Introduction

On a global scale, rice is one of the stable food crops cultivated on around 165.25 million hectares, with a production of 787.29 million tonnes1. India is a major producer and consumer of rice, accounting for 27.27% of the global rice cultivated area (45.07 million hectares) and 15.79% of production2. Global rice demand is expected to rise by more than 40% by 2050 to fulfil the needs of the world's growing population3. Transplanted rice is still the most common and traditional planting method in India, requiring a large amount of natural resources and nonrenewable energy sources. As a consequence, meeting the ever-increasing demand for rice in the context of dwindling natural resources is a big concern4. Direct Seeded Rice (DSR) is an alternative choice for rice growers around the globe in the face of limited water and energy resources5. However, weed infestation is a major hurdle to the successful deployment of DSR. Weed competition throughout the season results in 100% yield reduction in DSR6. In general, the critical weed-free period for DSR goes from 11 to 83 DAS, which is longer than for transplanted rice7. Effective weed management in direct-seeded rice necessitates a multifaceted strategy. Many authors suggested that it is challenging to effectively manage weeds in DSR with a single strategy8,9. In this context, adopting the Integrated Weed Management (IWM) strategy, which involves the synergistic integration of at least two components, emerges as a successful approach capable of addressing this challenge comprehensively10. A more competitive crop has an edge over weeds and lowers weed-related yield losses11,12,13.

Adoption of short-duration, highly competitive, and high-yielding rice hybrids would be more cost-effective in northern India's productive Gangetic plains, where the rice–wheat cropping system (RWCS) persists. The early vigor and phenotypic flexibility of short-duration high-yielding rice hybrids demand the right geometry for a better DSR establishment. It is widely acknowledged that wider spacing and single rice transplanting in the system of rice intensification (SRI) result in profuse tillering and higher yield14. Wider spacing in hybrids reduces seed rate and production cost12,15. The wider spacing also facilitates mechanical weed control in the spaces between rows; however, it takes a long time for the canopy to close compared to the narrower rows16,17, this leads to a longer crucial period for weed management. However, weed-competitive hybrids quickly close the canopy, provide shade, and prevent weed growth18. Hybrids are more vigorous than inbred; therefore, the weed suppression ability of hybrids may be utilized in DSR rice. In general, the recommended seed rate for inbred varieties shown in zero-till seeders or dry direct-seeded method is 25–30 kg ha–1 in the DSR system5. The seed rate, like inbred lines, increases production costs and reduces the net return in hybrids. Therefore, DSR uses square planting geometry to provide identical growing conditions and better weed management like SRI in rice. There are opportunities to use cultural practices for better weed management in DSR19. There is a clear association between weed emergence time and crop yield loss13. Yield losses are greater when weeds emerge earlier or simultaneously with the crop20. Despite chemical weed control methods achieved distinctive successes for weed management in field crops, herbicide use could pose hazards in the environment. Therefore, mechanical and manual weed control methods are still preferred. A hoe at crop emergence may suppress weeds that germinate early, providing a competitive edge to rice seedlings. Manual weeding is the most common technique in rice; however, it is tedious and not economically feasible21. The combination of hoe and hand weeding is most appropriate, especially for small farms and places where laborers are cheap22. Also, the integration between mechanical and cultural or chemical methods exhibited better weed control efficiency than the use of individual practice23.

The soil organic carbon loss is a major concern in tropical regions due to rapid mineralization24. The inclusion of fast-growing nitrogen-fixing crops as cover crops or co-cultures might enhance the organic carbon content of the soil and improve the available nutrient status25. Co-cultivation of fast-growing crops like Sesabnia aculeata will suppress the weeds and add nitro-gen to the soil. According to Gill and Walia26, the use of S. aculeate residues conserves soil moisture and adds roughly 15 kg N ha–1. The S. aculeata intercropping greatly reduce the weed density and biomass in DSR due to the low light transmission27. Residue retention enhances soil health by restoring the soil's physical characteristics28, and enhancing microbial activity and nutrient cycling29.

Mulching crop residue is a promising practice to suppress weed emergence and conserve moisture; however, this is almost impossible for large farms. The amount of rice straw is plentiful in the RWCS of northern India, and generally farmers burn the residues for easier and faster wheat planting30. The burning of residues pollutes the environment by emitting gases that are hazardous to human and environmental health5. There are several advantages in retaining rice residue. Rice straw can last longer in the field due to its higher lignin and silica content, which can help in managing weeds31. Furthermore, rice straw contains nutrients that can be recycled and utilized as organic fertilizer32,33, to improve soil fertility34,35. Retaining rice residue mulch provide an environmentally sound solution for managing weeds13,24. However, research on the effect of rice cultivars, planting geometry, and non-chemical weed management on weed density, diversity, and performance of hybrid rice cultivars is sparse.

