Interaction frequency and per-interaction effects as predictors of total effects in plant–pollinator mutualisms: a case study with the self-incompatible herb Linaria lilacina

Fo Pee Re iew In e ac ion equency and pe in e ac ion e ec s as p edic o s o o al e ec s in plan -pollina o mu ualisms: a case s udy wi h he sel -incompa ible he b Lina ia lilacina. Jou nal: Oecologia Manusc ip ID: OEC-KG-2010-0548.R3 Manusc ip Type: o iginal esea ch pape Da e Submi ed by he Au ho : n/a Comple e Lis o Au ho s: Sanchez-La uen e, Al onso; Uni e sidad de Se illa, Biologia Vege al y Ecologia Rod iguez-Gi ones, Miguel Angel; Es acion Expe imen al de Zonas A idas (CSIC) Pa a, Raquel; Uni e sidad de Se illa, Biologia Vege al y Ecologia Keywo ds: mu ualis ic ne wo ks, plan -pollina o in e ac ions, isi a ion a e, bou leng h, pollen deposi ion Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 1 In e ac ion equency and pe in e ac ion e ec s as p edic o s o o al e ec s in plan -pollina o mu ualisms: a case s udy wi h he sel -incompa ible he b Lina ia lilacina. Sho i le: In e ac ion equency and o al e ec s in Lina ia Al onso M. Sánchez-La uen e1, *, Miguel A. Rod íguez-Gi onés2 and Raquel Pa a1 1Depa amen o de Biología Vege al y Ecología, Facul ad de Biología, Uni e sidad de Se illa, A d. Reina Me cedes 9, 41012 Se illa, Spain 2Es ación Expe imen al de Zonas A idas (EEZA-CSIC), C a. de Sac amen o s/n, La Cañada de San U bano, 04120 Alme ía, Spain *Co esponding au ho email: al onso@sla uen e.es Fax: +34-953-294570 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1 Page 1 o 35 Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 2 Abs ac I is widely ecognized ha pollina o s a y in hei e ec i eness in pollina ion mu ualisms, due bo h o di e ences in lowe -pollina o mo phological i as well as pollina o beha iou . Howe e , pollina ion webs ypically ea all in e ac ions as equal, and we con end ha his me hod may p o ide misleading esul s. Using empi ical and heo e ical da a, we p esen he case s udy o a sel -incompa ible he b in which he numbe o lowe s isi ed by a pollina o canno be used as a su oga e o he o al e ec o a pollina o on a plan due o di e ences in pe - isi e ec i eness a p oducing seeds. In sel incompa ible species, he ela ionship be ween in e ac ion equency and pe -in e ac ion e ec may be inc easingly nega i e as mo e lowe s pe plan a e isi ed due o gei onogamous pollen ans e . We ound ha pollina o s making longe bou s (i.e. isi ing mo e lowe s pe plan isi ) had an o e all highe pollina ion success pe bou . Howe e , pe -in e ac ion e ec s ended o dec ease as he bou p og essed, pa icula ly o pollina o s ha cause highe pollen deposi ion. Since he same in e ac ion equency may esul om di e en combina ions o numbe o bou s (plan isi s) and bou leng h ( lowe s isi ed/bou ), pollina o s making epea edly sho e bou s may con ibu e mo e o plan ep oduc ion o he same numbe o lowe s isi ed. Consequen ly, he magni ude o he di e ences in numbe o in e ac ions o di e en insec ypes may be o e idden by he magni ude o he di e ences in e ec i eness as pollina o s, e en i he same pollina o s consis en ly in e ac mo e equen ly. We discuss wo p edic ions ega ding he alidi y o using in e ac ion equency as a su oga e o plan seed p oduc ion (as a measu e o o al e ec ) depending o he deg ee o sel -compa ibili y, plan size and lo al display. We sugges ha he ole o in e ac ion equency mus be es ed o di e en species, en i onmen s, and ac oss wide scales o alida e i s use as su oga e o o al e ec in plan -pollina o ne wo ks. Key wo ds: mu ualis ic ne wo ks, plan -pollina o in e ac ion, isi a ion a e, bou leng h, pollen deposi ion. 