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1.
被子植物的花回馈、雌雄蕊时空分离特征和花粉呈现式样等花部特征及传粉者效率会影响雄性适合度和有性繁殖过程。宁夏枸杞(Lycium barbarum)是中国宁夏、新疆、内蒙等干旱和半干旱地区分布的特有种。该研究对新疆喀什地区宁夏枸杞自然种群的花部综合征、花粉呈现式样、花回馈、传粉者行为与交配方式的关系进行观察及统计分析,以探讨其花粉逐步呈现的适应性及其在提高雌雄繁殖过程中的意义。结果表明:(1)宁夏枸杞的单花寿命为(4.07±0.15) d,而雄性持续时间(0.07±0.01 d)比雌性持续时间短(4±0.01 d);花寿命内雌蕊长度比雄蕊长,属柱头探出式异位类型;花粉呈现式样为不完全逐步呈现。(2)花寿命不同阶段花回馈间存在显著差异。(3)意大利蜜蜂(Apis mellifera)、熊蜂(Bombus sp.)、食蚜蝇(Syrphidae sp.)是宁夏枸杞在自然居群的主要访花者,其中熊蜂和食蚜蝇是主要传粉者,但传粉者效率低,属于高移出低沉积类型。(4)宁夏枸杞的花粉胚珠比(2 448.11±448.32)及授粉实验结果均表现出兼性异交特征;自发自交及人工自花授粉花的座果率及结籽率很低,属于自交不亲和类型;自然传粉花的座果率及结籽率比人工去雄异花低,存在其较高的花粉限制(40.71%)。研究发现,宁夏枸杞花部综合征表现出雌雄异位和花粉不完全逐步呈现式样,这是避免雌雄功能及雄蕊各花药间的干扰、减少花粉同步移出及保障其雄性适合度的有效途径,但自然居群的传粉者种类限制、传粉效率低以及自交不亲性是导致宁夏枸杞花粉限制及降低雌性繁殖成功的主要原因。  相似文献   

2.
在动植物的相互关系中,盗蜜行为被认为是一种不同于普通传粉者的非正常访花行为。动物之所以要采取这种特殊的觅食策略,有假说认为是由访花者的口器和植物的花部形态不匹配造成的,也有认为是盗蜜行为提高了觅食效率从而使盗蜜者受益。在盗蜜现象中,盗蜜者和宿主植物之间的关系是复杂的。盗蜜对宿主植物的影响尤其是对其繁殖适合度的影响归纳起来有正面、负面以及中性3类。与此同时,盗蜜者的种类, 性别及其掠食行为差异不仅与生境因素密切相关,而且会对宿主植物的繁殖成功产生直接或间接的影响。另外,盗蜜者的存在无疑对其它正常传粉者的访花行为也产生一定的影响,从而间接地影响宿主植物的繁殖成功, 而植物在花部形态上也出现了对盗蜜现象的适应性进化。作者认为, 盗蜜是短嘴蜂对长管型花最有效的一种掠食策略, 它不仅增加了盗蜜者对资源的利用能力, 而且由于盗蜜对宿主植物繁殖成功的不同的影响使其具有调节盗蜜者和宿主之间种群动态的作用, 两者的彼此适应是一种协同进化的结果。  相似文献   

3.
退化雄蕊是指没有花药或花药不可育的雄蕊,发现于被子植物32.5%的科以及54.4%的属中,它们在形态和生化组成上都与可育雄蕊有着显著区别。虽然丢失了产生可育花粉的能力、无法发挥雄性繁殖功能,某些退化雄蕊在进化过程中重新获得了一些有助于植物繁殖成功的新功能。本文将这些具有功能的退化雄蕊细分为8类:(1)信号型;(2)报酬型;(3)欺骗传粉型;(4)辅助传粉昆虫在花内活动;(5)辅助授粉;(6)协助花粉二次呈现;(7)保护其他花结构;(8)避免自交。退化雄蕊作为花结构的一部分,其功能集中于促进植物的繁殖成功,主要通过与传粉昆虫的相互作用来提高传粉效率。此外,某些植物的退化雄蕊也可能同时具有多种功能,并且其功能的强弱与传粉者的种类、行为、大小和频率相关。正确评估退化雄蕊对植物繁殖成功的影响,需要多学科手段来系统的研究,以便能更加深入的理解不同近缘关系的物种间退化雄蕊功能的差异,揭示退化雄蕊在被子植物系统进化中的意义。  相似文献   

