Feldman 1978; Craig 1979, 1983; Wade 1979;. Uyenoyama and Feldman 1980; Owen 1986). The present case is similar to the spread of a gene for altruistic ...
Behavioral Ecology and Sociobiology
BehavEcol Sociobiol(1989)25:437 444
. t ' S p r i n g e r - V e r l a g1 9 8 9
Colony level and within colony level selectionin honeybees A two allele population model for Apis mellifbru capensis Robin F.A. Moritz B a y e r i s c h eL a n d e s a n s t a l t f ü r B i e n e n z u c h t , B u r g b e r g s t r a s s e7 0 , D - 8 5 2 0 E r l a n g e n , F e d c r a l R e p u b l i c o f G e r m a n y Receivcd February 6, 1989i Acccpted June 18. 1989
Summary.Although honeybeeworkersare usually infertile, in queenlesscoloniessome workers can develop ovaries and produce offspring. Therefore the classicalDarwinian fitnessof workers is not zero. Experimentalstudiesin the Cape honey bce (Apis mellifera capensis)reveala huge geneticvariation for individualfitnessof workers.The present study with a one locus,two allelemodel for reproductive dominanceof workers shows that a balancedsystembetweencolony level and individual within colony selectionplausiblyexplainsthe phenomenonof a high geneticvarianceof worker fitness.In particular,a frequentoccurrcnceof queenlesscoloniesin the populationleadsto stablepolymorphic equilibria.Also the multiple mating system of the honey beequeensupportsthe propagation of allelescausingreproductivedominanceof workers.
Introduction Selection in natural populations of honeybees (Apis melliferetL.) operateson at leasttwo different levels:individual selectionand colony level selection (Owen 1986).The idea of colony level selection originatedwith Darwin (1S59),and Haldane (1932)explicitlyformulatedhow colony levelselection operatesin honeybees.In particular, social behaviorthat can be expressed only in groupsbut not in the individualinsect(eg.,temperatureregulation, defensivebehaviorshouldbe subjectto colony levelselection. Individual selectionacts not only on both sexual reproductives(queensand drones)but also on the usually infertile worker caste.The individual fitnessof honey bee workers has been discussed mainly in the context of inclusivefitnessand kin
selectiontheorysincethe fundamentalwork of Hamilton (1964a,b). Becauscof the male-haploidgenetic systemof Hymenopteraand the closeintracolonial relatedness, workers are expectedto gain particularlyfrom inclusivefitness.However,multiple mating of the honey beequeenreducesthe average intracolonial relationshipand weakensthe arguments of inclusive fitness theory. Furthcrmore, the classicalindividual fitness of workers is not zero. It is common that in many species of social insectsworkers produce male offspring (eg., Lin and Michener 1972; Oster and Wilson 1978; Wilson 1971).This is also true for honey bees.If a colony losesits queenand is not able to requeenitself,workerswill developovariesand start laying eggsin due time. In all known subspecies of A. mellfera, except A. m. c'upersls,these eggswill developinto drones.Although some of thesedronesmay not be as reproductivelysuccessful as queen produced drones (since they are smallerand are not alwaysproducedin the mating season),they are sexuallyreproductiveand definitely havea fitnesslargerthan zero(Pageand Erickson 1988).Consequently, laying workers gain a directindividual fitnessby producingolßpring. The speed of ovarian developmentshows a large variation among subspecies(Ruttner and Hesse1981).Workersof African racesof the honey beein particular show an extremelyrapid ovarian development.Workers of Apis melliJbraintermisstt in northernAfrica, for example,can initiate oviposition within 6 days after queen removal. Not all workersof a queenless colony will developovaries to a maturestage,and thereis a considerable variation for this characterwithin the colony.This phenotypicvariationcan be partitionedwith quantitative geneticalmethodsinto variation components of environmentalor geneticorigin. Moritz and Hillesheim(1985)were able to show that the abilitv
