Selfing rates in natural populations of Echium vulgare: a combined empirical and model approach

Transcription

1 Functional Ecology 1999 ORIGINAL ARTICLE OA 000 EN Selfing rates in natural populations of Echium vulgare: a combined empirical and model approach M. C. J. RADEMAKER, T. J. DE JONG and E. VAN DER MEIJDEN Institute of Evolutionary and Ecological Sciences, Leiden University, PO Box 9516, 2300 RA Leiden, The Netherlands Summary 1. We quantified geitonogamous selfing in Echium vulgare, a self-compatible, bumble-bee pollinated plant. A maximum estimate of selfing was determined using a paternity analysis with RAPDs. In the first experiment, bumble-bees visited a sequence of virgin flowers. The percentage selfing increased rapidly from 12% in the first flower visited, up to 50% in the 15th flower visited in the sequence. In the second experiment, when bees visited plants in a natural population, the average selfing of plants increased with the number of open flowers from 0% to maximally 33%. 2. The results obtained in both experiments are consistently lower than predicted by our model on pollen dynamics (Rademaker, de Jong & Klinkhamer 1997). We modified the model on pollen dynamics to link it more to the field situation with observations on flower stage, flower opening and bumble-bee preference, so that the bumble-bees encounter a variable number of pollen grains per flower. We also adjusted the parameters. If less pollen adheres to the bee (25% instead of 50%) after removal from the anthers, or if bees arrive at a plant with more pollen grains (6000 instead of 4448), the predictions of the model in regard to selfing could be improved but were still high compared with the observed selfing rates measured with RAPDs. 3. We suggest that the model is consistent with pollen dynamics in the field. However, post-pollination processes like selective abortion could play a role in E. vulgare. Key-words: Exponential decay model, geitonogamous selfing, RAPDs Functional Ecology (1999) Ecological Society Introduction The number of flowers that a plant produces determines its potential number of offspring. Large floral displays attract more pollinators and increase length of visitation sequences (Schmid-Hempel & Speiser 1988; Thomson 1988; Klinkhamer, de Jong & de Bruin 1989; Klinkhamer & de Jong 1990; Pleasant & Zimmerman 1990). However, at the same time it may be disadvantageous to produce many flowers because longer flower-visitation sequences induce more geitonogamous selfing and pollen loss within the plant (Dommee 1981; Crawford 1984; Dudash 1991; de Jong, Waser & Klinkhamer 1993; Harder & Barrett 1995; Snow et al. 1995). Geitonogamous selfing is generally considered non-adaptive in outcrossing plants as it has the same drawback as autogamy (inbreeding depression) but lacks its benefits (low costs). Many plant species are well adapted to avoid autogamy. Faegri & van der Pijl (1979) stressed that self-incompatibility is the most important mechanism to reduce self-fertilization. However, self-incompatibility mechanisms do not prevent a plant s pollen from landing on its own stigmas where it is unsuccessful. Several studies have shown the negative effects of self pollen on fitness when it clogs the stigma or interferes with outcross pollen grains in some other way (Galen, Gregory & Galloway 1989; de Jong et al. 1992; Broyles & Wyatt 1993). A common way to avoid self-pollination is by temporal and spatial separation of pollen and stigma within the same flower (dichogamy and herkogamy). Such adaptations have no effect on reducing geitonogamy when insects visit more flowers per plant. To reduce geitonogamy, plants may extend the flowering period and produce only a few open flowers at the same time. Furthermore, plants can synchronize their sex-expression (e.g. start to produce only male flowers per plant, followed by female flowers), which occurs in some umbellifers (Cruden & Hermann-Parker 1977). Pollinator behaviour may also influence the level of self-pollination. Bumblebees can often be seen rejecting certain flowers in an inflorescence, which reduces the number of flowers visited, resulting in a lower level of self-pollination. If bees choose between hermaphroditic flowers and 828

2 829 Selfing in Echium visit functionally female flowers before functionally male flowers, self-pollination is reduced. Plant architecture can play a part in this. On vertical inflorescences, bees usually move upwards. In the protandrous Foxglove (Digitalis purpurea) lower flowers open first. The bee will first meet the older flowers which are in the female stage and only as it moves up the inflorescence will it visit flowers in the male stage, which promotes outcrossing (Best & Bierzychudek 1982). Protandry of flowers in such an inflorescence thus constitutes a highly efficient outbreeding mechanism. Upward movement allows pollinators to avoid revisits, thus increasing their handling efficiency (Waddington 1981; Schmid- Hempel & Speiser 1988). On the other hand, plant architecture can also reduce pollinator handling efficiency. If the arrangement of the flowers is very complex, as in Echium vulgare (Boraginaceae), pollinators may miss some flowers and revisit others (Durrer & Schmid-Hempel 1994), and if they visit fewer flowers in a sequence self-pollination is reduced. Some