RESEARCH ARTICLE Regulation of behaviorally associated gene networks in worker honey bee ovaries

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1 124 The Journl of Experimentl Biology 215, Pulished y The Compny of Biologists Ltd doi: /je RESEARCH ARTICLE Regultion of ehviorlly ssocited gene networks in worker honey ee ovries Ying Wng 1, *, Srh D. Kocher 2, Timothy A. Linksvyer 3, Christin M. Grozinger 2, Roert E. Pge, Jr 1 nd Gro V. Amdm 1,4 1 School of Life Sciences, Arizon Stte University, Tempe, AZ 85287, USA, 2 Deprtment of Entomology, Center for Pollintor Reserch, Huck Institutes of the Life Sciences, Pennsylvni Stte University, University Prk, PA 16802, USA, 3 Deprtment of Biology, University of Pennsylvni, Phildelphi, PA 19104, USA nd 4 Deprtment of Chemistry, Biotechnology nd Food Science, Norwegin University of Life Sciences, 1432 As, Norwy *Author for correspondence (ying.wng.6@su.edu) Accepted 28 Septemer 2011 SUMMARY Severl lines of evidence support genetic links etween ovry size nd division of lor in worker honey ees. However, it is lrgely unknown how ovries influence ehvior. To ddress this question, we first performed trnscriptionl profiling on worker ovries from two genotypes tht differ in socil ehvior nd ovry size. Then, we contrsted the differentilly expressed ovrin genes with six sets of ville rin trnscriptomes. Finlly, we proed ehvior-relted cndidte gene networks in wild-type ovries of different sizes. We found differentil expression in 2151 ovrin trnscripts in these rtificilly selected honey ee strins, corresponding to pproximtely 20.3% of the predicted gene set of honey ees. Differences in gene expression overlpped significntly with chnges in the rin trnscriptomes. Differentilly expressed genes were ssocited with neurl signl trnsmission (tyrmine receptor, TYR) nd ecdysteroid signling; two independently tested nucler hormone receptors (HR46 nd ftz-f1) were lso significntly correlted with ovry size in wild-type ees. We suggest tht the correspondence etween ovry nd rin trnscriptomes identified here indictes systemic regultory networks mong hormones (juvenile hormone nd ecdysteroids), pheromones (queen mndiulr pheromone), reproductive orgns nd nervous tissues in worker honey ees. Furthermore, roust correltions etween ovry size nd neurl- nd endocrine response genes re consistent with the hypothesized roles of the ovries in honey ee ehviorl regultion. Supplementry mteril ville online t Key words: honey ee, ovry size, division of lor, socil ehvior, rtificil selection, ovrin trnscriptome, ecdysteroid signling. INTRODUCTION Ovries ply importnt roles in ehviorl regultion in nimls s diverse s mmmls (Kemnitz et l., 1989) nd insects (Cupp nd Collins, 1979; Hncock nd Foster, 2000; Klowden, 1990). Recently, it ws suggested tht ovries lso ffect complex ehviorl ptterns in functionlly sterile honey ee (Apis mellifer) workers (Amdm et l., 2006; Wng et l., 2009; Wng et l., 2010). The honey ee is the most-studied socil insect nd is model orgnism for understnding the regultion of ehvior (Amdm et l., 2006; Evns nd Wheeler, 1999; Giry nd Roinson, 1996; Hunt et l., 1995; Linduer, 1953; Pennisi, 2006). Worker honey ees progress through n ge-ssocited ehviorl sequence. They primrily conduct within-nest tsks during their first 2 3 weeks of dult life nd then trnsition to performing forging tsks outside the colony. The timing (ge) of forging onset vries mong individuls. Forging workers lso show different ehviors; some ees prefer nectr collection nd others prefer pollen collection (Pge nd Fondrk, 1995). This ehviorl plsticity is influenced y ovry size (Amdm et l., 2006; Wng et l., 2009; Wng et l., 2010). Workers tht receive n implnt of dditionl ovries, i.e. surgery to enhnce totl ovry mss, initite forging erlier thn shm controls (Wng et l., 2010). Bees with nturlly lrge ovries lso trnsition from nest tsks to forging t younger ges, nd they collect greter mount of pollen thn ees with smll ovries. These ssocitions re found within wild-type (unselected) Europen honey ees (Amdm et l., 2006), in crosses etween unselected Europen nd Africnized honey ees (Siegel, 2011), nd etween strins of two Europen honey ee genotypes tht were idirectionlly red for differentil forging ehvior (Hunt et l., 2007; Pge et l., 1995). These rtificilly selected genotypes re referred to s High vs Low pollen hording strins nd differ in severl trits: the High strins hve lrger ovries, forge erlier in life nd collect more pollen thn the Low strin ees. Thus, ovry size nd forging ehvior re heritle trits in honey ees (Amdm et l., 2009), nd vrition in oth of these phenotypes mps to overlpping genomic regions [quntittive trit loci (QTL)] (Grhm et l., 2011; Linksvyer et l., 2009; Wng et l., 2009). Linkge mpping of these trits hs een performed repetedly nd independently in crosses derived from different sources, i.e. from pollen-hording strin ees s well s Africnized nd Europen wild-type ees (Grhm et l., 2011; Linksvyer et l., 2009; Wng et l., 2009). The mpping studies hve provided positionl cndidte genes for phenotypic vrition in worker ovry size nd ehvior. Expression levels of some of these cndidte genes hve een exmined in worker rins nd ft odies (dominl dipose tissue). Ft ody expression of hormone receptor-like in 46 (HR46) nd phosphoinositide-dependent kinse-1 (PDK1) correltes with ovry size s well s worker division of lor (Wng et l., 2009). HR46 is possile nucler hormone receptor for ecdysteroid hormones

2 Behviorl gene networks in worker ovries 125 nd PDK1 is n element in the nutrient sensing trget of rpmycin-, epiderml growth fctor (Egf)- nd insulin-signling pthwys (Kmkur, 2011). However, lthough previous studies hve documented phenotypic, functionl genomic nd genetic evidence for the links etween honey ee division of lor nd reproductive physiology (Amdm et l., 2006; Wng et l., 2009; Wng et l., 2010), less is known out how ovrin tissue ffects worker ehvior per se. Here, we studied shred fetures of worker ovry nd rin trnscriptomes in order to egin to tese prt how ovries my function in honey ee division of lor. First, we nlyzed gene expression glolly, s well s loclly in co-expressed gene clusters etween ovries otined from High nd Low pollen-hording strin ees. This nlysis ws contrsted with six pulished rin trnscriptionl studies. Two of these studies descried ssocitions etween gene expression nd division of lor in the honey ee (Whitfield et l., 2003) nd in pper wsps (Toth et l., 2010). Four others exmined the pheromonl nd endocrine effects on worker ehviors: the dely of forging onset y queen mndiulr pheromone (QMP) (Grozinger et l., 2003; Kocher et l., 2010); the ccelertion of forging onset y methoprene, juvenile hormone (JH) mimic (Whitfield et l., 2006); nd honey ee ggression y lrm pheromone (Alux et l., 2009). Our comprtive nlysis generted list of cndidte iologicl processes for shred ehviorl nd ovrin gene regultion in honey ees. Finlly, s vrition in ovry size is ssocited with worker ehviorl differences (Amdm et l., 2006), we independently tested whether suset of genes ws lso differentilly expressed in wild-type worker ovries of different sizes. Our results show tht gene expression ptterns in worker ovries mirror rin trnscriptionl responses triggered y socio-environmentl fctors, nd identify severl physiologicl mechnisms tht my fcilitte the link etween ovrin ctivity nd division of lor in honey ee workers, including differences in metolic pthwys nd endocrine physiology. MATERIALS AND METHODS Microrrys Smple collection nd RNA extrction Honey ees, Apis mellifer L., from the High nd Low strins were mintined t Arizon Stte University, Phoenix, AZ, USA, nd t the University of Cliforni, Dvis, CA, USA. Two High strin colonies nd two Low strin colonies were used s donors for experimentl workers for the