BMC Evolutionary Biology

Transcription

1 BC Evolutioay Biology Bioed Cetal Reseach aticle Theoy of geomic impitig coflict i social isects David C Quelle* Ope Access Addess: Depatmet of Ecology ad Evolutioay Biology S-70, Rice Uivesity, P.O. Box 892, Housto TX U.S.A David C Quelle* - quelle@ice.edu * Coespodig autho Published: 8 July 2003 BC Evolutioay Biology 2003, 3:5 This aticle is available fom: Received: 8 Jue 2003 Accepted: 8 July Quelle; licesee Bioed Cetal Ltd. This is a Ope Access aticle: vebatim copyig ad edistibutio of this aticle ae pemitted i all media fo ay pupose, povided this otice is peseved alog with the aticle's oigial URL. Abstact Backgoud: Geomic impitig efes to the diffeetial expessio of gees iheited fom the mothe ad fathe (matigees ad patigees). The kiship theoy of geomic impitig teats paet-specific gee expessio as poducts of withi-geome coflict. Specifically, matigees ad patigees will be i coflict ove teatmet of elatives to which they ae diffeetly elated. Haplodiploid females have may such elatives, ad social isects have may cotexts i which they affect elatives, so haplodiploid social isects ae pime cadidates fo tests of the kiship theoy of impitig. Results: atigeic ad patigeic elatedesses ae deived fo idividuals affected i a vaiety of cotexts, icludig quee competitio, sex atio, woke layig of male eggs ad policig, coloy fissio, ad adoptio of ew quees. Numeous pedictios emege fo what cotexts should elicit impitig, which idividuals ad tissues will show it, ad the diectio of impitig effects. The pedictios ofte vay fo diffeet geetic stuctues (vayig quee ad mate umbe) ad ofte cotast with pedictios fo diploids. Coclusio: Because the cotexts diffe fom the omal impitig case, ad because othig is cuetly kow about impitig i social isects, these pedictios ca seve as a stog a pioi test of the kiship theoy of impitig. If the pedictios ae coect, the social isects, which have log seved as exemplas of coopeatio betwee idividuals, will also be show to be extaodiay examples of competitio withi idividual geomes. Backgoud Ogaisms ae omally vey cohesive etities i the sese that thei compoets wok togethe towad thei commo goal of suvival ad epoductio. Howeve, thee ae occasioal cicumstaces whee diffeet pats of a ogaism's geome may be i coflict because they have diffeet possible paths of epoductio [ 3]. Ogaella gees tasmitted oly though eggs may suppess polle fuctio. Dive elemets ca spead by killig off gametes lackig them. Tasposos that jump to othe places i the geome ca spead though iceased copy umbe eve at some cost to thei beae. Geomic impitig povides aothe likely case of withi-geome coflict. A impited gee is oe with paet-specific gee expessio; it is expessed diffeetly accodig to whethe it was iheited fom the mothe o the fathe [4]. Ofte oe copy o the othe is completely sileced. Diffeetial methylatio i the paetal gemlies is thought to udelie impitig. Whethe o ot a paet methylates a paticula gee i the gem lie may affect its expessio i the offspig by alteig the bidig of ehaces o epessos. Page of 23 (page umbe ot fo citatio puposes)

2 BC Evolutioay Biology 2003, 3 Haig's kiship theoy of impitig [5 8] explais how such impitig may be elated to withi-geome coflict via ki selectio. Ki selectio is the pocess wheeby a gee's actio affects the tasmissio of the gee to futue geeatios, ot though its effects o offspig, but though effects o othe elatives who shae the gee [9,0]. The powe of this pocess is popotioal to the elatedess betwee the acto ad the idividual affected. Ki selectio theoies have geeally assumed that mateally ad pateally iheited gees ae expessed idetically, so that the elevat elatedess coefficiets ae the aveage of those petaiig to gees iheited fom the mothe ad fathe. Howeve, Haig's kiship theoy of impitig explais how sepaate mateal ad pateal coefficiets take o meaig fo impited gees. This has bee woked out pimaily fo siblig competitio, whee a offspig takes esouces fom its mothe, at some cost to its sibligs. I the absece of impitig, the offspig is selected to weigh its ow gai by its elatedess to self () ad to weigh the cost by its elatedess to the sibligs affected (/2 fo full sibligs, /4 fo half sibligs). Suppose the cost falls o mateal half sibligs (with diffeet fathes) ad thee is impitig. The pateally deived gee is ot peset idetical by descet i the half siblig ( = 0) so if oly this allele is expessed, it will be selected to always be selfish, egadless of the cost to the half sibligs. The mateally deived allele has a 50% chace of beig peset i a half siblig ( = /2) so if it is the oly allele expessed, selfishess will have a et advatage oly whe the beefit is geate tha half the cost to the half siblig. Thee is theefoe potetial coflict betwee the pateally ad mateally iheited gees, with the pateal oes favoig selfish behavio ude boade coditios tha mateal oes. Of the vaious evolutioay theoies of geomic impitig, the ki coflict theoy sketched above seems to explai the available data most effectively [8,]. It accouts fo why impitig seems commo i mammals ad plats, taxa with pologed povisioig of offspig by thei mothe. It also accouts fo why so may of the kow impited gees ae expessed i embyos o i geetically simila o idetical suogates that act o behalf of the embyo, like placetas o edospems. ially, it explais why pateally expessed gees ted to icease the size of the offspig while mateally expessed gees usually ted to decease it. The kiship theoy of impitig would be geatly stegtheed if it could be tested i othe situatios i which it makes diffeet pedictios. o example, i species whee the male povides paetal cae, oe might expect impitig effects i the opposite diectio, with mateally deived gees beig moe selfish [2]. Quelle & Stassma [3] ecetly agued that the best ovel cotexts fo testig this theoy ae supplied by the haplodiploid social isects. They also suggested that social isect wokes could be so deeply divided by geomic impitig coflict as to scacely have ay uiquely idividual iteests. I this pape, I develop the udelyig theoy ad pedictios i geate detail. Social isects ae paticulaly iteestig fom this pespective fo two easos [3]. ist, they have a much wide vaiety of iteactios amog elatives tha the simple case of tasfe of utiets fom paet to offspig; social isects both compete ad coopeate with each othe i umeous cotexts. Secod, thee ae thee distict souces of the kids of elatedess asymmeties that might make mateally ad pateally deived gees coflict (igue ). Thee is multiple matig, as i the stadad impitig case (which woks oly with half sibligs). I social isects, multiple quees ca play a simila ole. I may social isects, coloies ae headed by elated quees who ae mated to uelated males. Thei offspig ae theefoe moe elated though the female side tha though the male side. ially, ats, bees ad wasps ae Hymeopteas who shae the haplodiploid geetic system. Haig [4] fist oted that haplodiploidy ceates asymmeties betwee mateal ad pateal gees that might favo impitig. I haplodiploid species, females ae diploid ad aise fom fetilized eggs while males ae haploid ad aise fom ufetilized eggs. As Hamilto (964) fist showed, this leads to a extaodiaily high elatedess of 3/4 amog full sistes, povidig a possible explaatio fo why females might wok to ea sistes istead of aisig thei ow offspig ( = /2). The elevated elatedess to full sistes aises because the haploid fathe cotibutes exactly the same gees to all his daughtes, with o eductio divisio. Haig theefoe agued that pateally expessed gees would be moe selected to favo caig fo sistes tha mateally expessed gees. The coditio eveses with sufficiet multiple matig by the quee, because the the pateal gees ae aely elated. uthemoe, because pateal gees i woke females ae abset fom thei bothes, they should be selected to favo highly female-biased sex atios [4]. ost wok o the ki coflict theoy of impitig has focused o how mateally ad pateally deived gees ae selected, assumig they have bee diffeetially labelled by the paets. A elated but distict questio is the evolutio of the labelig itself [2]. Whe should mothes ad fathes put a impit o thei gees? Oe possibility is that the oigial impitig itself has o immediate effects o ki ad is selected fo uelated easos o difts to fixatio. Alteatively, the placig of the impit by a paet may have a immediate effect o gee expessio ad social behavio i the offspig ad be selected fo those effects. o example, if a mothe places Page 2 of 23 (page umbe ot fo citatio puposes)