4.
毛姜花原变种花寿命对两性适合度的影响   总被引:3,自引:1,他引:2       下载免费PDF全文
植物的花寿命被认为是由雌、雄适合度的增长和维持花开放的花费之间的平衡来决定的。姜花属(Hedychium)是姜科唯一一个从热带到高海拔地区分布的大属, 属内不同种类植物的花寿命差异很大。毛姜花原变种(H. villosum var. villosum)的花寿命为5 d, 显著长于其它同域分布的姜科植物。通过人工剪除毛姜花原变种的柱头来使花朵具雌性功能的时间缩短, 结果显示: 在不同的处理中, 结实率随花朵具雌性功能时间的延长而增加, 开花1 d后剪除柱头的结实率为1.85% ± 1.59%, 极显著低于对照的结实率20.96% ± 4.13%, 说明其较长的花寿命能显著地增加传粉的成功率和结实率, 长达5 d的花寿命有利于雌性适合度的提高。同时, 毛姜花原变种开花1 d后, 剩余的平均花粉数和总平均花粉数没有显著差异, 而开花后2、3和4 d后剩余的平均花粉数则极显著少于总平均花粉数, 说明随着花寿命的延长, 花粉输出量也显著增加, 其长达5 d的花寿命也有利于其雄性适合度的提高。较长的花寿命在毛姜花原变种拓展新的生境、向更高海拔地区的扩散中也许起着重要的作用。姜科植物有着极其多样性的传粉和繁育系统, 花寿命在姜科植物传粉和繁育系统的多样性形成及其进化中起着重要作用, 同时, 较长的花寿命有效地提高了雌性适合度和雄性适合度, 从而使姜科植物能脱离热带生境, 向更高海拔的地区扩散, 花寿命在姜科植物从热带地区到高海拔地区的分布过程中也起着重要作用。  相似文献   

5.
传粉者的选择作用是花表型性状进化的重要驱动力, 解析选择作用的强度是理解花进化的关键。通过表型操控实验和表型选择研究能够分析花性状与其适合度的关系, 探究花性状的表型选择作用。为揭示花性状变化对雌性适合度的影响, 本研究处理展毛翠雀(Delphinium kamaonense var. glabrescens)花萼片大小, 并进行表型选择分析。结果表明: 人为减小展毛翠雀花萼片显著降低了传粉者的访花频率, 但是并没有影响种子产量(种子数和结籽率), 说明展毛翠雀花萼片的大小不影响种子产量, 可能主要吸引传粉昆虫输出花粉。通过雌性适合度(种子数量)估计表型选择梯度, 发现花萼片大小(长和宽)没有受到显著的直接选择梯度。但是, 花距长受到显著的线性选差和选择梯度, 表明花距的延长能够增加种子产量。本研究表明展毛翠雀花性状受到选择的作用, 但萼片和花距有不同的功能, 分别影响传粉者访问频率和种子产量。  相似文献   

6.
为了解樟科植物雌雄异熟的繁育系统特点,对3种樟科植物阴香(Cinnamomum burmannii)、紫楠(Phoebe sheareri)和浙江楠(Phoebe chekiangensis)雌雄异熟花的开花动态进行了比较研究。结果表明,3种植物雌性功能期的开始时间、雌性功能期和雄性功能期的时间分配有差异。3种植物的主要传粉者均为中华蜜蜂,在雌性功能期和雄性功能期均有访花;在雌性功能期第四轮退化雄蕊蜜腺和雄性功能期第三轮花丝基部的蜜腺分泌花蜜,不同开花阶段的花蜜蜜量和含糖量没有显著差异;柱头可授性和花粉活力在雌性和雄性功能期均较高;雌性功能期和雄性功能期均有自然花粉落置;座果率均是异交补粉自然套袋,表明都存在一定的传粉限制。因此,樟科植物雌、雄性阶段时间分配的不同,可能与退化雄蕊蜜腺和第三轮雄蕊附属蜜腺的分泌节律有关。  相似文献   

