Compensatory yield responses drive high performance of soybeans treated with seed-applied Soyfx ®: an on-farm experimental study

Plant growth-promoting bacteria are a promising tool for enhancing crop productivity while reducing dependence on synthetic agricultural inputs. This study evaluated the effects of the microbial consortia bioproduct inoculant Agrovive Biologicals ® Soyfx ®, applied as either a seed treatment or foliar spray, on soybean plant density, pod development, seed production, seed mass, and the accuracy of automated seed counting. The field experiment was conducted during the 2018 growing season under standard agronomic management. Three treatments were compared: untreated control, foliar application at the V2 growth stage (2.34 L ha -1 in 93.5 L ha -1 water), and seed treatment (1.30 mL kg -1 seed). Yield components were assessed through fixed-area sampling, pod classification, seed counting (manual and automated), and seed-size determination. Data were analyzed using appropriate statistical tests following assessment of normality. Seed treatment significantly reduced plant density from 32.6 to 23.2 plantsm -2 (−29%; p < 0.001) but increased average pod production per plant from 26.2 to 41.3 pods (+63%; p < 0.001) compared with the control. The number of seeds >6.35 mm increased from 986.4 to 1693.2 m -2 (+70%; p < 0.001), while 100-seed weight increased from 18 to 21.8 g (+21%; p < 0.001). As a result, seed treatment produced the highest yield (3.55 t ha -1), representing a 31% increase over the control (2.7 t ha -1; p < 0.022) and a 45% increase over the foliar treatment (2.45 t ha -1; p < 0.004). Despite a significantly lower plant density, total pod and seed production per unit area were maintained, indicating compensatory growth responses. Foliar application produced intermediate responses and did not differ significantly from the control. Pod-type analysis showed that seed treatment increased the frequency of three-spot pods of one-seed. Automated seed counts underestimated seed numbers relative to manual counts (p < 0.001). These results indicate that pre-sowing seed application of Agrovive Biologicals ® Soyfx ® improves soybean yield components and seed quality, providing an effective low-input alternative to foliar application.

As global food demand increases (Hamza et al., 2024), it is necessary to find ways to increase crop yields while avoiding environmental impacts from the over-application of chemical phytosanitaries and fertilizers. Soybean (Glycine max L.) high yields require substantial nitrogen (N) inputs, but relying on synthetic N-fertilizer is costly and environmentally damaging because it accounts for nearly 50% of fossil-fuel consumption in agriculture (Rodríguez-Navarro et al., 2011). The efficiency of N uptake by soybeans depends on multiple factors, including plant genetics, rhizobial strains, quality of the symbiosis and environmental conditions (Zimmer et al., 2016). A cost-effective and sustainable source of N for soybean cultivation is biological nitrogen (N 2) fixation, carried out by symbiotic soil bacteria, particularly Bradyrhizobium (Guriqbal Singh and Shivakumar, 2010). These bacteria form root nodules that enable the plant to fix atmospheric N 2, providing a low-cost and sustainable alternative to industrial fertilizers. Biological nitrogen fixation not only reduces fertilizer dependence but also enhances soil fertility when soybeans are grown in rotation or as an intercrop (Hamza et al., 2024). Therefore, plant growth-promoting bacteria (PGPB) have recently emerged as a viable means of enhancing efficiency and sustainability in modern agricultural production (Hamza et al., 2024). The PGPB include free-living bacteria, bacteria with specific symbiotic relationships with plants, bacterial endophytes that can colonize some plant’s interior tissues, and cyanobacteria (Fanai et al., 2024). Their renewable nature and lower ecological footprint make them suitable for supporting the transition to sustainable production systems and for meeting global sustainability goals (Priya et al., 2023).