3 BC Evolutioay Biology 2003, 3 =3/4 athe othe Othe mate othe's siste othe's siste's mate SEL ull siste Bothe Half siste Cousis Haplodiploid igue pedigee Haplodiploid pedigee. Coloig shows the elatioships of the idividual labelled "SEL". SEL's matigees ae coloed i pik ad patigees i blue. Gees uelated to SEL ae all show i white. Relatives beaig diffeet factios of pik ad blue ae those fo which thee may be coflict betwee SEL's matigees ad patigees. methyl goups i a ovel locatio, it might chage popeties at the bidig site of a pomote i he offspig. I this evet, oe eeds to coside the mothe's iclusive fitess iteests. These ae ot always the same as the iteests of a mateal gee i the offspig because that gee has udegoe segegatio; it "kows" it is i the offspig wheeas a gee i the mothe pio to segegatio has oly a 50% chace of beig tasmitted to that offspig. The impotace of the distictio betwee mateal ad mateally deived gees edes the temiology potetially cofusig. Haig [5] itoduced the tems "madumal" ad "padumal" to descibe the gees deived fom the mothe ad fathe, but these ae ot vey euphoious ad have ot bee adopted, so pehaps it is time fo aothe ty. I thei place, I will use the tems "matigeic" ad "patigeic" (Quelle & Stassma 2002). The "geic" suffix simultaeously evokes both the object of iteest (the gee) ad the fact that its souce (geesis) is what is impotat. They also have the advatage of havig coespodig ou foms: matigee ad patigee. With the additio of these tems, cofusio ca be avoided by usig mateal ad pateal to efe oly to the gees i the mothe ad fathe, o to the stategies of the mothe ad fathe. That beig said, the poblem is somewhat simplified i haplodiploids; because thee is o segegatio i males, pateal iteests ae idetical to patigeic iteests. The distictio is oly impotat o the female side. Page 3 of 23 (page umbe ot fo citatio puposes)

4 BC Evolutioay Biology 2003, 3 Table : Coefficiets of elatedess fo a haplodiploid female fo vaious female ad male elatives ull siblig Half siblig Ow offspig Offspig of full siste Offspig of half siste othe elated by qq, fathe uelated emales aveage 3/4 /4 /2 3/8 /8 qq /4 patigeic 0 /2 /2 0 0 matigeic /2 /2 /2 /4 /4 qq /2 ales aveage - /2 3/4 /4 qq /2 patigeic matigeic - /2 /2 qq These ae egessio coefficiets that do ot iclude epoductive value diffeeces betwee males ad females. The last colum is fo elatioships like cousis, with mothes elated by qq = 3/4 ad fathes uelated. Deivatio of the coflict coditios equies applicatio of ki selectio theoy. A allele is favoed ude ki selectio if it iceases iclusive fitess, which is the sum of all its fitess effects o elatives ( w i ), icludig itself, devalued by the coefficiet of elatedess of the acto to the idividual affected ( i ). I haplodiploids, a complete accout of iclusive fitess must also iclude two kids of epoductive value vaiables, as follows: wvs ii i i i > 0 (see [6,7]). S i is a adjustmet fo epoductive value owig to matig success of the two sexes. It takes o values popotioal to / fo females ad / fo males, whee ad ae the umbes o factios of females ad males i the populatio. ad could be icluded i diploid equatios as well, but ae usually omitted because they cacel out at sex-atio equilibium of =. They ae icluded hee because of the impotace of deviatios fom sex atio equilibium i social haplodiploids. V i is a distict sex-specific epoductive value adjustmet that applies egadless of sex atio. It coects fo the fact that diploid females ad haploid males cotibute diffeetly to distat futue geeatios. Ude most coditios, females (as a goup) cotibute twice as may gees to distat futue geeatio as males, so we will set V = / 2 fo haploid males ad V = fo diploid females. Thus, summig sepaately ove males ad females gives: w w m mm/ 2 f f/ > 0 ( 2) f Howeve, ude some coditios, such as whe wokes poduce some of the male eggs, the V's may take diffeet values [6]. I this pape, I will use equatio 2, uless othewise oted. Relatedess i haplodiploids has bee expessed i two ways [8,9]. The coefficiets used i () ae egessio coefficiets, ad ca be thought of, fo ay gee i the actos, as the egessio of its fequecy i beeficiaies o its fequecy i itself. Table lists the most impotat egessio 's used i this pape. ay eades will be moe familia with Hamilto's life-fo-life coefficiets, which ae the egessio measues with the stadad V adjustmets aleady made (i.e. multiplyig the egessio measue by 2 fo male-to-female elatedess ad dividig by 2 fo female-to-male elatedess). The easo fo keepig the 's ad V's distict is to accommodate those cases whee the V's ae ot i the stadad 2 to atio. Table lists the stadad egessio 's fo haplodiploid females, but also adds the sepaate egessio 's fo a female's patigees ad matigees. Oly female elatedesses ae icluded, fo two easos. ist, males pefom few social behavios i social Hymeoptea. Secod, males caot have coflict betwee matigees ad patigees because they lack the latte. The sepaate coefficiets ae calculated by dividig the fequecy (idetical by descet) of the gee i questio i the elative by its fequecy i itself (/2). The usual egessio coefficiet is the aveage of the patigeic ad matigeic coefficiets. Quelle & Stassma [3] used a diagammatic method whee the omal is istead the sum of two mateal ad pateal compoets, which wee half of the egessio values show hee. I fomal theoy it seems bette to employ the taditioal egessio-coefficiet fom, but which method is used makes o pactical diffeece because the facto-of-two diffeece applies to all 's, ad cacels out i applicatio of Hamilto's ule. A umbe of the esults deived below coce coloies with a multiply mated quee o with multiple quees. Relatedesses withi these coloies ae ofte aveages of coefficiets i Table. o example, if the quee is mated to x males ad thei spem is used equally the elatedess amog thei pogey is: Page 4 of 23 (page umbe ot fo citatio puposes)