species spread flower opening over the day, so that there is variation in the number of pollen grains in the flowers presented simultaneously on the inflorescence (Corbet 1978). This could reduce geitonogamy if bees accumulate self-pollen less rapidly or if this induces the bees to leave sooner and visit fewer flowers in succession. We will discuss this last point for E. vulgare in this paper. An individual plant of E. vulgare may produce hundreds of open flowers. Bumble-bees switch frequently between plants and only a small percentage (on average 5% on plants in dense populations, range 2 20%) of the flowers on a plant are visited in a sequence by a single bee during an approach (Klinkhamer & de Jong 1990). We have made an exponential decay model that describes pollen transfer between successive flower visits (de Jong et al. 1992; Rademaker et al. 1997), to predict the percentage self-pollination. In the model, pollen deposition, losses and removal are assumed to be fractions of the amounts carried by the pollinator and present in the anthers. The basic model assumes that all hermaphrodite flowers open simultaneously and contain equal amounts of pollen. The purpose of this study was threefold, i.e. to: (1) test our model on pollen dynamics in the field using virgin flowers and adjust the parameters to the field situation; (2) measure geitonogamous selfing in the field under natural conditions and compare these measurements with the model predictions; (3) adjust the model to the field situation. We therefore had to collect data on: (1) the temporal pattern of the flower opening during the day in E. vulgare; (2) the frequency of flowers of different stages (functionally or ), which differ in the number of pollen grains available; (3) the number of flowers visited by bumble-bees and their preference for flowers of different ages. Materials and methods THE PLANT Echium vulgare (Viper s Bugloss) is a self-compatible monocarpic perennial. Autogamy is prevented by protandry and spatial separation of anthers and style. We observed that plants in the greenhouse which were kept away from pollinators, produce no seeds. All plants studied were hermaphrodite, but malesteriles have been reported (Klinkhamer, de Jong & Wesselingh 1991). An individual plant may have one to 20 flowering stems (height cm). Each flowering stem may produce up to 50 cymes and each cyme carries c. 20 flowers. A plant may produce hundreds of flowers but only a small fraction (usually two to three flowers per cyme) is open at a specific moment of time. Flowers open throughout the day (Corbet 1978). Before and a few hours after opening, flowers are pink, turning into pink-blue during the first day. On the second day, flowers are blue, turning dark-blue when they begin to wilt on the third day (Corbet 1978; Klinkhamer & de Jong 1990; Klinkhamer et al. 1991), after which they may stay attached for a few more days. The hermaphroditic flowers are functionally male on the first day and functionally female on the second day. For simplicity we will use female or male stage instead of functionally female or male in what follows. In our study area, Meijendel (52 8 'N, 4 20 'E), a sand-dune system near The Hague, the Netherlands, E. vulgare was, in the year of our study, predominantly visited by bumble-bees like Bombus pascuorum (Scopoli) (64% of all pollinator visits) and Bombus terrestris L. (33% of all visits). FIELD OBSERVATIONS ON FLOWERING PHENOLOGY AND BUMBLE-BEE BEHAVIOUR Data were collected on flower opening during June and July For 30 plants we observed the daily pattern of flower opening. Every hour from h until h newly opened flowers were marked. This was repeated during four non-cloudy days with similar weather conditions. The average number of flowers that opened per cyme per hour was calculated. Data on flowering phenology were collected by counting the number of flowers per developmental stage of 100 plants, three times a day. We distinguished five consecutive stages on the basis of flower colour and the length of anthers and stigma (see Table 1). Data on pollen availability were collected for all stages. During 5 days 35 anthers were collected from every flower stage and stored in 70% ethanol. With a flowcytometer the number of pollen grains present in the anthers was counted (following de Laat, Gohde & Vogelzang 1987). Data on bumblebee preference were collected per flowering stage during 4 days. Flower visitation of 100 bumble-bees was observed. From these data we calculated the

3 830 M. C. J. Rademaker et al. Table 1. Description of the five different flower stages. The frequency distribution of flowers in each stage present on a plant (freq. flowers), the average number of pollen grains available (± SE) (pollen), the frequency distribution of visits to different stages, and the preference that denotes how often a given flower in a certain stage is visited by a bee, relative to a flower in the most frequently visited stage (stage 2) Freq. Pollen Freq. Flower stage (description) flower (%) (n = 34) visits (%) Preference 1. Flower pink, only small hole between petals visible (male stage) ± Style smaller then anthers (male stage) ± Style between small and large anthers (male stage-female ± receptive stage) 4. Style longer than anthers (female receptive stage) ± Flower starts