Plant growth-promoting bacteria enhance plant development either directly by improving resource acquisition or modulating plant hormone levels, or indirectly by reducing the detrimental effects of pathogenic organisms on plant growth and development, effectively functioning as biocontrol agents (Pérez-Montaño et al., 2025). The mechanisms through which PGPB enhance plant growth are nutrient solubilization, phytohormone production, reduction of plant stress via enzymes, and induction of plant resistance against pathogens (Glick, 2012; Poria et al., 2022). Providing mixed or reduced N forms, or relying on active N 2 fixation, greatly enhances N assimilation and seed N content, thereby improving overall biomass and productivity (Imsande, 1998). Hormonal dynamics also regulates seed filling in soybean, with large-seeded cultivars showing markedly higher abscisic acid and gibberellin levels associated with faster seed-filling rates (Liu et al., 2010). Crop productivity and seed quality are mainly influenced by varietal selection, seed inoculation with bacterial preparations, and use of growth regulators (Mazur et al., 2023). Particularly, it has been demonstrated that PGPB and a silicon–zinc nanocomposite enhance physiological performance, boost antioxidant activity, maintain nutrient balance, and improve yield components, thereby keeping crops more resistant to drought and salinity stress (Osman et al., 2021). Despite the large number of advantages of PGPB, only 0.1% of the created formulations were placed on the market in 2023, mainly due to the current agrochemical market climate and the registration procedures (Priya et al., 2023). Soybean yield productivity is determined by the number of pods per plant, the number of seeds per pod, and the seed weight and size. Especially, the number of seeds is the main determinant of final yield, being the number of pod formation –and retention– fundamental to assess yield potential (Vogel et al., 2021). Pod formation is the most yield-sensitive developmental stages in soybean (Vogel et al., 2021). Pod dehiscence or pod shattering occurs when drying pods accumulate internal tension and subsequently split open along their sutures and releasing the seeds which caused yield loss. Environmental stresses (e.g. elevated temperatures, elevated O 2, low humidity) sharply reduce productivity by limiting pod production and seed size (Burroughs et al., 2023; Hauser et al., 2025), and accelerates shattering (Zhang et al., 2018).

Therefore, this study aimed to evaluate the effect of the application of the microbial consortia bioproduct inoculant Agrovive Biologicals ® Soyfx ® on soybean seed as inoculant or foliar spray on plant density, pod formation, seed production, and final seed mass. The hypothesis was that the product application would enhance field yield by increasing the number of plants per acre, the number of pods per plant and the number and weight of seeds. The study also compares the automated and manual seed counting methods.

Experimental site, timeline, and agronomic management

The study was conducted during the 2018 growing season (from May to October) in Wheaton (Minnesota, USA; 45.84606 N 96.33759 W; Figure 1). The experimental field relied exclusively on natural rainfall, with no supplemental irrigation. Climatic conditions during the study period were moderate (Table 1).

Soybean seeds (Titan Pro, Variety 16L86; Clear Lake, Iowa, USA) were planted on May 12 th of 2018 at a variable seeding rate, with an average of 358,300 seeds ha -1. Standard agronomic management included a pre-emergent application of herbicide, Valor EZ (Valent U.S.A LLC, Headquartered in Walnut Creek, CA, USA) at 146 mL ha -1, followed by post-emergent herbicide applications of Liberty (BASF, Ludwigshafen, Germany) and Generic Dual (Syngenta, Basel, Switzerland) at 2.34 L ha -1 and 1.17 L ha -1, respectively.

Experimental treatments

The experiment included three treatments: an untreated control, a seed-applied treatment, and a foliar-applied treatment. The seed treatment was sown using MyYield seed previously treated with the microbial consortia bioproduct inoculant Agrovive Biologicals ® Soyfx ® (covered by U.S. Patent No. 11,980,183, Microbial Inoculant Compositions and Methods). According to the patent description, Soyfx ® is based on a consortium of microorganisms originally isolated from aquatic plant-associated environments and includes aquatic Pseudomonas spp. (including P. moraviensis and/or P. fluorescens) and Clostridium saccharobutylicum, together with additional taxa such as Delftia spp., Chryseobacterium spp., Sphingosinicella microcystinivorans, and Pseudomonas chlororaphis. The inoculant is produced through co-fermentation and is reported to contain approximately 3 × 10 8 CFU mL -1 before field application. The culture medium used during production contains iron and potassium nitrate as nutrient sources. The product was applied at 1.30 mL kg -1 of seed, with no additional binders added. The foliar application was done with the microbial consortia bioproduct inoculant Agrovive Biologicals ® Soyfx ® at the V2 (second trifoliate) growth stage, applied at a rate of 2.35 L ha -1 and tank-mixed with 37.9 L of water.

The control and seed-applied treatments were arranged in alternating planter rows across approximately 24.3 ha of the field, creating a spatially interspersed design intended to reduce the influence of field heterogeneity (Figure 1). The foliar treatment was established in a separate contiguous area (8.1 ha) to avoid spray drift and cross-contamination among treatments. This arrangement maintained treatment integrity while allowing comparisons under similar agronomic and environmental conditions.