microrry study. Ovries were collected from newly emerged worker ees (<24 h old) nd used for trnscriptionl profiling. Newly emerged workers hve encountered few dult stimuli tht could ffect their ovry physiology, thus potentil differences in the ovry etween strins should e primrily due to genotype or ovriole numer. Both ovries from ech worker were crefully dissected in sterile Ringers solution (on ice). For oth strins, ovries of 10 individul ees (five ees from ech of the two colonies) were pooled to form iologicl smple. Four iologicl smples were prepred from ech genotype. Ovries were flsh-frozen in liquid nitrogen (N 2 ) nd stored t 80 C. RNA ws extrcted using TRIzol Regent (Invitrogen, ct. no , Crlsd, CA, USA) (Koyshi et l., 2006; Michut et l., 2003). DNse (Qigen, Vlenci, CA, USA) tretment ws used to remove residul genomic DNA. The integrity of extrcted RNA ws tested y cpillry electrophoresis on n RNA6000 BioAnlyzer (Agilent Technologies, Plo Alto, CA, USA), nd only high-qulity smples were used for susequent nlyses. Identifiction of significntly regulted trnscripts RNA (200 ng) ws mplified with the MessgeAmp II RNA Amplifiction Kit (Amion, Austin, TX, USA). Amplified RNA (2 g) ws directly leled with Cy3 or Cy5 dye using Kretech leling kit (BioMicro, Slt Lke City, UT, USA). Leled proe (120 pmol) from two smples ws then hyridized to the wholegenome oligonucleotide rrys supplied y the W. M. Keck Center for Comprtive nd Functionl Genomics t the University of Illinois, Urn-Chmpign. The High nd Low ovries were hyridized with dye-swps (N 4 for ech group). Arrys were scnned using the Axon Genepix 4000B scnner (Moleculr Devices, Sunnyvle, CA, USA) nd GENEPIX softwre (Agilent Technologies, Snt Clr, CA, USA), nd rw dt were imported into SAS (SAS Institute, Inc., Cry, NC, USA) for nlysis. Fetures with n intensity elow 300 (the verge ckground intensity on the rrys) were removed from the nlysis. Genes with less thn six oservtions (out of possile 16) were lso removed. Dt were log-trnsformed nd normlized using mixed-model ANOVA (SAS) with the following model: y dye rry + lock + dye rry + e, where y is expression, e is error, dye nd lock re fixed effects, nd rry nd its interctions re rndom effects. Detection of significnce for differentil expression of residuls ws performed using mixed-model ANOVA with the model: y + genotype + spot + dye + rry + e, where y is the residul from the previous model, genotype nd dye re fixed effects, nd rry is rndom effect. P-vlues were corrected for multiple testing using flse discovery rte (FDR) djustment (proc MULTTEST, SAS). We chose n FDR threshold of 0.05, suggesting tht less thn 5% of the significnt trnscripts should e flse positives. Functionl nlysis nd mpping differentilly expressed gene clusters Gene ontology (GO) enrichment nlysis ws performed only on differentilly expressed genes in either High nd Low strin ovries. Only trnscripts (N 1534) identified s hving orthologs in Drosophil were included in the nlysis to exclude multiple trnscripts from the sme gene nd trnscripts for which the genomic loction hs not een ssigned. Genes were included s eing significntly differentilly expressed if the FDR-corrected P- vlues were Enrichment ws determined using GO-getter ( (Argst et l., 2009). The differentilly expressed genes were then mpped onto honey ee chromosomes for detecting genomic clusters. We used trnscripts (1794) tht hve een ssigned for genomic loctions nd tested whether these genes were clustered more thn expected nd whether such clusters were locted within the previously mpped QTL for forging ehvior (Hunt et l., 2007; Hunt nd Pge, 1995), sucrose sensitivity (Rueppell et l., 2006) nd ovry size (Linksvyer et l., 2009; Wng et l., 2009). Clustering ws ssessed cross ech chromosome y clculting chi-squre vlue for the oserved numer of significnt genes within sliding window of 15 loci nd step size of three loci, reltive to the expected numer of significnt genes within tht window, given the numer of significnt differentilly expressed genes for ech chromosome. We estlished conservtive 0.05 chromosome-specific significnce thresholds for the chi-squre sttistic using 10,000 rndom permuttions of the dt set with respect to significnce of differentil expression. Contrsting trnscriptomes from ovries nd rins We contrsted our list of 2151 differentilly expressed ovrin genes to four previously pulished rin trnscriptomes from wild-type worker ees, which were exposed to different ehviorl regultors

3 126 Y. Wng nd others (Grozinger et l., 2003; Kocher et l., 2010; Whitfield et l., 2006; Whitfield et l., 2003). We lso contrsted our ovrin trnscriptomes to rin trnscriptomes from pper wsps, which were relted to forging ehvior nd reproduction (Toth et l., 2010). Finlly, we used the results of study tht identified rin trnscriptionl chnges ssocited with exposure to lrm pheromone s negtive control (Alux et l., 2009). As there is no evidence tht lrm pheromone ffects reproductive physiology in honey ee workers, we did not expect overlp etween our results nd those of Alux et l. (Alux et l., 2009). Significntly overlpping genes, i.e. those tht were differentilly expressed in oth the ovrin nd rin trnscriptomes, were identified using right-tiled Fisher s exct test. Furthermore, GO nlyses were performed on the overlpping genes within ech pollen-hording strin, using GOToolBox ( (Alux et l., 2009). Verifiction of expression differences in cndidte genes in High vs Low strin ees Five genes [HR46, ftz trnscription fctor 1 (ftz-f1), tyrmine receptor (TYR), mjor royl jelly protein 1 (MRJP1) nd juvenile hormone-inducile protein 26 (JHi-26)] were chosen for verifiction of gene expression in smples tht were used for the rry. HR46 nd ftz-f1 re nucler receptors tht my ind ecdysteroid hormones produced y the ovry of dult femle insects, wheres TYR is G protein-coupled receptor (GPCR) predicted to ind tyrmine neurotrnsmitter. Both HR46 nd TYR re lso positionl cndidte genes in QTL regions tht influence forging ehvior. MRJP1, protein component in royl jelly, ffects queen worker differentition (Kmkur, 2011) nd potentilly influences ovry physiology in workers. JHi-26 is JH-inducile gene nd cn e triggered y methoprene, JH nlog. Ftz-f1, TYR, MRJP1 nd JHi- 26 were selected for profiling ecuse they were differentilly expressed etween High nd Low ovries in the microrry ssy (see Results). HR46 signls on the rry were too low to pss the threshold for the nlysis, ut HR46 cndidcy ws inferred from prior testing of HR46 expression in ovries from newly emerged ees of the High nd Low strins [for which ech iologicl smple consisted of 20 ovries (pooled) from 10 individul ees from two colonies per strin, N 12, Student s t-test: t 1, , P ; supplementry mteril Fig. S1]. Chrcterizing cndidte gene expression in lrge nd smll ovries of wild-type ees Both ovry size nd ehviorl phenotype ffect ovrin physiology nd gene expression. Using qrt-pcr, we tested whether reltive quntifiction (RQ) of the cndidte genes for ovry nd ehviorl regultion (HR46, ftz-f1, TYR, MRJP1 nd JHi-26) were ssocited with ovry size in wild-type, newly emerged ees. For these ees, we used five wild colony sources for testing the ssocition etween cndidte genes nd ovry size. After ovry dissections, ovriole numer ws counted using dissecting microscope (Leic, MZ 125, Bufflo Grove, IL, USA). In order to mximize the difference in gene expression etween ig nd smll ovries, we used five nd 12 s cut-off thresholds for the ovriole numer. Ovries from ees in which oth ovries hd either mny ovrioles (13±0.11, i.e. summing over the two ovries) or few ovrioles (4±0.06 in totl) were flsh-frozen in liquid N 2 nd stored t 80 C. Biologicl smples were mde y pooling 10 pirs of ovries within the sme size ctegory, nd these were ssigned to either lrge ovry (LAO) or