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Reproductive Biology |
2Laboratory of Plant Breeding, Graduate School of Life and Environmental Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8572, Japan; 3Genome Analysis Laboratory, Department of Forest Genetics, Forestry and Forest Products Research Institute, Tsukuba 305-8687, Japan; 4Environmental Biology Division, National Institute for Environmental Studies, Tsukuba 305-0053, Japan; 5Laboratory of Conservation Ecology, Department of Ecosystem Studies, Graduate School of Agricultural and Life Sciences, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 311-8657, Japan
Received for publication June 29, 2005. Accepted for publication October 21, 2005.
ABSTRACT
To evaluate the effects of flowering phenology on pollen flow distance and spatial genetic structure in a population of a bumblebee-pollinated herb, Primula sieboldii, we investigated the flowering phenology of 1712 flowers of 97 genets in a population in Nagano Prefecture, Japan, and constructed a mating model based on the observed mating pattern, which was revealed by paternity analysis using 11 microsatellite markers. The effects of flowering phenology were inferred by comparing estimated pollen flow distance and the level of heterozygosity in the next generation between two scenarios. In the first scenario, both the intergenet distance and flowering phenology influenced mating opportunity, while in the second scenario only intergenet distance influenced mating opportunity. Although the frequency distribution of pollen flow distance at the population level did not differ significantly between the two scenarios, the mean pollen flow distance of several flowers increased by more than 10 m as a result of variation in flowering phenology. Furthermore, accounting for flowering phenology predicted change in heterozygosity in the next generation from –0.04 to 0.07. The results showed that flowering phenology can affect pollen flow distance and spatial genetic structure.
Key Words: bumblebee • flowering time • heterostyly • mating model • microsatellite • Nagano Prefecture • paternity analysis • Primulaceae
Knowledge of effective pollen flow distance has great importance in evolutionary and conservation genetics, because pollen flow distance can strongly affect spatial genetic structure and hence the spatial scale of local adaptation and the total level of genetic diversity in a population (Loveless and Hamrick, 1984
). Many theoretical and simulation studies have shown that homozygous patches develop rapidly due to inbreeding and genetic drift when both seed and pollen flow are spatially restricted within a population (Wright, 1943
; Turner et al., 1982
; Sokal and Wartenberg, 1983
; Ohsawa et al., 1993
). However, most of these studies assumed that there is no variation in flowering phenology (i.e., flowering time and the number of flowers) among plants within a population. In reality, large variations in flowering phenology are often observed among plants within a population (Pors and Werner, 1989
; Dieringer, 1991
; Washitani et al., 1991
; Okayama et al., 2003
). These variations in flowering phenology may induce spatial and temporal variation in flower density and affect the degree of spatial restriction of pollen flow; researchers have shown that flower density can strongly affect pollen flow distance (Levin and Kerster, 1969
). For example, asynchronous flowering of neighboring plants may result in a longer distance of pollen flow between plants. Indeed, White and Boshier (2000)
reported a lower frequency of near-neighbor pollen flow due to asynchronous flowering of neighboring trees in a population of insect-pollinated American mahogany (Swietenia humilis Zucc.). Likewise, mass (synchronous) flowering of neighboring plants may increase the proportion of pollen flow between neighbors and hence may shorten the mean pollen flow distance.
The effect of flowering phenology on pollen flow distance may have significant consequences for spatial genetic structure (Schmitt, 1983
; Loveless and Hamrick, 1984
). Schmitt (1983)
predicted that long-distance pollinator movements early or late in the flowering season could have a significant impact on the spatial genetic structure of the annual herb Linanthus bicolor Greene, because long-distance pollen flow is likely to lead to fertilization between plants that are more distantly related. Therefore, consideration of flowering phenology is important for a proper understanding of the genetic processes that generate spatial genetic structure. However, no studies have quantitatively evaluated the effect of flowering phenology on pollen flow distance and on spatial genetic structure.
To accomplish this, it is necessary to distinguish the effect of flowering phenology from the effects of other factors. However, because the actual mating pattern is affected by various factors, we cannot infer the effect of flowering phenology solely from the observed mating pattern. Constructing a mating model and a simulation approach are essential for quantitative evaluation of the effect of flowering phenology on pollen flow distance and on spatial genetic structure.
