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Recently there have been many calls to approach the question of pollen sufficiency of plant reproductive success from a community perspective (e.g. Ashman et al., 2004; Hegland & Totland, 2008; García-Camacho & Totland, 2009; Dauber et al., 2010), and an equal number emphasizing the contributions of both pollen quantity and quality to pollen limitation (PL) of seed production (e.g. Ashman et al., 2004; Aizen & Harder, 2007; Alonso et al., 2010). However, analyzing the severity of PL and the relative roles of components of PL by applying the traditional experimental hand-pollination approach to multiple species may be complicated for several reasons. First, manipulation of pollen loads via hand-pollination on a wide range of species requires knowledge of the floral biology (e.g. timing of pollen dehiscence and stigma receptivity, and pollen viability), as well as the effects of emasculation on each (see the third paragraph of the Introduction section). Secondly, such community studies must include even ‘difficult to pollinate flowers’ (e.g. very small, short-lived flowers and/or those with complex or ‘closed’ floral morphology). Therefore, achieving equivalent application of hand-pollination treatments across numerous varied species of a community may be impossible. As a consequence, species-specific results may ultimately be a function of the interaction between ease of manipulation and the species itself.
In addition to the practical issues addressed above, the standard supplemental hand-pollination approach requires many considerations to reliably assess the PL of seed production (see discussions in Young & Young, 1992; Ashman et al., 2004; Wesselingh, 2007), of which we will highlight two. First, it can suffer from the confounding effects of resource limitation and/or reallocation of resources among flowers to fill seeds after heavy hand-pollinations (Knight et al., 2006; Wesselingh, 2007). Secondly, it does not distinguish between the quantity and quality components of PL, which is required to understand the repercussions of PL, especially when comparing plants within communities (Aizen & Harder, 2007; Alonso et al., 2010). The quantity component is directly related to factors such as pollen availability, pollinator visitation rates and the number of ovules per carpel (Burd et al., 2009). The quality component involves differences in pollen viability, germination, and tube development which affect fertilization potential. These components of quality can have a genetic or environmental basis (e.g. Young & Stanton, 1990; Walsh & Charlesworth, 1992; Dafni & Firmage, 2000; Edlund et al., 2004; Mazer et al., 2010; Lankinen & Madjidian, 2011 and references therein). Quality-related differences at the pollen–stigma interface or among tubes within the style are not only expected between compatible and incompatible donors in self-incompatible species (see Busch et al., 2010 and references therein), or between self and cross pollen in species with mixed mating systems (e.g. Lankinen & Armbruster, 2007; Mazer et al., 2010; Lankinen & Madjidian, 2011), but may also arise among pollen grains from different individuals (e.g. Marshall et al., 2007; Lankinen & Madjidian, 2011), or even among pollen grains from a single donor (Lankinen et al., 2009).
One proposal to overcome some of these limitations has been to assess the relative successes of open- and outcross-pollinated flowers (i.e. not supplemental pollination), combining the quantification of the relationship between natural pollen receipt and seed output with data on seed set after hand-pollination with outcross pollen only (Aizen & Harder, 2007). While this approach may better distinguish the quality and quantity components of PL, it does not alleviate the difficulties associated with floral manipulation (emasculation, effective collection and application of pollen to stigmas) of many species in community studies. It also requires enumeration of seeds, and thus still confounds post-zygotic effects of quality with pre-zygotic ones, as well as potential resource reallocation among flowers during seed filling. Another proposal for assessing the quantity and quality of PL is to record seed production of emasculated and control open flowers (Vaughton & Ramsey, 2010). However, this can be misleading if emasculation directly affects pollinator behavior, particularly in plants where pollen is the main reward to pollinators, and/or indirectly impairs pollen tube growth and ovule maturation, and thus fruit set (see Hedhly et al., 2009). Here, we propose an alternate nonmanipulative model-fitting approach for assessing the relative importance of the quantity and quality of pollen receipt in determining the natural pollination success of the pre-zygotic stage.
Our proposal involves analysis of pollen grain–pollen tube dose–response curves of naturally open-pollinated flowers. Thus, it does not require any floral manipulation or subsequent monitoring of seed production. As a result, it overcomes the limitations mentioned above in attempting (but not necessarily achieving) equivalent application of experimental manipulations across diverse sets of flowering species, and the confounding effects of resource reallocation during seed maturation. Further, it also avoids the inherent risk of losing experimentally pollinated flowers after pollinations as a result of the hazards experienced by marked plants in open wild habitats; for example, herbivory (Cahill et al., 2001).