Knowledge in these areas would make ecological weed management easier. To accomplish this, we hypothesise that the integration of cultivars, crop geometry, and non-chemical weed management approaches will result in sustainable rice production and weed management as well as healthy environment. The outcomes of this research can significantly contribute to the advancement of sustainable and economically viable agricultural practices. Therefore, a study was conducted with the following objectives: (1) to assess the influence of planting geometry, cultivars, and non-chemical weed management on crop performance, weed density and diversity of hybrid rice production (2) to analyze the economic implications of implementing these approaches in hybrid rice production. These objectives aim to offer valuable insights that can guide the development of economically viable and sustainable weed management practices in DSR.

Results and discussion

Weed flora

During the two-year study period, fourteen weed species from six different families were recorded at the experimental site. Among these, six species were grasses [i.e., bermudagrass (Cynodon dactylon (L.) Pers.), large crabgrass (Digitaria sanguinalis (L.) Scop), jungle rice (Echinochloa colona (L.) Link), barnyardgrass (Echinochloa crus-galli (L.) P. Beauv), goosegrass (Eleusine indica (L.) Gaertn.), and torpedograss (Panicum repens L.), five species were broadleaves [ i.e., blistering ammannia (Ammannia baccifera L.), pink node flower (Caesulia axillaris Roxb.), eclipta (Eclipta alba (L.) Hassk.), water primrose (Ludwigia parviflora Roxb.), and gulf leafflower (Phyllanthus fraternus G.L.Webster), and three species were sedges [i.e., smallflower umbrella (Cyperus difformis L.), flatsedge (Cyperus iria L.) and grasslike fimbry (Fimbristylis miliacea (L.) Vahl)]. The grasslike fimbry, blistering ammannia, jungle rice and bermuda grass were the dominant weed species and had the highest relative densities of 12.15%, 11.66%, 11.14%, and 11.12%, respectively (Fig. S1).

Weed density

Grasses, broadleaf, sedges, and total weed densities were significantly (p < 0.05) influenced by planting geometry, cultivars, and non-chemical weed management at 25 and 60 DAS (Table 1). At 25 DAS, grass, sedge, broadleaf, and total weed densities were 18.14%, 21.13%, 29.04% and 22.36%, lower respectively, for PN compared to PS geometry. In contrast, inverse occurred at 60 DAS, where PS observed 23.93%, 26.64%, 18.03%, and 22.67% lower weed densities of grasses, sedges, broadleaf, and total weeds, respectively, than PN. Lower weed densities in PS geometry may be due to weed growth smothering as a result of uniform plant-to-plant and row-to-row spacing30,36. Square planting further encourages crops to compete with weeds as a result of the better availability of space, light, and nutrients18,37,38. Nichols et al.39, and Dass et al.13, reported that a uniform row-to-row and plant-to-plant distance in rice had a lower weed-competition. Among cultivars, Arize 6444 (hybrid from Bayer) was more competitive with weeds than PHB 71 (hybrid from Pioneer) at 25 and 60 DAS. Faster emergence and robust seedlings of Arize 6444 were thought to be reasons for increased competitiveness. The cultivars that achieve early vegetative vigor and quick ground cover have a competitive advantage over weeds compared to varieties that have slow initial growth35,40. With regards to weed management treatments, HH + SC had the lowest grass, broad-leaf, sedge, and total weed densities at 25 DAS, with reductions of 90.61%, 91.81%, 89.05%, and 90.19%, respectively, compared to the weedy check.

Table 1 Weed density influenced by planting geometry, cultivar, and non-chemical weed management in rice.
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However, HH + WH treatment had the lowest weed densities at 60 DAS with 92.77%, 46.77%, 58.52% and 53.64% lower densities of grassy, broad-leaf, sedges, and total weeds compared to the weedy check. Further, treatments HH + MR4 and HH + MR6 recorded lower weed densities than WC at both the stages. Early prevention and suppression of weed germination and growth could be the reason for the lowest weed density in the HH + SC treatment. Keeping the weeds free at an early stage (hand hoeing at 12 DAS) and during the peak weed emergence period (manual weeding during the active tillering stage at 30 DAS) might have resulted in reduced weed competition and weed density of all the weeds at later stages12,18.