The purpose of this study was to evaluate the effect of flowering phenology on pollen flow distance and the level of inbreeding in the next generation of a population of Primula sieboldii E. Morren. Primula sieboldii is a spring-flowering clonal herb that grows in moist habitats throughout Japan and shows considerable variation in flowering phenology among genets within a population. To evaluate the effect of flowering phenology, we examined the spatial genetic structure within a population of P. sieboldii to understand the relationship between pollen flow distance and the inbreeding level in the next generation. Effective pollen flow (hereafter pollen flow) was revealed by means of paternity analysis using microsatellite markers. We then constructed a mating model that explains the observed mating pattern by intergenet distance and flowering phenology. Finally, the mating opportunities of flowers were estimated based on the mating model under two scenarios. In the first scenario, there is variation in flowering phenology among genets, and mating opportunity was determined by both intergenet distance and flowering phenology. In the second scenario, we assumed that flowering phenology does not vary, and as a result, mating opportunity was determined only by intergenet distance. The effects of flowering phenology were inferred by comparing the estimated pollen flow distance and level of heterozygosity in the next generation between the two scenarios.
MATERIALS AND METHODS
Plant species, study site
Primula sieboldii is a diploid clonal herb that is listed as vulnerable in the Japanese Red Data Book (Environment Agency of Japan, 2000
). Each genet of the species is composed of various numbers of physiologically independent ramets, which are clonally propagated by short rhizomes. This species is heterostylous and has two distinct mating types: long- and short-styled morphs. As is typical of heterostylous species, the species requires insect pollinators, especially queen bumblebees, Bombus diversus tersatus Smith (Washitani et al., 1995
), for pollination between the different morphs. Leaf emergence and flowering occur in early spring, and the plants bear fruit in summer. Each flowering ramet typically has 1–13 flowers on a 15-cm-long flower stalk, and one fruit produces 120 seeds at the maximum. Seeds of the species are dispersed about 10.4 cm from the maternal plants (Ishihama et al., 2003
). Therefore close relatives tend to be distributed near each other, and changes in pollen flow distance are likely to lead to changes in the inbreeding level of the next generation.
This study was carried out in a 30 x 100 m study site in a regional population of P. sieboldii in the University Forest of the University of Tsukuba (lat. 35°57' N, long. 138°27' E, 1400 m elevation), which is located on the side of Mt. Yatsugatake in Nagano Prefecture, central Japan (Fig. 1). In this regional population, P. sieboldii grows on moist forest floors dominated by deciduous Quercus mongolica subsp. crispula (Blume) Menitsky. In spring 2002, we recorded the locations of all flowering ramets to ±1 cm with reference to a square grid mapped onto the study site. The location of a flowering genet was defined by averaging the coordinates of all flowering ramets of the genet (Fig. 1). Because genet density varied considerably in this population, we divided the population into two areas on the basis of genet density: a high-density area and a low-density area (Fig. 1).
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We chose 17 genets (nine long-styled and eight short-styled) as the mother genets for use in the paternity analysis of this population. These mother genets were chosen to cover the full range of locations within the study site (Fig. 1) and to capture the variation in flowering time observed among the genets in this population. For the mother genets, we recorded both the opening and the closing date of each flower; the closing date of each flower was defined as the date when its corolla fell off in response to a soft touch. The flowering period of each flower was defined as the time between its opening and closing dates. For genets other than the mother genets, we defined the flowering period of each flower as 14 d, which was the mean flowering period for all recorded flowers.
Seed collection and germination
From late July to August 2002, we collected 1–5 mature fruits from each mother genet (mean per mother genet was 2.94, total 47 fruits). For these fruits, the mean number of seeds per fruit was 45.28 (SE = 3.06). Because the seeds were too small to extract a sufficient amount of DNA for PCR reactions, we germinated 1295 randomly chosen seeds (about 30 seeds per fruit) as follows. After 1 mo of moist-chilling treatment at 5°C, the seeds were stimulated to germinate by treatment with 1 mM gibberellin (GA3 in soluble granule, Kyowa Co., Tokyo, Japan). The seeds germinated on moist filter paper in petri dishes under favorable germination conditions for the species, with alternating temperatures (12 and 24°C) and a 12-h photoperiod (Washitani and Kabaya, 1988
). The final percentage germination averaged 91.1 ± 18.1% (mean ± SD). The seedlings were planted on peat-moss horticultural plates (15 x 20 x 3 cm, Sakatanotane Co., Yokohama, Japan) and raised to a size sufficient for DNA extraction. In total, 432 seedlings (about 10 seedlings per fruit) were sampled for the paternity analysis.