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 2 Page 2 o 35Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 3 In oduc ion In o de o p edic he e ec s o bio ic in e ac ions be ween species, i is impo an o ake in o accoun he quali a i e and quan i a i e componen s o he in e ac ion. The quali a i e componen accoun s o di e ences in he ai s o he in e ac ing indi iduals (e.g., ana omical o beha iou al, inna e o lea ned). The quan i a i e componen accoun s o di e ences in he in ensi y o he in e ac ion (e.g., equency and/o s eng h; see Be low e al. 2004; Vázquez e al. 2005). In plan -pollina o mu ualis ic in e ac ions, bo h componen s may ha e a signi ican in luence on ou come o plan -pollina o in e ac ion in e ms o ep oduc i e o demog aphic success o he in e ac ing species (e.g., He e a 1987, 1989; Colling e al. 2004; Aizen and Ha de 2007). The need o ake in o accoun bo h he quali a i e and quan i a i e componen s o plan -pollina o in e ac ions was al eady acknowledged in he well known 'Mos E ec i e Pollina o P inciple' (S ebbins 1970), which emphasised he ole o pollina o s as de e minan o he e olu ion o lowe specializa ion, p oposing ha he mos abundan and e ec i e agen s o pollen ans e be ween indi idual plan s we e he mos likely ones o de e mine hei e olu iona y pa hways. He e we a gue ha quali a i e and quan i a i e componen s o species in e ac ions also need o be aken in o accoun when analysing webs o in e ac ions be ween plan s and pollina o s. An inc easing numbe o s udies analyse whole plan -pollina o in e ac ions ne wo ks (Olesen and Jo dano 2002, Jo dano e al. 2003; Vázquez and Aizen 2004). These in e ac ion ne wo ks a e gene ally cha ac e ised by bina y ma ices, whe e each ow ep esen s a plan species and each column a pollina o species, and he cell a he in e ac ion be ween a ow (plan ) and column (pollina o ) is se equal o ze o (i he co esponding plan and pollina o species a e no known o in e ac ), o one (i he plan and pollina o a e obse ed o in e ac ). In his app oach no in o ma ion is gi en abou he quali a i e and quan i a i e componen s ha ac ually occu be ween in e ac o s. This bina y app oach, howe e , may be insu icien o p ope ly de ine he opology o an in e ac ion ne wo k, because no all ealized in e ac ions a e equally impo an , which has been pinpoin ed as one o he mos ecu en p oblems o pollina ion ne wo k s udies (e.g., Paine 1988, 1992, Memmo 1999, Blü hgen e al. 2006). A numbe o ecen pape s emphasize he need o include a sui able ep esen a ion o he quan i a i e componen o species in e ac ions (Jo dano 1987, Memmo 1999, Vázquez e al. 2005; see also Goldbe g e al. 1999), o assess he p ope ies o in e ac ion ne wo ks beyond hose add essed 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 3 Page 3 o 35 Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 4 solely om bina y ma ices. Se e al app oaches ha e been ecen ly used o include a sou ce o a ia ion in quan i a i e componen s when cha ac e izing in e ac ion ne wo ks, anging om di e si y indexes o a e ac ion me hods (e.g., Vázquez and Simbe lo 2002, He e a 2005). In plan -animal mu ualis ic ne wo ks, i has ecen ly been sugges ed ha one quan i a i e componen , he in e ac ion equency (de ined as he numbe o in e ac ion e en s pe ime uni ), may be used as a su oga e o he o al in e ac ion e ec (de ined as he pe -capi a ep oduc i e o seed dispe sal pe o mance o a plan species), when he pe -in e ac ion e ec is in a ian (Vázquez e al. 2005). The use o in e ac ion equency as a quan i a i e es ima e o o al in e ac ion e ec ha e been p oposed no only o plan -pollina o mu ualis ic ne wo ks bu also o o he in e ac ion ne wo ks, including plan -seed dispe se s (Jo dano and Schupp 2000), plan -an p o ec ion (Ness e al. 2006), and hos -pa asi e (Poulin e al. 2008). Howe e , a numbe o s udies ha e shown ha he mos abundan animal mu ualis s (i.e. hose who p esumably in e ac mo e equen ly) a e no necessa ily he mos e ec i e ones on a pe - isi basis (e.g., He e a 1987, 1989; Schupp 1993; May ield e al. 2001). Fo plan -pollina o in e ac ions, subs an ial a iabili y in pe in e ac ion e ec s may a ise because o (1) a ying abili ies o di e en pollina o g oups o pick up pollen om an he s and deli e i o s igma ( ela ed o hei beha iou , size, mechanical i , e c.; e.g., Wilson and Thomson 1991, Wilson 1995, Robe son e al. 2005); and (2) he composi ion o he pollen mix u e deli e ed by hose pollina o g oups (mos ele an in sel - incompa ible species, o in sel -compa ible ones wi h high le els o inb eeding dep ession; e.g., I ey e al. 2003, Colling e al. 2004; Williams 2007). This a ia ion in pe in e ac ion e ec is he esul o pollina o o aging s a egies and a e s ongly a ec ed by he pollina ion en i onmen (i.e., he bio ic and abio ic condi ions in which he plan -pollina o in e ac ion akes place; see Rod íguez-Gi onés and San ama ía 2010). In u n, he pollina