Interaction of planting geometry (PG) × cultivar (CV), CV × weed management (WM), and PG × CV × WM did not influence the weed density at 25 and 60 DAS (Table 1). However, planting geometry × weed management significantly (p < 0.05) influenced the broadleaf, sedge, and total weed densities at 25 DAS, and broadleaf weed density at 60 DAS (Table 1). The interaction of PG × WM revealed that PN and HH + SC combinations resulted in the lowest broadleaf, sedge, and total weed densities (Fig. 1a,b). This could be due to the lack of space available for weed growth in close spacing and smothering effect of sesbania co-culture treatments18,41. The lowest broadleaf density at later stage under PS and HH + WH combinations may be due to keeping the plots weed free in hand hoeing fb hand weeding treatments and faster crop growth when planted in the square pattern.

Figure 1
figure 1

Interaction effect of planting geometry × weed management on sedge, broadleaf and total weed densities at 25 DAS (a) and broadleaf density at 60 DAS (b). PN, sowing with seed drill at 18.5 cm row spacing; PS, square planting at 25 cm × 25 cm row to row and plant to plant spacing; W0, weedy check (no weed management); HH + WH, one hand hoeing at 12 DAS fb one hand weeding at 30 DAS; HH + SC, one hand hoeing at 12 DAS fb Sesbania aculeata co-culture and mulched 45 DAS; HH + MR4, one hand hoeing at 12 DAS fb rice residue mulching @ 4 t ha−1; HH + MR6, one hand hoeing at 12 DAS fb rice residue mulching @ 6 t ha−1. Means with different alphabets are significant (P < 0.05). Values shown in the figure are square-root [√(x + 0.5)]-transformed means.

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Weed diversity indices

Weed diversity indices such as dominance, evenness, and diversity were not influenced by PG, CV, or their interaction (Table 2). However, weed management (WM) had a significant effect on all the weed indices at 25 and 60 DAS. The HH + SC weed management treatment had the lowest Shannon–Wiener and evenness indices but the highest dominance index (Table 2). The lowest Shannon–Wiener and evenness indices values in HH + SC treatment indicate greater control of weeds42. Data on evenness (close to 1) indicates that weed species distribution in this experiment is more uniform across treatments. Weed evenness was not influenced by the interaction between PG and CV and PG, CV and WM at either evaluation date (25 or 60 DAS). However, at 25 DAS, PG × WM and CV × WM had a significant effect on evenness (Fig. 2a,b).

Table 2 Effect of planting geometry, cultivar and non-chemical weed management on weed diversity in rice.
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Figure 2
figure 2

Interaction effect of planting geometry × weed management and cultivar × weed management on evenness at 25 (a,b) and 60 DAS (c,d). PN, sowing with seed drill at 18.5 cm row spacing; PS, square planting at 25 cm × 25 cm row to row and plant to plant spacing; WC, weedy check (no weed management); HH + WH, one hand hoeing at 12 DAS fb one hand weeding at 30 DAS; HH + SC, one hand hoeing at 12 DAS fb Sesbania aculeata co-culture and mulched 45 DAS; HH + MR4, one hand hoeing at 12 DAS fb rice residue mulching @ 4 t ha−1; HH + MR6, one hand hoeing at 12 DAS fb rice residue mulching @ 6 t ha−1. Means with different alphabets are significant (P < 0.05).

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Likewise, at 60 DAS, the interaction of PG × WM and CV × WM had a significant effect on evenness (Fig. 2b,c), dominance (Fig. 3a,b), and the Shannon–Wiener index (Fig. 3b,c). Compared to other treatments, Ps and the HH + SC combination had significantly lower values of evenness and Shannon–Wiener index and the highest dominance value.

Figure 3
figure 3

Interaction effect of planting geometry × weed management and cultivar × weed management on dominance (a,b) and Shannon-Weiner index (c,d) at 60 DAS. PN, sowing with seed drill at 18.5 cm row spacing; PS, square planting at 25 cm × 25 cm row to row and plant to plant spacing; WC, weedy check (no weed management); HH + WH, one hand hoeing at 12 DAS fb one hand weeding at 30 DAS; HH + SC, one hand hoeing at 12 DAS fb Sesbania aculeata co-culture and mulched 45 DAS; HH + MR4, one hand hoeing at 12 DAS fb rice residue mulching @ 4 t ha−1; HH + MR6, one hand hoeing at 12 DAS fb rice residue mulching @ 6 t ha−1. Means with different alphabets are significant (P < 0.05).