smll ovry (SMO) group. We prepred 18 smples for ech of the LAO nd SMO groups. Protocols for RNA extrction nd DNse tretment were identicl to those descried ove for the microrry study. cdna ws synthesized using TqMn Reverse Trnscription Regents (Applied Biosystems, Foster City, CA, USA). Two-step qrt-pcr (rel-time) ws performed in triplicte using ABI Prism 7500 (Applied Biosystems), nd the dt were nlyzed using the Delt-Delt CT method (Pfffl, 2001) with ctin (GenBnk: XM_623378) s reference gene. This gene is stly expressed cross honey ee tissues, nd is stndrdly used for gene expression studies in the ee (Lourenço et l., 2008). By monitoring negtive control smples (without reverse trnscriptse) nd melting curves, we verified tht the qrt-pcr ssy ws not confounded y DNA contmintion or primer dimer (Vndesompele et l., 2002). The primer sequences of the five trget genes nd ctin were developed using Primer3 ( (see supplementry mteril Tle S1). Expression dt of cndidte genes were log trnsformed to confer pproximte normlity (Wng et l., 2009). The resulting vlues conformed to ssumptions of Student s t-test nd ANOVA s ssessed y norml proility plots of residuls, s well s y Brtlett s nd Levene s tests for homogeneity of vrince. Student s t-test ws used to compre the cndidte gene expressions in the ovry etween High nd Low strin ees. Onewy ANOVA ws used to compre the expression level of cndidte genes etween LAO nd SMO groups. The logtrnsformed expression level of cndidte genes ws dependent vrile nd ovry size (LAO or SMO) ws n independent vrile. Fisher s lest significnt difference (LSD) test ws used for post hoc comprisons. RESULTS Comprison of ovrin trnscriptomes etween honey ee strins, nd chromosome expression-mpping of genomic gene clusters We compred ovrin trnscript ptterns from newly emerged High nd Low pollen-hording strin ees using n estlished microrry pproch (Grozinger et l., 2003; Whitfield et l., 2002). We found tht 2151 trnscripts, 20.3% of the 10,586 trnscripts of the rry, were differentilly expressed etween the High nd Low strin sources t n FDR of 0.05 (supplementry mteril Tle S2). Thus, the ovrin trnscriptomes of the two pollen-hording strins were mesurly different during the first hours of dult life. GO nlysis reveled the functionl distriution pttern of differentilly regulted genes in High nd Low strin ovries nnotted ginst the Drosophil genome (supplementry mteril Fig. S2). A numer of functions were scried, including the ctegory sensory perception with 10 olfctory receptors nd two gusttory receptors expressed in ovries. It is possile tht the corresponding gene products incorporte into ovrin memrnes nd receive signls y inding molecules tht circulte in the insects hemolymph (lood). Such molecules cn e internlized from the environment or secreted from tissues. All differentilly expressed genes were ssigned to function groups within three functionl domins of the GO nlysis iologicl process, moleculr function nd cellulr component (Fig. 1). This comprison etween genotypes demonstrtes tht ovrin gene expression cn differ drmticlly etween young worker ees. Trnscripts puttively involved in defense responses (immune response) (P 0.033), regultion of poptosis (P 0.041), detection of iotic stimulus (P 0.010) nd electron trnsport (P 0.041) were significntly enriched in Low strin ovries, while

4 Behviorl gene networks in worker ovries 127 Biologicl function Moleculr function Cellulr component A High strin ovry Low strin ovry Electron trnsport Defense response Regultion of poptosis Ctolic process Detection of iotic stimulus B C Trnsferse ctivity trnsferring Endomemrne system Kinse inding ovrin inhiition nd less likely to complete egg development thn High strin workers (Amdm et l., 2006). Thus, ovrin gene expression differences detected erly in life (Fig. 1) my hve physiologicl implictions for honey ee workers. Using chromosome-wide thresholds of significnce (P 0.05), we found clusters of differentilly expressed genes in four genomic regions, one on ech of chromosomes 5, 9, 11 nd 14 (Tle 1). None of these clusters overlpped with previously identified QTL for ovry size or ehvior. Interestingly, on chromosome 11, the cluster contined six trnscripts (GB14888, GB11786, GB11890, GB16246, GB11022 nd GB14639) of the yellow protein fmily, which puttively encode the mjor royl jelly proteins 1, 4, 6, 2, 7 nd 8 (MRJP1, MRJP4, MRJP6, MRJP2, MRJP7 nd MRJP8, respectively). MRJPs re undnt in royl jelly, food secreted from hypophryngel (hed) glnds of workers. Yet, trnsgenic fruit flies with MRJP1 monomer expressed internlly (in ft) show ctivtion of Egf signling nd phenotypes (Kmkur, 2011), indicting internl roles of MRJP trnscripts perhps in vriety of tissues including ovries Log P-vlue Fig. 1. Comprison of gene ontology (GO) in the differentilly regulted genes etween High nd Low strins of worker honey ees in terms of (A) iologicl process, (B) moleculr function nd (C) cellulr component. The x-xis represents Log P-vlue (Shmir et l., 2005) nd P 0.05 ws used s cut-off for the sttisticlly enriched ctegory. The corresponding GO term is given eside ech horizontl r. Detiled results for P-vlues 0.10 re given in supplementry mteril Tle S3. Low strin ovries re typiclly smller thn High strin ovries nd, interestingly, there ws significnt overrepresenttion of ʻregultion of poptosisʼ in the Low strin ovries. kinse inding (P 0.016) ws significntly higher in High strin ovries (Fig. 1, see supplementry mteril Tle S3 for detils on sttistics). These results indicte tht Low strin worker ovries my e more sensitive to stimuli nd show higher levels of poptosis compred with High strin worker ovries. This interprettion mtches the finding tht Low strin workers re more sensitive to Contrsting trnscriptomes from ovries nd wild-type rins The genes tht were differently expressed etween ovries from the High nd Low strins were compred with previously pulished wild-type rin trnscriptomes regulted y QMP, nurse/forging ehvior nd tretment with methoprene ( JH mimic) (Grozinger et l., 2003; Kocher et l., 2010; Whitfield et l., 2006; Whitfield et l., 2003). We found significnt overlp etween ovrin nd rin dt (right-tiled Fisher s exct test; Tle 2). P-vlues less thn were significnt fter Bonferroni correction for multiple testing (P<0.004). We selected genes for GO nlysis tht were differently regulted in ovries of High or Low strin ees s well s regulted y QMP, nurse/forging ehvior or JH mimic in the rin of wild-type worker ees (Tle 2, groups with light, medium or drk shding, respectively; Fig. 2). Similr differences in iologicl processes were found etween High nd Low strin ovries in ech of the three comprisons. The overlp etween ovrin gene expression nd rin trnscriptomes ws ised towrds crohydrte, lipid nd mine metolism in High strin ees, wheres the corresponding Tle 1. Significntly (P 0.05) over-represented clusters of gene trnscripts on the honey ee chromosomes Gene ID Chromosome no. Physicl loction (MB) Annottion Genotype GB Secpin preproprotein Low GB CG8412 GB Trnscriptionl dpter 2B GB Antennl-specific protein 3c GB CG11658 Low GB CG4338 GB Olf186-M GB CG17233 GB Mjor royl jelly protein 1 Low GB Mjor royl jelly protein 4 GB Mjor royl jelly protein 6 GB Mjor royl jelly protein 2 GB Mjor royl jelly protein 7 GB Mjor royl jelly protein 8 GB ATP synthse et suunit High GB Hypotheticl protein isoform 2 GB CG18028 GB Similr to tyrosyl-trna synthetse A totl of 1794 significntly differentilly expressed genes were ssessed cross ech chromosome. Four gene clusters were found to e significntly over-represented on the honey ee chromosomes. Gry shding is used to distinguish different chromosomes. Low nd High genotypes indicte tht genes in the cluster were upregulted in Low or High strin ovries, respectively. MB, loction on the chromosome.