ion en i onmen may also a ec he in e ac ion equency, o example h ough he numbe o lowe s ha indi idual pollina o s isi pe plan (he ea e e e ed o as bou leng h; e.g. Robe son and Macnai 1995, G indeland e al. 2005, Williams 2007; see also Iwasa e al. 1995). Consequen ly, he pe in e ac ion e ec is no necessa ily an in a ian , inhe en , pa ame e o a gi en plan -pollina o pai , and dis ega ding i s in luence may limi he alidi y o using in e ac ion equency as he main p edic o o o al e ec . In his pape , we p esen empi ical da a o a case s udy illus a ing how he a ia ion in pe in e ac ion e ec may limi he p edic i e alue o in e ac ion equency as a su oga e o o al e ec s (plan seed se ) in plan -pollina o in e ac ions. We used he plan Lina ia lilacina (Plan aginaceae) and i s pollina o assemblage. 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 4 Page 4 o 35Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 5 L. lilacina is a sel -incompa ible he b; hus, only ou c ossed pollen is sui able o seed si ing. L. lilacina is isi ed ac oss i s ange by se e al bee species ha di e in abundance, beha iou , body size and o he mo phological ai s, which could a ec hei pe isi e ec i eness. We also de elop a gene al model o sel - incompa ible plan species aimed a calcula ing he ela i e con ibu ion o di e en pollina o s o seed p oduc ion as a unc ion o a iable bou leng h and pollen deposi ion abili y. Me hods S udy sys em and si es Lina ia lilacina Lange (Plan aginaceae) is a pe ennial he b endemic o moun ains in Sou h-eas e n Spain (Valdés 1970; Sáez and C espo 2005). This s udy was ca ied ou in 2005-2006 in he Jaén moun ains, in wo L. lilacina popula ions (Sillón del Rey [SR] and O iña [OT]) sepa a ed by ca. 3 km ( u he de ails can be consul ed in Sánchez-La uen e 2007). In hese popula ions plan s sp ou e e y season in mid win e and p oduce se e al o many simple o b anched s ems ( ange 5-156; mean±SE s ems/plan : 38.21±26.66; n= 195) o ca. 22 cm. in leng h, some o which may p oduce a a iable numbe o zygomo phic lowe s clumped a hei op ( ange 20-285; mean±SE lowe s/plan : 102.49±52.18; n= 146). Mo phologically, lowe s consis o an occluded, ubula co olla, wi h uppe and lowe whi ish lips, and colou ed nec a guides (blue o yellow, depending on he popula ion; Sánchez-La uen e and Alcán a a, unpub. da a). A spu is p esen o collec nec a p oduced by a nec a y loca ed unde he o a y inside he co olla. Func ionally, lowe s a e he maph odi ic and sel -incompa ible. F ui s a e a 2-locule capsule, dehiscing by al es. A e success ul pollina ion, he capsule de elops, con aining nume ous small b own, la ened, winged seeds ( ange 8-87; mean±SE seeds/ ui : 68.22±23.24; n= 2541). F ui ma u a ion akes be ween 18-24 days. In 2005, 15 plan s we e andomly selec ed in SR and 14 in OT. In 2006, he same plan s we e used in bo h popula ions, excep o 2 plan s los in OT and ha we e no subs i u ed. Composi ion, beha iou and e ec i eness o he pollina o assemblage In each season, we used he ea lies 2-3 ep oduc i e in lo escences o each agged plan du ing a week o p elimina y insec obse a ions, aimed o de ec he composi ion and abundance o he isi o assemblage, 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 5 Page 5 o 35 Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 6 and o analyse hei beha iou while isi ing plan s. O e all, we de ec ed 7 insec species, o which 4 we e analysed in u he de ail (see Resul s o a jus i ica ion). F om hese p elimina y obse a ions he expe imen al p ocedu e p oceeded as ollows. The emaining ep oduc i e in lo escences o he agged plan s we e co e ed wi h bags be o e lowe ing s a ed o a oid uncon olled lowe isi a ion by insec s while plan s we e no obse ed and o de e lo al he bi o es ha may damage co ollas be o e abscission (Sánchez-La uen e 2007). When he in lo escences s a ed o lowe , we emo ed bags on each census day and obse ed each plan in a andom o de wice a day in 20-minu es shi s du ing he ime o maximum pollina o ac i i y (12-18 h CET). Plan s in bo h popula ions we e obse ed be ween 1-8 hou s each season, depending on hei lowe ing phenology. O e all, pollina o censuses ex ended o 18 days in 2005 and 25 days in 2006, wi h 144 and 200 hou s o obse a ion espec i ely (bo h popula ions pooled). Du