Introduction

During the last five decades, there has been a large increase in grain production in Brazil. As a result, it has become one of the world’s biggest food producers and exporters, rather than a food importer. This was facilitated with the generation of new technologies for tropical conditions, including the transformation of acidic soils with a low nutrient content into the current production fields that have a built-up soil fertility resulting in a high crop yield1,2. However, there is still a need to increase and improve food production to satisfy the growing global demand. The increase in crop yield must be achieved in a sustainable way, with a reduction in the use of natural resources, such as land, nutrients, and water3,4. With the global food demand expected to double by 20505,6, many of the resources essential for food production may become increasingly scarce, including potassium (K)6.

Around 85% of soils in the Brazilian Savanna (Cerrado Region) have a low K content1. Some crops can extract K in a larger amount than nitrogen; it is also the most abundant cationic nutrient in plant tissue (up to 10% of the plant’s dry weight)7. It has been estimated that the global K reserves are sufficient for 5,800 years8. However, most of the K fertilizers are produced in only four countries i.e., Canada, Russia, Belarus, and China. These countries have about 76% of the world’s K reserves and produce about 74% of the total K fertilizers in the world6. In contrast, K reserves in Brazil are estimated to be less than 1% of the world’s total reserves6,8, and about 95% of the K fertilizer that is used in Brazil needs to be imported9. As a result, Brazilian agriculture is highly dependent on the import of potash fertilizer10. In the near future, global economic development may be limited by the reduction in K availability, as there will be a maximum peak in fertilizer production between 2029 and 2095, followed by a reduction6.

The concept of circular agriculture was initially conceived in Europe due to the need for a new and more sustainable agricultural production model11. It is expected that the adoption of circular practices can reduce the depletion of non-renewable resources and encourage the use of regenerative practices in agriculture, as well as recycling of by-products12. However, there are very few studies about circular agriculture that have been conducted at a farm level, especially under tropical conditions13,14, to validate the real impact of the adoption of circular practices. We expect that changing from linear to circular model will increase the use efficiency of K in large-scale commercial farms in Brazil by increasing the reuse and recycling of by-products that contain K. This could potentially reduce dependence on the import of K fertilizer in Brazil. Furthermore, it would contribute to a more sustainable management of global K resources for crop production10. To achieve long-term potash security, markets must be developed for renewable K fertilizers from manure and food waste6.

We present two case studies that were conducted on two large commercial Brazilian farms in which the concept of circular agriculture has been applied, even before the owners were aware of this term13. The farms initiated their activities more than 20 years ago with a continuing increase in their cultivated areas through incorporation of production fields that were previously occupied by degraded pastures and through the adoption of circular practices13,14. On these farms the field are 100% cultivated under NT, with a diversified cropping system that includes crop rotations. The soils are maintained through crop residues or cash and cover crops throughout the year as well as with maize intercropped with brachiaria grass (Urochloa ruziziensis). Both farms also have adopted an integrated crop-livestock system using agricultural products and by-products in beef cattle confinement. The goal of this study was, therefore, to assess how the adoption of circular agriculture practices can affect the K recovery in tropical conditions. Our hypothesis is that the adoption of circular practices increases the efficiency of K recovery under tropical conditions (Tables 1 and 2).

Table 1 Literature containing data on K content in dry matter (kg t− 1) of grains and residues and the harvest index.
Full size table
Table 2 Average dry matter (DM) yield and K content of cover crops based on studies conducted under conditions of the Brazilian cerrado.
Full size table

Results

The two farms, crops, yield, and management practices have been presented and discussed in two previous studies with focus on N and P13,14. In this study the focus is on the amount of K extracted by the crops, as well as the amount exported from the system and returned to the soil via residues and organic compost. Tables 3 and 4 show K content in the grains, residues, forage dry mass (DM), vines, and sweet potato roots, the DM yield of cover crops, and the amount of K extracted and exported per hectare. Most of the K extracted by the crops was accumulated in the shoots, i.e., residue. For instance, from the total accumulated K in the plant, the amount exported in the grain was only 30% for maize and sorghum and 15% for wheat (Table 5).