DNA extraction and genotyping
Genomic DNA was extracted from frozen leaves using a modified CTAB method (Murray and Thompson, 1980
). Genotypes of the 97 flowering genets and the 432 seedlings were determined by eight pairs of microsatellite PCR primers: ga0212, ga0218, ga0235, ga0668, ga1277, Pri0126, Pri0141, and Pri0146. The PCR conditions for each primer followed the protocol described by Ueno et al. (2003)
. The PCR products were run on a 3100 Genetic Analyzer with GeneScan software (Applied Biosystems, Foster City, California, USA). The characteristics of each marker are shown in Table 1.
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by using the software SPAGeDi (Hardy and Vekemans, 2002
). We defined 11 logarithmic distance classes of 0.5 interval, from ln(d) 
0.0 to 4.5 < ln(d) 5.0. These logarithmic distance classes were used because relatedness coefficients are expected to be proportional to the logarithm intergenet distance from the model of isolation by distance in a two-dimensional space (Rousset, 1997
). The significance of the deviation from the null hypothesis (spatial randomness of the pairwise relatedness) was tested by a randomization test that permuted individual locations 1000 times using SPAGeDi (Hardy and Vekemans, 2002
). We compared the actual average pairwise relatedness with the 1000 values generated by permutation.
Paternity analysis
The total exclusion probability calculated from the exclusion probabilities of the eight microsatellite loci was 0.998 (Table 1). Paternity of the seedlings was assigned by the simple exclusion method with CERVUS 2.0 software (Marshall et al., 1998
). For seedlings that had two or more pollen donor candidates at the study site, as determined by the results of this simple exclusion method, we performed a second analysis of the genotypes of the seedlings, their mother genets, and their pollen candidates using three additional microsatellite markers: ga0653, ga0666, and PS-2 (Table 1) following previously published protocols (Isagi et al., 2001
; Ueno et al., 2003
).
In addition, proportion of immigrating pollen was estimated by the method of Devlin and Ellstrand (1990)
. Because we previously determined the genotypes of 372 genets around the study site with the same eight microsatellite loci as used in this study (see details in Kitamoto et al., 2005a
), the allelic frequencies in the background population were estimated from the genotypic data of the 372 genets.
Modeling of the mating process
To understand the mating process of P. sieboldii, we constructed a mating model by modifying the neighborhood model (Burczyk et al., 1996
; Burczyk and Prat, 1997
). In this model, four factors were assumed to influence the mating opportunity of each outcross male (k): the morph (short- or long-styled morph), the distance of the outcross male from the mother genets, the degree of overlap of the respective flowering periods, and the number of flowers produced by the male. Because preliminarily hand-pollination experiments in a greenhouse showed that pollen vigor and stigma receptivity lasted 14 d from anthesis (N. Kitamoto and R. Ohsawa, University of Tsukuba, unpublished data), pollen viability and pistil receptivity were assumed to be constant during the flowering period of each flower. As a result of model selections by Akaike's information criterion (AIC; Akaike, 1998
), which quantifies the relative goodness-of-fit of statistical models, the individual mating opportunity of an outcross male k with a female flower j (
jk) was estimated as:
jk became zero when the kth male was the same morph type as the jth flower because mjk = 0. The parameter 
determines how intergenet distance influences mating opportunity, and the parameter 
, which mainly compensates for the low frequency of long-distance pollen flow, was added to improve the fit of the model. The effect of numjk on jk was assumed to follow a gamma distribution, because this distribution best fit the observed mating pattern in preliminary model fittings (data not shown): 
and ß relate to the shape of the distribution and determine how flowering phenology affects mating opportunity.
The mating process parameters, , , , and ß were estimated by fitting the model to the observed mating pattern using maximum-likelihood methods (Rao, 1973
) combined with the quasi-Newton method (Kennedy and Gentle, 1980
). Because we analyzed about 10 seedlings per fruit, there is a high probability of correlated mating for a single genet, assuming independent parentage for each seed within a fruit is clearly incorrect. Therefore, to avoid correlated mating, in the model fitting only one mating event was considered for each male parent that had more than two seedlings within the same fruit.