7.
花寿命的进化生态学意义   总被引:3,自引:0,他引:3       下载免费PDF全文
花寿命 (Floral longevity) 是指一朵花保持开放并具有功能的持续时间, 它作为一种重要的繁殖策略影响着植物的繁殖, 在植物繁殖策略的进化生态学研究中具有非常重要的意义。近年来, 进化生态学家开始重视花寿命的研究, 在传粉与非传粉因素对花寿命的影响、花展示和繁殖成功与花寿命的关系等方面取得了长足的进展。生活史进化模型表明, 最优花寿命取决于开花成本和两性适合度实现速率之间的权衡。大量的实验研究支持此模型。实验研究表明:授粉可导致某些植物的花寿命显著缩短, 但是, 花粉移除对花寿命一般没有显著影响;部分植物的花具有最短花寿命, 这可能是一种保证植物雄性适合度的机制;温度和水分等非传粉因素的变化, 因改变开花成本而影响到花寿命;在花的群体水平上, 植物根据传粉状况和资源状况, 会调节花序上不同花的开放时间, 进而改变花展示的结构和功能;长的花寿命是保障植物繁殖成功的重要机制之一, 但可能要付出一定的适合度代价。该文概述了花寿命进化生态学的理论和实验研究进展, 最后指出:在理论研究上, 雌雄利益冲突为理解花寿命的进化提供了新的视角。在实验研究中, 需要重视植物通过优化花寿命而增强雄性适合度的研究思路。对花寿命的成本-收益分析, 需要考虑单花与花展示的功能关系。  相似文献   

8.
草乌传粉过程中的广告效应与回报物质研究   总被引:2,自引:0,他引:2  
虫媒传粉植物与其传粉者之间的相互作用被认为是被子植物花多样性的一个重要选择压力。这种相互作用体现在植物对传粉者的吸引以及传粉者行为对花粉的转运两个方面。本项研究通过去除不同的花部器官研究了草乌(Aconitum kusnezoffii)对其传粉者的吸引, 并结合传粉者的访问行为和草乌花的生物学特性探讨了传粉过程与交配系统的适应。红光熊蜂(Bombus ignites)是草乌的有效传粉者。去除花萼片显著降低了红光熊蜂的访问频率, 但去除特化成蜜腺叶的花瓣并没有显著改变红光熊蜂的访问频率, 这表明草乌吸引红光熊蜂的主要结构是由5枚萼片组成的花部外观形态, 而非花瓣。花蜜是草乌提供给红光熊蜂的回报物质, 糖浓度为39.23%, 组氨酸浓度为0.25 μg/μL。草乌花较大、单花花期长、雌雄异熟、花粉寿命长, 是一个自交亲和但需传粉者传粉完成繁殖过程的异交物种。草乌花序是无限花序, 当上部的花处于雄性阶段时, 下部的花正好处于雌性阶段。而红光熊蜂在草乌花序上的访问顺序通常自下而上, 带来异交花粉为下部的花进行异花授精, 同时又带走上部花的花粉, 这就很好地促进了草乌的异交。草乌雄蕊自外向内逐渐成熟, 是一种有效的限制传粉者单次访问浪费大量花粉的花粉装配策略, 能提高植物通过花粉散布获得的雄性适合度。  相似文献   

9.
一些研究显示盗蜜对自交植物的结实和结籽没有显著影响。然而, 对于既有传粉者为其传粉实现异交又能通过自交实现生殖保障的兼性自交植物来说, 盗蜜对其生殖的影响还知之甚少。由于兼性自交植物可以自交, 盗蜜对其总体结实可能不会有显著影响, 但可能会通过影响传粉者行为而影响传粉者介导的结实。为了验证这一假说, 本研究以兼性自交的一年生角蒿(Invarvillea sinensis var. sinensis)为研究材料, 通过野外调查和控制实验, 探讨了盗蜜对传粉者介导的结实(传粉者行为)和总体结实率的影响。结果表明: 角蒿的盗蜜者和主要传粉者相同, 均为密林熊蜂(Bombus patagiatus)。熊蜂盗蜜频率平均为20.24% (范围为0-51.43%)。盗蜜对角蒿总体结实率、每果结籽数和每果种子重量没有显著影响。然而, 被盗蜜花的柱头闭合比率显著高于未被盗蜜花, 说明盗蜜影响传粉者的访花行为和传粉者介导的结实率。另外, 被盗蜜花的高度显著高于未被盗蜜花, 说明盗蜜者倾向于从较大较高的花上盗蜜。这些结果为全面认识盗蜜对植物生殖的影响提供了新的信息。  相似文献   