Table 3 Total cultivated area, grain, dry matter (DM) of residue and sweet potato yield, and total potassium extracted in grains, forage, sweet potato roots and in the DM residues of each crop for each growing season, i.e., summer and winter season, during three cropping years for farm 1.
Full size table
Table 4 Total cultivated area, grain and dry matter (DM) of residues, and total potassium extracted in grains, forage, and in the DM residues of crops for each growing season, i.e., summer and winter season, during three cropping years for farm 2.
Full size table
Table 5 Total beef cattle numbers during the confinement phase for each year, along with initial and final live weights, live weight gain per animal, total live weight gain per farm, and the amount of potassium exported in the live weight gained by the animals over the two years of confinement for farm 1 and farm 2.
Full size table

During three cropping years, 860 t K (Farm 1) and 307 t K (Farm 2) was applied as fertilizer (Tables 6 and 7), i.e., 169.3 on Farm 1 and 101 kg K ha− 1 year− 1 on Farm 2 (Figs. 1 and 2). For Farm 1, the amount of K that was added to the fields met the demand of the crops and increased the K content of the soil. From 2018/19 to 2020/21, the average K content in the soil increased from 74 to 101 mg dm− 3 for the 0–20 cm soil layer, from 35 to 45 mg dm− 3 for the 20–40 cm soil layer, and from 21 to 42 mg dm− 3 for the 40–60 cm soil layer. The estimated total amount of K in the 0 to 60 cm depth increased from 218 in 2018/19 to 313 kg ha− 1 in 2020/21. In contrast, the average K content for the 0–20 cm soil layer on Farm 2 decreased from 122 to 104 mg dm− 3, between the cropping years of 2018/19 and 2020/21. For the 20–40 cm layer, the reduction in K content in the same period was 91 to 61 mg dm− 3. The estimated amount of K in the 0 to 40 cm layer decreased from 357 to 276 kg ha− 1, from 2018/19 to 2020/21.

Table 6 Inputs of potassium from fertilizer, compost, and crop residues, and outputs of potassium in the grains, sweet potato, forage, and wheat straw to confinement for each growing season and the three cropping years for farm 1.
Full size table
Table 7 Inputs of potassium from fertilizer, compost, and crop residues, and outputs of potassium in the grains, forage, and wheat straw to confinement for each growing season and the three cropping years for farm 2.
Full size table
Fig. 1
figure 1

Summary of average inputs and outputs of potassium (kg ha− 1 year− 1) in the production system of Farm 1, based on the 2018/19, 2019/20 and 2020/21 cropping years and beef cattle production from 2020 to 2021. 1Stocking rate of 0.6 animal/ha.

Full size image
Fig. 2
figure 2

Summary of average inputs and outputs of potassium (kg ha− 1 year− 1) in the production system of Farm 2, based on the 2018/19, 2019/20 and 2020/21 cropping years and beef cattle production from 2020 to 2021. 1Stocking rate of 0.6 animal/ha.

Full size image

On Farm 1, 1532 t K was extracted in grains, sweet potato roots, forage, and leftovers (Table 6), i.e., 301.4 kg K ha− 1 year− 1 (Fig. 1). About 523 t K was exported in the grains and the sweet potato roots (Table 6), i.e., 102.8 kg K ha− 1 year− 1 (Fig. 1); this does not account for approximately 2.3 t of grains used in animal feed (Table S7). In total, around 524 t K was exported, considering the amount of K exported by beef cattle during the confinement period (Table 5).

On Farm 2, around 710 t K was extracted in grains, forage, and leftovers (Fig. 2), i.e., 233.1 kg K ha− 1 year − 1 (Fig. 2). The K total exported in grains represented 228.3 t K (Table 7), i.e., 72.9 kg K ha− 1 year− 1 (Fig. 2), minus the amount used to feed the animals on Farm 2 (Table S7). Thus, excluding the quantities used for animal feed, approximately 226 t of K were exported to the market in the form of grains and beef cattle by Farm 2. Around 822 t K for Farm 1 and 424 t K for Farm 2 was returned to the soil in the form of residues during the three cropping years (Tables 6 and 7). This is equivalent to 181.1 kg K ha− 1 year− 1 for Farm 1 and 151.8 kg K ha− 1 year− 1 for Farm 2 from residues (Figs. 1 and 2). Following the final harvest of the grains for the 2021 winter season, about 98.8 t of K for Farm 1 and 37.9 t of K for Farm 2 remained in the soil in the form of residues and was available for the following crop, i.e., the 2022 cropping season (Tables 6 and 7). This represented 19.4 kg K ha− 1 year− 1 for Farm 1 and 12.5 kg K ha− 1 year− 1 for Farm 2 for the 2022 summer season (Figs. S1 and S2).

