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

For Peer Review 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. Journal: Oecologia Manuscript ID: OEC-KG-2010-0548.R3 Manuscript Type: original research paper Date Submitted by the Author: n/a Complete List of Authors: Sanchez-Lafuente, Alfonso; Universidad de Sevilla, Biologia Vegetal y Ecologia Rodriguez-Girones, Miguel Angel; Estacion Experimental de Zonas Aridas (CSIC) Parra, Raquel; Universidad de Sevilla, Biologia Vegetal y Ecologia Keywords: mutualistic networks, plant-pollinator interactions, visitation rate, bout length, pollen deposition Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 1 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. Short title: Interaction frequency and total effects in Linaria Alfonso M. Sánchez-Lafuente1, *, Miguel A. Rodríguez-Gironés2 and Raquel Parra1 1Departamento de Biología Vegetal y Ecología, Facultad de Biología, Universidad de Sevilla, Avd. Reina Mercedes 9, 41012 Sevilla, Spain 2Estación Experimental de Zonas Aridas (EEZA-CSIC), Ctra. de Sacramento s/n, La Cañada de San Urbano, 04120 Almería, Spain *Corresponding author email: [email protected] 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 of 35 Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 2 Abstract It is widely recognized that pollinators vary in their effectiveness in pollination mutualisms, due both to differences in flower-pollinator morphological fit as well as pollinator behaviour. However, pollination webs typically treat all interactions as equal, and we contend that this method may provide misleading results. Using empirical and theoretical data, we present the case study of a self-incompatible herb in which the number of flowers visited by a pollinator cannot be used as a surrogate for the total effect of a pollinator on a plant due to differences in per-visit effectiveness at producing seeds. In self incompatible species, the relationship between interaction frequency and per-interaction effect may be increasingly negative as more flowers per plant are visited due to geitonogamous pollen transfer. We found that pollinators making longer bouts (i.e. visiting more flowers per plant visit) had an overall higher pollination success per bout. However, per-interaction effects tended to decrease as the bout progressed, particularly for pollinators that cause higher pollen deposition. Since the same interaction frequency may result from different combinations of number of bouts (plant visits) and bout length (flowers visited/bout), pollinators making repeatedly shorter bouts may contribute more to plant reproduction for the same number of flowers visited. Consequently, the magnitude of the differences in number of interactions of different insect types may be overridden by the magnitude of the differences in effectiveness as pollinators, even if the same pollinators consistently interact more frequently. We discuss two predictions regarding the validity of using interaction frequency as a surrogate for plant seed production (as a measure of total effect) depending of the degree of self-compatibility, plant size and floral display. We suggest that the role of interaction frequency must be tested for different species, environments, and across wider scales to validate its use as surrogate for total effect in plant-pollinator networks. Key words: mutualistic networks, plant-pollinator interaction, visitation rate, bout length, pollen deposition. 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 of 35Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 3 Introduction In order to predict the effects of biotic interactions between species, it is important to take into account the qualitative and quantitative components of the interaction. The qualitative component accounts for differences in the traits of the interacting individuals (e.g., anatomical or behavioural, innate or learned). The quantitative component accounts for differences in the intensity of the interaction (e.g., frequency and/or strength; see Berlow et al. 2004; Vázquez et al. 2005). In plant-pollinator mutualistic interactions, both components may have a significant influence on outcome of plant-pollinator interaction in terms of reproductive or demographic success of the interacting species (e.g., Herrera 1987, 1989; Colling et al. 2004; Aizen and Harder 2007). The need to take into account both the qualitative and quantitative components of plant-pollinator interactions was already acknowledged in the well known 'Most Effective Pollinator Principle' (Stebbins 1970), which emphasised the role of pollinators as determinant of the evolution of flower specialization, proposing that the most abundant and effective agents of pollen transfer between individual plants were the most likely ones to determine their evolutionary pathways. Here we argue that qualitative and quantitative components of species interactions also need to be taken into account when analysing webs of interactions between plants and pollinators. An increasing number of studies analyse whole plant-pollinator interactions networks (Olesen and