10.
蒙古沙冬青花序内性分配的变化、传粉者运动与繁殖成功   总被引:1,自引:0,他引:1  
性分配理论主要研究繁殖资源在雌雄功能间的最优分配,从雌雄功能的角度考虑其个体适合度.对花序内不同部位花的雌性与雄性资源分配变化的研究,对于我们理解植物采取哪种繁殖对策保障繁殖成功具有重要意义.本文对生长在中国科学院吐鲁番沙漠植物园内的蒙古沙冬青(Ammopiptanthus mongolicus)连续开花花序内不同部位...  相似文献   

11.
Nectar guides, contrasting patterns on flowers that supposedly direct pollinators towards a concealed nectar reward, are taxonomically widespread. However, there have been few studies of their functional significance and effects on plant fitness. Most previous studies focused on pollinator behaviour and used artificial flowers in laboratory settings. We experimentally investigated the role of putative nectar guides in a natural system: the South African iris Lapeirousia oreogena, whose flowers have a clearly visible pattern of six white arrow-markings pointing towards the narrow entrance of the long corolla tube, and its sole pollinator, a long-proboscid nemestrinid fly. We painted over none, some or all of the white arrow-markings with ink that matched the colour of the corolla background. Although arrow-marking removal had little effect on the approaches by flies to flowers from a distance, it dramatically reduced the likelihood of proboscis insertion. Export of pollen dye analogue (an estimate of male fitness) was reduced to almost zero in flowers from which all nectar guides had been removed, and fruit set (a measure of female fitness) was also significantly reduced. Our results confirm that the markings on L. oreogena flowers serve as nectar guides and suggest that they are under strong selective maintenance through both male and female fitness components in this pollination system.  相似文献   

12.
Pollinator‐mediated selection toward larger and abundant flowers is common in naturally pollen‐limited populations. However, floral antagonists may counteract this effect, maintaining smaller‐ and few‐flowered individuals within populations. We quantified pollinator and antagonist visit rates and determined a multiplicative female fitness component from attacked and non‐attacked flowers of the Brazilian hummingbird‐pollinated shrub Collaea cipoensis to determine the selective effects of pollinators and floral antagonists on flower size and number. We predicted that floral antagonists reduce the female fitness component and thus exert negative selective pressures on flower size and number, counteracting the positive effects of pollinators. Pollinators, mainly hummingbirds, comprised 4% of total floral visitation, whereas antagonist ants and bees accounted for 90% of visitation. Nectar‐robbers involved about 99% of floral antagonist visit rates, whereas florivores comprised the remaining 1%. Larger and abundant flowers increased both pollinator and antagonist visit rates and the female fitness component significantly decreased in flowers attacked by nectar‐robbers and florivores in comparison to non‐attacked flowers. We detected that pollinators favored larger‐ and many‐flowered individuals, whereas floral antagonists exerted negative selection on flower size and number. This study confirms that floral antagonists reduce female plant fitness and this pattern directly exerts negative selective pressures on flower size and number, counteracting pollinator‐mediated selection on floral attractiveness traits.  相似文献   

13.
Nectar is the most common floral reward that plants produce to attract pollinators. To determine the effect of nectar production on hawkmoth behavior, pollen movement, and reproductive success in Mirabilis multiflora, I manipulated nectar volumes and observed the subsequent foraging behavior of the hawkmoth Hyles lineata and the resulting pollen movement patterns. Individual hawkmoths visited significantly more flowers on plants with more nectar. The increase in flower visits significantly increased pollen deposition on stigmas and pollen removal from anthers when nectar volume was raised to twice the highest level found in nature. As hawkmoths visited flowers consecutively on a plant, the proportion of self pollen deposited on stigmas increased significantly and rapidly. Based on simulated hawkmoth visits, seed set was significantly reduced for flowers later in a visit sequence. A simple model combining these results predicts that the form of selection on nectar production varies depending on pollinator abundance. Using a multiple regression analysis a nearly significant (P < 0.08) effect of stabilizing selection was detected during a single season as predicted by the model for the prevailing hawkmoth abundance. Although increased nectar production may indirectly affect plant fitness by reducing resources available for other plant functions, the direct effect of high nectar production on pollinator behavior and self pollination may generally limit floral nectar production.  相似文献   