wilting (female receptive stage) ± probability that a flower of a certain stage was visited during an approach. Data on pollen load of the bumble-bees (B. pascuorum) were collected by counting the number of pollen grains on the bee s body (its head, vertex and thoracic and abdominal sternites) at arrival on a plant and at departure from an untreated flowering plant. In June 1998, in total 30 workers of B. pascuorum were captured, 20 workers at arrival and 10 workers at departure. The bees were chilled and cleaned three times with a piece of fuchsin glycerin jelly (Beattie 1972), to count the number of grains on the bee s body with a microscope. From the exponentional decline of pollen in the three slides it was estimated that the three samples contain 74% of the pollen on the bee and the data were corrected for this. Data on pollen accumulation on the bee s body were collected by applying the above procedure after the bees had visited between two and 11 virgin flowers full of pollen. In addition, pollen loss between flowers was calculated by inducing B. pascuorum workers to visit emasculated (female stage) flowers. We captured bees and determined pollen loads on the bees after they had visited between two and 11 emasculated flowers. SELFING WHEN BEES VISIT A SEQUENCE OF VIRGIN FLOWERS In the first experiment we induced bumble-bees to visit virgin flowers. The experiment was carried out in June and July 1996 in a common garden at the verge of the dune area. Plants were grown in 10 litre pots in a fine meshed cage to exclude insects. Bumble-bees from the field, which were foraging on natural E. vulgare plants (c. 98% of the pollen load was E. vulgare pollen) were offered plants with only virgin, receptive flowers. It was noted which flowers were visited and in what sequence. After an approach of a single bee to the plant the visited flowers were marked with numbered tags and the plant was returned to the cage. Six weeks after pollination the seeds were collected. Seeds were germinated in Petri dishes on moist filter paper at 20 /10 C with 16 h light. After 6 weeks, the third expanded leaf was collected and stored at 80 C for DNA extraction for paternity analysis. At the start of the experiment leaf material from all parent plants was collected and stored at 80 C. SELFING WHEN BEES VISIT OPEN-POLLINATED PLANTS IN THE FIELD The second experiment was carried out during July August 1997 in a natural population of 25 plants. Leaf material was collected in July from the parents for DNA extraction and we counted the number of open flowers 10 times. In August we harvested six plants, varying in number of open flowers. From each plant we collected the seeds and measured plant height, number of cymes, number of flowers per cyme and straw mass (mass of the plant without seeds after drying at 50 C for 2 days). From each parent 50 seeds were germinated in Petri dishes on moist filter paper at 20 /10 C with 16 h light. After 6 weeks, the third expanded leaf was collected for paternity analysis and was immediately used for DNA extraction. From each parent 24 seedlings were used in the DNA analysis. RAPDS FOR PATERNITY ANALYSIS DNA was extracted from samples of the frozen leaf material, collected in the first experiment, according to Cheung, Hubert & Landry (1993) with the addition of 2% PVP to the extraction buffer. In the second experiment DNA was isolated from samples of fresh leaves according to Walbot & Warren (1988). With the use of random amplified polymorpic DNA (RAPD) (Williams et al. 1990) we analysed whether the offspring was selfed (no additional bands compared to the mother) or outcrossed. We assumed that we could use RAPDs for paternity analysis on the basis of controlled crosses performed in an earlier experiment (Melser, Rademaker & Klinkhamer 1997). In this experiment we used the same method and primers for PCR reaction (Operon Technologies OPF4, OPF7, OPF9, OPF11, OPF12 and OPF16). For the bands scored we have checked if they were paternally inherited and only bands which also occur in other plants in the population were used to distinguish between selfed and outcross seedlings. To improve the reliability of the method, DNA of one family of offspring was

4 831 Selfing in Echium always put on a gel together with a sample of the mother to allow identification of non-maternal bands. To check further whether RAPDs could be used to distinguish between selfed and outcrossed seedlings we used controlled crosses between plants and tested four selfed seedlings from three different mothers with 10 primers. We found no additional bands. We therefore decided that RAPDs were suitable for quantifying selfing. In both experiments we scored the presence or absence of bands (not present in the mother) for each offspring. For the six analysed parents we found with six primers 21 bands which differed between parents in absence or presence. If bands in the offspring were present that were not present in the mother we concluded that the seed was outcrossed. The problem with this method is that some of the offspring with no extra bands that we classified as selfed, may in fact lack these bands by chance and are the result of outcrossing after pollination by individuals in the population that are genetically closely related to the mother. The method therefore gives a