5 BC Evolutioay Biology 2003, 3 = x x x ( 3 ) aveage ow othe whee ow is elatedess to the idividuals i oe's ow patilie, ad othe is elatedess to idividuals i the othe patilies. Simlaly, whe the pogey ae equally divided amog q quees: q q q = ( 4 ) aveage ow othe whee ow ad othe ow efe to matilies athe tha patilies. I will ot teat the moe complex case of societies with multiple, multiply mated quees, because these appea to be vey ae, but the piciples ae the same. Results The geeal pocedue adopted below is as follows. ist, idetify the classes of elatives affected by a behavio ad wite Hamilto's ule () o (2) i a suitable fom. Substitute i the elatedesses of the acto to the affected paties. These ae geeally daw fom Table, if ecessay aveagig usig (3) ad (4) fo multiple mates ad multiple quees, espectively. The solve fo the theshold b/c atio, the atio above which the behavio is favoed ad below which it is disfavoed. This is caied out sepaately fo uimpited, matigees, ad patigees, ad compaiso of the thesholds eveals which is pedicted to be selfish (o altuistic) ude the widest age of coditios. Also of iteest ae the coespodig b/c thesholds fo whe mothes ad fathes should impit. As oted above, the patigeic theshold i haplodiploids is the same as the pateal theshold. To solve fo the mateal theshold, I substitute elatedess of the mothe to the paties affected. Each sectio of the esults teats a diffeet categoy of iteactio defied i tems of what paties ae affected. The discussio gives moe detail o the specific kids of behavios that may apply to each categoy. Tade-offs betwee self ad female coevals I the stadad impitig coflict, offspig compete fo limited esouces, usually supplied by a paet, ad have effects o sibligs. Coside fist how this would wok i haplodiploids if the focal female gais at the expese of he sistes [4,20]. oe geeally, I will the coside ot just effects o sistes, but o ay female geeatio-mates which, fo lack of a bette tem, I will call coevals. Whe thee ae multiple quees i a coloy, coevals amog thei pogey might iclude cousis o eve o-elatives. Igoig the fist tem of expessio 2 because it petais to males, ad dividig the secod tem ito oe ivolvig effects o a focal female ad aothe ivolvig effects o he female coevals, we have w w co co > 0 (whee w co is the summed w i fo all affected female coevals, o the et cost). If the focal female gais fitess beefits at a fitess cost to coevals, w = b > 0 ad w co = -c co < 0, givig beefit/cost theshold of: b c co co > ( 5) If the focal female loses diect fitess ad he coevals gai, w = -c < 0 ad w co =b co >0, givig cost/beefit theshold of: c b co co > ( 6) o the momet, I focus o expessio (5) fo selfish behavios. Table 2 shows the theshold b/c atios fo thee kids of geetic stuctue. Colum is fo females who come fom a sigle oce-mated quee, that is, full sistes. The o-impited ule depeds o the co = 3/4 betwee full sistes ad = fo self. Note fist that it diffes fom the ule fo gees expessed i the mothe (last ow), which deives fom the fact that the mothe is equally elated to the focal female ad he coevals. Just as i stadad paet-offspig coflict [2,22], females ae selected to put moe of a cost o thei sistes, fo ay give beefit to self, tha thei mothe is selected to favo. Howeve, if thee is impitig, the offspig female has divided iteests: he matigees ad patigees ae selected to disagee because co is /2 fo matigees ad fo patigees (Table 2). atigees should be moe selfish tha patigees [4,20,3]. Specifically, matigees should favo beig selfish ad patigees should be opposed wheeve /2<b /c co <. As i the familia diploid case, the uimpited theshold is itemediate betwee the two impited thesholds. Howeve, seveal impotat diffeeces emege. ist, impitig coflict ca be impotat eve with sigle matig. Haplodiploidy by itself ceates the ecessay asymmety. Secod, i this haplodiploid case, it is the matigees that ae selected to be selfish ad the patigees that will be selected to modeate selfishess. The easo is of couse that the patigees ae the same i evey full siste, so they value full sistes as much as thei ow beaes. Thid, the patigees have a ally i battles agaist the matigees: the mothe. This may make it moe difficult fo matigees to wi. Now suppose the sigle quee has mated multiply, with x males who shae epoductio equally (Table 2, secod colum). co must ow be aveaged usig (3). Ude multiple matig, o-impited gees have a theshold that ages fom 3/4 fo oe mate to /4 fo may mates. As expected, as the factio of full sistes deceases, the egio whee selfishess is favoed iceases (theshold b/c atio Page 5 of 23 (page umbe ot fo citatio puposes)