5 128 Y. Wng nd others Tle 2. Significnt overlp etween ovrin trnscriptomes nd rin trnscriptomes in worker honey ees No. significnt No. upregulted in No. upregulted in Gene list trnscripts High ovries P Low ovries P Reference Nurse-ssocited < Whitfield et l., 2003 Forger-ssocited < Whitfield et l., 2003 Methoprene upregulted < < Whitfield et l., 2006 Methoprene downregulted < Whitfield et l., 2006 QMP upregulted < Grozinger et l., 2003 QMP downregulted < Grozinger et l., 2003 Upregulted in high QMP responders Kocher et l., 2010 Downregulted in high QMP responders Kocher et l., 2010 Wsp forging Toth et l., 2010 Wsp reproduction Toth et l., 2010 Alrm pheromone Alux et l., 2007 upregulted Alrm pheromone downregulted Alux et l., 2007 Previously pulished studies hve identified trnscriptionl differences ssocited with the regultion of nursing nd/or forging ehvior (Whitfield et l., 2003), methoprene exposure (Whitfield et l., 2006), nd queen mndiulr pheromone (QMP) (Grozinger et l., 2003; Kocher et l., 2010) nd lrm pheromone exposure (Alux et l., 2009). We serched for significnt overlp etween trnscripts differentilly expressed in newly emerged workers from High nd Low strins, nd the rin trnscriptomes in these studies. A rin trnscriptome from pper wsps (Toth et l., 2010) ws lso used to revel whether there ws ny overlp in the gene pttern cross species, which ws relted to reproduction nd forging ehvior. A right-tiled Fisher s exct test ws used to identify significnt overlp etween studies; P-vlues surviving Bonferroni correction (P 0.004) re highlighted in old. The overlpping genes from groups shded in the sme shde were pooled together for further gene ontology nnottion, which is descried in more detil in Fig. 2. overlp for Low strin ovries ws neurl network development nd responses to different stimuli, including ecdysone hormone response (Fig. 2). Thus, we found tht selection on pollen hording hs chnged ovrin expression of genes involved in metolic control nd signling, sensory physiology nd hormone responses, nd the sme genes respond in the rin during ehviorl plsticity in wild-type ees. There ws no significnt overlp etween ovrin trnscriptome in this study nd the lrm-pheromone rin trnscriptome selected s our negtive control (P>0.004; Tle 2). We lso contrsted our ovrin gene list to the pper wsp rin trnscriptomes relted to forging ehvior nd reproduction (Toth et l., 2010). We did not find significnt overlp in gene expression pttern relted to either forging or reproduction (Tle 2). These results re perhps unsurprising ecuse pper wsps (Polistes) nd honey ees hve fundmentl difference in reproductive physiologies (Toth et l., 2010) tht could differentilly ffect ehvior. However, the common mechnisms etween honey ees nd wsps my e etter reveled in the future y incresing the coverge of the wsp genome (Toth et l., 2010). Verifiction of expression differences in cndidte genes in High vs Low strin ees We selected five genes for expression verifiction tht re involved in metolic control nd signling, sensory physiology nd hormone responses (i.e. HR46, Ftz-f1, JHi-26, MRJP1 nd TYR; for summry on function, see Mterils nd methods). The results of ll five genes were consistent with the results from the rry (Fig. 3) ll hve significntly (P 0.05) higher expression in Low strin ovries thn in High strin ovries (one-tiled Student s t-test, TYR, P 0.039; ftz-f1, P ; HR46, P ; MRJP1, P ; JHi-26, P ). Chrcterizing cndidte gene expression in lrge nd smll ovries of wild-type ees Gene expression ws quntified in wild-type worker ovries of different size. These ovry size groups hd significnt effects on overll gene expression (one-wy ANOVA, F 5, , P<0.0001, N 16; Fig. 4). TYR mrna levels were significntly higher in the SMO group (Fisher s LSD, P ; Fig. 4A), wheres ftz-f1 nd HR46 were more strongly expressed in the LAO group (Fisher s LSD, P nd , respectively; Fig. 4B,C). MRJP1 nd JHi-26 expression, in contrst, did not vry y ovry size (Fisher s LSD, P nd , respectively; Fig. 4D,E). These outcomes suggest tht the ovrin expression levels of HR46, ftz-f1, MRJP1 nd JHi-26 re est explined y selection (genotype) in this study, wheres the mount of TYR trnscript cn e roustly ssocited with ovry size in the wild-type s well s the pollenhording strin ees. DISCUSSION Here, we descrie trnscriptionl differences etween the ovries of newly emerged ees from honey ee strins idirectionlly selected for ehvior. A numer of genes were ssocited with the iologicl process sensory perception or the functionl ctegory reproduction (GO nlysis, supplementry mteril Fig. S2). Differentilly expressed genes included ecdysone-inducile nucler hormone receptors nd olfctory nd gusttory receptors. Tken together, these results suggest tht the honey ee worker ovry is dynmic orgn (Wng et l., 2010), lthough it is often presumed to e inctive under norml socil conditions (Foster nd Rtnieks, 2001). Furthermore, the significnt overlp oserved etween the present study nd previously pulished rin trnscriptomes suggests tht oth ovry nd rin physiologies re ffected y systemic fctors such s JH, ecdysteroids nd QMP, nd further supports the

6 Behviorl gene networks in worker ovries 129 Response to QMP Relevnt processes to nursing ehvior A High strin ovry Low strin ovry Olfctory ehvior Response to ecdysone Regultion of cell differentition Antimicroil humorl response Response to other orgnism Nervous system development Negtive regultion of immune system process Regultion of metolic process Negtive regultion of response to iotic stimulus Cell development Trnsmission of nerve impulse Croxylic cid metolic process Nitrogen compound iosynthetic process Crohydrte ctolic process Cellulr mine metolic process Regultion of developmentl growth Lipid metolic process Protein metolic process B Aggressive ehvior Adptive immune response Lymphocyte medited immunity Centrl nervous system development Anion trnsport Croxylic cid metolic process Cellulr lipid metolic process Cellulr crohydrte ctolic process Sulfur compound ctolic process Fig. 2. Different ptterns of GO iologicl process etween High nd Low strins of worker honey ees in the ovry rin overlpping genes. (A) Response to queen mndiulr pheromone (QMP), which inhiits the ctivtion of the worker ovry nd ffects worker ehvior (Grozinger et l., 2003; Kocher et l., 2010). (B) Relevnt processes to nursing ehvior, which is regulted y systemic regultors including QMP, juvenile hormone (JH), ecdysteroid nd neurl systems (Whitfield et l., 2003). (C) Relevnt processes to forging ehvior/methoprene tretment, which ccelertes the ge t onset of forging (Whitfield et l., 2006). P 0.01 ws used s cut-off for the sttisticlly enriched ctegory. The GO term of ech ctegory is given y the corresponding r. Overll, the overlp etween rin trnscriptomes nd ovrin gene expression in the High strin ees ws ised towrds crohydrte, lipid nd mine metolism, wheres the corresponding overlps of Low strin ovries were neurl network development nd responses to different stimuli, including the ecdysone hormone response. Relevnt