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Weed control efficiency indices

Planting geometry had a significant effect (p < 0.05) on WMI, AMI, and IWMI, but did not influence the CRI and WPI (p > 0.05, Table 3). Compared to the zero-till seed drill sown method, the square planting (PS) method had a lower WMI, AMI, and IWMI, which indicates the effectiveness of this method on weed suppression. The lowest values of WMI, AMI, and IWMI indicate better weed control and a higher yield. The lowest values of WMI and AMI were recorded in earlier studies by Mishra et al.43 and Kumar et al.24 with treatments that efficiently reduced weeds and increased grain yield.

Table 3 Effect of planting geometry, cultivar and non-chemical weed management on weed control efficiency indices in rice.
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Cultivars influenced the CRI significantly (p < 0.05) compared to other indices. The cultivar Arize 6444 resulted in a higher CRI value than the cultivar PHB 71. CRI indicates increased vigor of crop plants due to weed control. Superior crop growth and biomass production of the Arize 6444 cultivar could be the reason for the higher CRI value. Garko et al.44 also reported a significant effect of different varieties on CRI in maize crop. The weed management treatments greatly influenced all the weed management indices. Among weed management treatments, HH + WH performed well; therefore, this treatment had a 169% higher CRI than the weedy check.

Furthermore, HH + WH treatment resulted in the lowest values of WPI, WMI, AMI, and IWMI over other treatments. The lower WPI, WMI, AMI, and IWMI indicate superior weed control.

The interaction effect of planting geometry × weed management revealed that PS × HH + WH had a lower value of WPI, WMI, AMI, and IWMI (Fig. S2a). Square planting and hand hoeing at the early stage fb hand weeding at peak weed emergence period could have resulted in better weed control than other combinations. The interaction of cultivar × weed management only had a significant effect on CRI (Fig. S2b). Greater suppression and control of weeds under the combination of Arize 6444 × HH + WH treatment might have led to a higher CRI.

Crop growth parameters

Planting geometry, cultivar, and weed management influenced the crop growth parameters (Table 4). However, the interaction effect of planting geometry, cultivar, and weed management did not influence except the number of tillers by planting geometry-by-cultivar and dry matter production by cultivar-by-weed management. The number of tillers (number m−2) and dry matter production (g running m−1) were (p < 0.05) 7.6% and 13.11% higher, respectively, for the square planting (PS) compared to the zero-till seed drill sown crop (PN). This could be due to optimum crop spacing that allowed the radiant energy, nutrients, and water to utilize; as a result, more tillers and robust crop growth were achieved under the square planting method6. On the other hand, De Datta45, reported that a higher seed rate in a seed drill-sown crop with normal spacing increases inter-and intra-plant competition, which leads to poor utilization of applied inputs, poor crop growth, and a lesser number of tillers. Furthermore, the square planting treatment decreased weed competition compared to zero-till seed drill-sown crop; this could also be the reason for the better growth and development. Cultivars only influenced the dry matter accumulation but not the number of tillers (Table 4). The Arize 6444 resulted in 8.41% higher dry matter production than the PHB 71; the higher dry matter for Arize 6444 could be the result of greater plants height and tiller production46.

Table 4 Effect of planting geometry, cultivar and non-chemical weed management on growth attributes and yield in rice.
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The weed management treatments, HH + WH and HH + SC resulted in the highest number of tillers and dry matter compared to other weed management treatments (Table 4). Hoeing and hand weeding at the early phases of crop growth might have nullified the early weed competition and ultimately led to a greater number of tillers and dry matter. Our findings are in agreement with Johnson et al.47 who reported that early-stage weed control in direct-seeded rice reduced weed pressure and increased grain yield. Growing S. aculeata and retaining its mulch in rice can suppress the weeds effectively48. Additionally, mineralization of residues provides available nutrients to crops at critical stages, which has a positive effect on crop growth at an early stage49,50.

Planting geometry × weed management had a significant effect on the number of tillers. The interaction effect of PS and HH + WH resulted in a maximum number of tillers, followed by PN and HH + SC and PN and HH + MR treatment combinations (Fig. 4a). Cultivar × weed management was found significant for dry matter accumulation. Arize 6444 and HH + WH, Arize 6444 and HH + SC combinations had a higher dry matter accumulation (Fig. 4b). The authors believed that this could be due to the synergistic effect of wider spacing in square planting and control of weeds by hand hoeing fb hand weeding, and hand hoeing fb Sesbania co-culture treatments.