ing each shi , we eco ded he ac i i y o all insec s isi ing lowe s. Fo each plan isi (i.e., each bou , he ea e de ined as he pe iod in which an insec was isi ing lowe s on he ocal plan ), we iden i ied he insec species and he lowe s i isi ed (i.e., he bou leng h). In o de o acili a e obse a ions, only one insec was allowed a a ime. Thus, when a plan was being isi ed by an insec , any o he insec in e es ed in ha plan was gen ly wa ed away. A e each bou , we pu a combina ion o colou ed wi es a ound he pedicel o all i gin lowe s isi ed, di e en o each isi o and acco ding o he o de in which hey we e isi ed. We conside ed he o de in which lowe s we e isi ed as a cue o assess he composi ion o he pollen mix u e deposi ed on s igmas. We assumed ha he i s lowe isi ed would ecei e he highes p opo ion o xenogamous pollen, while in subsequen lowe s isi ed on he same plan (i.e. gei onogamous isi a ions) he pollen mix u e deposi ed would be composed o an inc easingly highe p opo ion o au ogamous pollen (Ka on e al. 2009). Using his me hod, we could iden i y he lowe s isi ed in each bou , he o de in which hey we e isi ed, he isi o species and i s ela i e abundance, based on isi a ion a es. As we only allowed one isi pe i gin lowe , all lowe s isi ed once we e immedia ely closed by pu ing a small anspa en glue d op o obs uc he opening o he co olla ape u e. A he end o each shi , he ep oduc i e in lo escences we e bagged again. When all lowe s in an in lo escence had been isi ed, he pollina o bag was no emo ed again un il co olla abscission. Pollina o e ec i eness was es ima ed om he numbe o seeds p oduced pe ui . All lowe s we e su eyed e e y hi d day o check o o a y enla gemen . F ui s we e collec ed be o e dehiscence, and he 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 6 Page 6 o 35Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 7 numbe o seeds coun ed. Plan size, measu ed as o al lowe p oduc ion, was eco ded a he end o he season. De eloping ui s a e used by Gymnae on sp. (Cu culionidae, Coleop e a) wee ils o o oposi ion; hus we sp ayed all in lo escences wi h Syngen a Ka a e King ® (a lambda-cyhalo h in-based insec icide) when lowe s we e no longe unc ional o pollina ion. Sp ay was applied e e y hi d day. P e ious obse a ions demons a ed ha his p oduc is well ole a ed by bees when dilu ed and applied acco ding o he manu ac u e 's ins uc ions, and i is easonably e ec i e a p e en ing wee il a ack (Sánchez-La uen e 2007). Da a analyses Gene al linea mixed models we e used o es di e ences among pollina o g oups in (1) bou leng h, (2) seed p oduc ion pe plan in ela ion o he numbe o isi s pe plan , and (3) pe isi e ec i eness (seeds p oduced pe lowe ) in ela ion o lowe isi a ion o de in each bou . In he la e analysis, and since Apis made signi ican ly longe bou s han he o he pollina o g oups ( ange 1-9 lowe s/bou s. 1-4 lowe s/bou ; see Resul s), bou leng h was conside ed a con inuous a iable, a he han a ac o , o analyse he ull ange exhibi ed by Apis. All dependen a iables we e modelled as no mal. Pollina o g oup, season and popula ion we e included as ixed ac o s, while plan s we e conside ed as andom blocks. Plan lo al display (when es ing o di e ences among lowe o plan isi s) o o al lowe p oduc ion (when es ing o di e ences among whole plan s) we e used as co a ia es. All s a is ical analyses we e conduc ed using R 2.11.1. (R De elopmen Co e Team, 2010) and he nlme (Pinhei o e al. 2009) package. Model o pe in e ac ion e ec s Acco ding o Vázquez e al. (2005), he o al e ec (T) o a pollina o ype on a isi ed plan (in e ms o ep oduc i e pe o mance; e.g. seed p oduc ion) may be de ined as he p oduc o i s in e ac ion equency (I, numbe o lowe s isi ed du ing a imed obse a ion pe iod) and i s pe in e ac ion e ec (P, pe in e ac ion con ibu ion o seed p oduc ion): T= IP. In he da a-se ha Vázquez e al. (2005) analysed, T was co ela ed wi h I, and he e was no co ela ion be ween I and P, hus hey concluded ha he in e ac ion equency, I, can be used as a su oga e o he o al in e ac ion e ec s, T, ega dless o di e ences in e ec i eness among in e ac ions, P. Wi h he same p emises we de elop a model add essing he e ec o a ia ion in pe in e ac ion 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 7 Page 7 o 