The size of individual Delphinium flowers and the opportunity for geitonogamous pollination

Authors


†Author to whom correspondence should be addressed. E-mail: hishii@ucalgary.ca

Summary

  • 1Animal-pollinated plants influence their mating success through characteristics of their individual flowers and the arrangement of flowers into inflorescences. Previous studies of inflorescence function have focused on flower number, so the influences of traits of individual flowers on pollinator attraction and self-pollination between flowers remain unknown.
  • 2To investigate the effects of flower size and number on pollinator attraction and behaviour on inflorescences, we reduced the perianth size of flowers of Delphinium bicolor Nuttall and Delphinium glaucum S. Watson.
  • 3Reduction in flower size decreased the number of visits per inflorescence by bumble bees (Bombus spp.), but increased the number of probes per visit. In contrast, both attraction and probes per visit increased in a decelerating manner with number of open flowers. The average number of probes per flower, which combines the effects of pollinator attraction and behaviour on inflorescences, did not differ significantly between small- and large-flowered plants, or with flower number.
  • 4 The absence of significant variation among plants with different floral and inflorescence characteristics in visits per flower and nectar standing crop per flower indicate that bees achieved an ideal free distribution.
  • 5Our results suggest that large flowers reduce the incidence of geitonogamous pollination without reducing the frequency of probes per flower.

Introduction

Outcrossing, animal-pollinated angiosperms must attract pollinators to mate. Attraction enhances a plant's export of pollen to other plants (Harder & Wilson 1994) and assures that it imports sufficient pollen to fertilize its ovules and induce pollen-tube competition, resulting in the production of high-quality seeds (Winsor, Peretz & Stephenson 2000). The benefits of pollinator attraction have undoubtedly influenced the evolution of three visual aspects of floral displays: (1) the size and/or number of attractive organs, including showy perianths, involucre(s) and/or attractive sterile flowers (e.g. Hydrangea, Muscari, Viburnum, many Araceae); (2) the number of flowers open simultaneously; and (3) the density of open flowers. These features of floral displays probably evolve in concert, as pollinator attraction is a function of the entire plant, rather than of individual flowers (Harder et al. 2004).

Number of open flowers has been subject to more functional analysis than other aspects of floral display (reviewed by Ohashi & Yahara 2001; Harder et al. 2004). Plants that display many flowers typically attract more pollinators than few-flowered plants of the same species. However, the attractive benefit of displaying many flowers can be counteracted by the tendency of individual pollinators to visit more flowers, which increases the opportunity for geitonogamy (Harder & Barrett 1995; Karron et al. 2004; Harder & Johnson 2005). Geitonogamy can reduce mating success by using pollen that could otherwise have been exported to other plants (pollen discounting; Harder & Barrett 1995) and, in self-compatible species, by reducing both the production of outcrossed seeds (seed discounting) and average offspring performance due to inbreeding depression (Lloyd 1992). The aggravation of pollen discounting as a pollinator visits more flowers on a plant reduces the average export probability for every pollen grain that a pollinator removes from flowers (Iwasa, de Jong & Klinkhamer 1995). Consequently, attraction of many pollinators that each visit a few open flowers promotes total pollen export more than attraction of fewer pollinators that each visit many flowers, even if the number of visits per flower is identical (Iwasa, de Jong & Klinkhamer 1995). Intriguingly, the number of probes received by individual flowers often varies little with open-flower number, because enhanced attractiveness is often counterbalanced by a declining relation between the proportion of flowers probed by individual pollinators and increasing flower number (reviewed by Ohashi & Yahara 2001). This equalization of visitation to individual flowers is indicative of an ideal free distribution (Fretwell & Lucas 1970), in which consumers distribute themselves among resource patches so that all individuals realize an equal rate of resource intake (for examples involving pollinators see Dreisig 1995; Robertson & Macnair 1995; Ohashi & Yahara 2002).