Figure 4
figure 4

Interaction effect of planting geometry × weed management, and cultivar × non-chemical weed management on number of tillers (a), dry matter production (b) and production efficiency of rice (c,d). PN, sowing with seed drill at 18.5 cm row spacing; PS, square planting at 25 cm × 25 cm row to row and plant to plant spacing; WC, weedy check (no weed management); HH + WH, one hand hoeing at 12 DAS fb one hand weeding at 30 DAS; HH + SC, one hand hoeing at 12 DAS fb Sesbania aculeata co-culture and mulched 45 DAS; HH + MR4, one hand hoeing at 12 DAS fb rice residue mulching @ 4 t ha−1; HH + MR6, one hand hoeing at 12 DAS fb rice residue mulching @ 6 t ha−1. Means with different alphabets are significant (P < 0.05).

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Crop productivity

Compared to zero-till seed drill-sown crop (PN), square planting (PS) achieved a ~ 7.6% higher grain yield (Table 4). Vigorous crop growth, minimum inter-specific competition, a higher number of tillers, and greater weed suppression might be responsible for higher yields in the square planting method12,18,51. Previous studies reported that direct-seeded rice in the square planting method had a higher grain yield compared to normal planting52. Among cultivars, Arize 6444 produced a 10.7% higher grain yield than PHB 71. The higher grain yield for Arize 6444 could be attributed to increased dry matter accumulation, more tillers, faster crop growth, and better weed suppression15. With respect to weed management tactics, the HH + WH recorded the highest grain yields (4.85 t ha−1), followed by the HH + SC (4.68 t ha−1). Hoeing fb hand weeding during the critical crop-weed competition period might have reduced the weed competition and led to better crop performance14,53. Early weed control is crucial in DSR for improved crop growth and yield5,6. The hand hoeing fb either hand weeding or Sesbania spp. co-culture resulted in a weed-free condition and improved yield. Similarly, Maity and Mukherjee49, also reported that co-culture of Sesbania with rice smothered weeds and enhanced the grain yield of rice. Likewise, Baumann et al.27, and Gopal et al.54, observed a higher grain yield and available N content in soil under S. aculeata co-culture in direct seeding.

The interaction between planting geometry or cultivar and weed management tactics significantly influenced the grain yield. The treatment PS and HH + WH combination achieved the highest grain yield, followed by PS and HH + Sc, PN and HH + Sc, and PN and HH + WH (Table S1). Among weed management and cultivar interactions, the highest grain yield was observed for Arize 6444 × HH + WH and Arize 6444 × HH + Sc combinations (Table S2). Better crop growth, higher dry matter accumulation, and greater weed suppression ability of the Arize 6444 cultivar with square planting and hand hoeing fb hand weeding or hand hoeing fb Sesbania spp. co-culture could be the reasons for the higher grain yield.

Planting geometry, cultivar, and weed management had a significant impact on production efficiency. The results showed that square planting (PS) had the maximum production efficiency compared to zero-till seed drill-sown crops (PN). The higher yield with square planting could be attributed to improved production efficiency. Among cultivars, Arize 6444 resulted in higher production efficiency than PHB 71. The HH + WH achieved the highest production efficiency across weed management treatments and was comparable to HH + Sc. The increased crop yield per day was believed to be a reason for the higher production efficiency in HH + WH and HH + Sc. The PS and HH + WH interactions increased production efficiency (Fig. 4c). The cultivar × weed management interaction revealed that maximum production efficiency was recorded for Arize 6444 and HH + WH (Fig. 4d). This could also be because of the higher grain yield ha−1 day−1 and effective weed control12.