Jordano 2002, Jordano et al. 2003; Vázquez and Aizen 2004). These interaction networks are generally characterised by binary matrices, where each row represents a plant species and each column a pollinator species, and the cell at the interaction between a row (plant) and column (pollinator) is set equal to zero (if the corresponding plant and pollinator species are not known to interact), or one (if the plant and pollinator are observed to interact). In this approach no information is given about the qualitative and quantitative components that actually occur between interactors. This binary approach, however, may be insufficient to properly define the topology of an interaction network, because not all realized interactions are equally important, which has been pinpointed as one of the most recurrent problems of pollination network studies (e.g., Paine 1988, 1992, Memmott 1999, Blüthgen et al. 2006). A number of recent papers emphasize the need to include a suitable representation of the quantitative component of species interactions (Jordano 1987, Memmott 1999, Vázquez et al. 2005; see also Goldberg et al. 1999), to assess the properties of interaction networks beyond those addressed 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 of 35 Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 4 solely from binary matrices. Several approaches have been recently used to include a source of variation in quantitative components when characterizing interaction networks, ranging from diversity indexes to rarefaction methods (e.g., Vázquez and Simberloff 2002, Herrera 2005). In plant-animal mutualistic networks, it has recently been suggested that one quantitative component, the interaction frequency (defined as the number of interaction events per time unit), may be used as a surrogate for the total interaction effect (defined as the per-capita reproductive or seed dispersal performance of a plant species), when the per-interaction effect is invariant (Vázquez et al. 2005). The use of interaction frequency as a quantitative estimate of total interaction effect have been proposed not only for plant-pollinator mutualistic networks but also for other interaction networks, including plant-seed dispersers (Jordano and Schupp 2000), plant-ant protection (Ness et al. 2006), and host-parasite (Poulin et al. 2008). However, a number of studies have shown that the most abundant animal mutualists (i.e. those who presumably interact more frequently) are not necessarily the most effective ones on a per-visit basis (e.g., Herrera 1987, 1989; Schupp 1993; Mayfield et al. 2001). For plant-pollinator interactions, substantial variability in per interaction effects may arise because of (1) varying abilities of different pollinator groups to pick up pollen from anthers and deliver it to stigma (related to their behaviour, size, mechanical fit, etc.; e.g., Wilson and Thomson 1991, Wilson 1995, Robertson et al. 2005); and (2) the composition of the pollen mixture delivered by those pollinator groups (most relevant in selfincompatible species, or in self-compatible ones with high levels of inbreeding depression; e.g., Ivey et al. 2003, Colling et al. 2004; Williams 2007). This variation in per interaction effect is the result of pollinator foraging strategies and are strongly affected by the pollination environment (i.e., the biotic and abiotic conditions in which the plant-pollinator interaction takes place; see Rodríguez-Gironés and Santamaría 2010). In turn, the pollination environment may also affect the interaction frequency, for example through the number of flowers that individual pollinators visit per plant (hereafter referred to as bout length; e.g. Robertson and Macnair 1995, Grindeland et al. 2005, Williams 2007; see also Iwasa et al. 1995). Consequently, the per interaction effect is not necessarily an invariant, inherent, parameter of a given plant-pollinator pair, and disregarding its influence may limit the validity of using interaction frequency as the main predictor of total effect. In this paper, we present empirical data of a case study illustrating how the variation in per interaction effect may limit the predictive value of interaction frequency as a surrogate for total effects (plant seed set) in plant-pollinator interactions. We used the plant Linaria lilacina (Plantaginaceae) and its pollinator 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 of 35Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 5 L. lilacina is a self-incompatible herb; thus, only outcrossed pollen is suitable for seed siring. L. lilacina is visited across its range by several bee species that differ in abundance, behaviour, body size and other morphological traits, which could affect their per visit effectiveness. We also develop a general model for selfincompatible plant species aimed at calculating the relative contribution of different pollinators to seed production as a function of variable bout length and pollen deposition ability. Methods Study system and sites Linaria lilacina Lange (Plantaginaceae) is a perennial herb endemic to mountains in South-eastern Spain (Valdés 