Flower size can also affect pollinator attraction, with large-flowered plants typically attracting more pollinators than small-flowered plants (reviewed by Kudoh & Whigham 1998; Blarer, Keasar & Shmida 2002). However, the effects of flower size on a pollinator's behaviour once it arrives at a plant remains unexplored. As with flower number, the enhanced attractiveness of large flowers could result in visits to fewer flowers on an inflorescence by individual pollinators as visitors equalize nectar standing crop per flower within a plant population. In this manner, large flowers could reduce geitonogamy on plants that display many flowers. This hypothesis, and whether flower size and number act independently or interactively on pollinator behaviour, remain to be examined.

In this study, we manipulated the flower size of two Delphinium species to examine the effects of flower size and number on the attraction of bumble bee pollinators; the number of flowers probed by each bee attracted; and the average number of probes received by individual flowers. By considering bee behaviour and nectar standing crops, we also examined whether bees distribute themselves among plants in a manner consistent with an ideal free distribution. Development of this distribution requires that bees adjust their behaviour in response to the nectar abundance that they find on individual inflorescences, which we tested by examining the behavior of bees on inflorescences that had been excluded from pollinator access for brief periods. Based on the results of these experiments, we discuss the role of flower size in geitonogamous pollination and its consequences for flower-size evolution.

Materials and methods

study species and site

Both Delphinium glaucum S. Watson and Delphinium bicolor Nuttall are perennial, hermaphroditic herbs with purple, zygomorphic, spurred, protandrous flowers (Fig. 1). Flowers of both species have similar morphologies, with five large, petaloid sepals serving as the primary display organs, although D. bicolor flowers are much larger than those of D. glaucum (mean ± SE flower width, D. bicolor, 38·6 ± 0·71 mm, N = 20; D. glaucum, 25·8 ± 0·29 mm, N = 34). A flowering plant of D. glaucum produces 10–60 flowers in a single inflorescence (raceme), although some large plants produce a few basal, lateral inflorescences with one to 10 flowers. Flowers on lateral inflorescences open after most flowers on the main inflorescence have wilted. Our experiment considered plants with open flowers only on the main inflorescence. A flowering plant of D. bicolor produces one raceme with one to 15 flowers. Accordingly, a ‘plant’ in this study is synonymous with an ‘inflorescence’.

Figure 1.

Floral morphology of Delphinium bicolor (that of Delphinium glaucum is similar, but smaller). Flower size was manipulated by cutting sepals along the dashed lines.

We studied D. glaucum in a meadow at Sibbald Flat, Alberta, Canada (51°02′ N; 114°49′ W), and D. bicolor at the edge of an aspen (Populus tremuloides) forest, during 2005. Long-tongued bumble bees primarily pollinate these Delphinium species, although day-flying hawk moths (Hemaris sp.) visit occasionally. During our experiments, queens of Bombus californicus F. Smith pollinated D. bicolor, and workers of B. californicus and Bombus flavifrons Cresson pollinated D. glaucum.

experiments

We assessed the relative importance of open-flower number and size on pollinator behaviour, with an experiment that considered existing continuous variation in flower number and artificially induced discrete variation in flower size. This experiment considered 51 D. bicolor plants and 72 D. glaucum plants, which were selected to represent the range of open-flower number. We divided the selected plants randomly into two groups: intact plants and manipulated plants, on which we excised the distal half of each sepal of all open flowers to reduce perianth size (Fig. 1). This manipulation did not noticeably affect flower probing by bees, as bees rarely contacted the distal portion of the sepals. The average number of open flowers per inflorescence did not differ significantly between the flower-size treatments (D. bicolor, manipulated plants, mean = 20·5 flowers, lower SE (LSE) = 4·10 flowers, upper SE (USE) = 5·13 flowers; intact plants, mean = 28·2 flowers, LSE = 5·75 flowers, USE = 7·22 flowers; F1,49 = 1·01, P > 0·3; D. glaucum, manipulated plants, mean = 14·8 flowers, LSE = 1·07 flowers, USE = 1·15 flowers; intact plants, mean = 13·9 flowers, LSE = 1·00 flowers, USE = 1·08 flowers; F1,69 = 0·39, P > 0·5, based on ln-transformed data). We cut sepals and exposed flowers to pollinators at least 1 h before observing pollinator behaviour, so that the nectar standing crop during pollinator observations reflected the visitation frequency associated with the reduced perianth size.

