Introduction

Many crops depend totally or partially on pollinators for reproduction, even those initially thought to be fully or mainly self-pollinating1,2,3. Notably, this pollinator dependence is often related to aspects of flower biology (e.g., extent of self-compatibility), which tend to be overlooked in crop pollination studies4. One such aspect is premature pollen development (PPD), also known as precocious pollen germination. This is a phenomenon where pollen grains germinate and pollen tubes grow inside the anther, instead of the process taking place later, and as usual, on the stigma after pollen dispersal5. Despite its potentially profound reproductive consequences in both wild and domesticated plant species6,7,8, PPD is a surprisingly under-explored phenomenon.

PPD has been documented in a range of phylogenetically diverse plant taxa6,8,9,10,11,12,13,14,15 as well as in agriculturally important species like soybean and chickpea6,15. PPD can be triggered by plant genetics5,7,16,17,18 and environmental factors, such as temperature, nutrients, and humidity19,20,21. Nevertheless, the reproductive consequences of this phenomenon have not been empirically assessed.

PPD is generally considered a maladaptive trait, as it leads to reduced viability and precipitates pollen senescence7. Furthermore, even if such pollen reaches the stigma, fertilization may fail due to a temporal mismatch between stigma receptivity and pollen maturity5 or because PPD disrupts the developmental arrest necessary for pollen protection and survival during dispersal22.

Beyond its direct effects on pollen grain (male gametophyte) performance, PPD may influence a plant (sporophyte) mating system, impacting whether seed production relies primarily on autonomous self-pollination, i.e., pollen deposition on the stigma of the same flower, or cross-pollination in a broad sense, i.e., pollen deposition on the stigma of a different flower from the same or another plant6,8. On one hand, PPD could promote autonomous self-pollination and reproductive assurance when dehisced anthers containing germinated pollen contact the stigma, increasing the relative representation of selfed pollen and the likelihood of siring by this pollen8. A higher representation of selfed pollen on the stigma could be driven by two indirect mechanisms: first, the presence of numerous pollen tubes from germinated grains can obstruct the stigma, reducing the attachment of cross pollen8. Second, PPD can disrupt the developmental arrest needed for pollen dispersal, reducing pollen export to other flowers22. Conversely, PPD could hinder autonomous self-pollination and promote pollen transfer between flowers. First, PPD and anther dehiscence failure appear to be induced by similar environmental stimuli23,24, suggesting a shared regulatory basis. If PPD and anther dehiscence failure are correlated, pollen cannot be deposited on the stigma of the same flower. Additionally, PPD can cause a mechanical obstruction, where a “tangle” of unsuccessful pollen tubes traps non-germinated pollen grains within the anther, preventing their release and dispersal6. Both of these mechanisms could leave the stigma free to receive pollen from other flowers, promoting cross-pollination6.

We chose soybean (Glycine max L., Fabaceae), a globally cultivated crop grown primarily for its seeds, as our study system to explore three competing hypotheses. First, that PPD prevents autonomous self-pollination by causing male sterility. Second, that PPD promotes autonomous self-pollination. And third, that PPD prevents autonomous self-pollination and promotes cross-pollination by leaving space on the stigma.

Although soybean has traditionally been described as a predominantly autonomously self-pollinating crop [e.g.,15], recent discoveries challenge this notion, revealing substantial variation in its reliance on pollinators for pollen transfer and cross-pollination2,3,25,26. Strikingly, PPD is also described for this species15 (Fig. 1), yet the link between PPD and pollinator dependence has not previously been explored. Soybean, therefore, becomes an ideal study system to explore the consequences of PPD on plant pollination, both from a conceptual and an applied perspective. Conceptually, this work could enhance our understanding of how shifts in the normal timing of anther and male gametophyte development ecologically impact plant mating and plant-pollinator interactions [e.g.,26]. In an agricultural context, assessing the reproductive impact of PPD in crops like soybean can be relevant to understanding some of the developmental bases of male sterility28 and variable autogamous seed production29.

Fig. 1
figure 1

Pollen grain incipient germination (a) and tube development (b) in soybean anthers, and pollen-tube growth in the style (c). Note the mixture of premature and non-premature pollen grains present inside the anther locule. Some of the pollen grains that did not initiate germination inside the anther are indicated with an arrow.