35 Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 8 e ec s, and i s e en ual nega i e ela ionship wi h in e ac ion equency, wi h impac s on o al e ec s. Using a de e minis ic exp ession, i a pollina o ype i di e s in e ec i eness a seed p oduc ion among he di e en lowe s isi ed in each plan isi (i.e., in pe in e ac ion e ec ), he o al numbe o seeds (Ni) p oduced by pollina o ype i a e each bou may be calcula ed as: Ni=∑ =1 b Pi, (Eq. 1), whe e b is he bou leng h (i.e., numbe o lowe s isi ed/bou ) o pollina o ype i, and Pi, is he numbe o seeds p oduced by he - h lowe isi ed on he plan . Wi h a mo e gene al pe spec i e, we can calcula e Ni using a modi ied e sion o he model p oposed by de Jong e al. (1992) o e alua e he likelihood o seed p oduc ion by sel ing. As ou s udy species is sel - incompa ible, we ha e modelled he p oduc ion o seeds by c ossing as a measu e o he pe in e ac ion e ec , assuming a linea ela ionship be ween xenogamous pollen deposi ion and seed se . While he ela ionship be ween pollen deposi ion and seed se mus sa u a e when he e is enough pollen o e ilise all o ules, he linea ela ionship cons i u es a good app oxima ion when pollen is a limi ing esul , as was he case in ou expe imen (we only allowed a single isi pe lowe ) Fu he mo e, unlike de Jong e al. (1992), we ha e also assumed ha ans e o au ogamous pollen om an he s o s igmas wi hin he same lowe is likely om he e y i s lowe isi ed on a plan as a esul o he lowe handling by he isi o and gi en he close p oximi y o hese ep oduc i e s uc u es in ou s udy species. We i s conside ed a plan ha p oduces one seed pe lowe . When a pollina o a i es o he plan , i ca ies a ce ain amoun o xenogamous pollen om p e iously isi ed plan s (E), and i may also emo e a ac ion (k2) o he o al au ogamous pollen (A) p oduced by he cu en ly isi ed lowe . In hese calcula ions, we igno e any pollen ha is added o he bee’s “pollen baske ” and hence emo ed om he pollina ion ci cui . Because bo h E and k2A a e a ailable o deposi ion, he p opo ion o xenogamous pollen deposi ed is E/(E + k2A). This is also he p obabili y ha a xenogamous pollen g ain eaches and e ilises he o ule o he lowe . I , in each lowe , he pollina o deposi s a ac ion k1 o he pollen i ca ies, and he pollina o goes on o isi a second lowe on he same plan , upon a i al o ha lowe i will ca y amoun s (1- k1) E and (1- k1) k2 A o xenogamous and au ogamous pollen, espec i ely. A his second lowe , he pollina o will collec k2 A new 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 8 Page 8 o 35Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 15 plan (e.g., S ickle and Vinson 2000, Ka on e al. 2009; see also Rode e al. 1998), seed se o lowe isi n+1 is lowe han seed se o lowe isi n. The e o e, a e age pollina o e ec i eness is a dec easing unc ion o he numbe o lowe s isi ed pe plan . Thus, he h ee pollina o g oups seemed o be unc ionally equi alen in he i s lowe isi ed in each bou (Kendall and Smi h 1975, 1976; Die inge 1992), while e ec i eness p og essi ely dec eased in subsequen lowe s isi ed. The a e a which e ec i eness dec eases depends on he p opo ion o ca yo e pollen deposi ed a each lowe : he highe he p opo ion o pollen deposi ed a each isi , he as e he p opo ion o xenogamous pollen app oaches ze o and he as e pollina o e ec i eness dec eases. In ou sys em, pollina o e ec i eness dec eased as e o Apis han o An hopho a and Bombus. As we only allowed one isi pe pollina o g oup pe i gin lowe , and he e a e no di e ences in he amoun o o al pollen deposi ed among lowe s o each pollina o g oup (Sánchez-La uen e and Pa a, unpub. da a), he mos likely explana ion o his esul is ha Apis deposi s a highe ac ion o au ogamous pollen on each lowe (e.g., Rode e al. 1998; I ey e al. 2003; bu see Chambe lain and Schlising 2008) han Bombus and An hopho a, mos likely as a esul o he ways in which i handles lowe s, spending mo e ime pe isi , and pene a ing he lowe deepe , han Bombus and An hopho a (Sánchez-La uen e 2007, Sánchez-La uen e and Pa a, unpub. da a; see also Ha de 1990, Thos esen and Olesen 1996). A heo e ical model allows us o p edic how pe lowe seed se changes wi h he numbe o lowe s al eady isi ed on a plan , and wi h he pollen deposi ion abili y o he pollina o s. Con olling o