We observed experimental inflorescences for 5 h on each of 2 days (D. bicolor, 09.30–14.30 h on 14 June and 10.00–15.00 h on 16 June; D. glaucum, 10.30–15.30 h on 26 July and 10.00–15.00 h on 28 July). We observed different D. glaucum plants on both sampling days (36 plants per day), whereas we observed the same D. bicolor plants on both sampling days. For the D. bicolor plants an average (± SD) of only 0·20 ± 0·45 flowers opened and 0·40 ± 0·57 flowers wilted between sampling days, so that on 16 June most of the manipulated flowers had been in that state for 2 days. During each observation period, we recorded the number of pollinator visits per plant. For each visit, we also recorded the number of flowers that the bee probed.

After the pollinator observations on 16 June (D. bicolor) and 28 July (D. glaucum), we measured nectar standing crop with calibrated capillary tubes (Drummond Scientific, Broomall, PA, USA). Nectar was extracted from all flowers on D. bicolor inflorescences and five flowers selected uniformly along D. glaucum inflorescences. We also measured nectar concentration in the combined nectar from all flowers sampled from a plant with a sucrose refractometer (IN-50E, AS ONE, Osaka, Japan) when the volume of the aggregate sample exceeded 0·5 µl.

To investigate whether bees probe more flowers on inflorescences that receive few pollinator visits, independently of perianth size, we selected 50 plants and covered half of them, selected randomly, with mesh to prevent pollinator visits during the hour before observation. All flowers were left intact on both covered and uncovered plants. After removing the mesh from a covered inflorescence, we recorded the number of flowers probed by the first bee to visit that plant. We similarly observed the behaviour of the first bee observed visiting each continuously exposed inflorescence. These observations were conducted between 10.30 and 12.00 h on 29 July.

data analysis

We analysed the effects of open-flower number and perianth size on bee behaviour with generalized linear models (McCullagh & Nelder 1989: Genmod procedure of sas ver. 9·1·3, SAS Institute Inc., 2004). Analyses of the number of visits per plant and the number of flowers probed by individual bees considered a logarithmic link function and incorporated a Poisson error distribution. In contrast, the total flower probes per plant during 5-h observation periods tended to follow an aggregated distribution, so we analysed this response with a logarithmic link function and incorporated a negative-binomial error distribution. Inference concerning the effects of specific independent variables involved likelihood-ratio (G) tests. Analyses that involved repeated measurement of the same plant (all observations for D. bicolor and the number of probes per flower for D. glaucum) used generalized estimating equations (Liang & Zeger 1986) and a model of compound symmetry to account for correlated responses within plants. All analyses initially considered flower treatment (intact vs manipulated) and sampling date as categorical independent variables, the number of open flowers (ln-transformed) as a continuous covariate, and all interactions between these variables. We then simplified this model by backward elimination of non-significant interactions involving the covariate.

The preceding analyses allow direct tests of whether the behavioural responses varied in direct proportion to the number of open flowers on inflorescences. Given the ln-transformation of both dependent and independent variables, the behavioural response increased in direct proportion to the number of open flowers if the partial regression coefficient (b) of flower number (ln-transformed) does not differ significantly from 1. On the other hand, 0 < b < 1 indicates a decelerating increase, whereas b > 1 indicates an accelerating increase in behavioural response to the number of open flowers. We tested this expectation by considering whether the 95% confidence interval for the partial regression coefficient included 1.