6 BC Evolutioay Biology 2003, 3 Table 2: Thesholds fo favoig female behavios affectig a tade-off betwee self ad female coevals. Noimpited () Oe quee, sigly mated Patigeic atigeic (2) Oe quee, x mates 2 x 4x Pati. > ati. always x < 2 ateal (3) q quees, sigly mated 3 q 4q The umbes epeset the beefit/cost atio above which selfishess is favoed (expessio 5), ad the cost/beefit atio below which altuism is favoed (expessio 6). Low values ae moe selfish. Each colum defies oe kid of coloy stuctue ad each ow epesets selectio o a diffeet kid of gee, the fist thee i a female offspig ad the last i a quee. The "ateal" coditios ae fo whe a mothe would be selected to impit oe of he daughtes to pefom the actio i questio. athes would be selected to impit daughtes ude the patigeic coditios. is lowe). This chage comes etiely fom patigees. A matigee is equally elated to full sistes ad half sistes, so the matigeic b/c theshold emais at /2. I cotast, the patigee theshold dops to /x, eflectig thei zeo elatedess to half sistes. This meas the diectio of impitig effects should chage with mate umbe. With a sigle mate, as show above, the matigee should act moe selfishly tha patigees. With a effective mate umbe [23] of 2 o moe, matigees should be less selfish [3]. Now assume that the competig females come fom a polygyous society, whee the coeval females i questio deive fom q sigly mated, equally epoducig quees, elated to each othe by qq. The fathes ae assumed to be uelated to each othe ad to the quees. The elatedess values of the competig females must ow be weighted accodig to (4). The b/c thesholds ae give i the last colum of Table 2. The effect of multiple quees is athe like the effect of multiple males. As quee umbe x 2 q q 2q q < qq q q qq qq qq iceases, the uimpited theshold declies fom 3/4 to qq /4, so selfishess is easie to evolve. The coditio fo matigees is o loge ivaiat, but thee still appeas to be a poit at which the diectio of impitig switches: patigees will be less selfish tha matigees (lowe b/c theshold) whe q < / qq, (7) ad moe selfish whe the quee umbe is lage. This eflects the chage fom full sistes that ae moe elated though the patigees, to cousis that ae moe elated though the matigees. Thus, whe quees ae elated by 3/4, matigees i thei female offspig will be less competitive with at least two quees. If they ae elated as half sistes ( qq = /4) quee umbe must exceed 5. If the quees poducig the competig females ae uelated, the matigees should eve be moe competitive tha patigees. Howeve, i the Discussio sectio, I ote how a likage betwee q ad qq sometimes chages this coclusio. The mateal coditio ude multiple quees equies explaatio. If we wated to kow how a mothe quee would favo tasfe betwee females of the ext geeatio, ot kowig which is he offspig, the theshold would still be (i.e. b >c). Howeve, we ae iteested i whethe selectio would favo a mothe placig a impit that causes he ow daughte to do somethig affectig the daughte ad he daughte's female coevals. She caot impit the othe quee's daughtes. o the questio of placig a impit that acts though the daughte, the appopiate is the quee's elatedess to he ow paticula daughte, /2 while the appopiate co is the weighted aveage of the quee's elatedess to he ow daughtes ad to the daughtes of othe quees, usig (4). This diffeece will ecu i the sectios below wheeve the quee impits he daughte i a way that affects that daughte's ow fitess, but ot whe the impit causes the daughte to oly affect othe idividuals (as i the sex atio). The thesholds above apply whe females compete oly with othe females, paticulaly epoductive competitio amog adult females such as est foudesses o quees of multi-quee species. They ae ot geeally appopiate fo the cotext of female lavae solicitig food the cotext paallel to the stadad impitig coflict because that would omally also affect males. The moe complicated case with effects o both females ad males will be cosideed below. Because the sex-atio has impotat effects i this case, I will teat the sex atio fist. Page 6 of 23 (page umbe ot fo citatio puposes)

7 BC Evolutioay Biology 2003, 3 Sex atio: tade-offs betwee males ad females Sex atio is pehaps the best-studied kid of quee-woke coflict [6,24]. It also affects othe questios i haplodiploid social isects, icludig the oigi of sociality. o simplicity, thoughout this pape, I will assume that idividual males ad females ae equally costly. Whe they ae ot, the fomulas ca be adjusted by additio of a cost atio coectio, ad the esults should emai the same except fo beig expessed i tems of elative ivestmet athe tha elative umbes. I tems of equatio 2, we ca ask whe would it pay to aise oe male at the cost of oe female, ad vice vesa. Settig the w's to uity, it is bette to poduce a male whe m /2> f / ad bette to poduce a female whe the sig is evesed. The stable equilibium is whe the two sides ae equal o f. / 2 = ( 8 ) m The sex atio optima fo each paty ae show i Table 3. Each is the equilibium / that would esult if all selectio wee o oe kid of gee. Agai, the fist colum of eties is fo coloies with a sigle sigly mated quee. The top ad bottom ows i this colum summaize the most basic sex atio theoy fo haplodiploids [6,24]. othes will favo : sex atios because m = ad f = / 2, meaig they ae equally elated to thei sos ad daughtes oce the epoductive value diffeece is accouted fo (the 2 i equatio 8). Howeve, wokes i a coloy with oe sigly mated quee will be eaig full sistes ( f = 3/4) ad bothes ( m = /2), so equatio 3 pedicts a 3: atio of females to males. As peviously oted by Haig [4], the woke's patigeic ad matigeic alleles will be i coflict if they ae expessed diffeetially. o the matigees, m = ad f = /2, so a : atio is favoed. o the patigees, whee m = 0 ad f =, expessio (8) pedicts a ifiite atio, that is, complete ivestmet i females. This follows because a woke's patigee is uelated to bothes. Ude impitig, the, patigees should favo moe ivestmet i sistes tha matigees favo [4]. Thus, the covetioal 3: equilibium i the absece of impitig is ot a equilibium fo impited gees. At the 3: equilibium thee is o selectio o wokes at the idividual level; a bothe is just as valuable as a siste. But selectio will still opeate o impited woke gees because 3/4 is above the matigeic gee equilibium ad below the patigeic equilibium. Agai, the uimpited value ca be see as the aveage of the matigeic ad patigeic values, povided they ae expessed i popotio of females athe tha atios (3/4 = [0.5 ]/2). Now coside a quee who has mated multiply with x males who shae epoductio equally (Table 3, colum 2). Agai, /x of a woke's sistes will be full sistes, ad the emaide half sistes (expessio 3). Substitutig the weighted elatedess i (8) yields a ew equilibium fo a uimpited woke gee: / = (2 x)/x. Thus, as is well kow, as the umbe of mates iceases, the woke optimum appoaches the quee optimum of because wokes ae symmetically elated to half siste ad bothes. The othe optima ae uchaged fom the sigle matig case. The mateal optimum emais the same as multiple matig does ot chage he elatedess to offspig, ad the same is tue fo matigees i the woke. Cuiously, the patigeic optimum also emais uchaged at 8, eve though patigee elatedess to females deceases (fewe full sistes), because patigee elatedess to males emais at zeo. Hee is a istace whee the uimpited optimum is ot the aveage of the patigeic ad matigeic oes. Howeve, the uimpited optimum does still povide some measue of the elative impotace of matigees ad patigees. As x iceases, selectio o the patigees becomes elatively impotet; ay bias patigees ceate towads moe sistes gives them a small geetic payoff, as most of those sistes ae half sistes who do ot shae the gee. Table 3: Sex atio equilibia No-impited 3 () Oe quee, sigly mated (2) Oe quee, x mates (3) q quees, sigly mated Patigeic atigeic Pati. > ati. always always always ateal Each ety is the equilibial sex atio /, fom expessio (8), that would esult if oly the kid of gee specified i colum was selected. Colums ad ows as i Table 2. 2 x x 3 q q qq qq Page 7 of 23 (page umbe ot fo citatio puposes)