The operational definition of pollen limitation tested through customary experimental pollinations referred to above analyzes plant reproduction as an input (pollen arrival)–output (seed production) process (Ashman et al., 2004). Pollen tubes represent the underappreciated intermediate phase between pollen arrival and seed production that may better characterize the pollination phase of this two-stage process, without the confounding effects of the second phase (filling seeds after ovule fertilization) in which pollination success interacts with resource availability (Ashman et al., 2004; Wesselingh, 2007). The importance of pollen load size for pollen tube numbers has been extensively studied and pollen tubes have been recognized as a better proxy to estimate the reproductive success of flowers (Herrera, 2002 and references therein; Bernasconi et al., 2007). But the shape of the relationship between the number of conspecific pollen grains on the stigma and the number of pollen tubes in the style remains poorly understood in naturally pollinated plants (Aizen & Harder, 2007).
Our model proposes that a change in the relative importance of two factors – the quantity and quality of pollen receipt – underlies the shape of natural pollen grain–pollen tube dose–response curves, and that this can be deduced by use of breakpoint/piecewise regression analysis. We applied our method to two different study cases to demonstrate that piecewise regression is a robust model-fitting approach, which is at least as good as the global nonlinear functions previously applied to similar dose–response curves (e.g. Mitchell, 1997; Alonso, 2005; Aizen & Harder, 2007). The examples also illustrate how the parameters derived from this analysis can facilitate comparisons among morphs, populations, and/or species to discern whether and how they differ in the relative importance of pollen quantity or quality aspects of pollination success. Although not explored in detail here, we note that this approach can also be used to discern the effects of contextual features on pollen quality and quantity. For example, one can combine this analytical approach with experimental manipulations, such as differential pollinator exclosures, to assess the effects of certain floral visitors on pollen quality and quantity. Finally, we discuss some limitations in the application of the model and suggest further ways to relate the quantity and quality components of pollination success to the PL of plant reproduction and recruitment. The distinction between the quality of the pollen vectors and the overall quantity of floral visitors has been acknowledged (e.g. Herrera, 1987, 1988, 1989). However, the links between such quality and quantity components of pollination and plant reproduction are still understudied (but see e.g. Herrera, 2000; Gómez et al., 2007), and we suggest that this method can help to bridge this gap.
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The piecewise model-fitting approach provides an objective means to estimate the relative relevance of Qt and Ql during a plant reproductive event. In our study cases, piecewise regression provided a goodness of fit similar to the commonly used negative exponential nonlinear regression. However, it also has the distinct advantage of producing parameters that can be explicitly linked to underlying biological processes, and can be compared across multiple data sets in a straightforward fashion. In the following paragraphs we illustrate the utility of the proposed method for understanding how morphs, species, reproductive events, or environments can differ in the relative importance of the quantity and quality of pollen receipt as limiting factors of natural pollination success.
In the Lamiaceae example, the pollination success of R. officinalis was more limited than that of L. latifolia, and both quantitative and qualitative effects underlie this difference. Rosmarinus officinalis had a lower percentage of visited flowers, lower average pollen loads, and a lower frequency of visited flowers falling into region III where Qt < Ql (7.3% vs 49.7%; Fig. 4) than L. latifolia. Furthermore, the piecewise analysis indicated that the quality of pollen received by L. latifolia flowers was on average higher than in R. officinalis because their styles saturated more rapidly and with a higher number of tubes. This latter result in particular demonstrates the value of the piecewise approach, as previous analyses of pollen tubes alone (Herrera, 2004) did not reveal the pollination quality difference between the two species that was uncovered here.
The two sexual morphs of the gynodioecious D. laureola exhibited widely different patterns. Female flowers were quantitatively less successful than those of hermaphrodites, which conformed to expectations given that they are the less preferred morph by the main pollinator in the study area (Alonso, 2004). Specifically, females had ten times as many unvisited flowers, much lower pollen loads and a higher percentage of flowers falling into region I compared with hermaphrodites (Fig. 5). However, the initial slope of the pollen grains–tubes relationship was twice as steep in females as in hermaphrodites, indicating either a higher quality of pollen received or a stronger discrimination capacity of female styles. Females are expected to receive a higher quality of pollen than hermaphrodites because they receive only outcross pollen. Also, females may have more restrictive stigmas or more discriminating styles because their styles saturated at a lower number of pollen tubes. Experimental studies of pollen tube development are required to ascertain the mechanisms behind these patterns (see e.g. Lankinen & Madjidian, 2011).