Simulations: effect of flowering phenology on pollen flow distance
To clarify the effects of flowering phenology on pollen flow distance, we estimated the mating opportunities for all 1712 flowers in this population under two scenarios. In the first scenario, there is variation in flowering phenology among genets, and mating opportunity was determined by flowering phenology and intergenet distance (hereafter, the phenology–distance scenario). The mating opportunity under the phenology–distance scenario was estimated based on the aforementioned model with observed flowering data and actual spatial distribution. In the second scenario, we assumed an unrealistic situation in which there is no variation in flowering phenology among genets and, as a result, only the distance between the jth flower and the kth opposite-morph genet determines the mating opportunity (hereafter, the distance scenario). This scenario corresponds to the situation in which f(numjk, , ß) = 1 in the mating model. Therefore, the mating opportunity under the distance scenario was estimated by changing f(numjk, , ß) in the mating model to 1. The effect of flowering phenology was inferred by comparing the estimated pollen flow distance between the two scenarios.
To determine whether flowering phenology can affect pollen flow distance at the population level, we compared the frequency distribution of pollen flow distance between the phenology-distance scenario and the distance scenario using the Kolmogorov–Smirnov test. The frequency of pollen flow at distance class x was defined as:
0.0 to 4.5 < ln(d) 5.0 as well as the distance classes in the analysis of spatial genetic structure.
In addition, to understand the effect of flowering phenology on pollen flow distance at the flower level, we compared the mean pollen flow distance for the jth flower (µdj) between the two scenarios by a Mann–Whitney U test. The mean pollen flow distance for the jth flower was defined as
Simulations: effect of flowering phenology on the inbreeding level in the next generation
To determine whether flowering phenology could affect the inbreeding level in the next generation, we compared the mating opportunity with genets that were distributed within a spatial scale in which a significantly higher relatedness was observed between the two scenarios. We also compared the predicted heterozygosity of the next generation between the two scenarios using the Wilcoxon signed-rank test. The heterozygosity of the next generation for the jth flower at the lth locus (Hjl) was predicted as:
jk is the mating opportunity between flower j and male k, and Hjkl is the expected heterozygosity at the lth microsatellite locus when the jth flower mates with the kth male. The predicted heterozygosity in the next generation of the jth flower (Hj) was calculated by averaging Hjl over the eight microsatellite loci, and the predicted heterozygosity in the next generation of each genet (Hgenet) was calculated by averaging all the Hj values of the genet. RESULTS
Census for flowering phenology
Notable variation in flowering phenology was observed among the genets at the study site. The first date of flowering varied from 5 to 27 May among genets. The number of flowers of each genet also varied considerably (from 1 to 256). Almost half the genets (49%) had only one flowering ramet, but a few genets had more than 15. The flowering period for each genet also varied considerably (from 11 to 38 d). The first date of flowering for each genet was significantly negatively correlated with the length of the genet's flowering period (r = –0.57, P < 0.0001). There was no significant correlation between the number of flowers of a genet and the first date of flowering of the genet.
Spatial genetic structure within the population
The mean relatedness for the eight microsatellite loci indicated the presence of a significant genetic structure within 1 m of the focal genet (P < 0.05, Fig. 2). This significant genetic structure may indicate that genets within 1 m of the focal genet tend to be more closely related than randomly paired genets.
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Among the 341 seedlings with only one male parent within the study site, 36 (11%) and 2 (0.6%) seedlings resulted from self-fertilization and intramorph pollen flow, respectively. Most of the self-fertilization (31 of the 36 selfings) was observed within the mother genets in the low-density area, and the two examples of intramorph pollen flow were observed in the mother genets in the high-density area.
The frequency distributions for intermate distance differed significantly between the high- and low-density areas in which the mother genets were located (Kolmogorov–Smirnov test, P < 0.001, Fig. 3, top panel). The mean pollen flow distance was 5.24 m in the high-density area and 13.15 m in the low-density area (excluding self-fertilization). The maximum pollen flow distances observed in the high- and low-density areas were 46.23 and 47.81 m, respectively.
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= –0.283, = 0.005, = 2.015, ß = 1179.096, log10-likelihood = –109.52, AIC = 231.03, likelihood ratio test P < 0.0001) was fit well to the observed frequency distribution of pollen flow distance (Fig. 3, Kolmogorov–Smirnov test, P = 0.53). In this model, the mating opportunity of males decreased with increasing distance from the mother genets and reached a peak when numjk was 1196.
Simulations: effect of flowering phenology on pollen flow distance
The frequency distribution of pollen flow distance did not significantly differ between the phenology-distance scenario and the distance scenario (Kolmogorov–Smirnov test, P = 0.23). This result indicated that flowering phenology did not change the frequency distribution of pollen flow distance at the population level.