The effects of flower treatment and open-flower number (ln-transformed) on volume and concentration of nectar were analysed with two-factor ancova (Kutner et al. 2005: Mixed procedure of sas ver. 9·1·3), which also included flower position within the inflorescence as a non-experimental factor. Both analyses initially considered all effects and their interactions, with non-significant terms subsequently being excluded by backward elimination. The analysis of nectar volume considered the standing crop in each of five flowers per plant, so we used restricted maximum likelihood (Jennrich & Schluchter 1986) to characterize the covariance in nectar volume among flower positions. Based on Aikaike's information criterion, a model of compound symmetry (D. bicolor) or an unstructured variance–covariance matrix (D. glaucum) was more appropriate than one that depicted independent responses. The covariances estimated by these matrices represent the dependence among repeated measurements of individual plants. To account for this lack of independence, we adjusted the denominator degrees of freedom for F-tests of the general linear model using Kenward & Roger's (1997) approximation, which can result in fractional degrees of freedom. Nectar volume was square-root transformed before analysis to correct for normality.

Results

The two Delphinium species experienced rather different pollination environments. Delphinium bicolor flowers during spring when bumble bee queens are active, and individual plants received a median of three pollinator visits during the 5-h observation periods (Fig. 2a). Visitation varied extensively among D. bicolor plants, with six plants receiving no visits during 5 h and one plant receiving 11 visits. The probability of a plant being visited at least once varied significantly with the number of open flowers (ln-transformed, G1 = 4·01, P < 0·05, generalized linear model with binomial error distribution), but not between flower-size treatments (G1 = 3·15, P > 0·05). In contrast, D. glaucum flowered during summer, when it was visited by more abundant bumble bee workers, so that all experimental plants received at least one visit during 5-h observation periods (Fig. 2b). In particular, the median D. glaucum plant received four pollinator visits during a 5-h observation period, with much less variation among plants than was observed for D. bicolor (F95,71 = 2·11, P < 0·005; Fig. 2). Despite these differences in the incidence and certainty of pollinator visits, the following results demonstrate qualitatively similar effects of flower size and number on pollinator behaviour.

Figure 2.

Variation in visitation to (a) Delphinium bicolor and (b) Delphinium glaucum inflorescences during 5-h observation periods.

For both Delphinium species, the number of bees attracted to individual inflorescences during 5-h observation periods varied positively with flower size and flower number (Table 1; Figs 3a,b and 4a,b). Reduction of sepal length by ≈50% decreased the mean visitation rate to inflorescences by roughly 60%. Although inflorescences with many flowers attracted more bees than those with fewer flowers, the partial regression coefficient for ln(open flowers) was significantly <1 for both species (Table 1), indicating that the mean number of inflorescence visits increased in a decelerating manner with open-flower number (cf. Figs 3b and 4b). Flower size and number affected bee visitation to inflorescences independently, as indicated by non-significant interactions between flower-size treatment and flower number (D. bicolor, G1 = 0·56, P > 0·4; D. glaucum, G1 = 0·43, P > 0·5). Furthermore, the effects of flower size and number did not differ significantly between the two sampling dates for either species (D. bicolor, G1 = 2·93, P > 0·05; D. glaucum, G1 = 1·13, P > 0·25).

Table 1.  Effects of flower-size treatment (intact vs sepal reduction) and number of open flowers on three features of bumble bee behaviour while visiting Delphinium bicolor and Delphinium glaucum plants, based on analyses of generalized linear models
Species and dependent variableModel goodness of fitIndependent variableLikelihood ratio (1 df)Partial regression coefficient (95% CI)
  • *

    , P < 0·05;

  • **

    , P < 0·01;

  • ***

    , P < 0·001.

  • All analyses also initially considered the interaction between treatment and flower number and observation date, but these variables were excluded from the final models because they did not affect bee behaviour significantly. See Figs 2 and 3 for details of responses.