The animals ingested through grains and forages the equivalent of 30 t of K for Farm 1 and 7 t of K for Farm 2 (Table S1), while the K exported during the confinement period was 633 kg K for Farm 1 and 194 kg K for Farm 2 (Table 5). It was estimated that 29.4 t K for Farm 1 and 6.4 t K for Farm 2 were excreted in feces and urine by animals during two years.

Based on the compost analysis, 24.5 t K for Farm 1 and 16.5 t K for Farm 2 was made available to the soil, which is equivalent to 4.8 kg K ha− 1 year− 1 for Farm 1 and 5.4 kg K ha− 1 year− 1 for Farm 2 (Figs. 1 and 2). The compost piles received about 8.3 kg K ha− 1 year− 1 for Farm 1 and 3 kg K ha− 1 year− 1 for Farm 2 in the form of animal manure and about 9.9 kg K ha− 1 year− 1 for Farm 1 and 5.2 kg K ha− 1 year− 1 for Farm 1 in the form by-products and forage produced for animal feed but not consumed or stored. In addition, at the end of 2021, there was 500 t of DM of maize silage (5.3 t K) and 496 t of DM of wheat straw (7.7 t K) stored on Farm 1, which was equivalent to a 2.55 kg K ha− 1 year− 1 stored as forage (Fig. 1).

Potassium recovery on Farm 1 was 84.9%; this was calculated as the ratio between the K extracted by crops and all the K added through inorganic fertilizer, compost, and crop residue, i.e., [301.4 kg K ha− 1 year − 1] / [Kfertilizer (169.3) + Kcompost (4.8) + Kresidue (181.1 kg K ha− 1 year − 1)]. K recovery on Farm 2 was almost the same as on Farm 1, i.e. 90.2%, based on the following calculation: [233.1 kg K ha− 1 year − 1] / [Kfertilizer (101) + Kcompost (5.4) + Kresidue (151.8 kg ha− 1 year − 1)].

Discussion

Flow of potassium added to the soil

The amount of K added to the soil for Farm 1 during the three cropping years was sufficient to supply the crop demand for K and increased the K content in the soil (Tables 6 and 7). The average amount applied via fertilizers in Farm 1 (169 kg ha− 1 year− 1) was around 68% higher than the amount applied on Farm 2 (101 kg ha− 1 year− 1). As a result, the average K content of the soil on Farm 2 was reduced from 2018/19 to 2020/21. It is worth noting that the K content in the top 0–20 cm soil layer in 2020/21 was within the appropriate range for crop growth and development, i.e., 70 to 120 mg dm− 3, on both farms15.

The K+ ion is weakly adsorbed to the soil’s negative charges by ionic bonds and has greater potential to be lost via deep leaching, especially in coarse-textured soils16, and when a high amount of K fertilizer is applied8,17. We assumed that the potential risk of leaching losses during the study period was higher on Farm 1 than Farm 2 due to the higher amount of K fertilizer that was applied since the climate, soils, and crops of the two farms were similar. Although K losses were not measured, it can be assumed that they exist in clayey Oxisols such as those found on Farm 1 and Farm 2 (Figs. 1 and 2 and S1-S2)10. estimated that 16.6% of the K applied to Brazilian soils is lost through leaching (13.7%) and erosion (2.9%). However, for the two farms of this study erosion losses were minimal since the soils are covered with straw and crops that are grown throughout the year either as a cash or cover crop. This was due to the adoption of NT with crop rotations and maize intercropped with brachiaria ruzziensis. However, leaching losses can occur during the compost production process, especially in the compost piles, which were not recorded in this study.