1970; Sáez and Crespo 2005). This study was carried out in 2005-2006 in the Jaén mountains, in two L. lilacina populations (Sillón del Rey [SR] and Otiñar [OT]) separated by ca. 3 km (further details can be consulted in Sánchez-Lafuente 2007). In these populations plants sprout every season in mid winter and produce several to many simple or branched stems (range 5-156; mean±SE stems/plant: 38.21±26.66; n= 195) of ca. 22 cm. in length, some of which may produce a variable number of zygomorphic flowers clumped at their top (range 20-285; mean±SE flowers/plant: 102.49±52.18; n= 146). Morphologically, flowers consist of an occluded, tubular corolla, with upper and lower whitish lips, and coloured nectar guides (blue or yellow, depending on the population; Sánchez-Lafuente and Alcántara, unpub. data). A spur is present to collect nectar produced by a nectary located under the ovary inside the corolla. Functionally, flowers are hermaphroditic and self-incompatible. Fruits are a 2-locule capsule, dehiscing by valves. After successful pollination, the capsule develops, containing numerous small brown, flattened, winged seeds (range 8-87; mean±SE seeds/fruit: 68.22±23.24; n= 2541). Fruit maturation takes between 18-24 days. In 2005, 15 plants were randomly selected in SR and 14 in OT. In 2006, the same plants were used in both populations, except for 2 plants lost in OT and that were not substituted. Composition, behaviour and effectiveness of the pollinator assemblage In each season, we used the earliest 2-3 reproductive inflorescences of each tagged plant during a week for preliminary insect observations, aimed to detect the composition and abundance of the visitor 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 of 35 Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 6 and to analyse their behaviour while visiting plants. Overall, we detected 7 insect species, of which 4 were analysed in further detail (see Results for a justification). From these preliminary observations the experimental procedure proceeded as follows. The remaining reproductive inflorescences of the tagged plants were covered with bags before flowering started to avoid uncontrolled flower visitation by insects while plants were not observed and to deter floral herbivores that may damage corollas before abscission (Sánchez-Lafuente 2007). When the inflorescences started to flower, we removed bags on each census day and observed each plant in a random order twice a day in 20-minutes shifts during the time of maximum pollinator activity (12-18 h CET). Plants in both populations were observed between 1-8 hours each season, depending on their flowering phenology. Overall, pollinator censuses extended for 18 days in 2005 and 25 days in 2006, with 144 and 200 hours of observation respectively (both populations pooled). During each shift, we recorded the activity of all insects visiting flowers. For each plant visit (i.e., each bout, hereafter defined as the period in which an insect was visiting flowers on the focal plant), we identified the insect species and the flowers it visited (i.e., the bout length). In order to facilitate observations, only one insect was allowed at a time. Thus, when a plant was being visited by an insect, any other insect interested in that plant was gently waved away. After each bout, we put a combination of coloured wires around the pedicel of all virgin flowers visited, different for each visitor and according to the order in which they were visited. We considered the order in which flowers were visited as a cue to assess the composition of the pollen mixture deposited on stigmas. We assumed that the first flower visited would receive the highest proportion of xenogamous pollen, while in subsequent flowers visited on the same plant (i.e. geitonogamous visitations) the pollen mixture deposited would be composed of an increasingly higher proportion of autogamous pollen (Karron et al. 2009). Using this method, we could identify the flowers visited in each bout, the order in which they were visited, the visitor species and its relative abundance, based on visitation rates. As we only allowed one visit per virgin flower, all flowers visited once were immediately closed by putting a small transparent glue drop to obstruct the opening to the corolla aperture. At the end of each shift, the reproductive inflorescences were bagged again. When all flowers in an inflorescence had been visited, the pollinator bag was not removed again until corolla abscission. Pollinator effectiveness was estimated from the number of seeds produced per fruit. All flowers were surveyed every third day to check for ovary enlargement. Fruits were collected before dehiscence, and the 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 of 35Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 7 number of seeds counted. Plant size, measured as total flower production, was recorded at the end of the season. Developing fruits are used by Gymnaetron sp. (Curculionidae, Coleoptera) weevils for ovoposition; thus we sprayed all inflorescences with Syngenta Karate King ® (a lambda-cyhalothrin-based