Visits per inflorescence
D. bicolorinline image = 114·12Treatment 7·80** 
ln(open flowers) 7·76**0·662 (0·304–0·940)
D. glaucuminline image = 20·45Treatment15·64*** 
ln(open flowers) 8·25**0·397 (0·122–0·673)
Flower probes per inflorescence visit
D. bicolorinline image = 115·35Treatment10·61** 
ln(open flowers)12·38***0·432 (0·280–0·585)
D. glaucuminline image = 257·76Treatment26·58*** 
ln(open flowers)22·88***0·431 (0·318–0·544)
Total flower probes during 5 h
D. bicolorinline image = 112·70Treatment 0·91 
ln(open flowers)14·92***1·046 (0·762–1·331)
D. glaucuminline image = 72·95Treatment 2·32 
ln(open flowers)65·31***0·951 (0·762–1·141)
Figure 3.

Effects of flower-size manipulation (a,c) and mean (± SE) number of open flowers (b,d) on the number of bees visiting Delphinium bicolor inflorescences (a,b) during 5-h observation periods, and mean (± SE) number of flowers probed by individual bees (c,d). Solid lines (b,d) indicate the partial regression relations based on ln-transformation of both dependent and independent variables; dotted lines depict the specified ratios of dependent to independent variables. Statistical details are provided in Table 1.

Figure 4.

Effects of flower-size manipulation (a,c) and mean (± SE) number of open flowers (b,d) on the number of bees visiting Delphinium glaucum inflorescences (a,b) during 5-h observation periods, and mean (± SE) number of flowers probed by individual bees (c,d). Solid lines (b,d) indicate the partial regression relations based on ln-transformation of both dependent and independent variables; dotted lines depict the specified ratios of dependent to independent variables. Statistical details are provided in Table 1.

During a bee's visit to an inflorescence, flower size and number had contrasting effects on the number of flowers that it probed (Table 1; Figs 3c,d and 4c,d). Bees probed ≈25% fewer flowers on inflorescences with intact flowers than on inflorescences on which flower size had been reduced. In contrast, the number of flowers probed per inflorescence visit increased with flower number, although the proportion of flowers that bees probed declined with open-flower number, as indicated by partial regression coefficients for ln(open flowers) significantly <1 (Table 1; Figs 3d and 4d). The number of flowers probed per inflorescence visit did not vary significantly with either sampling date (D. bicolor, G1 = 1·29, P > 0·25; D. glaucum, G1 = 0·39, P > 0·5), or the interaction between flower-size treatment and ln(open flowers) (D. bicolor, G1 = 0·54, P > 0·4; D. glaucum, G1 = 1·18, P > 0·25).

The total number of flower probes on inflorescences during 5-h observation periods reflect the combined effects on inflorescence visitation and probes per inflorescence visit. For both species, the counteracting influences of the flower-size treatment on these two aspects of pollinator behaviour resulted in no significant treatment effect on the total number of probes (Table 1). Additionally, the total number of probes per inflorescence increased in direct proportion to open-flower number (partial regression coefficients not significantly different from 1; Table 1) because the partial regression coefficients for inflorescence visitation and probes per visit sum roughly to 1. Because of these effects, individual flowers received equivalent numbers of probes during the 5-h observation periods, regardless of flower size or open-flower number (median = 1·67 and 0·78 probes for D. bicolor and D. glaucum, respectively). The total number of flowers probed per observation period did not vary significantly with either sampling date (D. bicolor, G1 = 1·52, P > 0·2; D. glaucum, G1 = 3·62, P > 0·05), or the interaction between the flower-size treatment and ln(open flowers) (D. bicolor, G1 = 0·33, P > 0·5; D. glaucum, G1 = 2·17, P > 0·1).