The average rate of K used on Farm 1 and 2 (Figs. 1 and 2, and S1, S2) was considered high if they were to meet the demand of only one crop per year. However, on both farms two crops are grown per year (Table S1 to S6). For instance, just to meet the demand of common bean, maize, and soybean, 42, 75, and 100 kg K ha− 1 would be recommended, when the soil has a low nutrient availability15. In 2018/19, Farm 2 (122 mg dm− 3) had a higher K content than Farm 1 (74 mg dm− 3), which reflects the lower rate for Farm 2 since K was only applied only to meet the nutritional demand of the crops. Nevertheless, Farm 1 applied the nutrient to meet the nutritional crop requirements together with the amount necessary to increase the percentages of K in the CEC from 3 to 5%, as recommended for the region1,18.

The strategy of using a lower K rate on Farm 2 (Fig. 2) compared to Farm 1 (Fig. 1) without decreasing crop yield (Table S1 to S6), contributes to reducing the depletion of a non-renewable resources, such as the rocks that supply K12, as the higher the amount of K fertilizer applied, the greater the risk of losses due to leaching. The application of a lower fertilizer amount should be a crop management strategy, when technically possible, as it will contribute to a reduction in financial costs and an improvement of the environmental impact3.

Most of the K that was taken up by the crop was returned as residues to the soil (Tables 6 and 7), which was expected since the largest proportion of K uptake remains in the plant vegetative tissue, i.e., stems and leaves, rather than in the grains19,20,21,22. It was estimated that about 75 and 85% of the K that was taken up by maize and wheat was returned to the soil, respectively. In the case of common bean and soybean, about 59 and 56% of the amount taken up was returned to the soil through crop residues (Tables 6 and 7). Monocotyledonous require a higher amount of K in aboveground biomass compared to dicotyledonous but they export less through harvested, thus a larger amount of K to the soil following harvest8.

In a study carried out in an Oxisol under Brazilian Cerrado conditions with different maize hybrids, 74 to 89% of the total K taken up remained in crop residues19. In the case of common bean, the percentage in the residue was lower and ranged from 50 to 70% of the total extracted22. Some studies suggest that soybean crop exports 37% of the total K taken up in grains, while the remainder is returned to the soil through crop residue20. In the case of wheat, the proportion of K in the residues exceeds 82% of the total P taken up during the growing season20.

The K is released faster to the soil from the crop residues than P and N23. Normally, crop residues release 80% of the K in 30 days24. Under cold and dry conditions in Canada, approximately 90% of the K from crop residues was released into the soil after 52 days25, whereas under Brazilian conditions, 55% of the K was released from oat residues within just 15 days26. The K release from crop residue is rapid because it does not depend on the mining of soil organic matter. K is mainly found in the ionic form in the vacuole of plant cells and is not part of the structural components of the plant27.

In addition to crop residues, Farm 1 and Farm 2 received the equivalent of 4.8 and 5.4 kg K ha− 1year− 1, respectively, through the application of organic compost. This reduced the use of K inorganic fertilizer as non-renewable resource and associated production costs3,11,12,28,29. These contributions corresponded to 4.7% (Farm 1) and 7.4% (Farm 2) of the total amount of K exported in grains. It is estimated that 58.1, 21.8, 9.6, and 10.1% of the total K used in Brazilian agriculture came from K fertilizer, manure, waste from food, and from non-food industries10. However, it is believed that these numbers are very high for farms that only produce grain when compared with those obtained on Farm 1 and Farm 2 that had an integrated crop livestock system.

Potassium flows to grains and tubers, animals, and market

Although Farm 1 (524 t K) and Farm 2 (226 t K) exported a large amount of K to the market, a small amount was through the live weight of animals, e.g., between 0.19 and 0.38%. This small amount was due to the low animal stocking (0.6 to 1 animal/ha) as well as the low K content in the body of animals30. Thus, most of the exported K was through the grains and sweet potato roots on Farm 1 and through the grains on Farm 2, which is similar to previous studies.