8 BC Evolutioay Biology 2003, 3 The last colum of Table 3 shows the multiple-quee case, with q equally epoductive quees of the same geeatio, each mated oce. Relatedess is ow weighted accodig to (4). The o-impited equilibium is a complicated expessio that educes as expected to 3 whe q =. This same equilibium of 3 applies fo multiple uelated quees. Whe quees ae elated, the ivestmet atio appoaches : ude high quee umbes, a effect simila to multiple matig. The othe optima emai uchaged. Patigees i wokes ae elated oly to the /q siblig factio ( f = /q ad m = 0). The equilibium / emais ifiite. o matigees the equilibium / emais. Thus, as with multiple matig, havig multiple quees altes the optimal stategies of o-impited gees, but ot impited gees. Also like multiple matig, the o-impited optimum is ot the aveage of the patigeic ad matigeic oes, but does eflect the degee to which they become less potet though dilutio with cousis who ae eithe uelated (fo patigees) o less elated (fo matigees). Quees may also affect sex atios, but a quee's matigees ad patigees ae ot diffeetly elated to sos ad daughtes, so thee is o easo to expect them to be impited ude the coflict theoy. Tade-off betwee female vesus coevals of both sexes Whe a female stads to gai a fitess beefit, the cost ofte falls ot just o othe females (the case cosideed above) but o the coloy output as a whole. o example, if a female epoductive cosumes exta esouces, thee will be less left fo othe epoductives, both female ad male. Coside some paty whose elatedess to the focal female is ad whose elatedess to that female's coevals is co ad co fo females ad males espectively. This paty pefoms a behavio that causes the focal female's fitess to chage by w ad also causes a fitess chage of w co to each of co coeval females ad co coeval males. Note that ealie I used w to stad fo the summed effects o sistes, while hee it is moe coveiet to defie w as the pe siblig fitess chage, ad the multiply by thei umbe. Usig expessio 2, with the female tem split ito sepaate tems fo the coeval females ad the focal female, we have co w co co /2 co w co co / w / > 0. (9) If the female's behavio is selfish, b = w > 0 ad c co = - w co < 0. This gives a beefit/cost theshold of: b coco / coco / 2 > = coco coco cco / 2 ( 0 ) If the female's behavio is altuistic, w = -c < 0 ad w co = b co > 0, givig beefit/cost theshold of: c b co < coco co co 2 These esults paallel those i (5) ad (6), whee effects fall o sistes oly. Table 4 shows the theshold b/c (o c/b) atios fo a female actig to affect he ow fitess at the expese (o gai) of he coevals. The fial ow also shows the mateal thesholds fo the same fitess tasfes. Note fist that, if o males ae affected ( co = 0) the esults of Table 2 ae ecoveed (oce co is eplaced by to accout fo the chage fom total fitess to pe idividual fitess). The coditios i Table 4 deped ot oly o the female's elatedesses to he full sistes ad bothes, but also o the populatio sex atio, /, because that detemies the evetual elative matig success of males ad females. Coside fist coloies headed by a sigly mated quee (fist colum). The mateal theshold is highe tha the o-impited offspig theshold; that is, the mothe favos less selfishess o moe altuism by the daughte tha the daughte heself favos. The degee to which this is tue depeds o co / co ad /. The simplest, most atual case to coside is whe co / co = /, that is, whe the actio affects male ad female coevals i the same popotio as the populatio sex atio. Whe this is tue, the mateal theshold is exactly twice the oimpited offspig theshold. See Cozie ad Pamilo [6] fo exteded discussio of selectio o mothes ad o-impited offspig gees. The coditios fo matigees ad patigees diffe (Table 4, colum ), suggestig that impitig may be impotat. Howeve, if the acto affects female ad male coloymates i the same popotio as the populatio sex atio, co / co = /, the the two coditios both educe to co. Thus, if the effects fall o females ad males adomly with espect to thei fequecies i the populatio, o impitig effects ae expected. Howeve, impitig stategies ae expected to diffe if gees ae coditioally expessed i situatios whee the actos cosistetly ham sibligs who diffe fom the populatio sex atio. The matigeic theshold is lowe tha the patigeic oe whe / < co / co. So if the sibligs affected ae moe female biased tha the populatio as a whole, matigees ae selected to be moe selfish tha patigees. We aleady oted this fo the special case whe oly females expeiece the cost. I cotast, the matigeic b/c theshold is highe whe / > co / co. So if the sibligs affected ae moe male biased tha the populatio as a whole, matigees ae selected to be less selfish tha patigees. Page 8 of 23 (page umbe ot fo citatio puposes)