Economic analysis

A slightly higher cost of cultivation (COC) was registered for PN (600.55 US$) compared to PS (591.47 US$), which was due to the higher cost of hybrid seeds used under seed-drill sown crops (Table 5). Square planting had higher gross returns (GR) by 7.24%, net returns (NR) by 15.59%, and B: C ratio of 8.78% than zero-till drill sown crops. This was because of the lower COC coupled with a higher GR in PS than PN. Cultivars did not influence the COC due to similar seed rates, seed costs, and other inputs. However, higher GR, NR, and BCR were obtained for Arize 6444 compared to PHB 71 because of the higher yield under Arize 644412,18. The COC for weed control treatments ranged from 459.46 to 763.22 US$ ha−1; WC had the lowest COC and HH + MR6 had the highest. Rice straw was applied at a rate of 6 t ha−1 and the higher cost of rice straw was the reason for the higher COC in the HH + MR6 treatment. Higher GR (1398.26 US$ ha–1) and NR (851.03 US$ ha–1) were observed under HH + WH and HH + SC, and the least was with WC in both years. However, BCR was higher for HH + SC fb HH + WH treatment. These results could be the result of lower weed density under HH + WH and HH + SC14. The interaction effect between planting geometry × weed management was found to be significant for GR, NR and BCR (Fig. 5a–c). Highest GR, NR, and BCR were recorded under interaction of Ps and HH + WH as compared to other treatment combinations.

Table 5 Effect of planting geometry, cultivar and non-chemical weed management on cost of cultivation, gross return, net return and B: C ratio.
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Figure 5
figure 5

Interaction effect of planting geometry × weed management on gross return, net return and B:C ratio of rice. PN, sowing with seed drill at 18.5 cm row spacing; PS, square planting at 25 cm × 25 cm row to row and plant to plant spacing; WC, weedy check (no weed management); HH + WH, one hand hoeing at 12 DAS fb one hand weeding at 30 DAS; HH + SC, one hand hoeing at 12 DAS fb Sesbania aculeata co-culture and mulched 45 DAS; HH + MR4, one hand hoeing at 12 DAS fb rice residue mulching @ 4 t ha−1; HH + MR6, one hand hoeing at 12 DAS fb rice residue mulching @ 6 t ha−1. Means with different alphabets are significant (P < 0.05).

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Conclusions

The results emphasize the importance of selecting appropriate weed management strategies for sustainable DSR, taking into account both environmental considerations and economic feasibility. The findings from this study revealed that Arize 6444, the square planting system, and the hoeing fb hand weeding performed better in terms of yield than PHB 71, normal planting and other weed management practices. However, the higher cost of manual weeding and the unavailability of labors are the main drawbacks of the hoeing fb hand weeding system. Alternatively, Arize 6444, square planting geometry, and hoeing at 12 DAS fb Sesbania co-culture mulch at 45 DAS enhanced the productivity and profitability of DSR and significantly reduced weed density in the Eastern region of India. These findings contribute valuable insights to the ongoing efforts to promote sustainable and environmental friendly weed management practices, mitigating the risks associated with herbicide use and potential evolution of resistant weeds in direct-seeded rice systems. Development and research on precise seeding machines is a future research area for wider adoption of hybrids in DSR systems, higher weed control efficiency, and higher yield. Additionally, an assessment of the long-term impacts of the proposed weed management strategies on soil health, biodiversity, and overall ecosystem resilience is needed.

Materials and methods

Experimental site and weather conditions

Field experiments were carried out at the Agricultural Research Farm of the Institute of Agricultural Sciences, Banaras Hindu University, Varanasi (25,018′ N and 88,003′E), Uttar Pradesh, India, during the rainy seasons (June to October) in 2015 and 2016. The cropping system at the site has been rice followed by wheat for the last six years. The climate of the site is sub-tropical; May and June were the hottest months (maximum temperature 31–36 °C) and January was the coldest month (minimum temperature 7–14 °C). Annual rainfall averages 1036.8 mm and 87.3% of them are received between June and September (South-West Monsoon), and the remaining 13.7% is received between October and May (western disturbances and other climatological factors). The weather parameters are presented in Fig. S3. The soil type was a sandy clay loam (Typic Haplusteptiso-hyperthermic family, Inceptisol)55 with 0.4% organic carbon, 7.5 pH, 0.21 dsm–1 EC, 182.67 kg ha–1 available N, 22.12 kg ha–1 available P, and 216.5 kg ha–1 exchangeable K.