438
to develop ovariesin natural populationsof the most southernsubspecies of ,4. ntellifero,the Capc honey bee,is subjectto a strong gencticvariance. It is not yet clear whether this is a result of the specialreproductivestrategyof A. m. capensisor is a generalphenomenonin populationsof A. mellifbra. ln A. m. capenslslaying workers parthenogeneticallyproduce female offspring (thelytoky) whereasin all other known subspecies, the unfertilized eggs of laying workers developinto drones (arrhenotoky).This differencemay well have effectson the selectivevalue of laying workers,particularly sincequeenswith a full reproductivecapacity are rearedfrom the worker offspring. ln A. nt. c:open,sis, workerswith well-developed ovaries produce pheromonesidentical to those producedby the queen.Laying workerssynthesize both qualitatively and quantitatively queenlike amounts of 9-oxo-decenoic-acid(9-ODA), the queen substance, in their mandibular glands (Hemmling etal. 1979;Crewe and Velthuis 1980; Crewe 1982).This pheromonesuppresses ovary developmentin other workers and is thereforevcry closelylinked to classicalindividual fitnessof the layingworker. Reproductive"dominant" workcrs suppressthe reproductivecapacity of " subordinate" workers,which consequently do not develop their ovariesin the presenceof dominant workers. In this light, it was surprisingto find a high gcnetic variancefor this charactersincein populationsat equilibrium, the geneticvariancefor fitncss,and thereforeits selectability,is expectedto be small (Fisher 1930; Falconer1989).Indeed,Mousseau and Roff (1987) empirically showed that fitness componentshave a lower geneticvariance than traits more looselyconnectedwith fitness.Nevertheless,more than B0% of the total phenotypic varianceof 9-ODA production was due to genetic variance components (Moritz and Hillesheim 19 8 5 ) . A large geneticvariancefor fitnessin natural populationshas been explainedby many mechanisms.Among theseare frequencydepcndentselection (Bulmer 1980),highly variableenvironments (Ewing 19'79),mutation (Lande 1976; Turelli 1984), heterozygoteadvantage(Falconer 1981), and migration(Felsenstein 1976).Inan experimental analysis,Hillesheim(1987)and Hillesheimet al. (1989)found evidencethat selectionat the group or colony level might counteractindividual selection. For examplecoloniesof A. m. capensiscomposed exclusivelyof dominant workers lacked brood care. Workers removed eggs from brood cells and replacedthem with eggs of their own. Theseeggswere removedagain and brood never
"domideveloped into imagines. Furthermore, nant" colonieshad a dramaticallyreducedhoarding ability; workers did not store honcy, nor did they build combs.Coloniesof subordinateworkcrs werewell able to perform all typesof socialbehavior, suggestingthat these coloniesmight have a highergroup fitnessthan coloniescontainingdominant workers.The correlationbetweenindividual worker reproductivity and colony performance washighly significant.The increasedindividualfitworkershasa negativegenetnessof .4.m. capensis ic correlationto the group fitness(Hillesheim1987, Hillesheimet al. 1989).Only under this condition it is possible to experimentallydocument that group selectionactuallyis effective. The questionariseswhethera stableequilibrium betweengroup and individual selectioncan exist and if so, which conditionsmeet such an equilibrium in a naturalpopulation.A balancebetween both levels of selectioncould be an additional mechanismto keep the geneticvarianceof fitness componentsat a high level. Such a systemmay be particularly appropriate becauseof the close correlationbetweenindividual and colony fltness. Knowing that a one locus model is an extreme simplificationof the actualgeneticsysteminvolvcd in reproductivedominance,I set up a two allele system.This systemmay serve at least to show tendenciesof the effectsof the major componcnts that