processes to forging ehvior/methoprene tretment C Regultion of ecdysteroid metolic process Antimicroil humorl response Protein metolic process Orgn development Centrl nervous system development Neurogenesis Cell development Crohydrte ctolic process Cellulr lipid metolic process Androgen metolic process Cellulr mcromolecule ctolic process Log P-vlue hypothesis tht ech of these fctors re key prticipnts in regultory networks for socil ehvior in this species. Ecdysteroid hormones nd worker ovrin physiology Honey ee worker ovries produce ecdysteroids during the first dy of dult life (Amdm et l., 2010), nd the ecdysone receptor gene (EcR) is expressed in worker nd queen ovries (Tkeuchi et l., 2007). Ecdysteroids signl oogenesis in Triolium, Drosophil nd mosquitoes (Culex pipiens) (Bernrdi et l., 2009; Khter et l., 1994; Xu et l., 2010), ut oogenesis is uncommon in worker ees ecuse yolk uptke nd oocyte mturtion is suppressed pheromonlly when queen is present in the colony (Atkins et l., 1975). We found tht three genes ssocited with the ecdysteroid cscde [HR46, ftz-f1 nd ecdysone-induced protein 75 (E75)] were more highly expressed in Low pollen-hording strin ovries thn in the High strin. At dult emergence, Low strin ees lso hve the higher ecdysteroid titers, nd the plusile source of this hormone is the ovry (Amdm et l., 2010). Yet, elevted ecdysteroid signling nd/or sensing in Low strin ovries does not correlte with oogenesis (Amdm et l., 2006). Rther, ecdysteroids cn induce oocyte poptosis nd follicle tresi (Pul et l., 2005; Soller et l., 1999; Uchid et l., 2004), nd cn e supported y incresed poptosis regultion in Low strin ovries (Fig. 1A). This hypothesis is consistent with Low strin workers eing more redily inhiited from ctivting their ovries for egg lying (Amdm et l., 2006), perhps ecuse of heightened sensitivity to socil inhiition nd incresed rtes of follicle poptosis (Hunt et l., 2007). Future studies my nswer whether ecdysteroids regulte poptosis in honey ee ovries. Ecdysteroid titers re very low in the hemolymph of dult ees, suggesting tht ecdysteroids hve lost their function in dult workers (Hrtfelder et l., 2002). Recently, mny studies hve indicted tht ecdysteroid cscdes in the ft ody nd rin my e involved in socil ehvior (Velrde et l., 2009; Wng et l.,

7 130 Y. Wng nd others Log RQ (mrna) A D TYR MRJP1 B E ftz-f1 High Low High Low JHi-26 C High HR46 Low Fig. 3. Verifiction of expression differences in cndidte genes in High vs Low strin worker honey ees using reltive quntifiction (RQ). The sme smples used in the microrry were used for gene expression verifiction. (A) TYR, receptor of the neurl trnsmitter tyrmine; (B) ftz-f1, n ecdysteroid nucler receptor; (C) HR46, n ecdysteroid nucler receptor; (D) MRJP1, protein component in royl jelly; (E) JHi- 26, JH-inducile gene tht cn e triggered y methoprene. Brs represent mens ± s.e.m.; different letters ( or ) indicte significnt differences (one-tiled Studentʼs t-test, P 0.05). All cndidte genes showed higher expression level in Low strin ovries thn in High strin ovries, s ws the cse with the microrry High Low High Low 2009; Wng et l., 2010). In this study, we found significnt overlp of ecdysteroid-relted processes etween the Low ovrin nd rin trnscriptomes ssocited with QMP exposure (Fig. 2A) nd forging ehvior (Fig. 2C). This implies tht ecdysteroids my e involved in oth rin nd ovry physiologies relted to QMP nd forging ehvior. However, further investigtion is needed to test the role of ecdysteroids in honey ee rin regrding socil ehvior. QMP, JH-ecdysteroid hormone xes nd the worker ovry Our comprison etween ovrin nd rin trnscriptomes reltes iologicl processes of the ovry to rin mrna expression profiles ssocited with exposure to QMP, methoprene nd the nursing or forging ehviorl stte. In every comprison, similr ptterns of ovry rin overlp were found (Fig. 2). Ws this surprising? Worker ehvior, including nursing nd forging, is modulted y QMP (Pnkiw et l., 1998), JH (Hung et l., 1991) nd ovrin Log RQ (mrna) A TYR ftz-f1 HR46 B D LAO SMO LAO SMO MRJP1 E JHi-26 C LAO SMO Fig. 4. Chrcteriztion of cndidte gene expression in lrge nd smll ovries of wild-type honey ees using reltive quntifiction (RQ). Trnscript undnces of four cndidte genes were mesured in lrge ovries (LAO) nd smll ovries (SMO) of wild-type ees. (A) TYR; (B) ftz-f1; (C) HR46; (D) MRJP1; (E) JHi-26. Brs represent mens ± s.e.m.; different letters ( or ) indicte significnt differences (post hoc Fisherʼs lest significnt difference, P 0.05). Ftz-f1 nd HR46 were more highly expressed in LAO thn in SMO. TYR ws more highly expressed in SMO thn in LAO. There ws no difference in MRJP1 nd JHi- 26 expression etween LAO nd SMO LAO SMO LAO SMO

8 Behviorl gene networks in worker ovries 131 physiology (Amdm et l., 2006; Nelson et l., 2007; Roinson, 1992). Therefore, the overlp we reveled (Fig. 2) my e signture of (lrgely) systemiclly cting gene networks ssocited with the division of lor. Moreover, the cler seprtion etween pollen-hording strins in their overlp of ovry nd rin trnscriptomes supports the hypothesis tht the idirectionl selection on these strins cted on gene networks tht connect ehvior to physiology (Amdm et l., 2010; Pge et l., 1998). QMP emitted y honey ee queens inhiits ovry ctivtion (Hoover et l., 2003), influences ge-relted division of lor (Pnkiw et l., 1998) nd ffects rin development in worker ees (Morgn et l., 1998). The rin s trnscriptionl response to QMP is lso negtively correlted with worker ovriole numer (Kocher et l., 2010). This correltion points to unexplined connections etween rin function nd ovry size. We found tht the functionl ctegory olfctory ehvior ws over-represented in the overlp etween Low strin ovries nd rins regulted y QMP (Fig. 2A). Moreover, we identified 10 olfctory receptor (OR) genes differentilly expressed etween High nd Low strin ovries. ORs elong to the GPCR gene fmily, which is lso enriched in ovries of Low strin genotype ees (P ; supplementry mteril Tle S3). GPCRs comprise lrge protein fmily of trnsmemrne receptors tht ind light-sensitive compounds, odors, pheromones, hormones nd neurotrnsmitters. ORs re generlly expressed in cell memrnes of olfctory receptor neurons (ntenne) (Getz nd Akers, 1994; Murphy et l., 2003; Vosshll et l., 1999). However, dditionl functions of OR proteins hve een suggested (Feingold et l., 1999; Itkur et l., 2006; Xu et l., 2000) ecuse of their locliztion to different ectopic tissues (non-olfctory tissues), such s germ cells nd testis tissue in mmmls (Fukud et l., 2004; Mrchnd, 2003; Spehr et l., 2003; Vnderheghen et l., 1997; Ziegler et l., 2002). Recent experiments lso show tht one OR in honey ee ntennl neurons cn respond to component of QMP (Wnner et l., 2007). It is possile tht connections etween rin function nd ovrin trits in worker ees could e cused y correlted expression of ORs. This hypothesis cn e tested in future studies. JH is systemic hormone with effects on insect metolic iology, reproductive physiology nd dult ehvior. JH nd ecdysteroid