insecticide) when flowers were no longer functional for pollination. Spray was applied every third day. Previous observations demonstrated that this product is well tolerated by bees when diluted and applied according to the manufacturer's instructions, and it is reasonably effective at preventing weevil attack (Sánchez-Lafuente 2007). Data analyses General linear mixed models were used to test differences among pollinator groups in (1) bout length, (2) seed production per plant in relation to the number of visits per plant, and (3) per visit effectiveness (seeds produced per flower) in relation to flower visitation order in each bout. In the latter analysis, and since Apis made significantly longer bouts than the other pollinator groups (range 1-9 flowers/bout vs. 1-4 flowers/bout; see Results), bout length was considered a continuous variable, rather than a factor, to analyse the full range exhibited by Apis. All dependent variables were modelled as normal. Pollinator group, season and population were included as fixed factors, while plants were considered as random blocks. Plant floral display (when testing for differences among flower or plant visits) or total flower production (when testing for differences among whole plants) were used as covariates. All statistical analyses were conducted using R 2.11.1. (R Development Core Team, 2010) and the nlme (Pinheiro et al. 2009) package. Model of per interaction effects According to Vázquez et al. (2005), the total effect (T) of a pollinator type on a visited plant (in terms of reproductive performance; e.g. seed production) may be defined as the product of its interaction frequency (I, number of flowers visited during a timed observation period) and its per interaction effect (P, per interaction contribution to seed production): T= IP. In the data-set that Vázquez et al. (2005) analysed, T was correlated with I, and there was no correlation between I and P, thus they concluded that the interaction frequency, I, can be used as a surrogate for the total interaction effects, T, regardless of differences in effectiveness among interactions, P. With the same premises we develop a model addressing the effect of variation in per interaction 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 of 35 Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 8 effects, and its eventual negative relationship with interaction frequency, with impacts on total effects. Using a deterministic expression, if a pollinator type i differs in effectiveness at seed production among the different flowers visited in each plant visit (i.e., in per interaction effect), the total number of seeds (Ni) produced by pollinator type i after each bout may be calculated as: Ni=∑ v=1 b Pi,v (Eq. 1), where b is the bout length (i.e., number of flowers visited/bout) of pollinator type i, and Pi,v is the number of seeds produced by the v-th flower visited on the plant. With a more general perspective, we can calculate Ni using a modified version of the model proposed by de Jong et al. (1992) to evaluate the likelihood of seed production by selfing. As our study species is selfincompatible, we have modelled the production of seeds by crossing as a measure of the per interaction effect, assuming a linear relationship between xenogamous pollen deposition and seed set. While the relationship between pollen deposition and seed set must saturate when there is enough pollen to fertilise all ovules, the linear relationship constitutes a good approximation when pollen is a limiting result, as was the case in our experiment (we only allowed a single visit per flower) Furthermore, unlike de Jong et al. (1992), we have also assumed that transfer of autogamous pollen from anthers to stigmas within the same flower is likely from the very first flower visited on a plant as a result of the flower handling by the visitor and given the close proximity of these reproductive structures in our study species. We first considered a plant that produces one seed per flower. When a pollinator arrives to the plant, it carries a certain amount of xenogamous pollen from previously visited plants (E), and it may also remove a fraction (k2) of the total autogamous pollen (A) produced by the currently visited flower. In these calculations, we ignore any pollen that is added to the bee’s “pollen basket” and hence removed from the pollination circuit. Because both E and k2A are available for deposition, the proportion of xenogamous pollen deposited is E/(E + k2A). This is also the probability that a xenogamous pollen grain reaches and fertilises the ovule of the flower. If, in each flower, the pollinator deposits a fraction k1 of the pollen it carries, and the pollinator goes on to visit a second flower on the same plant, upon arrival to that flower it will carry amounts (1k1) E and (1k1) k2 A of xenogamous and autogamous pollen, respectively. At this second flower, the pollinator will collect 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 of 35Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 15 plant (e.g., Strickler and Vinson 2000, Karron et al. 2009; see also Rodet et al. 