determinethe selectivevalue of individual selection on the one hand and group selectionon the other. Both an analyticaland a simulationapproach are usedin the following study. Thegeneticslstenl Beforea geneticmodel can be constructed,the reproductive systemhas to be de{lned.Honeybces are haplo-diploidswith the male sexbeinghaploid. Virgin honeybeequeensare highly polyandrous and mate with a large number of drones (morc than 1l in A. melli/era,Adams eIal. l97l; up to 35 in tropical A. cerane.Woyke 1975)on their nuptual flight. The semenof thesedronesis thcn stored in the queen'sspermatheca.Studieswith geneticmarkersrepeatedlyshowedthat thc semen is mixed in the spermathecaand that there is no sperm clumping (Laidlaw and Page 1984; Moritz 1986a).For eachfertilizationa few spermsare released.In the analyticalmodel wc assumea homogenousmixing of semenin the spermatheca.For simplicityeachqueenis consideredto be inseminated by a very large number ol drones.Thus the gene frequencyin the semenmix in generation1 equalsthe gene frequencyin generationl-1 of
439
the femalepopulation.ln the computersimulation, discretenumbersof queensand dronesare drawn at random lrom the population in order to document the effectolmultiple mating on the dynamics of drift and selection. The genotypesof the queensthat are produced by laying workers are identical to the genotype of their mother workers.The mechanismof parthenogensisis an automictic fusion of the central polar body and the nucleus.In this type of automixis there is no recombinationof the chromosomal set, and mother and offspring are isogenic
Table l. Individualfitnessof workersand the colony fitnesses composedexclusively of the corresponding workers.Mixed colfollowingan additivemodel. oniesareassumed to havefitnesses ln the presenceof d/r/workers,r/i + and +i + workers will not reproduce;*/* workersonly reproduceifno did or di + workers are in the colony. lndividual fitnessof laying workers is limited by the colony fitness:thus, a r/rdworkerin a colony of did workcrsproducesno offspring Worker genotype
Individual fitness
Colony fltness
did
I 1i2 U
0 1i2 1
di+ -/-
for a given locus unless there (Verma and Ruttner 1980).
is crossing
Methods Analyticol model Let us consider one locus with two additive alleles. Let r/ be an allelc for reproductive dominance with a gene frcquency p, and + the alternative allclc for subordinalion with a frequency q in the population (Table 1). Workcrs homozygous for r/ will suppressdl + and +/+ workcrs; d/+ workcrs will suppress */* w o r k e r s . T h u s t h e c l a s s i c a ld i r e c t i n d i v i d u a l f i t n e s s o f + , r + w o r k c r s i s z e r o i n t h e p r e s e n c eo f t h c o t h e r g e n o t y p e s . Kin selection is not considered at this slage, since thc cffects o f i n c l u s i v c f i t n e s s a r e i d e n t i c a l f o r w o r k e r s i r r e s p c c t i v co f t h e i r genotype at the hypothetic locus under consideration T h e f i t n e s so f a q u e e n r i g h t c o l o n y w i l l d e p e n d o n t h c w i t h i n c o l o n y g e n o t y p e f r e q u e n c i e s .I f w e a s s u m c p l a i n a d d i t i v i t y , t h e gene frequency of the allele for subordinate behavior. 17,will be identical with the colony fitness l4lr (Table 2). A colony exclusively composed of rflrlworkcrs has a fitness of zero ir.r contrast to a colony of + / + workers with a group fitncss of l. A colony fitnessofzero will act epistatic over the individual fitness of laying workers. Thus a r/irlworker in a complete tlltlcolony will produce no offspring. Thc relative numbcrs o1' queens and drones produced by the colony is determincd by thc colony fitness. Thc drones produccd by the colony will havc genotypes corresponding to the old queen whereas the virgin queensare a random sample from thc lcmale genotypcs in the colony. Only queenright colonies can produce droncs corresponding to the colony fitness becausclaying workcrs of
