Modeling the amount of mineralized carbon from swine manure and wheat straw

A method capable of reducing the environmental damage caused by swine manure and the soil enrichment with nutrients is based on the use of these residues together with the crops straw in soils for agricultural production. Through the use of carbon mineralization curves, it is possible to determine the best intervals for the use of organic matter from manure to better adapt the use of soil and crops. Dynamics of carbon present in manure can help in the selection of the best management. The objective of this study was to compare the fit of three nonlinear models that describe the carbon mineralization in soil over time, in addition to assessing the carbon stock of wheat straw alone and combined with swine manure. The experiment was carried out in a randomized block design, with four replications and eight treatments. The following treatments were tested: T1 – soil (S), T2 – soil + straw on the surface (SSUR), T3 – soil + incorporated straw (INCS), T4 – soil + manure on the surface (MSUR), T5 – soil + incorporated manure (INCM), T6 – soil + incorporated manure + straw on the surface (INCMSSUR), T7 soil + incorporated manure + incorporated straw (INCMINCS), T8 – soil + straw on the surface + manure on the surface (SSURMSUR). Soil samples were incubated for 95 days, and ten observations were made throughout time. Carbon mineralization was described using nonlinear models Cabrera, Stanford and Smith and Juma, considering the autoregressive error structure AR (1), when necessary. The comparison of fit of models was made using the Akaike Information Criterion (AIC). The description of carbon mineralization of wheat straw and swine manure carried out by nonlinear models was satisfactory. The Cabrera model was the most appropriate to describe all treatments. The Stanford and Smith model, most used in the literature to describe the mineralization of organic waste in soil, did not achieve better results in relation to the other nonlinear models for the treatments under study. In general, the treatments with straw on the surface resulted in a larger carbon stock in the soil, and with the addition of manure to the wheat 1 Universidade Federal de Lavras (UFLA). Graduando em Agronomia. gustavo.paula1@agronomia.ufla.br. Departamento de Agricultura, Campus Universitário da UFLA, Lavras, Minas Gerais, 37200-000. 2 UFLA. Doutor em Estatística e Experimentação Agropecuária. edilsonmg3@hotmail.com. 3 UFLA. Doutoranda em Estatística e Experimentação Agropecuária. arianafruhauf@gmail.com. 4 UFLA. Doutorando em Estatística e Experimentação Agropecuária. ediposvm01@gmail.com. 5 UFLA. Professor Titular. joamuniz@ufla.br. 6 UFLA. Professor Titular. tales.jfernandes@ufla.br.


Introduction
Pig farming is an important agricultural activity that contributes significantly to the Brazilian economy, generating employment and income for producers and providing meat for domestic supply and for export. The participation of pig farming in agribusiness is relevant, considering that Brazil is the 4th largest pig producer in the world (EMBRAPA, 2018). In 2019, Brazilian pig production was expected to exceed 4 million tons, with exports of approximately 700 thousand tons (CONAB, 2019). Due to the high demand for pork, new farmers have appeared in different regions of Brazil. However, not all of them use the proper management for the disposal of residues generated by the animals, and as a consequence these residues are often the cause of river pollution. Several problems may arise from contamination of water courses. The high load of nutrients in water bodies, for example, can lead to eutrophication, mainly by the P and N present in the chemical composition of the material (CADONÁ, 2017). However, due to these problems, means were developed for the correct use of residues generated by pigs, representing an alternative to take advantage of the nutritional quality of liquid manure, mainly N, and use it as an organic fertilizer in agriculture. A practice that is becoming very common in Southern Brazil is the use of organic residues on the straw of winter crops, such as wheat, in no-till system for the production of corn and beans (LUZ, 2007).
No-till is a production system that brings various benefits to agriculture, providing several improvements in crops planting, in which straw has important functions, such as to protect the soil surface against direct action of the sun, increase soil organic matter content and reduce the impact of raindrops. For these reasons, it is important to conduct studies related to the decomposition of straw and liquid waste to seek improvements in the management of the system, since the speed of straw decomposition is important regarding whether the soil is bare or covered.
There is a colossal and varied number of microorganisms in soil, which are benefited from the input of organic matter through manure and straw, so that both carbon mineralization and immobilization can occur in soil, and this can vary depending on the relationship of several aspects of this material, such as: pH, chemical composition, C:N ratio, quantity, quality and incorporation or not of the added material. Nevertheless, decomposition also depends on several other factors present around the material to be decomposed, such as: the types of microorganisms in the area, the type of soil, the vegetation, that is, the entire soil ecosystem influences directly or indirectly on the decomposition of the material (MOREIRA et al., 2013).
The material to be decomposed contains labile compounds in its chemical composition, which are mineralized at the beginning of the decomposition, since they represent the most soluble fraction of the material used, and as this fraction decomposes, mineralization tends to become slower because microorganisms have more difficulties in mineralizing the resistant fraction of the remaining compounds (GIACOMINI et al., 2008;PULROLNIK, 2009). The behavior of the mineralization curve can be described by mathematical functions that constitute nonlinear regression models (FERNANDES et al., 2011;SILVA et al., 2019b;ZEVIANI et al., 2012;SOUZA et al., 2010;SILVA et al. 2020).
When the decomposition has two phases of mineralization, due to chemical composition, the Cabrera model has shown a good fit (SILVA et al., 2019b;2019c). Therefore, given the direct importance of soil management more favorable to the production of agricultural crops, it becomes relevant the understanding of the dynamics that involves the decomposition of organic residues in soil, and for this it is important to know the carbon mineralization curves over time.
In order to improve the productive capacity of the soil, it is necessary to understand the carbon dynamics during the decomposition of crop residues. The goal of this study was to compare the fit of three nonlinear models -Stanford and Smith, Cabrera and Juma -to describe the carbon mineralization in soil with wheat straw and swine manure over time, as well as to evaluate C mineralization of wheat straw alone and in combination with swine manure.