Sampling and data collected

Each field was randomly sampled by manual harvest on October 23, 2018. Five sampling locations (replicates) were randomly selected and distributed across each treatment area to capture within-field variability, resulting in a total of 15 samples across the three treatments. At each location, all plants within an area of 0.41 m² were harvested, resulting in a total sampled area of 2.03 m² per treatment. The width and spacing between rows were calculated following the Shaun Casteel methodology (Estimating Soybean Yields, Purdue University, College of Agriculture, https://ag.purdue.edu/news/department/agry/soybean-news/archive/estimating-soybean-yields.html#:~:text=The%20system%20is%20based%20on,be%2021%20inches%20in%20length). This approach is widely used in soybean agronomic assessments to estimate yield and yield components from representative field subsamples when harvesting entire treatment areas separately is not feasible.

Sampling was performed at the time of commercial harvest, as determined by the farmer based on crop maturity and seed moisture conditions. Therefore, a total of 15 samples were processed at the Agrovive Biologicals ® Laboratory (Harrisburg, SD, USA). Plants harvested in each sample were counted and density estimated per m². Then, pods were separated from plant material, counted, estimated per m², and classified according to developmental stage (mature or immature without seeds), empty (dehiscence pods), and the number of locular spots and seeds.

To minimize potential bias associated with the involvement of a company-affiliated author, field sampling followed a predefined protocol based on randomly selected sampling locations within each treatment area. Samples were identified using coded labels prior to laboratory processing, and laboratory measurements (plant counts, pod classification, seed counting, and seed-size determinations) were performed according to standardized procedures without reference to the study hypotheses or expected treatment outcomes. All observations were recorded directly from the harvested samples and subsequently analyzed by the academic authors independently of the commercial interests associated with the product under evaluation.

Pods were then opened and seeds were counted both manually and using an automatic seed counter for various seed shapes (CGoldenwall Automated seed counter machine SLY-C; CGoldenwall, China). Seeds were also estimated per m². Seeds’ mass in grams was estimated using the average weight of 10 subsamples of 100 seeds. Seed size distribution was determined using a 6.35 mm USA Standard sieve (ASTM E11), with volume standardized using a 1/8-cup measuring cup. Yield was estimated as the adjusted kg m -2 calculated as total kg m -2 multiplied by a moisture-correction factor. The kg m -2 were estimated using total seed mass and sample area. Moisture content of the seeds was determined as the mean of three measurements obtained with a Case IH Agriculture Moisture Tester 040 Grain (Agratronix; OH, USA).

Statistical analysis

Data files used for statistical analyses and statistical approach were independently reviewed by the academic authors. Data editing and statistical analyses were conducted in R software version 4.5.2 (R Core Team, 2025). The packages used to change the dataset characteristics were “dplyr” (Wickham et al., 2026) and “tidyr” (Wickham et al., 2025), and all figures were created with the package “ggplot2” (Wickham, 2016). Differences among treatments in plant density, pod density (total, mature, and filled), average pods per plant (total, mature and filled), seed density, seed greater than 6.35 mm density, 100-seed weight, and adjusted yield (t per ha) were assessed using one-way ANOVA (Stats package; R Core Team, 2025). Normality of residuals was checked using Q–Q plots and the Shapiro–Wilk test prior to conducting the ANOVA (Stats package; R Core Team, 2025). Least-square means (LS-means) were obtained using the “emmeans” package of R and multiple comparisons were adjusted with Tukey (Lenth and Piaskowski, 2025). A linear model was fitted to evaluate the effect of average filled pods per plant and treatments on the total seed production (Stats package; R Core Team, 2025).

Pod-type composition was evaluated using three complementary approaches. First, the overall compositional differences were assessed using a Permanova test on centered log-ratio-transformed data (pairwiseAdonis package; Martinez Arbizu, 2017). Then, the treatment effects on individual pod-type categories were tested using a Dirichlet regression model (DirichletReg package; Maier, 2014). Lastly, each pod-type category was analyzed using a generalized linear model with a quasi-Poisson distribution to account for overdispersion in the count data, with false discovery rate control via the Benjamini–Hochberg procedure (MASS package; Venables and Ripley, 2002). Significance was set at p ≤ 0.05 unless otherwise stated. Comparison between manual and machine-based seed counts was performed using the Wilcoxon signed-rank test (Stats package; R Core Team, 2025).