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In an experimental soybean field in Central Argentina, we explored the synergistic effects of premature pollen development (PPD) and pollinator abundance on the pollination dynamics and the pollinator dependence of this crop. Since a sizable proportion of pollinator visits were from diverse wild insects—primarily small bees and syrphid flies that better fit the soybean flower size (Fig. 2)—we separately assessed the effects of Apis mellifera and these wild pollinators on soybean pollination dynamics. We specifically investigated whether PPD promotes autonomous self-pollination or reduces it, and whether pollinators—both wild and managed (A. mellifera)—can compensate for any negative consequences of PPD. To make informed inferences about the real impact of PPD and pollinator abundance on soybean yield in our study, we were required to evaluate (1) the degree of pollen limitation experienced by soybean plants under field conditions, and (2) how much they depend on insect-mediated pollination for producing seeds. Hence, this study includes assessments of pollen limitation and pollinator dependence in the study cultivar under field conditions.

Fig. 2
figure 2

Insects comprising 98% of the pollinator assembly of soybean in our studied field. Visitation frequencies for each pollinator are indicated. Apis mellifera (a), Augochlora spp., Lasioglossum spp. (Halictidae) (b, c), and Toxomerus duplicatus (Syrphidae) (d). A soybean flower is also included for size comparison with pollinator body size. Scale bar = 1 cm.

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Results

Pollinator visitation frequency

A total of 50 flower visits were observed across the 15 sampled plots. Apis mellifera accounted for 64% of all visits. The remaining 36% of visits were distributed among small wild bees (20% Augochlora spp, and Lasioglossum spp.: Halictidae), syrphid flies (14%, Toxomerus duplicatus: Syrphidae) and a single visit by the carpenter bee Xylocopa splendidula: Apidae (2%)  (Supplementary Information S1). While more than one species of Augochlora and Lasioglossum coexisted in the surrounding area, species-level identification was not possible because the recorded pollinators were not trapped. The visitation frequency by domesticated honeybees ranged between 0 and 0.048 visits/ flower * 5 min (mean ± SD = 0.022 ± 0.015) and by wild insects, considered together, between 0 and 0.043 visits/ flower * 5 min (mean ± SD = 0.013 ± 0.010). There was no evidence of an association between visitation frequency by honeybees and wild insects across the 15 plots (r = 0.051, P = 0.858). This facilitates evaluation of the effects of each of these two classes of pollinators on the number of pollen tubes in the style. Other potential soybean pollinators were recorded in the experimental field and its surroundings, using insect traps. These included 16 different bee species in 10 genera spread across Apidae, Andrenidae, and Halictidae (Supplementary Information S1).

PPD, visitation frequency, and their effects on pollination

PPD and the number of pollen tubes in the style varied largely across the sampled flowers. The proportion of germinated pollen in the anther, considered as an indication of the extent of PPD (hereafter pPPD) ranged between 0 and 1 (mean ± SD = 0.623 ± 0.215), whereas the average number of pollen tubes in the style ranged between 0 and 47 (mean ± SD = 12.548 ± 8.554).

Backwards model selection30 resulted in a reduced model that included the effects of pPDD and visitation frequency by wild pollinators as explanatory factors of the variation in the number of pollen tubes in the style. This model also included an interaction between pPPD and visitation frequency by wild pollinators (z = 3.283, P < 0.005). The effect of visitation frequency by A. mellifera, as well as the interaction between pPPD and visitation frequency by A. mellifera were not significant and were, therefore, excluded during the backward model selection process. The effect of flower shape, a proxy of flower age and morphogenesis, was also excluded during backward model selection (Supplementary Information S2). The reduced model suggests that pPPD significantly reduced the number of pollen tubes in the style when wild pollinator visitation was low (Fig. 3). However, this negative effect of PPD reversed with increasing visitation frequency by wild pollinators (Fig. 3).

Fig. 3
figure 3

Effects of the proportion of prematurely developed pollen grains (i.e., pPPD) and wild pollinator visitation frequency on the number of pollen tubes in the style. The predicted values and standard errors correspond to the reduced model obtained using backward model selection. The fixed terms in this model included pPPD, wild pollinator visitation frequency, and their interaction on the number of pollen tubes in the style. (a) The effect of pPPD on the number of pollen tubes in the style for each of three terciles of wild pollinator visitation frequency is shown. Raw data and standard errors for the predicted number of pollen tubes in the style are included. (b) Isoline panel where the number of pollen tubes in the style (the dependent variable) as a function of pPPD and the visitation frequency of wild pollinators is represented by a color gradient.