bou leng h, pollina o s wi h highe capabili ies o pollen deposi ion (la ge k1; including bo h ou c ossed and au ogamous pollen) ha e lowe no malised cumula i e seed se s pe bou , since he cumula i e seed se app oached i s asymp o ic alue a e he i s 3-4 lowe s isi ed/bou (e.g. Ka on e al. 2009). In con as , lowe deposi ion abili ies lead o highe asymp o ic cumula i e seed se , which is app oached a e a g ea e numbe o isi s. Fo example, he ela ionship be ween bou leng h and no malised cumula i e seed se is almos linea o bou leng hs o up o 9 isi s (Fig. 3), and he a e age pollina o e ec i eness is li le a ec ed by bou leng h. Compa ing model p edic ions wi h da a on seed se pe lowe , we can also es ima e he p opo ion o a ailable pollen ha bees deposi a each lowe . When pollen deposi ion abili y (k1) is la ge, he e ec o bou leng h on pollina o e ec i eness can be su icien ly high o b eak he ypical posi i e co ela ion be ween in e ac ion equency and o al e ec . Fo example, i ing ou model o he seed p oduc ion da a in Fig. 1 leads o alues o pollen deposi ion o 0.12, 0.16 and 0.31 o Bombus, An hopho a and Apis, espec i ely. Wi h hese 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 15 Page 15 o 35 Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 16 alues o pollen deposi ion we ound ha , while he in e ac ion equency o Apis was he highes among all he isi o g oups, a less abundan pollina o (An hopho a), making sho e bou s, con ibu ed mo e o seed p oduc ion. Al hough Bombus also made sho e bou s han Apis, and he e o e had highe a e age pe in e ac ion pollina ion e ec i eness, he e ec was no su icien ly s ong o compensa e o he much lowe in e ac ion equency o Bombus, which consequen ly had he lowes o al e ec o he h ee g oups. Simila esul s ha e been ound o ano he sel -incompa ible plan species in which pollina o e ec i eness has been s udied. May ield e al. (2001) compa ed he e ec i eness a seed p oduc ion and pollen expo in he sel - incompa ible Ipomopsis agg ega a (Polemoniaceae) o Bombus apposi us and se e al hummingbi d species o which his plan species was supposedly adap ed. They ound ha B. apposi us isi ed ewe lowe s pe plan han hummingbi ds. Howe e , hey we e 4.04 imes mo e e ec i e a seed p oduc ion, and 2.75 imes mo e e ec i e a pollen expo pe lowe isi , han he bi ds. Consequen ly, al hough hei o e all isi a ion equency could be be ween a hi d and a qua e ha o hummingbi ds in some seasons, B. apposi us had a highe o al e ec on plan ep oduc i e success. Di e ences among pollina o g oups in bou leng h and pollen deposi ion abili y may in luence pe in e ac ion e ec independen ly o each o he . In u n, a ia ion in pollina o abundance may be ela ed o he o al numbe o in e ac ions o each pollina o g oup. The ou come in e ms o he measu ed o al e ec may esul om a combina ion o hese h ee pa ame e s. Fo ins ance, in Fig. 5 he o al e ec o a pollina o wi h a bou leng h (b) o 4 lowe s pe plan isi and a pollen deposi ion abili y (k1) o 0.47 is ac ually compa able o ha o a pollina o wi h b= 8 and k1= 0.02, despi e he la ge di e ences in bo h pa ame e s. Bu , di e ences in pollen deposi ion abili y may e en ually be mo e impo an han di e ences in bou leng h o gene a e a ia ion in pe in e ac ion e ec s. Thus, while we would no expec lo al display and/o plan size o se a limi on he pollen deposi ion abili y o a gi en pollina o g oup when isi ing plan s o he same species, hose pa ame e s may se a limi on he a ia ion in bou leng h (e.g., Wase and P ice 1991; Di Pasquale and Jacobi 1998, S ickle and Vinson 2000; G indeland e al. 2005; Ka on e al 2009). Fo example, Pellmy and Thompson (1996) ound di e ences in numbe o in e ac ions and e ec i eness among se e al insec g oups isi ing he sel -incompa ible he b Li hoph agma pa i lo um (Saxi agaceae). Howe e , because no di e ences occu ed among insec ypes in hei bou leng h, gi en he small lo al display exhibi ed by he s udy species a any one ime, no a ia ion in pe in e ac ion e ec , associa ed wi h a ia ion in bou leng h would be expec ed. Thus, 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 16 Page 16 o 35Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 17 only he numbe o bou s pe plan (bu no he bou leng h) was esponsible o he a ia ion in in e ac ion