Study limitations

This study was conducted during a single growing season at one rainfed location, and therefore the results should be interpreted within the environmental and management conditions evaluated. Detailed soil physicochemical and biological characteristics were not measured and may have influenced treatment responses. Although the alternating-row arrangement of the control and seed-treated plots was intended to reduce the influence of small-scale spatial heterogeneity, the foliar treatment was established in a separate field section to avoid spray drift and may therefore have been more susceptible to field-related variation. In addition, germination, seed vigor, and seedling emergence were not measured, preventing identification of the mechanisms responsible for the reduced plant density observed in the seed-treated plots. Finally, yield estimates were derived from fixed-area sampling rather than whole-plot harvests. Consequently, additional multi-year and multi-location studies incorporating comprehensive soil characterization and crop establishment measurements are needed to confirm the robustness and general applicability of these findings.

Descriptive statistics

Descriptive statistics are displayed in Table 2. Regarding the plants and pods, the number of plants m -2 ranged from 23.2 ± 1.3 (seed treatment) to 32.6 ± 3.7 (control). The total pods m -2 ranged from 804.6 ± 118.2 (foliar treatment) to 955.8 ± 118.7 (seed treatment). The total mature pods m -2 ranged from 755.6 ± 111.6 (foliar treatment) to 881.2 ± 116.6 (seed treatment). The total filled pods m -2 ranged from 707.7 ± 125.5 (foliar treatment) to 860.9 ± 116.2 (seed treatment). The average total pods per plant ranged from 25.3 ± 4.8 (foliar treatment) to 41.3 ± 6.2 (seed treatment). The average mature pods per plant ranged from 23.8 ± 4.5 (foliar treatment) to 38.2 ± 6.2 (seed treatment). The average total filled pods per plant ranged from 22.2 ± 4.6 (foliar treatment) to 37.3 ± 6.3 (seed treatment).

Regarding the seeds, the number of seeds m -2 ranged from 1571.1 ± 266.5 (foliar treatment) to 1869.1 ± 239.9 (seed treatment). The number of seeds greater than 6.35 mm ranged from 881.2 ± 169.1 (foliar treatment) to 1693.2 ± 246.3 (seed treatment). The average weight per 100-seed ranged from 18.0 ± 0.5 (control) to 21.9 ± 0.5 (seed treatment). The tons of seeds ha -1 ranged from 2.4 ± 0.4 (foliar treatment) to 3.5 ± 0.5 (seed treatment).

The identified pod-type categories were: blank pods (no mature pods) from 16.0 ± 4.5 (control) to 30.2 ± 11.1 (seed treatment); empty/dehiscent pods from 8.2 ± 6.9 (seed treatment) to 19.4 ± 11.4 (foliar treatment); one-spot one-seed from 4.0 ± 2.0 (foliar treatment) to 4.8 ± 1.8 (seed treatment); two-spot one-seed from 26.0 ± 5.2 (foliar treatment) to 32.6 ± 15.3 (control); two-spot two-seed from 68.4 ± 17.9 (control) to 74.6 ± 21.8 (foliar treatment); three-spot one-seed from 11.0 ± 4.5 (control) to 24.8 ± 7.6 (seed treatment); three-spot two-seed from 75.4 ± 20.1 (foliar treatment) to 115.4 ± 14.3 (seed treatment); three-spot three-seed from 91.8 ± 10.1 (foliar treatment) to 105.6 ± 16.6 (control); and four-spot four-seed pods from 0.2 ± 0.4 (foliar treatment) to 2.0 ± 0.7 (control).

Analysis of variance

Results revealed that several traits significantly differed among treatments, particularly between the seed treatment and the control or the foliar treatment. The seed treatment surface had fewer plants per m 2 (p < 0.001) than the control or foliar treatment (Figure 2a). Nevertheless, all three treatments showed no significant differences in total (p = 0.150; Figure 2b), mature (p = 0.238; Figure 2c), or filled (p = 0.185; Figure 2d) pods per m 2. They also achieved a similar total number of seeds per m 2 (p = 0.406; Figure 2e). In contrast, the seed treatment had a higher number of big seeds (i.e., greater than 6.35 mm m -2; p < 0.001; Figure 2f), and increased the average number of pods per plant, the total number (p < 0.001; Figure 3a), the mature (p < 0.001; Figure 3b) and filled (p < 0.001; Figure 3c) pods per plant. After accounting for plant density, the seed treatment produced fewer seeds per pod than the control (p = 0.023) and showed a tendency for the foliar treatment (p = 0.098), whereas the foliar treatment did not differ from the control (p = 0.526; Figure 3d). The seed treatment also revealed a greater average weight of 100-seeds (p < 0.001; Figure 4a) and total tons ha -1 of seeds than the control (p = 0.022; Figure 4b) or foliar (p = 0.004; Figure 4b) treatment.