9 BC Evolutioay Biology 2003, 3 Table 4: Thesholds fo favoig female behavios that affect self ad both sexes of coevals. () Oe quee, sigly mated (2) Oe quee, x mates (3) q quees, sigly mated No-impited 3co co 4 4 ( 2 x) co co 4x 4 ( 3 ( q ) ) 4q q 4q qq co qq co Patigeic co co x co q atigeic Pati. > ati. ateal co co 2 2 co < cof co co co co 2 2 < co cof co co q 2q 2 x < x cof co q q qq co q ( q ) qq co co qq qq co The umbes epeset the beefit/cost atio above which selfishess is favoed (expessio 0), ad the cost/beefit atio below which altuism is favoed (expessio ). Low values ae moe selfish. Colums ad ows as i Table 2. Ude multiple matig (colum 2 of Table 4) the oimpited selfishess coditio becomes easie to meet (ad the altuism coditio hade to meet) because of the loweed elatedess to the sibligs expeiecig the cost. This loweig comes etiely fom the patigeic side of the acto's geome, so the patigeic side becomes moe selfish elative to the matigeic side. I fact, fo x > 2, the patigeic coditio is always moe selfish tha the matigeic oe, o matte what the elatioship betwee bo / ad sis /. Similaly, with multiple quees (colum 3 of Table 4), the o-impited b/c coditio is easie to meet tha with a sigle quee (colum ) because of the loweed elatedess amog sibligs with multiple quees. I this case, both matigeic ad patigeic elatedess is loweed, but the patigeic moe so because patigeic gees ae ot at all elated to the pogey of othe quees. Agai, the effect is to accetuate patigeic selfishess elative to matigeic selfishess. The coditio fo whe the patigeic theshold is highe (Table 4, Row 4, Colum 3) shows depedece o the populatio sex atio as befoe. Howeve, the ight had side is egative whe q > / qq, which meas ude this coditio, the patigeic theshold is lowe (patigees should be moe selfish), iespective of sex atios. Thus, povided quee elatedess is ot low, matigees should be less selfish tha patigees wheeve thee ae moe tha a few quees. At the limit of zeo quee elatedess, the sigle-quee coditio is estoed because effects o uelated idividuals ae selectively ielevat. The same fitess tade-off ca be viewed fom the viewpoit of a woke. Should she favo a focal female coeval if this has costs o othe female ad male coevals? o example, should wokes allow oe of thei coevals to become a epoductive whe this imposes some cost o the esidet quee's epoductio? The same expessios, (0) ad (), ca be used, but ow the elatedesses ae fo wokes to the paties affected. I this case, the woke's elatedess to the focal female beig helped is the same as its elatedess to the coeval females beig hamed, = co, so: b c co > co co co co 2 ( 2) o if the focal female suffes a cost to beefit coevals c b co < co co co co. ( 3) 2 Page 9 of 23 (page umbe ot fo citatio puposes)

10 BC Evolutioay Biology 2003, 3 The impotat chage is that wheeas matigees ad patigees ae equally elated to self, they ae ofte diffeetly elated to coevals. Table 5 shows the thesholds. These thesholds ae geeally highe tha i Table 4 (i.e. favo the focal female less) because the beefit is goig to a female coeval istead of to self (except fo the mateal thesholds, which ae idetical because it is the same fitess tadeoff fom the mothe's poit of view). Relatedesses to this coeval female ae ot the same fo matigees ad patigees, addig aothe souce of impitig coflicts. So, ude oe sigly mated quee (Table 5, colum ), whee the oly impitig effects i Table 4 wee due to sex atio, thee is ow cosistet impitig. Now the patigeic theshold is always lowe tha the matigeic. So, fo example, patigees should moe ofte be selected to favo a siste becomig a quee i the coloy, ad matigees should moe ofte be selected to suppess such a actio. The same is tue ude multiple matig (Table 2, colum 2) ad multiple quees (colum 3). Tade-off betwee male vesus coevals of both sexes It is also woth cosideig actios that aid a focal coeval male at a cost to othe coeval males ad females. Hee we do ot coside the viewpoit of the focal male himself, because a haploid male has o pateal gees ad caot have paet specific gee expessio. Istead we focus o the woke poit of view. Should, fo example, a woke espod to a male's demad fo moe food if that would impose a cost o othe male ad female bood? om (2), we obtai a expessio paallel to (9) co w co co /2 co w co co / w /2 > 0 (4) diffeig oly i the fial tem applyig to a male istead of a female. The woke's elatedess to the focal male beig helped is the same as he elatedess to othe coeval males beig hamed, = co, so: b c co co co co 2 > ( 5) co o if the focal male suffes a cost to beefit coevals c b co co co co 2 >. ( 6 ) co Table 6 shows the thesholds. The key featue with espect to impitig is that woke patigees ae uelated to the males poduced by the quees ( co = 0). Theefoe woke patigees would always favo suppessio of bothes. This esult, coupled with the pevious oe i which matigees ted to suppess sistes, is closely elated to the sex atio esult deived ealie. But it shows that simila logic applies ot just fo pue fitess tasfes betwee the sexes, but also whe a idividual of oe sex is favoed at a cost to both sexes of its sibligs. Table 5: Thesholds fo woke behavios that affect tade-offs betwee oe of thei female coevals vesus both male ad female coevals. No-impited () Oe quee, sigly mated (2) Oe quee, x mates (3) q quees, sigly mated co co 3 co x co 2 x co ( ( q ) qq ) co 3 q ( qq ) Patigeic co co co atigeic co co co co co co Pati. > ati. eve eve eve ateal co co co co co co The umbes epeset the beefit/cost atio above which favoig the oe female coeval is selected (expessio 2), o the cost/beefit atio below which disfavoig he is selected (expessio 3). Low values favo the focal female ad high value favo the male ad female coevals. Colums ad ows as i Table 2. Page 0 of 23 (page umbe ot fo citatio puposes)