The amount of K exported to the market in the live weight of the animals ranged from 2.1 to 2.8% of the amounts of the nutrient ingested by the animals. Thus, most of the K was excreted in the animals’ feces and urine, contributing to the high K concentration in animal manure. For pastures conditions, 95% of K can return to the soil as feces and urine3130. found that the efficiency of K used by beef and dairy cattle and poultry was only 2.7%; this low value is related to the low K content of meat, milk, and eggs. These results highlight the need for studies seeking to increase the use efficiency of K by animals. The adoption of livestock farming integration can take advantage of the nutrient from the manure and, thus, reduce the use of chemical fertilizers28. This could reduce the depletion of global K sources, increasing K recycling, as recommended through the principles of circular agriculture3,11,12,29. This in turn can reduce food production costs since 95% of the K fertilizers that are used in Brazil are imported10.

Flow of K recovered and K losses in the soils

The K recovery observed on Farm 1 (84.9%) and Farm 2 (90.2%) was much higher than the values found in other studies in Brazil. Recent studies have estimated that K recovery in Brazil at 66%32 and 73%10. Farm 2 was slightly more efficient in using K than Farm 1 because Farm 2 applied a smaller amount of K fertilizer than Farm 1 (Figs. 1 and 2). K recovery can decrease as the rates of applied fertilizers increase8,17. Even with the lower K fertilizer rate, yield on both farms was very similar as discussed by13. These results show that even with efficient production systems, it is always possible to increase the use efficiency of nutrients.

The higher K recovery in both farms occurred because of circular agricultural practices such as no-till, crop rotations, crop diversification, cover cropping, and intercropping with brachiaria. The deep roots of grasses, such as brachiaria and millet, can extract K that may have been leached into deeper soil layers33. In addition, combining grasses with other crops, such as those found on Farm 1 and Farm 2, is also known to improve K recovery efficiency [17; 8]. Monocots commonly require a higher amount of K in their aboveground biomass but export less in the harvested grain compared to dicots. Hence, a greater amount of K is returned to the soil8 that can then be taken up by the dicot crop in the rotation following a monocot crop. On both farms, K from plant residues was very important in plant nutrition in succession, as K is readily washed from plant residues into the soil in the presence of moisture23,24,27. On Farm 1 and Farm 2, most of the K taken up by maize (75%) and wheat (85%) was returned to the soil through crop residues. In the case of common bean and soybean, around 60% of the amount taken up by the crop was also returned to the soil through crop residues (Tables 6 and 7).

Overall, the association of NT, with crop rotation practices, cover crops, and maize intercropped with brachiaria kept the soil covered throughout the year and reduced problems such as weeds, pests and diseases, in addition to increasing nutrient recycling34 Environmental services from crop rotation have replaced the use of pesticides in some places3. Nevertheless, on many Brazilian farms, the diversification of the cropping system has also been adopted because the monoculture could bring serious soil and crop management problems34 Thus, a simple way to encourage the adoption of these circular agriculture practices would be to demonstrate their importance in reducing common agronomic problems. Moreover, the economic benefits can also be used to convince farmers to adopt circular agricultural practices3.

Finally, this assessment provides valuable insights regarding the potassium flow within integrated crop-livestock systems. Nevertheless, a few limitations of the assessment must be acknowledged. For instance, potassium losses through leaching and during compost production were not directly measured for this study; instead, we have estimated these rates based on previous studies. It is also worth noting that this is an on-farm study developed on commercial farms, thus there is a lack of control treatments, which may also limit the study. Moreover, the findings are specific to the edaphoclimatic conditions of the Brazilian Cerrado, characterized by highly weathered, clay-rich Oxisols and a tropical climate with distinct wet and dry seasons. These factors may constrain the direct applicability of the results to temperate agricultural systems. Yet, we believe that the outcomes are relevant to other tropical and subtropical regions with savanna-type vegetation and similar environmental characteristics. Within this context, the study offers significant contributions to the understanding of potassium dynamics in sustainable agricultural systems under tropical conditions and may serve as a foundation for future research incorporating direct measurements, controlled comparisons, and broader agroecological assessments.