Overall, flowers of both species presented equivalent nectar standing crops per flower immediately after the 5-h periods of bee observation, regardless of flower-size treatment or number of open flowers (Table 2). This conclusion applies to both nectar concentration and volume per flower. Unlike nectar concentration, which we measured for aggregate samples from inflorescences, we measured nectar volume for individual flowers. Analysis of the standing nectar volume in individual flowers detected significant variation within inflorescences, regardless of whether the flowers were intact or manipulated (Table 2). Specifically, for both species, uppermost flowers contained less nectar than those at all other positions (Fig. 5, based on Tukey's multiple comparisons, P < 0·05). For D. glaucum, flowers within the second-highest fifth of the inflorescence also offered less nectar than the lowermost flowers.

Table 2.  Effects of flower-size treatment, number of open flowers and flower position within Delphinium bicolor and Delphinium glaucum inflorescences on the concentration and volume of nectar standing crop
Dependent variableIndependent variableD. bicolorD. glaucum
  • ***

    , P < 0·001.

Nectar concentrationFlower sizeF1,16 = 2·07F1,26 = 3·28
ln(open flowers)F1,16 = 0·20F1,26 = 2·09
Size × ln(open)F1,16 = 1·36F1,26 = 2·92
Nectar volumeFlower sizeF1,60·2 = 0·21F1,32 = 1·39
ln(open flowers)F1,62 = 0·52F1,32 = 1·21
Size × ln(open)F1,53 = 0·11F1,32 = 0·95
Flower positionF4,105 = 7·78***F4,32 = 17·10***
Figure 5.

Relation of mean (± SE) volume of nectar in Delphinium bicolor and Delphinium glaucum flowers after 5-h observation periods to a flower's relative position within the inflorescence (D. bicolor, 1 = fifth lowest flower, ... 5 = top flower; D. glaucum, 1 = bottom fifth of inflorescence, ...  5 = top fifth).

Bees detected differences in the recent visitation history of D. glaucum inflorescences, and visited more flowers on inflorescences that had been excluded from visitation during the preceding hour (mean = 3·9 flowers, LSE = 0·38 flowers, USE = 0·43 flowers) than on inflorescences that had been exposed continuously (mean = 2·5 flowers, LSE = 0·30 flowers, USE = 0·34 flowers, G1 = 7·65, P < 0·01). As we observed in other experiments, bees also visited more flowers on inflorescences that displayed more flowers (G1 = 9·00, P < 0·05; partial regression coefficient ± SE = 0·483 ± 0·164), but this effect did not differ significantly among exposure treatments (G1 = 0·19, P > 0·5).

Discussion

Delphinium bicolor and D. glaucum differ considerably in flower size (D. bicolor > D. glaucum) and number of open flowers (D. bicolor < D. glaucum), but these aspects of floral display influenced pollinator attraction and behaviour during inflorescence visits similarly for both species. In general, plants with larger flowers attracted more bees, but each bee probed fewer flowers on large-flowered plants, so the average visitation rate to individual flowers did not vary significantly with flower size (Table 1). In addition, plants that displayed many flowers attracted more bees than few-flowered plants, and individual bees visited more flowers on large inflorescences (Table 1). However, neither response kept pace with variation in flower number, so that the number of bees attracted per flower and the proportion of flowers probed by individual bees both declined with increasing flower number (Figs 2 and 3). As a result, the average visitation rate to individual flowers did not vary significantly with flower number. For both Delphinium species, flower size and number influenced pollinator behaviour independently. We now consider the implications of these effects for bee behaviour and reproduction by bee-pollinated plants.