Treatment details and crop management

The experiments were arranged in a split-split plot design with three trial factors (planting geometries, cultivars, and non-chemical weed management) in three replications. Two planting geometries [normal (PN) and square planting (PS)] were arranged in the main-plots, two cultivars (Arize 6444 and PHB 71) in the sub-plots, and five non-chemical weed management treatments [weedy check (WC), single hoeing (1 HH) at 12 DAS fb one hand weeding (1 HW) at 30 DAS (HH + WH), 1 HH at 12 DAS fb Sesbania co-culture and its mulching (HH + Sc), 1 HH at 12 DAS fb rice straw mulching @ 4t ha−1 (HH + MR4), and 1 HH at 12 DAS rice straw mulching @ 6 t ha−1 (HH + MR6)] in the sub-subplots (Table 1). The main plot size was 40 m × 5 m, the sub-plot size was 20 m × 5 m, and the sub-sub plot was 4 m × 5 m. The field was prepared with one pass of moldboard plough fb disk to uproot established perennial weeds. Finally, two passes of cultivator and planking were done to provide a good tilth suitable for a DSR crop. The sowing dates were June 22, in 2015 and June 28, in 2016. Nitrogen (150 kg ha−1), P2O5 (60 kg ha−1), and K2O (60 kg ha−1) were applied at the recommended rates through urea (NH2)2CO), di-ammonium phosphate ((NH4)2HPO4) and muriate of potash (KCl), respectively. Half of the recommended nitrogen and full doses of phosphorus and potassium were applied at the time of sowing. The remaining nitrogen was given in two equal portions at the tillering and panicle initiation stages. The crop was harvested manually on 28th October in 2015 and 5th November in 2016 (Table 6).

Table 6 Description of planting geometry, cultivar and weed management options adopted in the experiment.
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Weed observations

Weed density and composition

In each plot, two quadrates (1 m2) were placed randomly for weed observations (25 and 60 DAS). Weeds were classified as grass, broadleaf, and sedge after identification. At 60 DAS, the relative density of various weed flora was calculated by dividing the weed density of each weed species by the overall weed density in the weedy check plot and multiplying the result by 100.

Weed diversity indices

Weed dominance, diversity and evenness were assessed at 25 and 60 DAS by estimating the Simpson’s index56, Shannon–Wiener index57 and Pielou’s measure58, respectively using the Past software (v.4.03) (Eqs. 1–3).

$$\mathrm{Simpsons index }({\text{D}})=\sum \frac{(ni (ni-1))}{(N (N-1))}$$
(1)
$$ {\text{Shannon}}{-}{\text{Wiener index}}\;\left( {\text{H}} \right) = - \sum pi{\text{In}}pi $$
(2)

where ni is the number of species i, pi is the proportion of the species i in total number of species, N is the total number of individuals in a sample.

$$ {\text{Pielous}}\;{\text{measure}}\;{\text{of}}\;{\text{evenness}}\;\left( {\text{E}} \right) = {\text{H}}/{\text{In}}\;{\text{S}} $$
(3)

where H is the species diversity index (i.e., Shannon–Wiener index), and S is the species richness (number of weed species present in a plot).

Weed control indices

The weed control efficiency indices were calculated using weed dry matter and density data as well as crop dry matter and yield data at 25 and 60 DAS59,60 (Eqs. 4–8).

$${\text{CRI}}=\frac{{{\text{DMC}}}_{{\text{T}}}}{{\text{DMC}}_{\text{C}}}\times \frac{{\text{DMW}}_{\text{C}}}{{\text{DMW}}_{\text{T}}}$$
(4)

where, CRI = Crop Resistance Index, DMCT = Dry matter of crop in treated plot, DMCC = Dry matter of crop in control plot (weedy), DMWC = Dry matter of weed in control plot, DMWT = Dry matter of weed in treated plot.

$${\text{WPI}}=\frac{{{\text{DMW}}}_{{\text{T}}}}{{\text{DMW}}_{\text{C}}}\times \frac{{\text{WC}}_{\text{C}}}{{\text{WC}}_{\text{T}}}$$
(5)

where, WPI = Weed Persistence Index, DMWT = Dry matter of weed in treated plot, DMWC = Dry matter of weed in control plot, WCC = Weed count in control plot, WCT = Weed count in treated plot.

$${\text{WMI}}=\frac{\frac{{{\text{Y}}}_{{\text{T}}}-{{\text{Y}}}_{{\text{C}}}}{{{\text{Y}}}_{{\text{C}}}}}{\frac{{{\text{DMW}}}_{{\text{C}}}-{{\text{DMW}}}_{{\text{T}}}}{{{\text{DMW}}}_{{\text{C}}}}}$$
(6)

where, WMI = Weed Management Index, YT = Crop yield in treated plot, YC = Crop yield in control plot, DMWC = Dry matter of weed in control plot, DMWT = Dry matter of weed in treated plot.