maximum estimate of the percentage selfing; the real selfing rate can only be lower than this value not higher. Knowing the inheritance pattern and population frequency of alleles it would be possible to estimate selfing exactly within confidence limits, or to make statements about the average selfing level in the population. Correcting the data with MLDT, a program which estimates outcrossing rates with dominant markers (Ritland 1990) indicated that we could not estimate selfing accurately, owing to small family sizes, and that zero selfing was within the confidence limits. For this reason, we decided to present only the maximum selfing rates in this paper. On average, the outcross offspring had four bands not present in the mothers. Therefore assuming heterozygosity of all bands (1/2) 4 = 6 25% gives a rough estimate of the fraction of the seedlings that we classified as selfed, but may in fact be outcrossed, missing the unique bands of their father by chance. We present the uncorrected data in the figures. THE MODEL ON POLLEN DYNAMICS We used the exponential decay model on pollen transfer (Lertzman & Gass 1983; Crawford 1984; de Jong et al. 1992; Robertson 1992; Barrett, Harder & Cole 1994; Harder & Barrett 1995; Rademaker et al. 1997) to predict the percentage self-pollination. In our model, pollen deposition, losses and removal are assumed to be fractions of amounts carried by the pollinator and the anthers. Respectively, k 1 denotes the fraction of pollen on the bee s body deposited on the stigma per flower visit, k 2 the fraction of pollen removed from the anthers per flower visit, k 3 the fraction of pollen removed from the anthers that adheres to the pollinator, and k 4 the fraction of pollen on the bee that is lost during the flight between flowers, passively and through grooming (Rademaker et al. 1997). The outcross-pollen load on the bee when it arrives on the plant is denoted A. This only includes pollen on the head and vertex and thoracic and abdominal sternites of the bee, i.e. those parts of the body that may come in contact with the stigma, and not the pollen collected in the baskets on the legs. B is the total amount of pollen present in the anthers of a fresh flower. The values for the different parameters are presented in Table 2. Many of the above authors that used this model, assume at some point that the bumble-bee is saturated. This does not mean that the bee is full with pollen; bees foraging on E. vulgare carry on their body several thousands of grains while there is space for many more (see later). It does mean that, on average, for each flower visited pollen uptake equals pollen loss, so that there is an equilibrium. Bees should then carry Ā= k 2 k 3 B(1 k 4 )/(k 1 + k 4 k 1 k 4 ) eqn 1 pollen grains just before visiting a flower. In this equation k 2 k 3 B denotes the number of pollen grains that adheres to the bee in every successive flower visited. When B is variable, dynamic equilibrium implies that, on average, the bees leave the plant with as much pollen as they arrive with. If bees are saturated and when losses on the stigma (k 1 ) are very small compared to other losses (k 4 ) (Rademaker et al. 1997), we can use the approximation S n =1 [1 (1 k 4 ) n ]/k 4 n eqn 2 Table 2. The values for the different parameters first estimated (± SD) under controlled conditions in a vault (Rademaker et al. 1997) and later estimates in the field. Year in which measurements were made is given between brackets Controlled conditions Field Parameters B. terrestris B. pascuorum and B. terrestris A: number of pollen on the bee s body 4448 ± ± 2000 both species (1996) 4748 ± 1923 B. pascuorum (1998) B: number of pollen in the virgin receptive flowers (see Table 1, 1997) k 1 : fraction of pollen deposited on the stigma ? k 2 : fraction of pollen removed from the anthers not measured 0 14 both species (1996, unpublished results) 0 16 both species (Klinkhamer et al. 1991) k 3 : fraction of pollen removed from the anthers that B. pascuorum (1998, see Results Fig. 3) adheres to the pollinator k 4 : fraction of pollen on the bee lost between flowers B. pascuorum (1998, this paper)

5 832 M. C. J. Rademaker et al. to estimate selfing (Crawford 1984; Robertson 1992; Barrett et al. 1994), in which S n is the average plant selfing rate and n the number of open flowers visited in a sequence on that plant. This approximation holds in our case for E. vulgare as k 1 is much smaller than k 4 (Rademaker et al. 1997). As follows from equation 2, if the pollen on the bumble-bees is in equilibrium, only reducing k 4 reduces the percentage selfing. On the other hand, if bees leave the plant with more and less grains than at arrival the situation is complex. Then we can still compute selfing by counting all pollen flows for the different flowers visited. The results obtained with the model then also depend on k 2 k 3 B and A. We modified the exponential decay model (Rademaker et al. 1997), in which bumble-bees visited a sequence of identical virgin flowers, by including flowering phenology and the behaviour of the bumble-bees. The flowering phenology of the plant is important because five different stages can be distinguished in E. vulgare. All flower stages differ in the amount of pollen present (B) and in the probability of being visited by a bumble-bee (Table 