being a woman caused one to be rejected from the graduate school at Berkeley.Butresearchersnotedthatineverydepartmentwomenwereno morelikelytoberejectedthanmen,thewomensimplyappliedtotougher departments.Beingawomanwascorrelatedwithavariablethatactually broughtabouttheeffectinquestion. SoberandWilsonofferasimplifiedversionofwhathappenedatBerke- leyasananalogytowhatisgoingonintheirmodel.Theyhaveusimagine   : ⁄  35 that a hundred individuals, ten men and ninety women apply to a tough department with a thirty percent acceptance rate,whileanotherhundred individuals, this time ten of them women and ninety of them men apply to an easier department with a sixty percentacceptancerate.Neitherde- partmentdiscriminates,sothirty-threewomenareacceptedtothegradu- ateschoolalongwithsixtymen.SoberandWilsonwrite: A bias exists in the two departments combined, despite the fact that it does not exist in any single department, because the departments contribute unequally to the total number of applicants who are ac- cepted.Injustthesameway,altruistscanincreaseinfrequencyinthe two groups [in their model] combined, despite the fact that they de- creaseinfrequencywithineachgroup,becausethegroupscontribute unequallytothetotalnumberofoffspring. Sober and Wilson’s analogy is misplaced, and to see why, we need to flesh out the supposed parallel in more detail. Sober and Wilson tell us thatthebiasinthetwogroupsofapplicantscombinedisowingtothefact that each group contributes unequally to the total number of applicants who are accepted. This explanation fits with their explanation of what’s going on in their biological model: altruists can survive and reproduce becausethesubgroupofaltruistsgrowslargerfasterthanthuscontributes morememberstotheglobalpopulation.Butitiseasytoofferadifferent set of numbers that shows a supposed bias in the total number of appli- cantsacceptedtoBerkeleydespitethefactthateachdepartmentcontrib- utes the same number of applicants to the total. Consider the following hypotheticalsituationinwhichahundredpeopleareacceptedatBerkeley, fifty-six men and forty-four women. Each department contributes fifty applicants to this total. The English department is tough, with a forty percentacceptancerate,whilethephysicsdepartment,havingasixtyper- cent acceptance rate, is relatively easy to get into. All that is left is to gerrymander the remaining numbers. To make things work out,let’ssay that there are eighty-three applicants to the physics department and a hundredandtwenty-fiveapplicantstotheEnglishdepartment.Oftheap- plicants to the physics department, seventy-two are men and eleven are women; of the applicants to the English department, thirty-two are men and ninety-three are women. That makes a hundred and four applicants ofeachgender.Thephysicsdepartmentacceptsforty-threemenandseven women. The English department accepts thirteen men and thirty-seven women. Each department contributes an equal number of individuals to the total number of acceptances, fifty people each. But the total number ofacceptancesstilllooksbiased,despitethefactthatthesamenumberof womenappliedasmen,ahundredandfoureach.Fifty-sixmen,andonly forty-fourwomen,areacceptedtoBerkeley. 36   Whether or not each department contributes unequally to the total number of acceptances is irrelevant to the operation of Simpson’s para- dox, as the above hypothetical scenario shows. On the above numbers, thegraduateschoollooksbiased,despitethefactthatneitherdepartment is biased, and also despite the fact that each department contributes an equalnumberofapplicantstotheoveralltotalofacceptances.Soberand Wilson have misunderstood how Simpson’s paradox operates, and it is worthwhilespendingsometimetoclarifyjustthat. Simpson’s paradox is notreallya paradoxsincethereisa clearexpla- nationforwhatisgoingoninsuchscenarios.Apurportedcause,beinga man, does not lead to its purported effect, getting accepted at Berkeley, becauseoftheoperationofanothercausethatworkstoskewthenumbers. In the Berkeley case, the alternate cause in operation is applying to easy departments.Itturnsoutthatbeingamaniscorrelatedwithapplyingto easydepartmentsandbeingawomaniscorrelatedwithapplyingtotough departments. That is what explains the overall bias in the acceptance of candidates to the graduate school. Sober and Wilson explicitly assume geneticdeterminismintheirmodel(1998,22),sotheonlytraitsthatmake a difference to the evolution of altruism in their model are the genes for altruism and selfishness along with the two traits, being among mostly nonaltruists, and being grouped with the majority of altruists, that are acquiredwhenthepopulationdividesintosubgroups.Thedistributionof these last two traits is what is responsible for the success of the altruists overthenonaltruists.Beingsurroundedbyaltruistsincreasesfitness,and altruismiscorrelatedwithbeingsurroundedbyaltruistswhileselfishness iscorrelatedwithbeingsurroundedbynonaltruists. The upshot of the Berkeley case and other situations in which Simp- son’s paradox is at work is that a purported cause, a characteristic that lookstobecausallyconnectedtoanothercharacteristicbasedonstatistical evidence, turns out not to be a cause of the effect at all. Instead, it turns outtobeacharacteristicthatiscorrelatedwithanothercharacteristicthat istherealcauseoftheeffect.2ThisisnotthemoralthatSoberandWilson want to draw with respect to their model. The upshot of Sober and Wil- son’smodelisnotthataltruismdoesnotcausethereproductionofaltru- istsorthereplicationofaltruisticgenes.SoberandWilson’smodelislike the Berkeley case insofar as there is another cause other than altruism relevant to the effect in question that is at work in their model, namely 2.InordertoavoidSimpson’sparadox,advocatesofprobabilistictheoriesofcausality, suchasCartwright(1979)whomSoberandWilsonciteasthesourceoftheBerkeley example, adopt the contextual unanimity clause, stating that causal relationscanbe inferredfromcorrelationsonlyforthosesituationsthatarehomogenouswithrespect toothercausesoftheeffectinquestion.