titers re often negtively correlted in insects, with opposing regultion demonstrted in Drosophil melnogster (reviewed y Riddiford, 1996), mosquitoes (Aedes troplpus) L (Birnum et l., 1984) nd honey ees (Remold, 1987). Using rin trnscriptome dt from exposure to methoprene ( JH mimic), we found tht Low strin ovries is functionl processes towrds ecdysteroid nd neurl regultion in contrst to the High strin ees (Fig. 2C). It hs previously een demonstrted tht worker sensitivity towrds JH responses is conditionl on their Low vs High genotypes (Amdm et l., 2007; Amdm et l., 2010), i.e. Low strin worker ees show reduced JH sensitivity, perhps ecuse of the genetic is towrds ecdysteroid signling tht is suggested y our results. Genomic gene clusters Our study presents genomic mpping pproch tht cn e used on lrge-scle trnscript dt. This method cn enhnce functionl genomic studies y dding sptil informtion s to where significntly expressed genes re locted in the genome. Using this method, we found four genomic clusters of differentilly expressed genes, suggesting tht, in these regions of the genome, nery genes re consistently nd differentilly expressed etween High nd Low genotypes (Tle 1, supplementry mteril Fig. S3). Similr gene clusters re often co-regulted (Cohen et l., 2000; Spieth et l., 1991; Tkder et l., 1996). According to our conservtive chromosome-wide thresholds, previously mpped QTL for worker ehvior nd ovry size do not contin puttively co-regulted gene clusters, s would e expected if the QTL led to chnges in cis regultion of groups of genes. More quntittive mesures of differentil gene expression, i.e. with RNA sequencing nd susequent genome mpping, my etter revel genomic ptterns of gene expression nd the degree to which gene clusters re coregulted. Alterntively, the identified QTL my ffect ovriole numer during ovry development in lte lrvl stges. Becuse we used newly emerged ees in this study, we might hve missed the developmentl window when the QTL ffect the ovriole numer. One of the clusters we detected contined MRJP-encoding genes. A few MRJP trnscripts re generlly expressed in honey ee reproductive tissues, suggesting roles in sex-specific reproductive mturity (Drpeu et l., 2006). We found the gene cluster to e upregulted in Low strin ovries. Ecdysteroid signling, which presumly is lso upregulted in Low strin ovries, enhnces the royl-jelly-producing (nd strongly MRJP-expressing) hypophryngel glnds of workers in ddition to influencing ovrin physiology (Wegener et l., 2009). Cross-fostering studies indicte tht low strin nurse workers provide different nutritionl environments to developing lrve thn high strin nurse workers (Linksvyer et l. 2009, 2011), perhps s result of differentil MRJP1 expression. The elevted expression of MRJP genes in Low strin ovries might, in other words, e n ecdysteroid-driven response. An MRPJ1 monomer influences honey ee development when secreted in lrvl food (Kmkur, 2011). MRJP1 ws not differentilly expressed in wild-type ovries of different sizes (Fig. 3D), suggesting tht it is not involved in ssocitions etween ovry size nd ehvior in worker ees. Yet, cndidte gene expression is reltive quntity, n mount corrected towrds housekeeper genes tht re eqully present per unit totl RNA. Between individuls, however, the summed totl RNA of vrily sized tissues cn correlte with orgn size, e.g. if the lrger-sized orgns hve more cells. Lrge ovries hve more cells tht mke up the ovriole count. This considertion could e relevnt for trnslted proteins such s MRJP1, s lrger ovries might relese more product thn smll ovries. Genotype, ovry size nd specific ptterns of gene expression Ovriole numer plys role in socil ehvior (Amdm et l., 2006; Wng et l., 2010) nd ovrin physiology (Mkert et l., 2006) in honey ees. However, High nd Low pollen-hording genotypes cn lso e fctors influencing the ovrin trnscriptomes. Therefore, we tested the ssocition etween ovry size nd the expression of five cndidte genes in wild-type ees: HR46, ftz-f1, TYR, MRJP1 nd JHi-26. For the two ltter genes, no ssocition ws supported. For HR46 nd ftz-f1, differences were significnt ut levels were opposite to those predicted y the verge ovriole numer of High nd Low strin genotypes, suggesting tht differentil expression of these genes cn e influenced y the genetic ckground. TYR, however, showed consistent reltionships with ovry size etween wild-type nd the selected stocks. It ws suggested previously tht selection for pollen-hording strins hs influenced reltionships etween HR46, Ftz-f1 nd ovry size in newly emerged ees (Wng et l., 2009). HR46 nd ftz-f1 mrna levels coincide with signling y ecdysteroid hormones (Velrde et l., 2009), nd ecdysteroid titers re shifted in lte pupl stges nd during erly dult life etween High nd Low pollenhording strin ees (Amdm et l., 2010). This shift my lso chnge the induction of HR46 nd ftz-f1 reltive to ovry size when

9 132 Y. Wng nd others A B Egg Lrv Pup Nurse N nd G Ovry size? JH + Ecdy Environment (E) Nutrition (N) Genotype (G) Ecdy? N nd G Vg + Ovry signling Forging O/P Vg Forging O/P JH QMP Egg production JH Vg Ovry signling Forging O/P Forger Ecdy? Time QMP Forging ctivity Queen mndiulr pheromone (QMP) Fig. 5. Model to explin roles of ovries in regultory network of socil ehvior. Ovry size is determined y nutrition (N) sttus nd colony genotype (G) t the lst lrvl stge, which is ffected y systemic hormone, JH (Bloch et l., 2000; Schmidt-Cpell nd Hrtfelder, 1998). Results from the present study nd those from Wng et l. suggest tht ecdysteroids (Ecdy) my e involved in poptosis for shping ovry size (Wng et l., 2009). Queen mndiulr pheromone (QMP) inhiits egg production in nurses nd slows workers to forge in their lter lives. Nutrition nd genotype lso ply importnt roles in regulting ovry signling nd vitellogenin (Vg) titers in dult workers, which ffect ge of forging onset (O) nd forging preference (P). Vg regultes forging O/P directly or through feedck loop with JH (Amdm et l., 2004; Amdm nd Omholt, 2003; Ihle et l., 2010). Worker ovries cn ccelerte forging O/P, in which ecdysteroids my function. There re lso neurl regultions etween the ovry nd rin, which my e involved in these ehviorl networks. selected strins re compred with wild type. Similr phenomen re known from other systems (Toledo-Rodriguez et l., 2004). TYR, which is ctivted y the neurotrnsmitter tyrmine, ws consistently negtively ssocited with ovriole numer in the two selected strins nd in wild-type ees. TYR is positionl cndidte gene in the QTL Pln2 tht is geneticlly linked to forging ehvior nd ovry size (Hunt et l., 2007; Linksvyer et l., 2009). Tyrmine, furthermore, influences honey ee sucrose responsiveness, which diverges etween pollen-hording strins, nd predicts forging ehviorl trits in wild-type ees (Pnkiw nd Pge, 2003; Scheiner et l., 2002). These connections might point to systemic ptterns in TYR-dependent signling. Yet, the modlity of TYR expression differs etween the rin nd ovry of the pollenhording strins (supplementry mteril Fig. S4), which