1). A bumblebee accumulates most self pollen grains in flowers in the male stage 1 and 2. It is only in stage 3 and 4 that pollen can be deposited on the receptive stigma to fertilize ovules. The calculation of the selfing rate is depicted in Fig. 1. The number of flowers visited is calculated from the number of simultaneously open flowers using the equation lny = lnx (Klinkhamer & de Jong 1990). In this equation lnx denotes the natural logarithm of the number of open flowers and lny denotes the natural logarithm of the number of flowers visited in a sequence. This equation was based on the most extensive data set we have available and was consistent with the more limited data on visitation we obtained in the summer of For every arriving bumble-bee random numbers determined the stage of the flower visited with probabilities corresponding to the frequency of visits in Table 1. For every bumblebee we kept count of the number of self and outcross pollen grains on its body during its visit to the plant, according to the exponential decay model. The parameter values (k 1, k 3, k 4, A, B) from this model were measured in an earlier experiment under controlled conditions in a vault (Rademaker et al. 1997). For the stage 3 and 4 flowers we kept count of the number of deposited self and outcross pollen grains on the stigma. We did not keep count of pollen remaining in the anthers after removal. The idea is that, because flowers open and age continuously over the day, the frequency distribution of flowers in different stages is similar for bees arriving at the plant at different times of the day (Table 1). After many bumble-bee visits the percentage self pollination could be calculated for a plant with a known number of open flowers by adding the numbers of self and outcross pollen deposited on Fig. 1. Description of the calculation of the average percentage selfing in the field, with flowers in different stages.

6 833 Selfing in Echium each stage 3 and 4 flower, then calculate the percentage selfing for each flower separately and average over flowers to obtain a plant estimate of selfing. Results FIELD OBSERVATIONS ON FLOWERING PHENOLOGY AND BUMBLE-BEES The flower-opening pattern during the day is given in Fig. 2. On average, 18 flowers per plant opened during the day, that is about 0 4 flowers per cyme per day. On average, only two flowers per plant opened outside the observation period (during the evening and the night). During the day flowers change from functionally male to functionally female. The last stage flowers (stage five) can be attached to the plant for several days and, as a rule, two flowers are present on a cyme during the day. The five consecutive stages of flower development differed in the frequency in which they were present on the plant, pollen content and bumble-bee preference (Table 1). Throughout the day new flowers opened and aged. The proportion of flowers in each of the five stages stayed roughly the same during the day. The flower stages differed in the probability of being the first flower visited in the sequence (χ 2 [4] = 37 6, Fig. 2. Average number of flowers that opened per cyme per hour (n = 30). The average was calculated by adding data for the 30 plants over 4 days. n = 100, P < 0 001). Apparently bumble-bees distinguish between flowers when approaching a plant. Flower stages 2, 3 and 4 had a higher chance to be visited first, while especially the old flowers (stage 5) were avoided. The relative frequency distribution over stages of the last flower visited was identical to that of all flowers visited (χ 2 [4] = 3 27, n = 100, P = 0 55), which means that the tendency to leave the plant did not differ between flower stages. Pollinators clearly distinguish between stages when foraging on the plant. A flower in stage 5 receives times fewer visits than a flower in the most preferred stage 2 (Table 1). Field estimates were made of the pollen load on bees (± SD), that arrived and departed at a field plant, with flower stages and pollen in its flowers corresponding to Table 1. Arriving bees (B. pascuorum) carried on average 4748 ± 1923 (n = 20) pollen grains and departing bees on average 7313 ± 2728 (n = 10) pollen grains. These figures suggest that bees loose 35% of the pollen on their body when flying between plants (ANOVA, F [1,28] = 8 91, P = 0 006). A field estimate of k 3 was obtained by counting the number of pollen grains on the bee s body when visiting a sequence of virgin flowers. Workers of B. pascuorum were induced to visit up to 11 virgin flowers. Figure 3 shows that for every successive visit (x) to a flower the number of grains on the bee s body (y) increased with 1485 grains (y = x, n = 10, P = 0 01). As this amount is equal to k 2 k 3 B, it can be calculated that, with k 2 = 0 16 (Klinkhamer et al. 1991) and B = (see Table 2, field data), k 3 = In a small field experiment in 1998 we observed that a fraction of 0 05 of the pollen on the body of the bee (B. pascuorum) was lost between visits to a pair of flowers when bees foraged on a plant with emasculated flowers, which is comparable to k 4 = 0 06 which was previously found for B. terrestris measured under controlled conditions (Rademaker et al. 1997). We summarized all available data on the parameters of our exponential decay model. Table 2 shows that some