$${\text{AMI}}=\frac{\frac{{{\text{Y}}}_{{\text{T}}}-{{\text{Y}}}_{{\text{C}}}}{{{\text{Y}}}_{{\text{C}}}}-\frac{{{\text{DMW}}}_{{\text{C}}}-{{\text{DMW}}}_{{\text{T}}}}{{{\text{DMW}}}_{{\text{C}}}}}{\frac{{{\text{DMW}}}_{{\text{C}}}-{{\text{DMW}}}_{{\text{T}}}}{{{\text{DMW}}}_{{\text{C}}}}}$$
(7)

where, AMI = Agronomic Management Index, YT = Crop yield in treated plot, YC = Crop yield in control plot, DMWC = Dry matter of weed in control plot, DMWT = Dry matter of weed in treated plot.

$${\text{IWMI}}=\frac{{\text{WMI}}+{\text{AMI}}}{2}$$
(8)

where, IWMI = Integrated Weed Management Index, WMI = Weed Management Index, AMI = Agronomic Management Index.

Crop studies

At 90 DAS, the number of tillers in each plot was counted from a 1 m2 area. To calculate the dry matter accumulation, destructive plant sampling was performed from a meter row. These samples were sun-dried and then oven-dried at 65 °C for 72 h to achieve a constant dry weight. The plant dry weight is expressed in g m−1 row length. At harvest, plot-wise produce was threshed independently, and grain yield was measured in kg ha–1. The production efficiency was calculated (kg ha−1 day−1) by dividing the grain yield by the number of days needed for each treatment to reach maturity.

Economic analysis

The economics were computed using current market input prices and the return on the final output (grain and straw yield). The production cost includes human labour, tilling, seeding, seed, straw, fertilizer, irrigation, harvesting and threshing, and the cost of transportation to market (Table S3). The following formulae were used to calculate the gross and net returns and the benefit-cost (B: C) ratio (Eqs. 9–11)24.

$$ {\text{Gross}}\;{\text{returns}}\;\left( {{\text{US}}\$ \;{\text{ha}}^{ - 1} } \right) = ({\text{Grain}}\;{\text{yield}}\;\left( {{\text{t}}\;{\text{ha}}^{ - 1} } \right) \times {\text{sale}}\;{\text{price}}\;\left( {{\text{US}}\$ \;{\text{t}}^{ - 1} } \right) + ({\text{Straw}}\;{\text{yield}}\;\left( {{\text{t}}\;{\text{ha}}^{ - 1} } \right) \times {\text{sale}}\;{\text{price}}\;\left( {{\text{US}}\$ \;{\text{t}}^{ - 1} } \right) $$
(9)
$$ {\text{Net}}\;{\text{return}}\;\left( {{\text{US}}\$ \;{\text{ha}}^{ - 1} } \right) = {\text{Gross}}\;{\text{returns}}\;\left( {{\text{US}}\$ \;{\text{ha}}^{ - 1} } \right){-}{\text{Cost}}\;{\text{of}}\;{\text{cultivation}}\;\left( {{\text{US}}\$ \;{\text{ha}}^{ - 1} } \right) $$
(10)
$$ {\text{Benefit}}\;{\text{Cost}}\;{\text{ratio}} = {\text{Gross}}\;{\text{return}}\;\left( {{\text{US}}\$ \;{\text{ha}}^{ - 1} } \right)/{\text{Cost}}\;{\text{of}}\;{\text{cultivation}}\;\left( {{\text{US}}\$ \;{\text{ha}}^{ - 1} } \right) $$
(11)

All economic analyses were expressed in US$ by converting 1 USD = 67 Indian rupees (INR).

Statistical analysis

The data were subjected to analysis of variance (ANOVA) as described by Gomez and Gomez61. The normality of weed data was confirmed using the Shapiro–Wilk test (p < 0.05) and it was found non-normal. Therefore, the square-root transformation √(x + 0.5) was performed. Weed diversity indices such as dominance, diversity and evenness were calculated using the PAST software (version 4.03). In ANOVA, planting geometry, cultivars, weed management, and year were considered as the fixed effects, and replication was considered as the random effect. We did the combine analysis of data and found that there was no significant effect (p > 0.05) of years on weed density, diversity indices, weed control efficiency indices, available NPK in soil, number of tillers, dry matter production, grain yield, production efficiency and economics. Therefore, we did the pooled analysis of years. The treatment means were compared using Fisher’s LSD test at a 5% level of significance. All the analysis was performed using R software (version 4.0)62.

Authors have confirmed that all the plant studies were carried out in accordance with relevant national, international or institutional guidelines.