Pod-type analysis

All three analyses performed on the pod-type composition highlighted significant differences among treatments. Permanova results showed treatment effects when considering all pods or when restricting analysis to mature or filled pods. Despite the control and seed treatment revealed a similar overall composition of pod-types (p = 0.580), there were differences between the foliar and the seed treatments (p = 0.040). Moreover, foliar treatment tended (p = 0.068) to a different overall composition of pod-types compared to control. Dirichlet regression (Table 3) revealed similar composition of pod types between the foliar treatment and the control. However, the seed treatment had higher number of blank pods (p = 0.043) and three-spot pods containing a single seed (p = 0.018) than the control. Analyses of individual pod-type categories (Figure 5) did not showed significant differences between treatments and control in any pod-type. However, the “three-spot, one-seed” pods (Three_one) tended to be higher in seed treatment than the control or the foliar treatment (p = 0.061), in agreement with the Dirichlet results (Table 3). Pods with four spots and four seeds (Four_four) also tended to be more frequent in the control than the seed or foliar treatment (p = 0.061).

Manual versus machine seed counting

The automated counter underestimated seed number compared with manual counting (p < 0.001; Figure 6). Points located on the 1:1 line indicate perfect agreement between methods, whereas deviations from the line reflect differences between machine and manual counts. The manual seed count presented a 1.04-fold increase compared to the automated counter, indicating that the automated method underestimated seed number by 3.8%.

Soybean yield is determined by the interaction of several key components, including plant density, pods per plant, seeds per pod and seed size, all of which directly influence final productivity (Painkra et al., 2018; Vogel et al., 2021). In the current study, although the seed treatment reduced plant density, this reduction did not translate into lower total pod or seed production per m 2. The mechanisms responsible for the lower plant population were not specifically evaluated in this study and therefore cannot be determined with certainty. Potential explanations include effects of the seed coating process on germination or seedling emergence (Santos et al., 2021), changes in seed water uptake during germination (Upretee et al., 2024), or interactions between the microbial inoculant and environmental conditions during crop establishment (Jarecki, 2021; Fiodor et al., 2023). However, germination, seed vigor, phytotoxicity, and mechanical seed damage were not directly assessed, preventing definitive conclusions regarding the cause of the reduced stand density. Field establishment is influenced by multiple factors, including soil moisture, temperature, seedbed conditions, and microbial interactions, and the observed reduction in plant density may therefore reflect a combination of treatment and environmental effects rather than a direct negative effect of the microbial inoculant itself. This observation is consistent with the broader understanding that yield is primarily determined by seed number per unit land area and seed weight, with seed number being the dominant driver of yield variation across environments (Vogel et al., 2021). The importance of the reproductive period in determining yield (Painkra et al., 2018), may explain this compensation, as plants under seed treatment appear to maintain pod and seed output despite reduced plant establishment.

Seed size and early seedling performance are critical physiological determinants of yield formation. Larger seeds consistently show superior germination vigor, faster early growth, and greater physiological robustness (Wang et al., 2025). Although seed size did not influence germination percentage or germination rate indices in soybean (Vange et al., 2016), multiple studies demonstrate that large seeds produce seedlings with longer roots and shoots, increased dry matter, and greater stress-tolerance capacity (Wang et al., 2025; Vange et al., 2016). This enhanced early vigor often translates into increased pod initiation, resource acquisition, and ultimately higher yields. In the present study, seed treatment increased pod number per plant and overall bean weight, aligning with the well-established relationship between improved pod formation and enhanced yield potential (Painkra et al., 2018). Although the seed treatment resulted in fewer seeds per pod and fewer seeds per plant compared with the control, the combined effect of more pods and larger bean size ultimately produced a higher yield. This aligns with previous observations that seed number, pod number, and seed mass compensate for one another to stabilize yield, a phenomenon particularly pronounced in soybean (Painkra et al., 2018; Vogel et al., 2021).

When contrasted with published agronomic benchmarks, the present study reveals notable differences in how seed and foliar treatments influence soybean stand establishment and yield components. Kolisnyk et al. (2024) reported a plant density of 77.4 plants m - ² under foliar fertilization, whereas our results showed that seed treatment reduced plant density (23.2 plants m -2) but maintained pod and bean production per surface at levels comparable to the control. This suggests a strong compensatory response in reproductive allocation, consistent with the well-established dominance of seed number per unit area and seed weight as primary drivers of soybean yield (Vogel et al., 2021). Regarding seed weight, our findings with both treatments (seed treatment, 1000-seed weight of 218 g; foliar treatment, 1000-seed weight of 183 g) outperformed those from Kolisnyk et al. (2024), who reported 1000-seed weights of 106.4–116 g under foliar feeding. This pattern agreed with the understanding that compensatory adjustments—particularly increases in pod production or seed size—can offset reductions in seed number, resulting in stable or enhanced yield outcomes. Such physiological compensation enables crops under seed-based treatments to achieve yields comparable to those obtained under more intensive foliar fertilization regimes.