of the parameters measured under controlled conditions (Rademaker et al. 1997) differ from the parameters measured in the field. We used the most reliable data and varied the other parameters over the range suggested by the different measurements. Fig. 3. Increase in the number of pollen grains on the body of workers of Bombus pascuorum after different numbers of virgin flowers visited. THE MAXIMUM PERCENTAGE SELFING OBTAINED WITH RAPDS Selfing when bees visit a sequence of virgin flowers In the controlled pollination experiment, in which bumble-bees visited virgin flowers, the maximum percentage selfing increased significantly with the position of the flower in the sequence. We found 12 5% selfing in the first flower visited and up to 50% selfing in the 15th flower visited on a plant (y = x; Kendall τ = 0 40, one sided P = 0 025; Fig. 4).

7 834 M. C. J. Rademaker et al. Fig. 4. Relationship between the percentage selfing predicted with the model and the flower sequence position when bumble-bees visit virgin flowers. Parameters were estimated by Rademaker et al. (1997) for B. terrestris under controlled conditions: A = 4448, k 1 = , k 2 = 0 16, k 3 = 0 5, k 4 = 0 061, B = The solid line gives results with these parameters. The dotted line with reduced k 3 (k 3 = 0 25), the broken line with reduced k 4 (k 4 = 0 04), and the broken, dotted line with increased A(A= 8000). For further explanation see text. The maximum percentage selfing estimated with RAPDs from the plants on which bees visit a sequence of virgin flowers is plotted in the figure (open dots). Selfing when bees visit open-pollinated plants in the field In Fig. 5a the maximum percentage selfing for six plants which differed in flower number and consequently in flowers visited per approach is plotted. The maximum percentage selfing (y) of individual plants in E. vulgare varied from 0 to 33%, and averaged 12 5%. Selfing tends to increase with the number of flowers visited per approach (x) on a plant (y = x; Kendall τ = 0 55, one sided P = 0 06), although this result is not significant. The percentage selfing seems to be lower in the natural population than in the controlled experiment with virgin flowers. If we increase A, up to a level of 8000 pollen grains on the bee at arrival at the plant, selfing is reduced (Fig. 4). Reducing k 4 has a negligible effect on the selfing rate (Fig. 4), even if k 4 approaches zero. Because bees are not in equilibrium, but quickly accumulate pollen, the speed at which the selfing rate approaches one, depends more strongly on the pollen that adheres to the bee in each flower (k 2 k 3 B) than on k 4. If we consider the values for B and k 2 as correct and note that k 1 and k 4 have little effect, then increasing A and decreasing k 3 simultaneously has most effect on the fit. For A = 6000 and k 3 = 0 25 selfing is reduced to 79% in the tenth flower, but the model still overestimates the maximum selfing rate estimated with RAPDs. Selfing when bees visit open-pollinated plants in the field Figure 5a shows the predictions of the model, if bumble-bees visit a sequence of flowers which differ in the number of pollen grains available and receptiveness of the stigma, i.e. a typical E. vulgare plant in the field, and also the data on selfing in the field obtained PREDICTIONS AND SENSITIVITY OF THE MODEL Selfing when bees visit a sequence of virgin flowers Figure 4 shows the predictions of the model if bumblebees visit a sequence of virgin flowers. We started off with the field value for pollen per virgin flower (B = 55000) and the other parameters as determined under controlled conditions in the vault for B. terrestris ( standard parameters ). The maximum percentage selfing obtained with RAPDs is lower than predicted by the model with the standard parameters (Fig. 4). The value of parameter k 1 is very small and changing it has no effect on the predicted selfing rate. If less pollen adheres to the bee s body, this does have an effect on selfing. The amount of pollen adhering to the bee comes as one parameter, k 2 k 3 B. As the values k 2 and B are best estimated, we varied k 3, but, of course, reducing k 3 by 50% had the same effect as reducing k 2 or B by 50%. If k 3 is reduced from 0 5 to 0 25 the fit of the model improves (Fig. 4). With k 3 = 0 15 it improves further but the predicted selfing is still too high. Fig. 5. (a) Relationship between the percentage selfing predicted with the model and the number of flowers visited per approach. Parameters were estimated by Rademaker et al. (1997) for B. terrestris under controlled conditions: A = 4448, k 1 = , k 2 = 0 16, k 3 = 0 5, k 4 = 0 061, B = variable as in Table 1. The solid line gives results with these parameters and the identical results if B = , which is the average amount of pollen encountered in the flowers visited by the bee. The dotted line gives results with reduced k 3 (k 3 = 0 25) and the broken line with k 3 = For further explanation see text. The maximum percentage selfing obtained with RAPDs from the field population is plotted in the figure (solid dots). (b) Effect of A (A= 4448 solid line, A = 6000 broken line, A = 8000 dotted line), which is the number of pollen grains on the bee at arrival at the plant, on the predicted percentage selfing for plants with flowers with on average B = pollen grains.