14.
The relationship between plant and pollinator is considered as the mutualism because plant benefits from the pollinator's transport of male gametes and pollinator benefits from plant's reward.Nectar robbers are frequently described as cheaters in the plant-pollinator mutualism,because it is assumed that they obtain a reward (nectar) without providing a service (pollination).Nectar robbers are birds,insects,or other flower visitors that remove nectar from flowers through a hole pierced or bitten in the corolla.Nectar robbing represents a complex relationship between animals and plants.Whether plants benefit from the relationship is always a controversial issue in earlier studies.This paper is a review of the recent literatures on nectar robbing and attempts to acquire an expanded understanding of the ecological and evolutionary roles that robbers play.Understanding the effects of nectar robbers on the plants that they visited and other flower visitors is especially important when one considers the high rates of robbing that a plant population may experience and the high percentage of all flower visitors that nectar robbers make to some species.There are two standpoints in explaining why animals forage on flowers and steal nectar in an illegitimate behavior.One is that animals can only get food in illegitimate way because of the mismatch of the morphologies of animals'mouthparts and floral structure.The other point of view argues that nectar robbing is a relatively more efficient,thus more energy-saving way for animals to get nectar from flowers.This is probably associated with the difficulty of changing attitudes that have been held for a long time.In the case of positive effect,the bodies of nectar robbers frequently touch the sex organs of plants during their visiting to the flowers and causing pollination.The neutral effect,nectar robbers' behavior may destruct the corollas of flowers,but they neither touch the sex organs nor destroy the ovules.Their behavior does not affect the fruit sets or seed sets of the hosting plant.Besides the direct impacts on plants,nectar robbers may also have an indirect effect on the behavior of the legitimate pollinators.Under some circumstances,the change in pollinator behavior could result in improved reproductive fitness of plants through increased pollen flow and out-crossing.  相似文献   

15.
Plant-pollinator interactions promote the evolution of floral traits that attract pollinators and facilitate efficient pollen transfer. The spatial separation of sex organs, herkogamy, is believed to limit sexual interference in hermaphrodite flowers. Reverse herkogamy (stigma recessed below anthers) and long, narrow corolla tubes are expected to promote efficiency in male function under hawkmoth pollination. We tested this prediction by measuring selection in six experimental arrays of Polemonium brandegeei, a species that displays continuous variation in herkogamy, resulting in a range of recessed to exserted stigmas. Under glasshouse conditions, we measured pollen removal and deposition, and estimated selection gradients (β) through female fitness (seeds set) and male fitness (siring success based on six polymorphic microsatellite loci). Siring success was higher in plants with more nectar sugar and narrow corolla tubes. However, selection through female function for reverse herkogamy was considerably stronger than was selection through male function. Hawkmoths were initially attracted to larger flowers, but overall preferred plants with reverse herkogamy. Greater pollen deposition and seed set also occurred in reverse herkogamous plants. Thus, reverse herkogamy may be maintained by hawkmoths through female rather than male function. Further, our results suggest that pollinator attraction may play a considerable role in enhancing female function.  相似文献   

16.
Ecological interactions between flowers and pollinators greatly affect the reproductive success. To facilitate these interactions, many flowers are known to display their attractive qualities, such as scent emission, flower rewards and floral vertical direction, in a rhythmic fashion. However, less is known about how plants regulate the relationship between these flower traits to adapt to pollinator visiting behavior and increase reproduction success. Here we investigated the adaptive significance of the flower bending from erect to downward in Trifolium repens. We observed the flowering dynamic characteristics (changes of vertical direction of florets, flowering number, pollen grain numbers, pollen viability and stigma receptivity over time after blossom) and the factors affecting the rate of flower bending in T. repens. Then we altered the vertical direction of florets in inflorescence of different types (upright and downward), and compared the pollinator behaviors and female reproductive success. Our results showed that florets opened sequentially in inflorescence, and then bend downwards slowly after flowering. The bending speed of florets was mainly influenced by pollination, and bending angle increased with the prolongation of flowering time, while the pollen germination rate, stigma receptivity and nectar secretion has a rhythm of “low-high-low” during the whole period with the time going. The visiting frequency of all the four species of pollinators on upward flowers was significantly higher than that of downward flowers, and they especially prefer to visit flowers with a bending angle of 30°–60°, when the flowers was exactly of the highest flower rewards (nectar secretion and number of pollen grains), stigma receptivity and pollen germination rate. The seed set ratio and fruit set ratio of upward flowers were significantly higher than downward flowers, but significantly lower than unmanipulated flowers. Our results indicated that the T. repens could increase female and male fitness by accurate pollination. The most suitable flower angle saves pollinators’ visiting energy and enables them to obtain the highest nectar rewards. This coordination between plants and pollinators maximizes the interests of them, which is a crucial factor in initiating specialized plant-pollinator relationships.  相似文献   