1998), seed set of flower visit n+1 is lower than seed set of flower visit n. Therefore, average pollinator effectiveness is a decreasing function of the number of flowers visited per plant. Thus, the three pollinator groups seemed to be functionally equivalent in the first flower visited in each bout (Kendall and Smith 1975, 1976; Dieringer 1992), while effectiveness progressively decreased in subsequent flowers visited. The rate at which effectiveness decreases depends on the proportion of carryover pollen deposited at each flower: the higher the proportion of pollen deposited at each visit, the faster the proportion of xenogamous pollen approaches zero and the faster pollinator effectiveness decreases. In our system, pollinator effectiveness decreased faster for Apis than for Anthophora and Bombus. As we only allowed one visit per pollinator group per virgin flower, and there are no differences in the amount of total pollen deposited among flowers for each pollinator group (Sánchez-Lafuente and Parra, unpub. data), the most likely explanation for this result is that Apis deposits a higher fraction of autogamous pollen on each flower (e.g., Rodet et al. 1998; Ivey et al. 2003; but see Chamberlain and Schlising 2008) than Bombus and Anthophora, most likely as a result of the ways in which it handles flowers, spending more time per visit, and penetrating the flower deeper, than Bombus and Anthophora (Sánchez-Lafuente 2007, Sánchez-Lafuente and Parra, unpub. data; see also Harder 1990, Thostesen and Olesen 1996). A theoretical model allows us to predict how per flower seed set changes with the number of flowers already visited on a plant, and with the pollen deposition ability of the pollinators. Controlling for bout length, pollinators with higher capabilities of pollen deposition (larger k1; including both outcrossed and autogamous pollen) have lower normalised cumulative seed sets per bout, since the cumulative seed set approached its asymptotic value after the first 3-4 flowers visited/bout (e.g. Karron et al. 2009). In contrast, lower deposition abilities lead to higher asymptotic cumulative seed set, which is approached after a greater number of visits. For example, the relationship between bout length and normalised cumulative seed set is almost linear for bout lengths of up to 9 visits (Fig. 3), and the average pollinator effectiveness is little affected by bout length. Comparing model predictions with data on seed set per flower, we can also estimate the proportion of available pollen that bees deposit at each flower. When pollen deposition ability (k1) is large, the effect of bout length on pollinator effectiveness can be sufficiently high to break the typical positive correlation between interaction frequency and total effect. For example, fitting our model to the seed production data in Fig. 1 leads to values of pollen deposition of 0.12, 0.16 and 0.31 for Bombus, Anthophora and Apis, respectively. With these 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 of 35 Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 16 values of pollen deposition we found that, while the interaction frequency of Apis was the highest among all the visitor groups, a less abundant pollinator (Anthophora), making shorter bouts, contributed more to seed production. Although Bombus also made shorter bouts than Apis, and therefore had higher average per interaction pollination effectiveness, the effect was not sufficiently strong to compensate for the much lower interaction frequency of Bombus, which consequently had the lowest total effect of the three groups. Similar results have been found for another self-incompatible plant species in which pollinator effectiveness has been studied. Mayfield et al. (2001) compared the effectiveness at seed production and pollen export in the selfincompatible Ipomopsis aggregata (Polemoniaceae) of Bombus appositus and several hummingbird species for which this plant species was supposedly adapted. They found that B. appositus visited fewer flowers per plant than hummingbirds. However, they were 4.04 times more effective at seed production, and 2.75 times more effective at pollen export per flower visit, than the birds. Consequently, although their overall visitation frequency could be between a third and a quarter that of hummingbirds in some seasons, B. appositus had a higher total effect on plant reproductive success. Differences among pollinator groups in bout length and pollen deposition ability may influence per interaction effect independently of each other. In turn, variation in pollinator abundance may be related to the total number of interactions of each pollinator group. The outcome in terms of the measured total effect may result from a combination of these three parameters. For instance, in Fig. 5 the total effect of a pollinator with a bout length (b) of 4 flowers per plant visit and a pollen deposition ability (k1) of 0.47 is actually comparable to that of a pollinator with b= 8 and k1= 0.02, despite the large differences in both parameters. But, differences in pollen deposition ability may eventually be more important