equency among pollina o g oups, and he o al e ec could be accu a ely p edic ed om he in e ac ion equency alone. Many ecological p ocesses ela ed o ep oduc i e success, demog aphy o na u al selec ion (among o he s) in wild popula ions a e con ex -dependen . This implies he occu ence o a numbe o a iable ou comes depending on he pa icula condi ions in which hese p ocesses ake place (e.g., Rey e al., 2006; Alonso e al. 2007; see also Thompson 1994, 2005). Unde s anding he ela ionship be ween pollina o e ec i eness and bou leng h is also impo an i we a e o explain a iabili y in ep oduc i e success be ween plan s, popula ions and yea s. The heo e ical model can be applied no only o assess seed p oduc ion o sel -incompa ible plan species, bu also o es ima e he p opo ion o sel ed and ou c ossed seeds p oduced in sel -compa ible species. In he p esence o la e -ac ing inb eeding dep ession, hese es ima es a e essen ial o quan i y pollina o e ec i eness, as ou c ossed seeds a e mo e aluable han sel ed ones. By measu ing seed se o a andom sample o lowe s isi ed by a single pollina o o a gi en plan species, we can ob ain an unbiased es ima e o his species' pollina ion e ec i eness. Bu plan s and en i onmen al ai s, such as lo al display and plan densi y, may a ec bou leng h (e.g. Oha a and Higashi 1994, I ey e al. 2003). The es ima e pe in e ac ion e ec ob ained in one popula ion will obscu e he ac ha he same pollina o species has di e en pollina o e ec i eness o plan s o di e en sizes, and i will be impossible o ex apola e om one popula ion measu ed one yea , o o he popula ions o yea s. Fo example, we ound ha bou leng h was di ec ly ela ed o lo al display (see also Robe son and Macnai 1995, G indeland e al. 2005, Williams 2007), while plan isi a ion was no . Consequen ly, di e ences in lowe ing phenology o synch ony among plan popula ions o he same plan species, o igina ing by en i onmen al o bio ic ac o s, o by di e ences among plan s sizes, may di ec ly be esponsible o he a ia ion in bou leng h and numbe o bou s o he same pollina o species (e.g. S ickle and Vinson 2000), wi h p esumed in luences in he among- lowe a ia ion in seed numbe and/o quali y (e.g. Ka on e al. 2009). A leas wo complemen a y and es able p edic ions o plan -pollina o in e ac ions may a ise om ou esul s. Fi s , we p edic ha in e ac ion equency will be a wo se p edic o o o al e ec in sel -incompa ible han in sel -compa ible species, while in sel -compa ible species he p edic i e alue o he in e ac ion equency as a su oga e o o al e ec s will dec ease as he le el o inb eeding dep ession inc eases. In bo h cases, a 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 17 Page 17 o 35 Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 18 lowe mean pe in e ac ion e ec may be expec ed as mo e lowe s a e isi ed pe bou , because he amoun o au ogamous pollen will inc ease wi h bou leng h. Second, because bou leng h is o in e es o de ine he a ia ion in pe in e ac ion e ec s, and hence i s in luence on o al e ec s, he alidi y o he in e ac ion equency as a p edic o o o al e ec s in such plan species may be educed as plan size and/o lo al display inc ease, as a la ge numbe o lowe s open a any one ime may allow pollina o s o inc ease hei bou leng h. These p edic ions could also a ise om he da ase used by Vázquez e al. (2005), e en hough hey combined sel -compa ible and sel -incompa ible species. Thus, al hough mos o he 22 species included in he da ase used we e sel -compa ible (ca. 70%), he co ela ion be ween in e ac ion equency and pe in e ac ion e ec s was nega i e o mos o he sel -incompa ible ones. In cases o a posi i e co ela ion, his could be due o he absence o di e ences among pollina o s in bou leng h, as sugges ed abo e. Howe e , he co ela ion be ween in e ac ion equency and o al e ec was posi i e in all cases, and Vázquez e al. (2005) concluded ha pe in e ac ion e ec s could be dis ega ded o explain o al e ec s. Howe e , as shown in Fig. 2 om ou empi ical da a, a posi i e co ela ion be ween in e ac ion equency and o al e ec does no gua an ee ha he pollina o wi h he highes equency would also con ibu e he mos o o al e ec s. A c i ical pa ame e o e alua e whe he a pollina o g oup may con ibu e mo e han o he o seed p oduc ion may be he a