suggests more complex, tissue-specific function of TYR nd tyrmine tht re supported y previous studies (e.g. Hung et l., 2004; Nykmp nd Lnge, 2000; Thompson et l., 2007). Tken together, our results support TYR s cndidte gene for ssocitions etween ovry size nd ehvior in worker ees. Conclusions Ovry size is ffected y genetic nd environmentl fctors nd influences socil ehvior in honey ee workers. Socil environmentl signls (such s QMP) nd physiologicl systems (such s the ecdysteroid nd JH xes) regulte worker ovrin development nd physiology. Yet, the worker ovry my lso e n ctive endocrine signling system nd trnscriptionl feedck genertor (Fig. 5). Therefore, our study supports the hypothesis tht oth ovries nd rins prticipte in the regultory networks, which respond to the systemic stimuli such s hormones nd pheromones, nd modulte honey ee division of lor. These insights provide pltform for further functionl studies tht cn determine how ovrin processes influence rin function nd socil ehvior. LIST OF ABBREVIATIONS Egf epiderml growth fctor E75 ecdysone-induced protein 75 FDR flse discovery rte ftz-f1 ftz trnscription fctor-1 GO gene ontology GPCR G protein-coupled receptor HR46 hormone receptor-like in 46 JH juvenile hormone JHi-26 juvenile hormone-inducile protein 26 LAO lrge ovry LSD lest significnt difference MRJP mjor royl jelly protein MRJP1 mjor royl jelly protein 1 OR olfctory receptor PDK1 phosphoinositide-dependent kinse-1 QMP queen mndiulr pheromone QTL quntittive trit loci RQ reltive quntifiction SMO smll ovry TYR tyrmine receptor gene ACKNOWLEDGEMENTS We thnk N. Mutti nd M. K. Fondrk for experimentl ssistnce nd we re lso grteful to Z. Simões, C. S. Brent, A. Dolezl, K. Trynor nd K. Dolezl for helpful comments on the mnuscript. FUNDING This reserch ws supported y the Reserch Council of Norwy [180504, ] nd The PEW Chritle Trust [to G.V.A.], the Ntionl Institute on Aging [NIA P01 AG22500] nd the Wissenschftskolleg zu Berlin [to G.V.A., T.A.L. nd R.E.P.] nd the Ntionl Science Foundtion-CAREER grnt [NSF to C.M.G.]. Deposited in PMC for relese fter 12 months. REFERENCES Alux, C. nd Roinson, G. E. (2007). Alrm pheromone induces immedite-erly gene expression nd slow ehviorl response in honey ees. J. Chem. Ecol. 33, Alux, C., Le Conte, Y., Adms, H. A., Rodriguez-Zs, S., Grozinger, C. M., Sinh, S. nd Roinson, G. E. (2009). Regultion of rin gene expression in honey ees y rood pheromone. Genes Brin Behv. 8, Alux, C., Sinh, S., Hsdsri, L., Hunt, G. J., Guzmn-Novo, E., DeGrndi- Hoffmn, G., Urie-Ruio, J. L., Southey, B. R., Rodriguez-Zs, S. nd Roinson, G. E. (2009). Honey ee ggression supports link etween gene regultion nd ehviorl evolution. Proc. Ntl. Acd. Sci. USA 106, Amdm, G. V. nd Omholt, S. W. (2003). The hive ee to forger trnsition in honeyee colonies: the doule repressor hypothesis. J. Theor. Biol. 223, Amdm, G. V., Norerg, K., Fondrk, M. K. nd Pge, R. E., Jr (2004). Reproductive ground pln my medite colony-level selection effects on individul forging ehvior in honey ees. Proc. Ntl Acd. Sci. USA 101,

10 Behviorl gene networks in worker ovries 133 Amdm, G. V., Csondes, A., Fondrk, M. K. nd Pge, R. E., Jr (2006). Complex socil ehviour derived from mternl reproductive trits. Nture 439, Amdm, G. V., Nilsen, K. A., Norerg, K., Fondrk, M. K. nd Hrtfelder, K. (2007). Vrition in endocrine signling underlies vrition in socil life history. Am. Nt. 170, Amdm, G. V., Ihle, K. E. nd Pge, R. E. (2009). Regultion of honey ee (Apis mellifer) life-histories y vitellogenin. In Hormones, Brin nd Behvior, Vol. 4 (ed. D. Pfff, A. Arnold, A. Etgen, S. Fhrch nd R. Ruin), pp Sn Diego, CA: Elsevier Acdemic Press. Amdm, G. V., Pge, R. E., Jr, Fondrk, M. K. nd Brent, C. S. (2010). Hormone response to idirectionl selection on socil ehvior. Evol. Dev. 12, Argst, G. M., Croy, C. H., Couts, K. L., Zhng, Z., Litmn, E., Chn, D. C. nd Ahn, N. G. (2009). Plexin B1 is repressed y oncogenic B-Rf signling nd functions s tumor suppressor in melnom cells. Oncogene 28, Atkins, E. L., Bnker, R., Butler, C. G., Cle, G. H., Cle, G. H., Jr, Crne, E. nd Ddnt, C. C. (1975). The Hive nd the Honey Bee. Hmilton, IL: Dtnt & Sons. Bernrdi, F., Romni, P., Tzertzinis, G., Grgiulo, G. nd Cvliere, V. (2009). EcR-B1 nd Usp nucler hormone receptors regulte expression of the VM32E eggshell gene during Drosophil oogenesis. Dev. Biol. 328, Birnum, M. J., Kelly, T. J., Woods, C. W. nd Imerski, R. B. (1984). Hormonl regultion of ovrin ecdysteroid production in the utogenous mosquito, Aedes troplpus. Gen. Comp. Endocrinol. 56, Bloch, G., Borst, D. W., Hung, Z., Roinson, G. E., Cnni, J. nd Hefetz, A. (2000). Juvenile hormone titers, juvenile hormone iosynthesis, ovrin development nd socil environment in Bomus terrestris. J. Insect Physiol. 46, Cohen, B. A., Mitr, R. D., Hughes, J. D. nd Church, G. M. (2000). A computtionl nlysis of whole-genome expression dt revels chromosoml domins of gene expression. Nt. Genet. 26, Cupp, E. W. nd Collins, R. C. (1979). The gonotrophic cycle in Simulium ochrceum. Am. J. Trop. Med. Hyg. 28, Drpeu, M. D., Alert, S., Kuchrski, R., Prusko, C. nd Mleszk, R. (2006). Evolution of the Yellow/Mjor Royl Jelly Protein fmily nd the emergence of socil ehvior in honey ees. Genome Res. 16, Evns, J. D. nd Wheeler, D. E. (1999). Differentil gene expression etween developing queens nd workers in the honey ee, Apis mellifer. Proc. Ntl. Acd. Sci. USA 96, Feingold, E. A., Penny, L. A., Nienhuis, A. W. nd Forget, B. G. (1999). An olfctory receptor gene is locted in the extended humn et-gloin gene cluster nd is expressed in erythroid cells. Genomics 61, Foster, K. R. nd Rtnieks, F. L. (2001). Convergent evolution of worker policing y egg eting in the honeyee nd common wsp. Proc. R. Soc. Lond. B 268, Fukud, N., Yomogid, K., Oke, M. nd Touhr, K. (2004). Functionl chrcteriztion of mouse testiculr olfctory receptor nd its role in chemosensing nd in regultion of sperm motility. J. Cell Sci. 117, Getz, W. M. nd Akers, R. P. (1994). Honeyee olfctory sensill ehve s integrted processing units. Behv. Neurl. Biol. 61, Giry, T. nd Roinson, G. E. (1996). Common endocrine nd genetic mechnisms of ehviorl development in mle nd worker honey ees nd the evolution of division of lor. Proc. Ntl. Acd. Sci. USA 93, Grhm, A. M., Mundy, M. D., Kftnoglu, O., Pge, R. E., Jr, Amdm, G. V. nd Rueppell, O. (2011). Support for the reproductive ground pln hypothesis of socil evolution nd mjor QTL for ovry trits of Africnized worker honey ees (Apis mellifer L.). BMC Evol. Biol. 11, 95. Grozinger, C. M., Shrsh, N. M., Whitfield, C. W. nd Roinson, G. E. (2003). Pheromone-medited gene expression in the honey ee rin. Proc. Ntl. Acd. Sci. USA 100 Suppl. 2, Hncock, R. G. nd Foster, W. A. (2000). Exogenous Juvenile hormone nd methoprene, ut not mle ccessory glnd sustnces or ovriectomy, ffect the lood/nectr choice of femle Culex nigiriplpus mosquitoes. Med. Vet. Entomol. 