Recommendations for use
Given the intrinsic variability among flowers in pollen grains and tubes, achieving convergence and narrow confidence intervals for parameters of the piecewise analysis requires large sample sizes, larger than in most studies that use the standard hand-pollination approach. From our intensively studied cases, we conclude that a sample size of c. 150–200 visited flowers can be used as a rough guide. Lack of convergence emerged as the most common problem with small or largely unbalanced data sets, as a result of reduced possibilities of collecting samples in all the regions of the pollen grains–tubes relationship. This problem may be overcome with larger sample sizes (e.g. n = 200–600), a judicious analysis of outliers, deletion of single data points for which pollen grains appeared underestimated (i.e. pollen tubes >> pollen grains), and/or intensive grid searches of the initial parameters.
One should acknowledge, however, that absence of convergence of the piecewise model may actually indicate a strong influence of quality or quantity effects on pollination success on a given data set. This can be evaluated by plotting all data on a common scale. Indeed, a balance between quantity and quality effects would be predicted mainly in species with mixed mating systems (Goodwillie et al., 2005). In these species, stigmas are expected to receive mixtures of self and outcross pollen from many genetically distinct conspecific individuals and thus the broadest variation in pollen tube performance (Mazer et al., 2010). Species with a strong propensity to autonomously self-pollinate may be the most problematic, because the amount of pollen received would not directly reflect the activity of pollinators. In extreme cases, for example, species with closed flowers, or prior self-pollination, it may not be possible to fit a curve to the relationship between pollen grains deposited on the stigma and pollen tubes in the style. One option in these species is to emasculate flowers before anthesis (if pollen is not the main reward for pollinators) and/or just before the assurance mechanism is triggered (in species with delayed autonomous selfing) (Fenster & Martén-Rodríguez, 2007) so that only pollinator-mediated pollen deposition is assessed.
Linkages of Qt and Ql with seed production
The relationship between components of pollination success and plant reproduction can be verified by relating pollen receipt to seed production (Mitchell, 1997; Kalla & Ashman, 2002; Aizen & Harder, 2007). The piecewise approach provides an explicit connection between these two stages of the process. As a first step, a low percentage of unvisited flowers suggests little influence of pollen quantity on limitation of seed production in species with a single ovule per flower. In addition, and perhaps more importantly, we can predict that, in species with multiple ovules per flower, flowers to the left of the breakpoint will have fewer seeds per fruit than those to the right of the breakpoint. We explored this prediction with an L. latifolia data set (from the same population but a different year) where styles and ripe fruits were collected from the same flowers. Based on pollen tubes (pollen loads were not scored) we divided the sample into two regions defined by the number of tubes at breakpoint (k = 15) as the BCa were very small and few flowers fell in the narrow region II (Fig. 4). As predicted, the percentage of ovules producing seeds was significantly lower in flowers from below than above the breakpoint (25.3% ± 2.3 vs 43.2% ± 4.1; F1,123 = 15.47, P < 0.0001). Furthermore, the relationship between the percentage of ovules leading to seeds and the number of tubes was highly significant below (F1,87 = 49.57, P < 0.0001, adjusted without intercept), but not above (F1,35 = 0.35, P = 0.55) the breakpoint. These results indicate a strong link between the quantity and quality limitation at the pre-zygotic and early post-zygotic phases of pollination success in L. latifolia. Such relationships are also likely to hold in other species (see also Kalla & Ashman, 2002).
Both pollination quantity and quality have consequences for seed production and potentially for population recruitment. The study of the two-stage relationship between pollen grains and pollen tubes and then between tubes and the quantity and quality of seeds under natural conditions will be logistically limited to species suitable for individual flower monitoring after style collection and environments with a low risk of predation on developing fruits. Piecewise regression provides a tractable quantitative method with which to characterize the extent to which the first step in the pollination process is achieved, and to predict the pollen load threshold at which the pollination process changes from being dominated by quantity effects to being dominated by quality effects. The method provides a direct means to objectively compare multiple species, populations or reproductive events. In particular, we foresee that, by simultaneously scoring pollen grains and tubes of wilted naturally pollinated flowers and analyzing their relationship with piecewise regression, we will be able to more rigorously assess the effects of pollination quantity and quality in plant reproduction from a community perspective. Such work is imperative if we are to better understand this important ecosystem service and the potential consequences that pollinator disruptions may impose (Kremen & Ricketts, 2000 and references therein).