ideal free distribution of pollinators

The behaviour of bees visiting both Delphinium species and lack of variation among plants in average nectar standing crop per flower both suggest that bees distributed their visits among plants according to an ideal free distribution. Flower size had contrasting influences on plant attractiveness and the number of flowers probed by individual bees, resulting in equal numbers of flower probes on large- and small-flowered plants during 5-h observation periods. In addition, the average number of probes per flower varied little with flower number, because both a plant's attractiveness and the number of flowers probed by individual pollinators increased in a decelerating manner with the number of open flowers, as has been shown by many previous studies (reviewed by Ohashi & Yahara 2001). Together, these responses eliminated variation in nectar standing crop per flower among large- and small-flowered plants, and among few- and many-flowered plants (Table 2). Thus both bee behaviour and nectar distribution among plants indicate that bees responded to variation in flower size and number by distributing their visits among plants in a manner that equalized their nectar-intake rate, as expected with an ideal free distribution (Fretwell & Lucas 1970). This distribution is a common feature of bee–plant interactions (Dreisig 1995; Robertson & Macnair 1995; Ohashi & Yahara 2002).

How might an ideal free distribution arise? Plants with many or large flowers may be more attractive simply because they are more conspicuous than their neighbours. Bee eyes have limited resolving power because the minimum visual angle that they can detect is about 5° (Giurfa et al. 1996; Spaethe & Chittka 2003), depending on the insect's body size (Spaethe & Chittka 2003) and the object's colour and contrast with its background (Giurfa et al. 1996). Thus bees probably detect plants with large outlines more readily than smaller plants. In addition, if plants have remained unvisited during an appreciable period (e.g. at dawn), bees will prefer both large-flowered plants because they tend to offer more nectar per flower (Harder 1988; Cohen & Shmida 1993; Blarer, Keasar & Shmida 2002: although not in our experiment) and many-flowered plants to reduce flight costs between flowers (Ohashi & Yahara 2001). However, as plants receive visits, individuals that have received frequent visits will tend to have a higher proportion of flowers with small nectar standing crops, at least for a while. This correlation in nectar standing crop among flowers within inflorescences allows bees to determine whether a particular inflorescence is currently rewarding, based on their experience probing only a few flowers (Pyke 1978, 1982; Waddington 1981; Dreisig 1989; Smithson 2002; Smithson & Gigord 2003), especially on vertical inflorescences, such as those of Delphinium, on which bees routinely follow an upward path (Pyke 1978; Waddington 1981). Bees exhibited this response to nectar correlations within plants by visiting more flowers on plants that we had excluded from pollinator access for 1 h to allow undisturbed nectar accumulation (Fig. 3). Such facultative responses by bees to the standing nectar crop would tend to equalize nectar standing crop per flower among plants with different flower sizes and numbers.

The equalization of nectar volumes among plants contrasts with the consistent pattern of lower standing crops in upper flowers on inflorescences of both Delphinium species (Fig. 5). This pattern probably reflects the lower rate of nectar secretion by young, upper flowers in Delphinium inflorescences (Pyke 1978). As a result, the positive correlation in nectar volumes within inflorescences that promotes the development of an ideal free distribution will weaken in the upper portion of Delphinium inflorescences.

strategies that reduce successive probes by a pollinator

The results of our experiments indicate that, because bees achieve an ideal free distribution, plants with large flowers relative to the average flower size in a population probably experience less geitonogamy than small-flowered individuals. Large flowers reduce the number of flowers probed per pollinator without affecting the overall visitation rate experienced by a plant's individual flowers. Because flower size affects pollinator behaviour independently of flower number, increased flower size provides an effective means to reduce geitonogamy and its associated negative effects on pollen export, without compromising the frequency of visits to individual flowers. As a result, a large-flowered variant should be able to invade an outcrossing plant population because of its reduced self-pollination and enhanced pollen export. As this advantage depends on the size of the variant's flowers relative to the prevailing size in the population, rather than their absolute size, spread of a variant with larger-than-average flowers increases mean flower size and creates the opportunity for invasion of a variant with still larger flowers. However, such selection should eventually be counteracted by a variety of costs of large flowers, including increased physiological costs of maintenance (reviewed by Galen 1999); reduced flower number if a fixed investment in flower production imposes a size-number trade-off (e.g. Worley & Barrett 2000; Andersson 2005); allometric changes in the lengths of stamens and/or pistils (e.g. Conner 2002) that reduce the precision of contact between pollinators, anthers and stigmas; and increased attraction of flower and seed predators by large flowers (reviewed by Strauss & Whittall 2006).