14, Hrtfelder, K., Bitondi, M. M. G., Sntn, W. C. nd Simões, Z. L. P. (2002). Ecdysteroid titer nd reproduction in queens nd workers of the honey ee nd of stingless ee: loss of ecdysteroid function t incresing levels of socility? Insect Biochem. Mol. Biol. 32, Hoover, S. E. R., Keeling, C. I., Winston, M. L. nd Slessor, K. N. (2003). The effect of queen pheromones on worker honey ee ovry development. Nturwissenschften 90, Hung, Z. Y., Roinson, G. E., Yoi, S., Strmi, C., Strmi, A. nd Sty, B. (1991). Hormonl regultion of ehviourl development in the honey ee is sed on chnges in the rte of juvenile hormone iosynthesis. J. Insect Physiol. 37, Hung, Z. Y., Hnley, A. V., Pett, W. L., Lngenerger, M. nd Dun, J. J. (2004). Field nd semifield evlution of impcts of trnsgenic cnol pollen on survivl nd development of worker honey ees. J. Econ. Entomol. 97, Hunt, G. J. nd Pge, R. E., Jr (1995). Linkge mp of the honey ee, Apis mellifer, sed on RAPD mrkers. Genetics 139, Hunt, G. J., Pge, R. E., Fondrk, M. K. nd Dullum, C. J. (1995). Mjor quntittive trit loci ffecting honey-ee forging ehvior. Genetics 141, Hunt, G. J., Amdm, G. V., Schliplius, D., Emore, C., Srdesi, N., Willims, C. E., Rueppell, O., Guzmn-Novo, E., Arechvlet-Velsco, M., Chndr, S. et l. (2007). Behviorl genomics of honeyee forging nd nest defense. Nturwissenschften 94, Ihle, K. E., Pge, R. E., Frederick, K., Fondrk, M. K. nd Amdm, G. V. (2010). Genotype effect on regultion of ehviour y vitellogenin supports reproductive origin of honeyee forging is. Anim. Behv. 79, Itkur, S., Ohno, K., Ueki, T., Sto, K. nd Knym, N. (2006). Expression of Golf in the rt plcent: possile impliction in olfctory receptor trnsduction. Plcent 27, Kmkur, M. (2011). Roylctin induces queen differentition in honeyees. Nture 21, Kemnitz, J. W., Gier, J. R., Lindsy, K. A. nd Eisele, S. G. (1989). Effects of ovrin hormones on eting ehviors, ody weight, nd glucoregultion in rhesus monkeys. Horm. Behv. 23, Khter, H. M., Gd, A. M. nd Hssn, A. N. (1994). Effect of juvenile hormone nd ecdysone on inititing lood mel-dependent vitellogenic ovrin cycles in utogenous nd nutogenous Culex pipiens (Dipter: Culicide). J. Egypt. Pulic Helth Assoc. 69, Klowden, M. J. (1990). The endogenous regultion of mosquito reproductive ehvior. Experienti 46, Koyshi, M., Michut, L., Ino, A., Honjo, K., Nkjim, T., Mruym, Y., Mochizuki, H., Ando, M., Ghngrekr, I., Tkhshi, K. et l. (2006). Differentil microrry nlysis of Drosophil mushroom ody trnscripts using chemicl ltion. Proc. Ntl. Acd. Sci. USA 103, Kocher, S. D., Ayroles, J. F., Stone, E. A. nd Grozinger, C. M. (2010). Individul vrition in pheromone response correltes with reproductive trits nd rin gene expression in worker honey ees. PLoS ONE 5, e9116. Linduer, M. (1953). Division of lour in the honeyee colony. Bee World 34, Linksvyer, T. A., Fondrk, M. K. nd Pge, R. E., Jr (2009). Colony-level selection in honey ees produces coevolved socilly intercting gene complexes. Americn Nturlist 173, Linksvyer, T. A., Rueppell, O., Siegel, A., Kftnoglu, O., Pge, R. E., Jr nd Amdm, G. V. (2009). The genetic sis of trnsgressive ovry size in honeyee workers. Genetics 183, Linksvyer, T. A., Kftnoglu, O., Akyol, E., Bltch, S., Amdm, G. V. nd Pge, R. E., Jr (2011). Lrvl nd nurse worker control of developmentl plsticity nd the evolution of honey ee queen worker dimorphism. J. Evol. Biol. 24, Lourenço, A. P., Mckert, A., Sntos, C. nd Simões, Z. L. P. (2008). Vlidtion of reference genes for gene expression studies in the honey ee, Apis mellifer, y quntittive rel-time RT-PCR. Apidologie 39, Mkert, G. R., Pxton, R. J. nd Hrtfelder, K. (2006). Ovriole numer- predictor for differentil reproductive success mong worker sufmilies in queenless honey ee (Apis mellifer L.) colonies. Behv. Ecol. Socioiol. 60, Mrchnd, A. P. (2003). Chemistry. Dimondoid hydrocrons-delving into ntureʼs ounty. Science 299, Michut, L., Flister, S., Nee, M., White, K. P., Cert, U. nd Gehring, W. J. (2003). Anlysis of the eye developmentl pthwy in Drosophil using DNA microrrys. Proc. Ntl. Acd. Sci. USA 100, Morgn, S. M., Butz Huryn, V. M., Downes, S. R. nd Mercer, A. R. (1998). The effects of queenlessness on the mturtion of the honey ee olfctory system. Behv. Brin Res. 91, Murphy, C. T., McCrroll, S. A., Brgmnn, C. I., Frser, A., Kmth, R. S., Ahringer, J., Li, H. nd Kenyon, C. (2003). Genes tht ct downstrem of DAF-16 to influence the lifespn of Cenorhditis elegns. Nture 424, Nelson, C. M., Ihle, K., Amdm, G. V., Fondrk, M. K. nd Pge, R. E. (2007). The gene vitellogenin hs multiple coordinting effects on socil orgniztion. PLoS Biol. 5, Nykmp, D. A. nd Lnge, A. B. (2000). Interction etween octopmine nd proctolin on the oviducts of Locust migrtori. J. Insect Physiol. 46, Pge, R. E. nd Fondrk, M. K. (1995). The effects of colony-level selection on the socil orgniztion of honey ee (Apis mellifer L.) colonies: colony-level components of pollen hording. Behv. Ecol. Socioiol. 36, Pge, R. E., Roinson, G. E., Fondrk, M. K. nd Nsr, M. E. (1995). Effects of worker genotypic diversity on honey ee colony development nd ehvior (Apis mellifer L.). Behv. Ecol. Socioiol. 36, Pge, R. E., Jr, Erer, J. nd Fondrk, M. K. (1998). The effect of genotype on response thresholds to sucrose nd forging ehvior of honey ees (Apis mellifer L.). J. Comp. Physiol. A 182, Pnkiw, T. nd Pge, R. E., Jr. (2003). Effect of pheromones, hormones, nd hndling on sucrose response thresholds of honey ees (Apis mellifer L.). J. Comp. Physiol. A 189, Pnkiw, T., Hung, Z.-Y., Winston, M. L. nd Roinson, G. E. (1998). Queen mndiulr glnd pheromone influences worker honey ee (Apis mellifer L.) forging ontogeny nd juvenile hormone titers. J. Insect Physiol. 44, Pul, R. K., Tkeuchi, H., Mtsuo, Y. nd Kuo, T. (2005). Gene expression of ecdysteroid-regulted gene E74 of the honeyee in ovry nd rin. Insect Mol. Biol. 14, Pennisi, E. (2006). Honey ee genome illumintes insect evolution nd socil ehvior. Science 314, Pfffl, M. W. (2001). A new mthemticl model for reltive quntifiction in rel-time RT-PCR. Nucleic Acids Res. 29, e45. Remold, H. (1987). Cste specific modultion of juvenile hormone titers in Apis mellifer. Insect Biochem. 17, Riddiford, L. M. (1996). Moleculr Aspects of Juvenile Hormone Action in Insect Metmorphosis. Sn Diego, CA: Acdemic Press. Roinson, G. E. (1992). Regultion of division of lor in insect societies. Annu. Rev. Entomol. 37, Rueppell, O., Chndr, S. B., Pnkiw, T., Fondrk, M. K., Beye, M., Hunt, G. nd Pge, R. E. (2006). The genetic rchitecture of sucrose responsiveness in the honeyee (Apis mellifer L.). Genetics 172, Rueppell, O., Metheny, J. D., Linksvyer, T., Fondrk, M. K., Pge, R. E. nd Amdm, G. V. (2011). Genetic rchitecture of ovry size nd symmetry in Europen honey ee workers. Heredity 106, Scheiner, R., Pluckhhn, S., Oney, B., Blenu, W. nd Erer, J. (2002). Behviourl phrmcology of octopmine, tyrmine nd dopmine in honey ees. Behv. Brin Res. 136, Schmidt-Cpell, I. C. nd Hrtfelder, K. (1998). Juvenile hormone effect on DNA synthesis nd poptosis in cste-specific differentition of the lrvl honey ee (Apis mellifer L.) ovry. J. Insect Physiol. 44,

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