8 835 Selfing in Echium with RAPDs. To obtain the data depicted in Fig. 5a the average selfing rate of all flowers visited at different positions in a sequence is plotted against the number of flower visits per approach. Again the percentage selfing predicted by the model was high compared to the data on selfing obtained with RAPDs. Simplifying the model by using the average number of grains present in the flowers visited by the bee (B = 13400) produced results very similar to the model in which pollen per flower differed between stages (solid line) (Fig. 5a). k 1 is again so small that it has no effect on selfing. Reducing k 4 results in smaller selfing rates but, with the standard values, the effect is still small. Reducing k 4 with 50% to 0 03 lowers the plant selfing from 50% to 48% when 10 flowers are visited per approach. Lowering k 3 reduces selfing rates again, improving the fit with the data (Fig. 5a). With k 3 = 0 25 bees accumulate pollen, arriving with 4448 pollen grains and departing with 7188 pollen grains after 10 flowers visited. With k 3 = 0 15 bees are close to equilibrium, they leave the plant with 4653 pollen grains. As we have seen before that bees accumulate pollen on field plants (Fig. 3), this value of k 3 is clearly too low. Increasing A also reduces selfing. If we increase A from 4448 to 8000 the predicted selfing is still higher than observed (Fig. 5b). With A = 8000 at arrival, bees still accumulate pollen and after 10 flowers they carry pollen grains. Simultaneously adjusting k 3 and A has most effects on the fit. With k 3 = 0 25 and A = 6000, the bees are accumulating pollen, carrying 7207 pollen grains if they leave after the tenth flower. Selfing on plants on which 10 flowers are visited per approach is then down to 30%, close to the observed maximum selfing estimates with RAPDs but still an overestimate. The margins of the parameters A and k 3 are quite small. Higher values of A are unrealistic when comparing the data on captured bumble-bees in Table 2. If we choose a lower value of k 3, bees in the model do not accumulate pollen. Discussion WHY IS THE PREDICTED SELFING TOO HIGH? We could think of several factors influencing our results. All these factors make the difference between predicted and observed maximum selfing rates even greater than we found. These factors are listed below. First, the model assumed complete mixing of pollen on the bee s body. If layering plays a part, outcross pollen will be covered by self pollen after a flower visit, which will increase the predicted level of selfing. Second, we assumed that on a plant with 300 open flowers all bumble-bees visit exactly 10 flowers in a sequence. If the first bee visits, for instance, only five flowers and the second one 15 flowers, the average level of selfing brought about by the two bees will be higher than when two bees each visit 10 flowers in succession. Therefore variation in the number of flowers visited will increase the predicted level of selfing. Third, as we noted before our estimates on selfing are maximum estimates of the selfing rate. The problem with RAPDs is that some of the offspring with no extra bands, that we classified as selfed, may in fact miss these bands by chance and are the result of outcrossing. Fourth, the equation (Klinkhamer & de Jong 1990) used to calculate the number of flowers visited per approach from the number of open flowers was a minimum estimate of the number of flowers visited per approach. In a population with isolated plants bumble-bees make longer visitation sequences (Klinkhamer & de Jong 1990) and the predicted selfing will even be higher. All these factors make the difference between predictions and observations only larger and not smaller! Post-pollination events like differential pollen tube growth and selective abortion might explain why the model overestimates the observed percentage selfing. Melser et al. (1997) have shown that the impact of selective seed abortion seems to be small for the whole population as for E. vulgare no difference was found in seed set of selfed and outcrossed pollinations, both in a single and mixed donor experiment in a growth room. However, three out of 10 genotypes were found to be selective with respect to outcross vs self-pollination, producing more seeds with outcross pollen (Melser et al. 1997). We cannot rule out the possibility that in the field selective abortion could play a part. In the growth room pollination was less abundant compared to the field and there is less light. Also, with the six plants for which we determined the maximum percentage selfing, we may have picked some genotypes that select against selfing. In Melser et al. s (1997) experiment the number of seeds per flower in the three selective genotypes was maximally a factor 0 