Correlation-based evidence supports the interpretation that pod number, seed number, and seed mass are key targets for yield improvement. Painkra et al. (2018) reported strong positive correlations between yield and pods per plant, seeds per plant, seeds per pod, and 100-seed weight, emphasizing that improving these components leads to significant gains in productivity (Painkra et al., 2018). In our study, treatments enhanced pod production or increased seed size clearly achieved higher yield per m 2, consistent with this framework. The finding that the foliar treatment did not differ significantly from the control in seed per pod further supports the idea that pod number and seed size, more than seeds per pod, were the primary drivers of treatment differences (Painkra et al., 2018).

Regarding final yield, our results also fit within the broader global and regional ranges reported in the literature. Foliar fertilization in the Forest-Steppe region produced yields between 2.68 and 3.29 t ha -1 (Kolisnyk et al., 2024), while pre-sowing seed treatment in Ukraine achieved 2.91 t ha -1 for the variety ‘Sandra’ and 2.51 t ha -1 for ‘Legend’ (Mazur et al., 2023). These values are consistent with long-term increases in global average soybean yield, which rose from 1128 to 2769 kg ha -1 over the past six decades (Vogel et al., 2021), as well as the wide environmental yield range of 1.3–3.6 t ha -1 observed from rainfed to irrigated conditions across temperate Europe (Karges et al., 2022). Even under contrasting management systems, such as those evaluated by Zimmer et al. (2016), where yields reached 1.63 t ha -1 under conventional management and 2.46 t ha -1 under organic management, the variability is driven largely by differences in resource availability, environmental conditions, and cultivar adaptation. Within this context, our results demonstrate that seed treatment can achieve competitive yield performance (3.55 t ha -1) while offering economic and operational advantages—namely lower application costs, reduced water use, and simplified implementation—positioning it as an efficient alternative to foliar treatment in soybean production systems. Beyond physiological and morphological determinants, yield also responds to nutrient management and cultivation practices. Mazur et al. (2023) highlighted that optimizing soil physicochemical conditions, maintaining adequate nutrient supply, and implementing balanced fertilization regimes significantly improve soybean growth, seed quality, and yield potential.

Economic considerations also play an important role in treatment selection. Kolisnyk et al. (2024) demonstrated that foliar fertilization strategies can be profitable in certain environments, yet our results contrast with these findings: seed treatment was more cost-effective, requiring lower application costs while improving yield performance. Additionally, seed application reduced water requirements relative to foliar treatment, aligning with the broader need for resource-efficient systems in modern soybean production.

In agreement with the existing literature, the automated counter underestimated seed number compared with manual seed count, however the degree of underestimation was quite low. The primary drivers of undercounting described are overlapping seeds in images (Ghimire et al., 2023) and small seed size (Zu et al., 2025). Seed overlap is the most direct cause of underestimation: when seeds touch or overlap in an image, contour-based algorithms merge them into a single object, systematically reducing the count below the true value (Ghimire et al., 2023).

The present results suggested that, under the specific environmental, management, and field conditions evaluated in this single-site, single-season study, seed treatment for soybean offers an integrated set of agronomic, physiological, and economic advantages, and confirms the underestimation of the automated counter. Seed treatment promoted higher pod production per plant, larger bean size, increased occurrence of three-seed pods, improved overall yield, and reduced input costs, even though individual plants produced fewer seeds per pod or per plant. Despite a lower plant density, seed treatment maintained pod and seed production per unit area and resulted in higher yield than foliar treatment, suggesting that compensatory mechanisms involving pod production and seed size effectively offset reductions in stand establishment. These findings reinforced the central concept that soybean yield is shaped by flexible and compensatory interactions among pod number, seed number, and seed size. However, because the effectiveness of microbial inoculants can be strongly influenced by meteorological conditions, soil characteristics, and their interactions, these results should be interpreted within the specific context of the present study. Further multi-year and multi-location experiments are needed to confirm the consistency and broader applicability of these responses across different production environments.