than differences in bout length to generate variation in per interaction effects. Thus, while we would not expect floral display and/or plant size to set a limit on the pollen deposition ability of a given pollinator group when visiting plants of the same species, those parameters may set a limit on the variation in bout length (e.g., Waser and Price 1991; Di Pasquale and Jacobi 1998, Strickler and Vinson 2000; Grindeland et al. 2005; Karron et al 2009). For example, Pellmyr and Thompson (1996) found differences in number of interactions and effectiveness among several insect groups visiting the self-incompatible herb Lithophragma parviflorum (Saxifragaceae). However, because no differences occurred among insect types in their bout length, given the small floral display exhibited by the study species at any one time, no variation in per interaction effect, associated with variation in bout length would be expected. 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 of 35Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 17 only the number of bouts per plant (but not the bout length) was responsible for the variation in interaction frequency among pollinator groups, and the total effect could be accurately predicted from the interaction frequency alone. Many ecological processes related to reproductive success, demography or natural selection (among others) in wild populations are context-dependent. This implies the occurrence of a number of variable outcomes depending on the particular conditions in which these processes take place (e.g., Rey et al., 2006; Alonso et al. 2007; see also Thompson 1994, 2005). Understanding the relationship between pollinator effectiveness and bout length is also important if we are to explain variability in reproductive success between plants, populations and years. The theoretical model can be applied not only to assess seed production of self-incompatible plant species, but also to estimate the proportion of selfed and outcrossed seeds produced in self-compatible species. In the presence of later-acting inbreeding depression, these estimates are essential to quantify pollinator effectiveness, as outcrossed seeds are more valuable than selfed ones. By measuring seed set of a random sample of flowers visited by a single pollinator of a given plant species, we can obtain an unbiased estimate of this species' pollination effectiveness. But plants and environmental traits, such as floral display and plant density, may affect bout length (e.g. Ohara and Higashi 1994, Ivey et al. 2003). The estimate per interaction effect obtained in one population will obscure the fact that the same pollinator species has different pollinator effectiveness for plants of different sizes, and it will be impossible to extrapolate from one population measured one year, to other populations or years. For example, we found that bout length was directly related to floral display (see also Robertson and Macnair 1995, Grindeland et al. 2005, Williams 2007), while plant visitation was not. Consequently, differences in flowering phenology or synchrony among plant populations of the same plant species, originating by environmental or biotic factors, or by differences among plants sizes, may directly be responsible for the variation in bout length and number of bouts of the same pollinator species (e.g. Strickler and Vinson 2000), with presumed influences in the among-flower variation in seed number and/or quality (e.g. Karron et al. 2009). At least two complementary and testable predictions for plant-pollinator interactions may arise from our results. First, we predict that interaction frequency will be a worse predictor of total effect in self-incompatible than in self-compatible species, while in self-compatible species the predictive value of the interaction frequency as a surrogate for total effects will decrease as the level of inbreeding depression increases. In both 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 of 35 Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 18 lower mean per interaction effect may be expected as more flowers are visited per bout, because the amount of autogamous pollen will increase with bout length. Second, because bout length is of interest to define the variation in per interaction effects, and hence its influence on total effects, the validity of the interaction frequency as a predictor of total effects in such plant species may be reduced as plant size and/or floral display increase, as a larger number of flowers open at any one time may allow pollinators to increase their bout length. These predictions could also arise from the dataset used by Vázquez et al. (2005), even though they combined self-compatible and self-incompatible species. Thus, although most of the 22 species included in the dataset used were self-compatible (ca. 70%), the correlation between interaction frequency and per interaction effects was negative for most of the self-incompatible ones. In cases of a positive correlation, this could be due to the absence of differences among pollinators in bout length, as suggested above. However, the