11 BC Evolutioay Biology 2003, 3 Table 6: Thesholds fo woke behavios that affect tade-offs betwee oe of thei male coevals vesus both male ad female coevals. No-impited co () Oe quee, sigly mated (2) Oe quee, x mates (3) q quees, sigly mated 3co co ( 2x ) co Patigeic atigeic co co co co co qco Pati. > ati. co 0 co 0 co 0 ateal co co co co co co co 2 q q co The umbes epeset the beefit/cost atio above which favoig the oe male coeval is selected (expessio 5), o the cost/beefit atio below which disfavoig him is selected (expessio 6). Low values favo the focal male ad high values favo the male ad female coevals. Colums ad ows as i Table 2. Table 7: Thesholds fo a woke eplacig oe of the quee's male eggs with he ow male egg. No-impited () Oe quee, sigly mated (2) Oe quee, x mates (3) q quees, sigly mated 2 Patigeic atigeic q qq q q Pati. > ati. eve eve eve ateal q 2 qq q q 2 qq q q 2 q 2 The umbes epeset the beefit/cost atio above which eplacemet is favoed (expessio 7), so low values favo eplacemet. Colums ad ows as i Table 2. Tade-offs betwee males of mateal vesus daughte geeatios Oe epoductive optio that emais ope to may wokes i haplodiploids is the layig of male eggs, which does ot equie wokes to be isemiated [8,24]. Hee I will assume the simplest case whee the wokes have the optio of eplacig a quee-laid male. Woke layig of male eggs chages the sex-specific epoductive values, so that females ae o loge exactly twice as valuable as males. Theefoe we use the moe geeal expessio () istead of expessio (2). Let b w be the beefit to the wokes so ad c q be the cost the quee's so, while w ad q ae the coespodig elatedesses to these males. Replacig a quee's male with a woke male is favoed whe b V w w c V q q b w q o 7 c > > q The epoductive value of males depeds o the factio of males that ae poduced i the populatio [6,25], but hee it cacels out because thee ae o females affected. If wokes sometimes mistakely eplace a quee's female egg, o if thee ae othe costs to the coloy esultig i educed female poductio, the tems fo effects o females would eed to be icluded, ad epoductive values would eed to be etaied. w Page of 23 (page umbe ot fo citatio puposes)

12 BC Evolutioay Biology 2003, 3 Table 8: Thesholds fo a woke pevetig aothe woke fom eplacig a quee's so with he ow so (woke policig). No-impited () Oe quee, sigly mated (2) Oe quee, x mates (3) q quees, sigly mated 2 Patigeic atigeic q qq q q Pati. > ati. eve eve eve ateal q 2 qq q q 2 qq q q 2 q 2 The umbes epeset the beefit/cost atio above which eplacemet is favoed (expessio 8), so low values favo eplacemet. Colums ad ows as i Table 2. Table 7 shows the thesholds. With a sigle oce-mated quee, the coditio fo o-impited woke gees to eplace a quee-laid male is b/c > /2. As is well kow, a female is moe elated to he ow so ( = ) that to the quee's so ( = /2), so she will eplace it uless the b/c atio is low. Similaly, the quee is twice as elated to he so as to he woke's so, so he b/c theshold fo allowig the woke to eplace he egg is 2. If the behavio simply substitutes oe feshly laid male egg by aothe, the b may be about the same as c. The o-impited coditio is the aveage of b/c > fo matigees ad b/c > 0 fo patigees. Thus, layig of male eggs by wokes will be selected moe o patigees, eflectig the fact that a woke's patigee is eve peset idetical by descet i he bothes, who have o fathe. ultiple matig does ot chage these coditios. The mates, sigle o multiple, do ot cotibute to the males beig eplaced. With multiple quees, elatedess is diluted by the pesece of the additioal quees, but the elative positios of the fou paties emai the same. With espect to impitig, it emais tue that patigees should be selected to eplace the quee's males, while matigees should do so oly ude sticte beefit/cost coditios. If wokes do ty to lay male eggs, othe wokes have the choice of eithe acceptig it o tyig to pevet it [26]. The latte is called woke policig, ad it could take the fom of wokes destoyig each othe's eggs, o of wokes pevetig each othe fom becomig epoductively active. Policig is favoed whe: c b w q q <. ( 8) w This is the same theshold as (7) but with two chages. ist, the quee's sos get the beefit istead of the cost. Secod, we ow take the pespective ot of the layig woke, but of aothe woke, so the elevat elatedesses ae fo a o-layig woke to a layig woke's sos ad to the quee's sos. Table 8 shows the thesholds. ateal thesholds ae geeally uchaged fom Table 7, because fom the quee's poit of view, this is the same tade-off betwee a quee so ad a woke so. The exceptio is the multiple-quee case because, as oted peviously, the mothe ca put a impit oly o he daughtes. Woke thesholds ae diffeet because ow we ae cosideig a o-layig woke's viewpoit. With oe sigly mated quee (colum ) o-impited gees will ot geeally favo policig because wokes ae less elated to the quee's so ( q = /2) tha to aothe woke's so ( w = 3/4). But patigees ad matigees diffe. Patigees ae completely uelated to the quee's sos ad theefoe do ot favo policig of othe wokes. atigees ae twice as elated to the quee's sos ( q = ) tha to othe woke's sos ( w = /2) ad will theefoe ted to favo policig. ultiple matig (Table 8, colum 2) teds to pomote policig i o-impited gees because wokes become less elated to each othe. The well-kow uimpited pedictio is that if b = c, wokes should police each othe oly if the umbe of mates exceeds 2 [26]. Howeve, the impited coditios ae idepedet of mate umbe. The matigees ae always twice as elated to the quee males as to woke males ad so they would be selected to Page 2 of 23 (page umbe ot fo citatio puposes)