Conclusion

Two large-scale commercial farms from the Brazilian Savanna region were considered in this study with K recovery for Farm 1 around 85% and for Farm 2 around 90%; these high K recovery values reflect the circular practices adopted by both farms. Most of the K taken up by maize (75%), wheat (85%), common bean (59%) and soybean (56%) was returned to the soil through crop residues. About 98% of the K consumed by the animals in the dry matter of the feed was excreted in the feces and urine and transformed into organic compost to be reused as organic fertilizers in the production fields. The quantities exported by the animals while in confinement represented 0.2% for Farm 1 and 0.4% for Farm 2 of all K that was exported. This study showed that the adoption of circular agricultural practices such as cropping system diversification via rotation, cover cropping, intercropping with deep root grasses, no-till, continuous soil coverage, and crop-livestock integration improved the K use efficiency and recovery under tropical conditions.

Materials and methods

Characterization of the farms

Data collected were obtained from two commercial farms, i.e., Fazenda 3 W Agronegócios (Farm 1) and Fazenda Santa Helena (Farm 2). Both farms are in the Campos das Vertentes region in the Minas Gerais State, Brazil. Farm 1 is located at 21° 23’ S and 44° 39’ W, Itutinga County, at 1017 m above sea level, while Farm 2 is located at 21° 15′ 39″ S and 44° 31′ 04″ W, Nazareno County, 1020 m above sea level. Details about the climatic conditions, soil type, and vegetation of the farms were previously presented in13,14.

Data for each production field from the 2018/19, 2019/20, and 2020/21 cropping seasons—including cultivated area, crop type, fertilization rate, and crop productivity for both Farm 1 and Farm 2—are provided in the supplementary material (Tables S1–S6).There are two cropping seasons in one single year where the study was conducted: September to February, i.e., the first season or summer season, and March to August, i.e., the second season or winter season. At Farm 1, during the first season, 1559 ha was cultivated in 2018/19, 1675 ha in 2019/20, and 1848 ha in 2020/21. During the second season, 1299 ha was cultivated in 2018/19, 1437 ha in 2019/20, and 1787 ha in 2020/21. At Farm 2, during the first season, 903 ha was cultivated in 2018/19, 1025 ha in 2019/20, and 1,116 ha in 2020/21. During the second season, 739 ha was cultivated in 2018/19, 1025 ha in 2019/20, and 1021 ha in 2020/21. For both farms, agricultural practices were adopted to improve soil fertility and reduce soil compaction during the year when degraded pastures were converted into cropland prior to cultivating any cash or cover crop.

The initial soil fertility conditions, as well as the amendments rates used were presented by13. For instance, limestone doses (usually > 9 t ha− 1) and gypsum were applied and incorporated into the 0–40 cm soil layer with two harrow passes, followed by subsoiling and two slight disc harrow passes35. In addition, prior to planting the first crop, each field is corrected for P, K, and micronutrients. In the specific case of potassium, the K content ranged from 31 to 54 mg dm− 3. Potassium fertilization consisted of K rates to correct the soil to reach 4% of the potential CEC18 plus the quantities of K that were exported in the grains of each crop36,37,19. Immediately following the incorporation of soil amendments, millet (Pennisetum glaucum) was sown at the beginning of September as the first crop of the cropping system and used as a cover crop to protect the soil against erosion. Common bean (Phaseolus vulgaris) was the second crop that was grown, and it was the first cash crop with planting in January. The soil was tilled only once during this process and only to incorporate the amendments. Then, all fields were managed under continuous NT13. The entire history of fertilization, use of cultivars and plant protection products such as herbicides, insecticides and fungicides, during this study have been described by13.

Assessments of crop yield and nutrient absorption

After harvesting the crops, the farmers took the entire production to the grain silos for removal of impurities, weighing, moisture measurements, drying, and storage. After cleaning and drying, grain yield was obtained by dividing the total production of each production field by its area. Sweet potatoes were produced on Farm 1 only and to obtain the average yield, the total production was weighed and divided by the total harvested area. 83% of all sweet potatoes harvested were classified as market standard and 17% were ground for animal feed or used in compost, when not consumed by the animals.