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Pollen limitation and pollinator dependence

Average seed set (average proportion of ovules that developed into seeds in each plot) ranged between 0.820 and 0.938 (mean + SD = 0.882 ± 0.037). Seed set tended to increase with the number of pollen tubes in the style (z = 1.842, p = 0.065, N = 15) (Fig. 4a). Therefore, pollen receipt likely limits soybean yield in the study area.

Fig. 4
figure 4

Assays were conducted to determine pollen limitation and pollinator dependency for this study. Effect of the number of pollen tubes in the style on seed set across the 15 plots examined (a). Effect of the pollination treatment (enclosed plants versus plants exposed to pollinators) on seed set (b). The number of pollen tubes in the style and seed set were averaged for each plot. Raw data, along with the standard errors of the predicted values for seed set, are included in the plots.

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Seed set decreased after pollinator exclusion. On average, seed set was 8.26% higher in open-pollinated plots compared to excluded plots (Fig. 4b) (z = 2.822, P < 0.005). This indicates that soybean depends partially on insect pollination for seed production.

Discussion

In the context of understanding how flower biology impacts crop pollination and, by extension, yield4, our study uncovered a significant role of premature pollen development (PPD) within the anther locule of soybean. In particular, PPD appears to influence the soybean breeding system by decreasing autonomous self-pollination and, when highly prevalent, promoting cross-pollination by wild insects (Fig. 3).

At low wild pollinator visitation frequencies, where autonomous self-pollination is critical, our results indicate that PPD considerably reduced the number of pollen tubes growing in the style (Fig. 3). This reduction suggests that PPD hinders autonomous self-pollen deposition6. Our observation of mixed non-premature and premature pollen grains in anthers (Fig. 1a, b) supports the idea that premature pollen tubes obstruct anther pollen release, thus impeding non-germinated pollen attachment to the stigmatic surface6. However, the precise mechanism affecting autonomous self-pollination remains to be fully elucidated. We also found that high wild pollinator visitation frequencies seem to overcome the negative effect of PPD on self-pollination, especially when the incidence of PPD is remarkably high (Fig. 3). Nevertheless, the results concerning the role of wild pollinator visits on the soybean breeding system must be interpreted with caution. While we extensively sampled undehisced anthers to assess the effect of PPD on pollen tube growth, the time allocated for assessing pollinator visits—by both wild insects and A. mellifera—was limited compared to other studies [e.g.,31]. Indeed, other species of potential soybean pollinators were recorded in the sampled field and its surroundings outside the observation periods; consequently, we may be missing their contribution to soybean pollination (Supplementary Information S1).

Counterintuitively, we observed a reduced number of pollen tubes growing in the style under conditions of high wild pollinator visitation and low PPD incidence. This is surprising, as low PPD should be related to higher pollen viability and/or reduced clumping, factors expected to increase the potential for autonomous self-pollination, even with abundant pollinator activity. A key insight came from examining the pollen carried by field-collected honeybees and wild pollinators: the few samples analyzed contained only non-germinated soybean pollen grains (Supplementary Information S3). This suggests that non-germinated pollen may be more readily dislodged from the anther and adhere to pollinators before the dehisced anthers contact the stigma, thus diminishing autonomous self-pollination in these flowers. While previous research has focused on factors such as pollenkitt properties and pollen ornamentation (e.g., spines) that influence adhesion [e.g.,32,33], our findings highlight an additional, potentially crucial factor: the timing of pollen development relative to anther aperture. Interestingly, the presence of protruding structures on pollen grains, such as spines, enhances both the spreading area of pollenkitt (increasing their adhesive surface) and Van der Waals attraction forces. Both factors contribute to pollen adhesion and retention within the anther33. Pollen grains with protruding pollen tubes may experience a similar effect, diminishing their propensity to be dislodged from the anther. More extensive pollinator sampling and detailed anther and pollen grain examination are essential to elucidate such mechanisms.

Although we found putative effects of PPD and wild pollinator visitation frequencies on the number of pollen tubes in the soybean style, the absolute pollen deposition on soybean stigmas was limited, never exceeding 50 pollen grains (Fig. 3a)—a finding that aligns with other research conducted in Argentina34. This contrasts sharply with studies from other parts of the world, where pollen counts on the stigma can exceed 60035. Low pollen counts in both our study and in Huais et al.34 are likely a consequence of the reduced number of pollinator visits to Argentine soybean fields, which is probably due to natural habitat loss and heavy pesticide use3,36. This aligns with the relatively high pollen limitation reported for this crop in the region26.