However, the mean pollen flow distance at the level of individual flowers (µdj) was altered by flowering phenology, especially in the low-density area. In the high-density area, the differences of the µdj between the two scenarios (= the µdj in the phenology–distance scenario – the µdj in the distance scenario) ranged from –1.59 to 4.59 m, while that in the low-density area ranged from –21.36 to 14.88 m. In the low-density area, the µdj of 77 flowers (4.5% of the total flowers at the study site) was increased by more than 5 m, and the µdj of 48 flowers (2.8% of total flowers at the study site) was decreased by more than 5 m under the phenology-distance scenario. In total, the µdj values of 662 flowers (38.7%) were significantly different between the two scenarios at a 5% level (Mann–Whitney U test). Most of these significantly different flowers were observed early or late in the flowering season in the low-density area. Although these effects of flowering phenology generated the variation in the µdj between flowers within a genet, the variances in the µdj among genets were not significantly different between the two scenarios (F test, F = 0.928, P = 0.721).
Figures 4–11 illustrates how flowering phenology affected the pollen flow distance. For an early-flowering flower (5 to 13 May) of a genet in the high-density area, asynchronous flowering of neighboring genets led to longer-distance pollen flow (Figs. 5, 9) than was predicted on the basis of the distance model (Figs. 4, 8). However, a flower of the same genet that bloomed later (20 to 31 May) mated with the nearest genet (Fig. 6) because the relative effect of intergenet distance became larger (Fig. 10). Furthermore, for a flower of a different genet in the high-density area that bloomed later (20 May to 1 June), mass (synchronous) flowering of neighboring genets increased pollen flow between neighbors and decreased the pollen flow distance (Figs. 7, 11).
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The variation in flowering phenology changed the predicted heterozygosity of the next generation of each genet from –0.04 to 0.07. The predicted heterozygosity in the next generation for each genet differed significantly between the two scenarios (Wilcoxon signed-rank test, z = –3.554, P < 0.001). Sixty of the 97 flowering genets showed higher heterozygosity in the next generation in the phenology–distance scenario than in the distance scenario, although the increase was slight (the mean predicted heterozygosity of the next generation over all genet means was 0.699 for the phenology– distance scenario and 0.691 for the distance scenario).
When the predicted heterozygosity in the next generation of each genet (Hgenet) and the mating opportunity with males within 1 m were compared between the two scenarios, significant negative correlation between the degree of increase in the Hgenet and the mating opportunity was found (r = –0.423, P < 0.01). This result indicated that the change of pollen flow distance induced by variation in flowering phenology could affect the level of inbreeding in the next generation.
DISCUSSION
Mating model
The predicted pollen flow distance based on the mating model was fit well to the observed pollen flow distance (Fig. 3). Because we did not include selfing in the mating model, we probably overestimated the predicted heterozygosity in the next generation. To include the selfing rate in future mating models for P. sieboldii, at least two factors should be considered: the total mating opportunity and the genetic variation in self-incompatibility. At our study site, selfing flowers tended to have a low total mating opportunity, which can be represented by the denominator of each flower in equation 1 (the mean and SD of the total mating opportunity for the selfing and the nonselfing flowers were 58.27 x 10–6 ± 85.64 x 10–6 and 291.13 x 10–6 ± 269.22 x 10–6, respectively). Therefore, it is likely that the selfing rate was affected by the total mating opportunity. Furthermore, a previous study based on hand-pollination experiments in a greenhouse suggested that there was genetic variation in self-incompatibility among genets within a natural population of P. sieboldii (M. Nagai et al., University of Tokyo, unpublished data). The effects of this genetic variation in self-incompatibility on the selfing rate should be clarified in a future study.
Moreover, variation in fecundity among genets was not considered in this model. Consequently, the predicted effect of flowering phenology on spatial genetic structure may be different from the actual effect. In particular, because seed production is often positively correlated with plant density (Antonovics and Levin, 1980
; Nishihiro et al., 2000
; Ishihama et al., 2003
; Watanabe et al., 2004
), seed set of genets in the low-density area may be lower than genets in the high-density area. To understand the effect of flowering phenology on spatial genetic structure, the effect of plant density on fecundity should be considered in the future model.
Effect of flowering phenology on pollen flow distance
Our study showed that the mean pollen flow distance for each flower (µdj) can be strongly affected by the number of flowers and the degree of overlap of their flowering period with that of opposite-morph neighbors (Figs. 4–11). However, observed variation in flowering phenology did not dramatically change the frequency distribution of pollen flow distance at the population level because flowering phenology both increased and decreased the pollen flow distance for each flower.