Large flowers often produce more nectar, and bees can learn this association (Harder 1988), but our experiment did not include this association. Would a large-flowered variant whose flowers did not produce more nectar than those of average plants in the population still have a selective advantage? For example, bees might learn that large-flowered plants are no more productive than small-flowered plants, and visit them indiscriminately. Our results for D. bicolor argue against this possibility. For this species, we examined the same plants on 14 and 16 June, and most of the flowers during the 16 June observations had been manipulated on 14 June. Thus bees had 2 days to learn that small-flowered (manipulated) plants were not less productive than large-flowered (intact) plants. Nevertheless, the differential response of bees to large- and small-flowered plants did not differ between the two sampling dates, indicating that the lack of association between flower size and nectar production did not affect bee behaviour significantly. Thus the effects of flower size on bee behaviour seem to occur regardless of any learned associations between flower size and nectar production, probably because large-flowered plants are more obvious than small-flowered plants. Therefore the scenario for the evolution of large flowers outlined above is unlikely to be affected by such associations.

As a means of reducing successive probes by a pollinator, flower size offers advantages not provided by the two other classes of floral mechanism that can serve this role: displaying few flowers simultaneously, and offering pollinators low or variable foraging returns. Many studies have found that pollinators visit fewer flowers on inflorescences with few open flowers (Figures 3d and 4d; Ohashi & Yahara 2001). Open-flower number depends on both the rate of flower opening and floral longevity (Ishii & Sakai 2001a; Meagher & Delph 2001; Harder & Johnson 2005), so that plants that display a small fraction of their flowers simultaneously open few flowers at once and/or have short-lived flowers. Exposing few flowers has two disadvantages as a means of limiting geitonogamy. First, brief floral longevity reduces the opportunity for pollinator visits per flower, which can increase the chance that pollen in anthers and ovules remains unfertilized (Ishii & Sakai 2001b). Second, exposing a small fraction of flowers simultaneously necessarily extends a plant's total flowering period (de Jong, Klinkhamer & van Staalduinen 1992; Ishii & Sakai 2001a), which may not allow sufficient time for subsequent seed development and dispersal. This time constraint is not shared by the alternative strategy to reduce geitonogamy, of offering pollinators low or variable foraging returns per energetic expenditure by producing limited or variable nectar per flower (Pyke 1978, 1982; Biernaskie, Cartar & Hurly 2002; Smithson 2002; Smithson & Gigord 2003; Biernaskie & Cartar 2004), complex floral structures that require extended probing time per flower (Ohashi 2002), and low flower density within a plant's display (Ishii & Sakai 2001b). However, these mechanisms also have obvious negative consequences for the visitation rate to individual flowers, because they reduce the number of flowers probed per visit without increasing pollinator attraction.

In contrast to other mechanisms that limit geitonogamy, production of large flowers promotes pollinator attraction without affecting visitation to individual flowers. Similar benefits should be realized by small-flowered species with specialized organs for attraction, such as the conspicuous involucre of many Araceae, attractive sterile flowers, or the retention of old flowers to enhance the floral display (Harder & Barrett 1996). Together, these mechanisms illustrate that the evolution of floral traits, such as flower size, depends not only on the interaction between pollinators and individual flowers, but also on the contributions of each flower to the performance of the entire floral display (cf. Harder et al. 2004).

Acknowledgements

We thank Ralph Cartar for useful comments on the manuscript. This research was funded by a Postdoctoral Fellowship (0124) from the Japan Society for the Promotion of Science for Research Abroad (H.S.I.) and a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (L.D.H.).

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