Table 2. Off .spring matrix and fitness values (14/, to Wr) for thc corresponding colonies. d :allele for reproductive dominance * :allele lor subordinate behavior p - allele frequency in males for r/ in generation / - 1 Q :allele frequency in males for * in generätion l- 1 P , Q . a n d R : f e m a l e g e n o t y p e f r e q u c n c i c si n g c n c r a t i o n I Bccause the number of drones produced by a colony depends on l4l (colony fitncss) we obtain
P- (P W ,+ + Q Wr \i ( P W ,- r Q W ,+ R W3 ) and
q : G Q W ,+ R W) i e w | + Q W ,+ R W3 ) Queen genotype
possiblefemalcoflspring
frequency vector
queenright(c)
dd
D
d+
O
T T
R
w i t h t r ' t :r il -, p 1 2 , Queengcnotypc
Wr:i-pi2,
dd
d+
PWt
4Wr Wrl2 PW:
(pi2)rv. 0
frcqucncyvcctor
dd
D
d+
o
T T
R
0 (ql2)W' QWt
quecnlcss (1
r')
,ld
d+
--
wr w2 0
U U w3
U 0 0
W r : 1 - p 1 2 : t h i sc o n d e n s et o s: possiblclcmalc offspring (.44)
U)
over
dd
d+
jq(cp+1-c) (1-t*(1- c +)cp) U
*q'
ic(}+ q) (1-\rp)(cp+1 c)
++ 0 1,q()+q) (.1(1 t*)
440 Queen S u r v i v oI
Table 3. Flow diagram of simulation program
c
choice of parameters population size polyandry queen survival gene liequency
0.1 0.5 o.7 o
o
o
I
o.84
U.3
o L
J
o.9
establishinitial population
I
o
select queens & drones
t5
20
i
Generolion
matlng
Fig. l. Analytical modcl: The change of the gene frcquency for the worker-dominance allele, p( f-axis), depcnds on the prop o r t i o n o f q u e e n l e s sc o l o n i e s i n t h e p o p u l a t i o n ( 1 - c )
o
-
J
l
queens' offspring quccns & droncs
o c o 5 o l"L
I
determine colony fi tness
I laying workers' offspring quecns only
AR
'. = J
o ul
ö
o . 5 1 Survivolof eueens
Fig.2. Analytical model : Depcndencc of the equilibrium frequency lor thc worker-dominance allele ( f-axis) on the proportion of queenright colonies in thc population (X-axis)
Apis melliJbra c'apensis produce exclusivcly female offspring. The direct individual fitness of drones is assumed not to correlatc with either queen or colony fitness. Laying workers will appear only in those colonies that arc q u e e n l e s s .I f c i s t h e l r e q u e n c y f o r q u e e n r i g h t c o l o n i e s t h a t produce olfspring queens and drones, then 1 c is the frequency for qucenless colonies that produce queens in the population (colonies that do not succeed in producing sexual reproductivcs are not considered). Because initially the worker genotype freq u e n c i c si n t h e c o l o n y w i l l n o t c h a n g e a f t c r t h e l o s s o f a q u e e n , also the colony fitness is considered not to change until the first offspring queen of a laying worker is produced. Virgin qucens produced by laying workcrs will always be of thc d// or d/+ type, dcpcnding mainly on thc mother quccn's genotype.Onlyrfnodid ordi + workersareinthecolonyare+/+ workers expected to produce offspring. In ordcr to obtain a rccursion equation, the contribution o f b o t h q u c c n r i g h t a n d q u c c n l e s sc o l o n i e s h a v e 1 o b e c o n s i d cred. Combining the information lrom Tablc 2 and using the notation of Boorman and Levitt (1980) - with p,, e,, and R, reprcsenting the fiequencies ol dd, r/+, and * * fcmales in generation I wc obtain the following recursion equätion: (P,, Q,, R,):f,-,
M/J,-,
(l)
wherc./is the frcquency vector, M is the 3 x 3 matrix in Table 2. and J, , is the normalizing scalar for making Pt+Qt+Rt:7.
Somc courscs of gcne frequency changes are shown in Fig. 1. The initial frequency is at p:11.5 in order to document positive or negative effects of c on the allele frequency morc clcarly. We see that thc cquilibrium frequency depends on the percentage of queenright colonies in thc population. At c:0.84 the frequency does not change and thc population maintains its high gcnctic variability. I n o r d c r t o d e t c r m i n c t h e c o n d i l i o n s a t c q u i l i b r i u n - r ,( P , , R, ,) should be met. Rcsolving (1) for this Q,, R)--(P,,, case and fbr 0