This study also indicated that the effect of flowering phenology on pollen flow distance depended on the genet density. In the low-density area, the mean pollen flow distance of many flowers in the phenology-distance scenario became longer than that predicted by the distance scenario. Because genets in the low-density area had few neighbors, the probability of flowering asynchronously with the neighbors was high. It is possible that the high probability of flowering asynchronously with the neighbors would increase the mating opportunity with distantly distributed genets and lead to longer-distance pollen flow. In contrast, the effect of flowering phenology on pollen flow distance in the high-density area was small because genets in the high-density area had many neighbors, and hence the probability of flowering asynchronously with all these neighbors was low. Because the number of flowers in the low-density area was small in this population, the mean pollen flow distance at the population level did not change dramatically.
Schmitt (1983)
predicted that long-distance pollen flow would occur early or late in the flowering season in a population of the annual herb L. bicolor because the pollinator's flight distance increased early or late in the flowering season. In contrast, the mean pollen flow distance for most flowers in the high-density area did not change for flowers that bloomed early or late in the flowering season in this population. These flowers had in common synchronously flowering neighbors within 3 m, indicating that the local density of flowering genets is more important in determining pollen flow distance than the density of flowering genets across the whole population.
Effect of flowering phenology on the inbreeding level and spatial genetic structure of the population
Because seed dispersal of P. sieboldii is spatially restricted (Ishihama et al., 2003
), close relatives tend to be distributed near each other. Indeed, significant spatial genetic structure was detected within 1 m at this study site (Fig. 2). Many theoretical and simulation studies have shown that homozygous patches develop rapidly because of inbreeding and genetic drift when both seed and pollen flow are spatially restricted within a population (Wright, 1943
; Turner et al., 1982
; Sokal and Wartenberg, 1983
; Ohsawa et al., 1993
). Ohsawa et al. (1993)
adopted the formula f = k · exp(–kd) to fit the data reported in the literatures for 11 insect-pollinated plant species and describe the degree of restriction of pollen flow. In this equation, f represents the probability of mating, d is the distance from the pollen source, and k is a constant. Ohsawa et al. (1993)
showed that the estimated value of k varied from 0.076 to 0.787 among plant species (mean = 0.408). By fitting this formula to our observed data, the value of k in our population of P. sieboldii was estimated to be 0.131. This value indicates that the degree of spatial restriction of pollen flow in this population of P. sieboldii was relatively low compared with the 11 plant species.
Ohsawa et al. (1993)
also showed that homozygous patches did not develop with k = 0.13 given a large population size (N = 10 000), synchronized flowering, uniform plant density, and no overlapping of generations. Accordingly, if there had been no variation in flowering phenology in the population of P. sieboldii, homozygous patches would not develop. In addition, our study revealed that the degree of spatial restriction of pollen flow was affected by flowering phenology (Figs. 4– 11). Therefore, it is likely that the inbreeding level in the next generation will vary among genets and even among flowers within a genet. Indeed, for genets near mass-flowering genets, the degree of spatial restriction on pollen flow increased (Figs. 7, 11), the mating opportunity with males within 1 m increased from 25% to 62%, and the predicted heterozygosity in the next generation decreased from 70% to 66%. On the other hand, for a genet that bloomed simultaneously with a male within 1 m for only 3 d, the mating opportunity with males within 1 m decreased from 30% to 1%, and the predicted heterozygosity in the next generation increased from 68% to 75%. These results indicated that the probability of development of homozygous patches varied among genets.
Conclusion
Our study showed that pollen flow distance and the inbreeding level in the next generation can be altered by flowering phenology. Although the frequency distribution for pollen flow distance at the population level did not change dramatically in this population of P. sieboldii when flowering phenology was accounted for, the mean pollen flow distance of several flowers increased by more than 10 m. Furthermore, the inclusion of flowering phenology in the scenario changed the predicted heterozygosity in the next generation of each genet from –0.04 to 0.07. These results suggest that consideration of flowering phenology is very important for a proper understanding of the genetic processes that generate spatial genetic structures.
FOOTNOTES
The authors thank Drs. K. Uchida and Y. Kuroda for their support during our fieldwork at the University Forest of University of Tsukuba. Financial support was provided by the Environmental Research and Technology Development Fund of the Ministry of the Environment, Government of Japan. 
6 Author for correspondence (e-mail: osawaryo{at}sakura.cc.tsukuba.ac.jp
)
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