Pollen limitation and pollinator dependency likely affected seed set in the studied cultivar and field (Fig. 4), indicating that PPD and wild pollinator visits can significantly impact soybean yield. The significant contribution of pollinators to soybean pollination and yield agrees with general findings in the literature2,3,31. These studies suggest that despite soybean’s perceived self-pollinating nature, its yield—which may be influenced by mechanisms such as PPD—partially depends on pollinator-mediated pollen transfer. However, the magnitude of this effect in our study appears to be on the lower end: the pollinator contribution observed here (an 8.26% increase in seed set) is lower than the 40% average reported for other cultivars in Argentina3. Additionally, our observed pollen limitation seems less severe when compared to studies where pollen supplementation increased seed set up to 50%26. Ultimately, since pollen limitation and pollinator dependence vary across cultivars and sites2,3, the economic impact of the mechanisms proposed here (PPD and wild pollinator visits) may be cultivar- and site-dependent. Indeed, differences in pollinator-mediated pollen deposition do not always translate into differences in crop yield, as shown by other studies34,37. Testing these mechanisms in other cultivars and geographic locations would prove valuable for assessing the real impact of PPD and wild pollinator visits on soybean yield. Additionally, incorporating data from other crop yield estimates, such as fruit set, would prove beneficial for a better assessment.

Shifting the focus from the ecological and potential economic consequences of PPD in soybean, we briefly address the putative evolutionary origin of this trait in the crop. Understanding this origin carries significant implications for managing the incidence of PPD through breeding and genetic engineering29. PPD is a common characteristic across numerous lineages of cleistogamous plants9,11,38,39,40,41,42,43, and given soybean’s innate tendency toward cleistogamy15,44,45, PPD in this crop may represent an ancestrally inherited trait with downstream effects on reproduction and yield. PPD in natural plant populations might not necessarily have a negative effect on autonomous self-pollination. Indeed, in plant species with only a few prematurely developing pollen grains, e.g., Woodfordia fruticosa (L.) Kurz (Lythraceae)14, PPD could even reinforce autonomous self-pollination. The high incidence of PPD in soybean, and its negative impact on autonomous self-pollination, may instead be an unintended consequence of modern breeding practices. Soybean cultivars are frequently selected for earlier flowering times to escape frost or enable multiple harvests44,46. Considering that reproductive transitions at various levels within the plant (from transition to flowering to anthesis) share regulatory mechanisms47, selection for early flowering may have inadvertently reinforced cleistogamy and PPD in soybean.

In conclusion, this study demonstrates that PPD can influence pollination and mating of soybean, a crop commonly perceived as fully autogamous. Our findings reveal that PPD can both hinder autonomous self-pollination and promote cross-pollination, particularly when wild pollinators are present. Whether PPD, synergistically with pollinator visits, significantly contributes to variation in soybean yield might be context-dependent, as pollen limitation and pollinator dependency vary geographically and across cultivars. The possibility that PPD is an ancestrally inherited trait and that the observed high prevalence of PPD in soybean may be an indirect consequence of breeding for early flowering, stresses the crop’s dependence on pollinators for pollen transfer. Ultimately, our work underscores the importance of not overlooking flower biology when understanding the relevance of plant-pollinator interactions even in crops perceived as pollinator-independent. It also highlights a crucial role of wild pollinators in soybean reproduction and emphasizes the importance of preserving pollinator habitats to ensure high yields and maintain productivity, even in seemingly autogamous crops.

Materials and methods

Study system

This study was conducted at an experimental field of the National Agricultural Technology Institute (INTA) located in Marcos Juárez, Córdoba Province, Argentina (32°42’48’’S; 62°03’40’’W). The sowing date for the experimental field was mid-November 2023 at a seeding density of 35 cm between rows. On January 3, 2024, the crop was at the onset of flowering.