Crop residues were estimated using harvest index values reported in peer-reviewed scientific studies conducted in the Cerrado region of Brazil (Table 1). Nutrient contents of the crop grains and crop residues were also extracted from the Brazilian literature. Crop grains and residues used in the diets of the animals were analyzed at 3rlab Laboratory (www.3rlab.com.br) of Lavras, Minas Gerais State, Brazil, from samples collected on the farms. The K content of dry mass (DM) and DM yield of the cover crops [millet, oat (Avena strigose), and brachiaria] were calculated based on the average K concentration that was obtained from the Brazilian literature under Cerrado conditions (Table 2).

The average amount of K exported by each crop (kg ha− 1 year− 1) was obtained by dividing the total amount of this nutrient present in the grains produced during the three cropping years by the area cultivated in the summer season during the three cropping years. In this case, 5082 ha was cultivated during the three cropping years on Farm 1 and 3044 ha on Farm 2. The average amount of K (kg ha− 1 year− 1) that entered the production fields as fertilizers, residues, and compost were also estimated by dividing the total input in the three cropping years by the area cultivated in the summer season of each farm. It was assumed that the nutrients that were present in the residues produced in the crop of previous harvest would be the K inputs for the next crop.

Similar to the method used for N recovery by13 and P recovery by14, K recovery was calculated during the three cropping years as the ratio among all K extracted by the crops for all K inputs into the soil, i.e., K from fertilizer + K from compost + K from residue (Eq. 1).

$${\text{Krecovery}}=\frac{{\left( {{\text{K~Crop}}} \right)}}{{\left( {{\text{K~~Fertilizer}}+{\text{~K~Compost}}+{\text{~K~Residue~}}} \right)}}~$$
(1)

.

In the Eq. 1, Kcrop was considered the average quantity of K exported by crops (kg ha− 1 year− 1); Kfertilizer was the average quantity of K from commercial fertilizers (kg ha− 1 year− 1); Kcompost was the average quantity of K from organic compost (kg ha− 1 year− 1); and Kresidue was the average quantity of K from residue (kg ha− 1 year− 1) produced during three cropping years.

The quantity of K in kg per ha per year in compost piles were estimated by the difference between the quantity of K in by-products plus K in forage produced for animal feed minus the amount of K that was not consumed or stored.

Beef cattle in confinement

The animal production started in 2020 with the integration into the production of both farms with confined beef cattle using the Nellore breed (Bos indicus). To feed the animals, all the leftovers from grain silos, e.g., broken grains and straw from pre-cleaning the grains, were used, in addition to part of the straw from the wheat crop, which was transformed into hay after the grains were harvested. On Farm 1, around 17% of the leftover sweet potatoes that was classified as unfit for the market, were used as animal feed. To balance the diet of the animals as discussed by13 part of the grains produced on both farms was also used, as well as maize silage and snaplage. Some by-products were purchased on the market when it was economically advantageous, such as sorghum and soybean meal, and cotton seed, among others. In turn, the animal component of the production system contributed manure that was added to the compost piles. Leftover animal feed and by-products such as wheat and sweet potato waste that were not used for food in the confinements, were collected daily and composted together with all the manure produced in the confinements.

Farm 1 confined 1460 beef cattle in 2020: 686 animals in phase 1, i.e., growth before the fattening phase, and 774 animals in phase 2, i.e. the fattening phase. The total number of animals increased to 2244: 1214 in phase 1 and 1030 phase 2 in 2021. Farm 2 started its activities with 236 beef cattle in 2020: 148 animals in phase 1 and 88 animals in phase 2. In 2021, 1001 animals were confined: 492 animals in phase 1 and 509 animals in phase 2. The animals in each confinement phase, i.e., growth vs. fattening, required different diets that were balanced by veterinary nutritionists, as presented by13.

Based on the K content in the live weight of Nelore animals59 and the live weight gained by the animals during the average confinement period, i.e. 85 days on Farm 1 and 76 days on Farm 2, the quantities of K exported by each group of animals were estimated. The average K exported in the live weight of the beef cattle and the K inputs in the diet and output in the excreta, calculated as kg ha− 1 year− 1, were obtained by dividing the total amounts by the total cropland on Farm 1, i.e., 5,082 ha, and Farm 2, i.e., 3,044 ha. The K total in the excreta (feces and urine) produced by beef cattle were calculated through the difference between the total amount of K ingested by animal minus the total amount of K exported in the live weight of the animals.