5 lower with self-pollination than with cross-pollination. This suggests that in the field the observed selfing could be 50% lower than the fraction of self-pollen deposited on the stigma. Despite the fact that our exponential decay model overestimated the percentage selfing in the field it seems to be a suitable model for predicting pollen dynamics. First, the model is consistent with the accumulation of pollen grains on the bee s body in the field (with the adjusted parameters k 3 and A). Second, the predictions of our exponential decay model are comparable to the data on dye-transfer (Rademaker & de Jong 1998). To measure pollen transfer we marked a fixed number of flowers (anthers with pollen) with dye on a small, medium and large plant (number of open flowers). After a fixed period of time stigmas were collected from all plants in the population, including the marked plants, and the number of dye particles was counted. The data showed that on average 33% of the dye particles were retrieved on the stigmas within the plant and 67% were retrieved on

9 836 M. C. J. Rademaker et al. stigmas of flowers on other plants in the population, which corresponds, under some assumptions (de Jong et al. 1993), to 33% self-pollination. This suggests again that post-pollination events could be responsible for the difference between model predictions and the observed selfing rates. DOES FLOWER OPENING OVER THE DAY REDUCE GEITONOGAMY IN ECHIUM? We showed that increasing pollen adherence to the bee (k 2 k 3 B) affects selfing. In this way one would expect that opening flowers through the day, so that few pollen are available in most flowers, would reduce selfing compared to a situation in which all flowers open simultaneously in the morning. However, one should realize that in the model we changed one parameter and kept others the same. Many authors assume equilibrium ( saturation ) in the exponential decay model (Crawford 1984; Robertson 1992; Barrett et al. 1994). Under this assumption the parameters are not independent of each other. If a plant puts less of its pollen on the bee, the bee arrives with a lower amount of pollen grains (A) at the next plant in the population. Thus A changes also with a change in any of the parameters according to equation 1. This leads to the paradoxical result that selfing in the population is independent of all parameters, except k 4 and the number of flowers visited after an approach (equation 2). In that case the selfing rates in an E. vulgare population in which plants have only virgin flowers and in a population with plants with few pollen grains per flower, or even with a variable number of pollen grains per flower, are all the same. To conclude whether pollen presentation affects geitonogamy, we need to know if pollen exported on the bee is proportional to pollen presented (as in our model) or that non-linearities exist as some authors have suggested (Thomson & Thomson 1992). In the first case presenting flowers simultaneously do not increase geitonogamy. If E. vulgare plants were to open all flowers in the morning, then the quality of flowers (the number of pollen grains present) would decrease through the day. If the quality of the flowers is high in the morning, bees may visit more flowers in a sequence, which would affect geitonogamy. For E. vulgare we observed that bumble-bees visited only a small fraction (on average 5%, range between 2% and 20%) of the open flowers on the field plants. In a field experiment with an artificial plant we observed that bees preferred unvisited (virgin) flowers over visited flowers (Rademaker & Taal 1998). Moreover, on an artificial plant with only virgin (unvisited) flowers twice as many flowers were visited in a sequence, as compared to a plant with visited flowers from the field in stage 1 5. Bees stay longer on the plant if they encounter fresh flowers. Pappers et al. (in press) also found that bees had a smaller chance of leaving an E. vulgare plant after they had visited a flower with a high nectar content. As a result the presence of different flower stages simultaneously present on a plant, reduces the number of flowers visited in a sequence, which reduces selfing. If E. vulgare were to open all flowers in the morning, bees would be expected to visit more of these fresh flowers per approach, resulting in more geitonogamy compared to the actual situation in which flowers open through the day. Opening flowers throughout the day is therefore a strategy to reduce geitonogamous selfing. Acknowledgements We thank Saskia van Bodegom and Pieter Pelser for help with collecting data, Judith Batenburg and Johan van Nes for collecting data on pollen loads and Peter Klinkhamer for helpful comments on the manuscript. 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