The approximately 24-hectare experimental field was sowed with the soybean monogenetic cultivar DM 46E21 STS of maturity group IV (seeds provided by DONMARIO Semillas). The whole experimental field was divided into a grid of 1-hectare plots. Fifteen of these plots were strategically selected to create a gradient of pollinator identity and abundance, ranging from areas close to honeybee hives to those located near a remnant of natural grassland (Supplementary Information S4). The center of each of these 15 plots was marked as a sampling point, where data on pollinator visitation frequency, pollination, and seed set were collected. More specifically, this spatial design allowed us to assess how varying levels of pollinator availability influenced pollen germination on the stigma, ultimately affecting crop yield. We also established a pollinator exclusion treatment in five of the 15 plots that were undergoing open pollination by enclosing plants in a 1 m³ mesh enclosure in each plot. This treatment was later used to assess the degree of pollinator dependence.

Field sampling

Pollinator monitoring and flower sampling were conducted once a week on four consecutive weeks during flowering, between the beginning and end of January, and pod collection at the end of March. All 15 study plots were monitored for flower visitation by Apis mellifera and wild pollinators. Pollinator visit censuses were conducted on sunny days between 9 am and 5 pm. To ensure coverage of the entire daily period of insect activity, the census time for each plot varied between sampling days. On four separate sampling dates, we conducted three 5-minute censuses per plot, totaling one hour of census time per plot. During each census, we estimated the number of visits a flower received by observing a group of approximately 10 randomly selected flowers from different plants that were never reused. We conducted a total of 15 h of observations on pollinator visitation frequency.

On the same dates as the pollinator censuses, we collected at least 30 soybean flowers per plot from three different locations within a 20-meter radius of the plot’s center. These flowers were preserved in 70% ethanol in plastic vials. We collected a total of 477 open individual flowers, evenly spread across the four sampled weeks.

During the harvest on March 27 and 28, we haphazardly collected and counted seeds from a random sample of 100 pods from each of the 15 plots. Additionally, we counted seeds from 100 pods from each meshed enclosure across the five treated plots. In total, we examined 2,000 pods: 1,500 from plants in all 15 plots that were exposed to insect-mediated pollination, and 500 from the meshed plants in the five treated plots that were excluded from pollinators. The 1,500 pods from open-pollinated plants were later used in an analysis to assess the incidence of pollen limitation in the field. The 500 pods from the exclusion treatment, along with the 500 pods from the corresponding open-pollination treatment in these five plots, were used to assess the pollinator dependency of the studied cultivar.

Pistil and anther examination

In the laboratory, the 477 flowers collected in the field were stained using decolorized aniline blue48 and then dissected to separate the gynoecium from the remaining floral parts. The gynoecium was then placed on a slide, squashed with a coverslip, and observed at 200x on a Leica DMLB microscope equipped with a fluorescent light and the appropriate filter sets. We counted the number of pollen tubes protruding through the stigma and growing in the upper portion of the style as a measure of pollination success.

For calculating the proportion of premature pollen grains inside the anther, we used two to four undehisced anthers from at least 11 flowers per plot (a total of 186 out of 477 sampled flowers). We ensured that all examined anthers were undehisced to accurately classify pollen grains as non-premature or premature. This step was taken to avoid misclassifying pollen grains that may have started germinating on the stigma as premature. The undehisced anthers of each flower were placed on a slide, squashed with a coverslip, and observed under fluorescent light at 100x magnification. Between two and four photomicrographs were obtained using an Axiocam CCD monochromatic digital camera (one photograph per anther). Each photograph was taken to encompass the majority of the anther and the outline of the pollen grains remaining after squashing it. Pollen grains were classified as premature if they showed a protruding pollen tube, a small protrusion, or one or several stained knobs (Fig. 1a, b), and as non-premature if they showed no staining at all (Fig. 1a, b). The proportion of premature pollen grains (hereafter pPPD​) was calculated as the number of premature pollen grains divided by the total number of pollen grains (non-premature + premature). pPPD​ was obtained by analyzing images with ImageJ’s counting tools49 from an average of 113.753 pollen grains per flower.

Before flower dissection, the corolla and calyx of the 186 flowers were photographed with the Leica M420 magnifying glass, equipped with a Leica color camera. Based on these images, we measured the vertical lengths of the calyx and the corolla using ImageJ49 and calculated the ratio corolla length/calyx length. We used this ratio as a proxy for flower ontogeny (as the corolla extends beyond the calyx during development and post-anthesis) to account for potential effects of flower age and morphogenesis on PPD, stigma receptivity, and stigmatic pollen receipt.

Data analysis

Pearson correlation test between visitation frequencies by A. mellifera and wild pollinators

We used a Pearson’s correlation test to evaluate an eventual correlation between the visitation frequency of honeybees and wild insects across the 15 plots. Absence of a significant correlation facilitates the use of visitation frequencies of honeybees and wild insects as separate independent variables in our models, avoiding problems arising from collinearity30.