13 BC Evolutioay Biology 2003, 3 favo policig. The patigeic elatedess to woke sos chages with mate umbe, but its elatedess to the quee's sos is always zeo. Patigees ae theefoe always selected ot to police (favoig othe woke's males ove the quee's) but the stegth of this selectio is expected to weake with mate umbe because the patigee will also be uelated to may of the woke males beefited. Simila esults hold fo multiple quees (Table 8, colum 3). Agai, the o-impited coditio switches fom ot favoig policig at low quee umbes (whe q =, c/b must be less tha 2/3) to favoig policig at high quee umbes (c/b must be less tha 2). The patigee emais opposed to policig at all c/b levels. The matigee coditio has become depedet o quee umbe, but the c/ b theshold is always geate tha, so that matigees still geeally favo policig. Ki ecogitio Distiguishig coloy-mates fom o-elatives will omally be favoed by both matigees ad patigees. Impitig might be expected to be ivolved i coloy ecogitio oly whe eighboig coloies ted to be elated though oe paet but ot the othe. o example, if adjacet coloies wee poduce by buddig, ad the quees of these coloies mate with males who have dispesed, patigees i the quees' female pogey would be moe favoed to ecogize ad exclude membes of eighboig coloies. emales could gai iclusive fitess by favoig thei closest elatives withi thei coloy, fo example favoig full sistes ove half sistes, though thee is little evidece that they do (Kelle 997). Reeve [27] suggested that impitig ad the accompayig disageemet betwee matigees ad patigees might be elevat to this absece of withi-coloy discimiatio. om expessio (2), gees affectig a close coloymate ad moe distat coloymate ae expected to be selected accodig to: c b distat close close distat <. ( 9) Table 9 shows the elevat thesholds fo two kids of withi-coloy discimiatio. Colum is fo favoig a female of oe's ow patilie ove a female of aothe patilie. I wods, patigees value full sistes vey highly, while matigees have o elatedess stake i favoig full sistes, favoig them oly if the beefit exceeds the cost to half sistes. Hece the failue to see such discimiatio could esult fom matigeic esistace [27]. The same explaatio is ot so stog fo discimiatio of matilies i multiple-quee coloies (Table 9, colum 2). I this case, the thesholds apply both to discimiatio of females ad discimiatio of males (by females). Agai, patigees ae moe stogly selected to discimiate (uless qq = 0). Howeve, matigees ae also moe elated to thei ow matilie tha to othe matilies, so c/b atios may ofte be i a egio whee matigees would favo discimiatio. I this age, thee would be o coflict betwee patigees ad matigees. Table 9: Thesholds fo favoig oes ow matilie o patilie ove aothe i the same coloy. () Oe quee, mates; favo females of ow patilie No-impited 3 (2) q quees sigly mated; favo ow matilie Patigeic atigeic qq Pati. > ati. always always ateal qq The umbes epeset the beefit/cost atio above which discimiatio is favoed (expessio 9). Low values favo moe discimiatio. Colums ad ows as i Table 2. Discussio Haig [4] fist poposed that haplodiploidy would make social isects poe to impitig effects fo both sex atio ad fo helpig behavio. Quelle & Stassma [3] suggested that impitig effects would be moe pevasive, coveig most aeas of social coflict. The iclusive fitess expessios i the peset pape povide a moe igoous foudatio fo this claim. Numeous pedictios follow about impitig effects i social isects, may of which ae summaized i Table 0. While mechaistic studies ae equied to tell us how impitig woks, Haig's ki coflict theoy povides us with a plausible "why". I additio, it offes pomisig pedictios as to who, what, whee, ad which diectio. What behavioal cotexts ae expected to lead to ki coflict betwee matigees ad patigees. Who ae the expected playes? Whee do we expect to see the coflict expessed; what tissues will show paet-specific gee expessio? Which way will matigees ad patigees push i each cotext? 3 qq Page 3 of 23 (page umbe ot fo citatio puposes)

14 BC Evolutioay Biology 2003, 3 Table 0: Pedictios about impitig effects i haplodiploid social isects. Behavio Expessed i Ude coditio(s) Actio of patigees Actio of matigees Suppessig excess demads by female lavae (Table 5) Suppessig excess demads by male lavae (Table 6) Wokes Ay quee o mate umbe Less suppessive oe suppessive Wokes Ay quee o mate umbe oe suppessive Less suppessive Competitio amog coeval quees o foudesses (Table 2) Repoductive females Oe quee, sigly mated Less competitive oe competitive Oe quee, mated moe tha twice ultiple elated quees, sigly mated ultiple uelated quees, sigly mated oe competitive Usually less competitive No impitig Less competitive Usually moe competitive No impitig Sex atio: e.g. killig male lavae, haassig male adults (Table 3) Helpig quee(s) o leavig to epoduce (Table 4) Addig a daughte quee, o eplacig old quee with daughte quee (Table 2 o 4) Become a woke o a quee (Table 2 o 4) Divisio of coloy betwee mothe quee ad daughte (Table 4) Wokes Ay quee o mate umbe avo females avo males Quees Ay quee o mate umbe No impitig No impitig emales Oe quee, sigly mated, beefits ot sex-biased Oe quee, sigly mated, beefits female biased Oe quee, sigly mated, beefits male biased Oe quee, sigly mated, split sex atios No impitig oe altuistic oe selfish oe altuistic i femalebiased; moe selfish i malebiased No impitig oe selfish oe altuistic oe selfish i female-biased; moe altuistic i male-biased Oe quee, moe tha 2 mates oe selfish oe altuistic ultiple quees, beefits ot oe selfish oe altuistic sex-biased Wokes (Table 5) All Aid selfishess oce helpig Daughte quee to be added Oe quee, sigly mated No impitig o less i favo No impitig o moe i favo Oe quee, moe tha 2 mates oe i favo Less i favo ay elated quees Depeds o specific coditios Depeds o specific coditios Old quee Ay quee o mate umbe No impitig No impitig Wokes (Table 5) Ay quee o mate umbe avos daughte quees moe avos old quees moe emale affected Oe quee, sigly mated No impitig o woke No impitig o quee Oe quee, moe tha 2 mates Quee Woke ay elated quees, ew Usually quee Usually woke quees fom sigle geeatio of old quees Old quee Ay quee o mate umbe No impitig No impitig Wokes (Table 5) Ay quee o mate umbe avos quee moe avos woke moe Daughte quee Oe quee, sigly mated No sex atio bias Uimpited Uimpited Daughte quee Oe quee, multiply mated avo self moe avo mothe quee moe othe quee Ay mate umbe Uimpited Uimpited Wokes (Table 5) Ay mate umbe avo daughte quee moe avo old quee moe Excess food demads (Table 4) emale lavae Oe quee, sigly mated, o No impitig No impitig sex bias Oe quee, moe tha 2 mates oe demadig Less demadig Page 4 of 23 (page umbe ot fo citatio puposes)