correlation between interaction frequency and total effect was positive in all cases, and Vázquez et al. (2005) concluded that per interaction effects could be disregarded to explain total effects. However, as shown in Fig. 2 from our empirical data, a positive correlation between interaction frequency and total effect does not guarantee that the pollinator with the highest frequency would also contribute the most to total effects. A critical parameter to evaluate whether a pollinator group may contribute more than other to seed production may be the ratio of mean per visit effectiveness (i.e., the mean per interaction effect). The ratio of mean per interaction effects of Anthophora and Apis is 2.66. For any given interaction frequency, Apis would be more valuable than Anthophora at seed production if it visits more than 2.66 times as many flowers as the latter. However, under this critical value, Anthophora would be of greater value, despite Apis still having a higher interaction frequency. As the ratio of the difference in number of flowers visited by these pollinator groups was below the critical value in both seasons (in 2005: 237 flowers visited by Apis / 151 flowers visited by Anthophora = 1.57; in 2006: 227 flowers visited by Apis / 155 flowers visited by Anthophora = 1.46), Anthophora consistently contributed more to seed production than Apis, despite the latter visiting more flowers. However, if we compare Bombus to Apis, we find a critical value of 1.78. As the ratio of the difference in number of flowers visited by these pollinator groups is always above this critical value (in 2005: 237 flowers visited by Apis / 63 flowers visited by Bombus = 3.76; in 2006: 227 flowers visited by Apis / 80 flowers visited by Bombus = 2.84), the pollinator making more visits (Apis) is, in this case, more valuable at seed production. Thus, as in Vázquez et al. (2005), we also found positive correlations between interaction frequency and total effect for all the pollinator groups tested, but it was the ratio 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 of 35Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 19 between per interaction effects what finally determined what pollinator contributed the most to total effects. Overall, because differences in interaction frequency may be overridden by differences originating from variation in bout length and/or pollen deposition ability, it is clear that behaviour (Herrera 1987; RodríguezGironés and Santamaría 2010) may explain pollinator contribution to plant reproduction better than the number of interactions. Our results suggest that, at least for self-incompatible plant species, the predictive value of the interaction frequency in plant-pollinator interactions may be a “moving target” because it is context dependent. In other words, we do not expect the same distribution of all its components under different environmental conditions, even when the same participants are involved. For simplicity, our model assumes a linear relationship between pollen deposition and seed production. That is, it fits species with post-zygotic mechanisms of self-incompatibility, while in cases of pre-zygotic mechanisms, the results may be approximate. However, even in these cases the relationship between pollen deposition and seed set may still be linear (depending on each particular system) and the model may accurately predict the total effects, as observed for our example species. Our study assess the importance of different insect types as pollinators based upon their effectiveness at seed production at plant level, as measured through behavioural and morphological features. However, our study does not address the synergistic effect of each insect type in presence/absence of the rest of the insect types. In other words, we have not tested how interactions among different insect types may influence their value as pollinators, as suggested by Aigner (2001). Because plants are pollinated by a number of insect types constituting an assemblage, these interactions may be important to define functional groups, rather than individual pollinator types, as valuable contributors to plant fitness (see Fenster 2004). A precondition for the definition of a functional group of pollinators is that all pollinators in such group should have additive effects on plant fitness, and this can only be tested by varying the presence/absence or abundance of different insect types, and analysing the fitness consequences of such variation. Consequently, we suggest that the role of the interaction frequency, as a suitable predictor of total effects, must be tested for different pollination systems, in different pollination environments, for different pollinator assemblages, and across wider scales, to validate its generalised use as a quantitative measure in plant-pollinator interaction networks. Acknowledgements 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 of 35 Oecologia For Peer Review Sánchez-Lafuente et al. Interaction frequency and total effects in Linaria - 20 We thank Rebecca E. 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