The effects of PPD and pollinator visitation on pollination

We investigated the effects of pollinator visitation frequency (separately for managed honeybees and wild pollinators), and their interactions with PPD on the number of pollen tubes in the style (our dependent variable) to explore how these factors affect pollination dynamics in soybean. We did so by using backward model selection30.

Backward model selection

Backward model selection is an iterative procedure for simplifying a statistical model30. This process begins with a full model containing all potential predictor variables and then systematically removing the least significant variable one at a time. The process continues until all remaining variables are statistically significant and their removal would substantially worsen the model’s fit to the data. This method helps to identify the most parsimonious model, which is the simplest model that best explains the data30 (from here on, we call it the “reduced” model).

For our backward model selection, the full model assessed the separate contribution of each pollinator group, A. mellifera and wild pollinators, to the number of pollen tubes in the style. As mentioned above, A. mellifera and an array of wild, small-sized pollinators co-existed at the study site (Fig. 2), and their visitation frequencies were not correlated (see Results). In addition to the main effects of pPPD and visitation by each of these two pollinator groups on the number of pollen tubes in the style, the model included two interaction terms: (1) pPPD × visitation frequency by A. mellifera, and (2) pPPD × visitation frequency by wild pollinators. Corolla length/calyx length was included as a covariable representing flower development. A z-score standardization was applied to all continuous variables in this model to achieve appropriate model convergence.

Our full model, and all subsequently simpler models, also included “plot” as a random factor to account for spatial variation in the number of pollen tubes growing in the style. An autoregressive AR1 structure, based on the week of sampling, was also incorporated within the random effects to account for temporal autocorrelation. Both additions improved model fit (Supplementary Information S5). Because we observed significant overdispersion (dispersion parameter = 4.7195, p < 0.0001), a generalized linear mixed model (GLMM) with a negative binomial distribution and a log link function was employed as our full model. Linear overdispersion was preferred over quadratic overdispersion, based on the AIC criterion (Supplementary Information S6). The full model and all subsequently simpler models were fitted using the glmmTMB function in R (library: glmmTMB;50.

Full model validation

Before conducting backward model selection, we performed a bootstrap analysis of the fixed effects of the full model to confirm the reliability of its parameters51. The confidence intervals of non-significant parameters consistently included zero, while those of significant parameters did not (Supplementary Information S7).

Fixed terms of the reduced model under the three PPD scenarios

Table 1 presents the fixed terms expected to be significant and retained in the final (reduced) model, including their predicted signs, under three alternative scenarios formulated in this study: the hypothesis that PPD prevents autonomous self-pollination due to male sterility; the hypothesis that PPD promotes autonomous self-pollination; and the hypothesis that PPD prevents autonomous self-pollination, thereby facilitating the receipt of crossed pollen on the stigma.

Table 1 The three scenarios (hypotheses) for the consequences of PPD on soybean reproduction, along with the fixed structure of the reduced model expected after conducting backward model selection. Significant fixed effects and their signs (in parentheses) are shown. The dependent variable, “number of pollen tubes in the style”, is represented by “x”.
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Estimates of pollen limitation and pollinator dependency

We used two separate models with the same dependent variable, average seed set per plot, to investigate two things: first, the extent to which soybean plants were pollen-limited (meaning seed production was limited by pollen deposition, not plant resources); and second, the extent to which the studied soybean cultivar depends on pollinator-mediated cross-pollination. Because the soybean cultivar used in this study had a fixed number of three ovules per ovary in all 477 flowers examined, we estimated seed set as the average number of seeds per plot divided by three. This response variable was continuous, bounded between 0 and 1, but not binary as in most binomial regressions; therefore, we used weights equal to the number of pods sampled in each plot (100 in each) in the two generalized linear models (GLM), with a binomial error distribution and a logit link function30. Both models were run using the glm function from the stats R library52. In the first model, we investigated the impact of the number pollen tubes in the style on soybean seed set in the 15 examined plots. The independent variable was the number pollen tubes in the style, averaged over all the pistils examined in each of the 15 plots. In the second model, we investigated the effect of pollination treatment (open pollination versus exclusion from pollinators) on seed set in the five sampling plots where these open pollination and pollinator exclusion treatments were conducted.