17.
The relationship between plant and pollinator is considered as the mutualism because plant benefits from the pollinator’s transport of male gametes and pollinator benefits from plant’s reward. Nectar robbers are frequently described as cheaters in the plant-pollinator mutualism, because it is assumed that they obtain a reward (nectar) without providing a service (pollination). Nectar robbers are birds, insects, or other flower visitors that remove nectar from flowers through a hole pierced or bitten in the corolla. Nectar robbing represents a complex relationship between animals and plants. Whether plants benefit from the relationship is always a controversial issue in earlier studies. This paper is a review of the recent literatures on nectar robbing and attempts to acquire an expanded understanding of the ecological and evolutionary roles that robbers play. Understanding the effects of nectar robbers on the plants that they visited and other flower visitors is especially important when one considers the high rates of robbing that a plant population may experience and the high percentage of all flower visitors that nectar robbers make to some species. There are two standpoints in explaining why animals forage on flowers and steal nectar in an illegitimate behavior. One is that animals can only get food in illegitimate way because of the mismatch of the morphologies of animals’ mouthparts and floral structure. The other point of view argues that nectar robbing is a relatively more efficient, thus more energy-saving way for animals to get nectar from flowers. This is probably associated with the difficulty of changing attitudes that have been held for a long time. In the case of positive effect, the bodies of nectar robbers frequently touch the sex organs of plants during their visiting to the flowers and causing pollination. The neutral effect, nectar robbers’ behavior may destruct the corollas of flowers, but they neither touch the sex organs nor destroy the ovules. Their behavior does not affect the fruit sets or seed sets of the hosting plant. Besides the direct impacts on plants, nectar robbers may also have an indirect effect on the behavior of the legitimate pollinators. Under some circumstances, the change in pollinator behavior could result in improved reproductive fitness of plants through increased pollen flow and out-crossing. __________ Translated from Acta phytoecologiaca Sinica, 2006, 30(4): 695–702 [译自: 植物生态学报]  相似文献   

18.
Nectar spurs have an important role in floral evolution and plant–pollinator coadaptation. The flowers of some species possess spurs curving into a circle. However, it is unclear whether spur circle diameter is under direct selection pressure from different sources, such as pollinators and nectar robbers. In this study, we quantified selection on some floral traits, such as spur circle diameter in Impatiens oxyanthera (Balsaminaceae) using phenotypic selection analysis and compared the relative importance of pollinators and nectar robbers as selective agents using mediation analysis. The study showed that pollinators caused significant selection on corolla length, spur curvature and spur circle diameter while nectar robbers only imposed strong selection on spur circle diameter. Pollinators favored flowers with large corolla, curly spurs and large spur circle while nectar robbers preferred flowers with small spur circle. More pollinator visits resulted in higher female reproductive success, while robbery reduced female fitness. Conflicting selection on spur traits from pollinators and nectar robbers was not found. Mediation analysis showed that selection on floral traits through nectar robbing was stronger than selection through pollination. The results suggested that pollinators and nectar robbers jointly mediated the directional selection for large spur circle, and nectar robbers caused stronger selection than pollinators on floral traits.  相似文献   

19.
Without changing their allocation to male function, plants can increase male fitness by increasing the number of visits they receive, attracting more efficient pollinators, or by changing their schedule of dispensing of pollen to floral visitors. We explore the strength of selection on the different components of pollen-dispensing schedules using sensitivity analysis. We find that changes in both the efficiency of pollinators and the expected mean number of visits produce large changes in male fitness. Our results suggest there may be strong selection on features that allow pollen to be available to multiple visitors and that selection is probably weak for mechanisms that would promote near optimal dispensing schedules.  相似文献   

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