io o mean pe isi e ec i eness (i.e., he mean pe in e ac ion e ec ). The a io o mean pe in e ac ion e ec s o An hopho a and Apis is 2.66. Fo any gi en in e ac ion equency, Apis would be mo e aluable han An hopho a a seed p oduc ion i i isi s mo e han 2.66 imes as many lowe s as he la e . Howe e , unde his c i ical alue, An hopho a would be o g ea e alue, despi e Apis s ill ha ing a highe in e ac ion equency. As he a io o he di e ence in numbe o lowe s isi ed by hese pollina o g oups was below he c i ical alue in bo h seasons (in 2005: 237 lowe s isi ed by Apis / 151 lowe s isi ed by An hopho a = 1.57; in 2006: 227 lowe s isi ed by Apis / 155 lowe s isi ed by An hopho a = 1.46), An hopho a consis en ly con ibu ed mo e o seed p oduc ion han Apis, despi e he la e isi ing mo e lowe s. Howe e , i we compa e Bombus o Apis, we ind a c i ical alue o 1.78. As he a io o he di e ence in numbe o lowe s isi ed by hese pollina o g oups is always abo e his c i ical alue (in 2005: 237 lowe s isi ed by Apis / 63 lowe s isi ed by Bombus = 3.76; in 2006: 227 lowe s isi ed by Apis / 80 lowe s isi ed by Bombus = 2.84), he pollina o making mo e isi s (Apis) is, in his case, mo e aluable a seed p oduc ion. Thus, as in Vázquez e al. (2005), we also ound posi i e co ela ions be ween in e ac ion equency and o al e ec o all he pollina o g oups es ed, bu i was he a io 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 18 Page 18 o 35Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 19 be ween pe in e ac ion e ec s wha inally de e mined wha pollina o con ibu ed he mos o o al e ec s. O e all, because di e ences in in e ac ion equency may be o e idden by di e ences o igina ing om a ia ion in bou leng h and/o pollen deposi ion abili y, i is clea ha beha iou (He e a 1987; Rod íguez- Gi onés and San ama ía 2010) may explain pollina o con ibu ion o plan ep oduc ion be e han he numbe o in e ac ions. Ou esul s sugges ha , a leas o sel -incompa ible plan species, he p edic i e alue o he in e ac ion equency in plan -pollina o in e ac ions may be a “mo ing a ge ” because i is con ex dependen . In o he wo ds, we do no expec he same dis ibu ion o all i s componen s unde di e en en i onmen al condi ions, e en when he same pa icipan s a e in ol ed. Fo simplici y, ou model assumes a linea ela ionship be ween pollen deposi ion and seed p oduc ion. Tha is, i i s species wi h pos -zygo ic mechanisms o sel -incompa ibili y, while in cases o p e-zygo ic mechanisms, he esul s may be app oxima e. Howe e , e en in hese cases he ela ionship be ween pollen deposi ion and seed se may s ill be linea (depending on each pa icula sys em) and he model may accu a ely p edic he o al e ec s, as obse ed o ou example species. Ou s udy assess he impo ance o di e en insec ypes as pollina o s based upon hei e ec i eness a seed p oduc ion a plan le el, as measu ed h ough beha iou al and mo phological ea u es. Howe e , ou s udy does no add ess he syne gis ic e ec o each insec ype in p esence/absence o he es o he insec ypes. In o he wo ds, we ha e no es ed how in e ac ions among di e en insec ypes may in luence hei alue as pollina o s, as sugges ed by Aigne (2001). Because plan s a e pollina ed by a numbe o insec ypes cons i u ing an assemblage, hese in e ac ions may be impo an o de ine unc ional g oups, a he han indi idual pollina o ypes, as aluable con ibu o s o plan i ness (see Fens e 2004). A p econdi ion o he de ini ion o a unc ional g oup o pollina o s is ha all pollina o s in such g oup should ha e addi i e e ec s on plan i ness, and his can only be es ed by a ying he p esence/absence o abundance o di e en insec ypes, and analysing he i ness consequences o such a ia ion. Consequen ly, we sugges ha he ole o he in e ac ion equency, as a sui able p edic o o o al e ec s, mus be es ed o di e en pollina ion sys ems, in di e en pollina ion en i onmen s, o di e en pollina o assemblages, and ac oss wide scales, o alida e i s gene alised use as a quan i a i e measu e in plan -pollina o in e ac ion ne wo ks. Acknowledgemen s 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 19 Page 19 o 35 Oecologia Fo Pee Re iew Sánchez-La uen e e al. In e ac ion equency and o al e ec s in Lina ia - 20 We hank Rebecca E. 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