Material and methods
Data used for fitting the models were extracted from Luz (2007), and correspond to the results in means of an experiment that evaluated carbon mineralization in different treatments involving doses of swine manure in soil and wheat straw. The experiment was carried out in Santa Maria, state of Rio Grande do Sul, in the Soil and Environment Microbiology Laboratory, Soil Department, University of Santa Maria.
The soil used is classified as arenic dystrophic red argisol, and was collected in the 0-10 cm layer on July 1, 2006. The area in which the soil was collected had been grown with corn since 1998, in no-till system. After removing the crop residues remaining on the soil surface, soil was collected and transported to the laboratory for homogenization and sieving through 4.0 mm mesh, remaining stored moist in plastic bags, at room temperature, until incubation. The contents of C and N were determined by dry combustion, and the excess 13 C, by mass spectrometry. Values of the contents of C and N were: 42.7% and 0.65% (C/N = 65) respectively, and the excess 13 C, 2.016%. There was determination of the nitrate content (NO3-N) of the water-soluble fraction of straw, by colorimetry, representing 16.2% total nitrogen content. Liquid swine manure was collected from a farm in the city of Restinga Seca, state of Rio Grande do Sul. The levels of organic C, total N, ammonia N, dry matter and pH values of swine manure were determined according to the methodology described in Tedesco et al. (1995).
In addition to these treatments, three flasks containing the NaOH solution (blank) were incubated to capture the C-CO2 from the internal atmosphere of the flasks of all treatments. Thirtytwo experimental units were set up (8 treatments and 4 replications), consisting of acrylic containers, 5.0 cm high and 5.0 cm diameter, with a capacity of 110.0 mL, added with soil of each treatment. To each acrylic container was added 131.0 g soil with 15.0 % moisture, equivalent to 117.8 g soil dried at 105 °C. Moisture was maintained at field capacity.
The C-CO 2 released in each treatment was captured in 10.0 mL of a 1 mol L -1 NaOH solution placed in a 37.0 mL glass vial, suspended on the top of each flask. The excess NaOH in each sampling interval was titrated with a solution of 1 mol L -1 HCl, after precipitation of carbonate with a solution of 1 mol L -1 BaCl 2 .
Nonlinear models evaluated are: Cabrera (1), Juma (2) and Stanford and Smith (3) with the following equations: at which: u i = ϕ 1 u i-1 + ... + ϕ p u i-p + ε i , with i= 1, 2, ..., n and n is the number of times measurements were taken; u i is the residual of the fit in the i-th time; ϕ 1 is the autoregressive parameter of order 1; u i-1 is the residual of the fit of time immediately before the i-th measurement; ϕ p is the autoregressive parameter of order p; u i-p is the residual of the fit in p times before the i-th measurement; ϕ i is the blank residue, with normal distribution, N(0,σ 2 ).
In the models, when the residuals are independent, the parameters ϕ i will be null, and consequently u i = ε i (MAZZINI et al., 2003;GUEDES et al., 2004).
In equations (1), (2) and (3), y i defines the average value of the mineralized carbon amount in times t i in days; C 0 indicates the value of the potentially mineralizable carbon amount; C 1 is the easily mineralizable carbon amount; k, k 1 , k 0 are mineralization rates; v is half-life; t i refers to the time of the i-th measurement, expressed in days (PEREIRA et al., 2005). In addition, the Cabrera model considers two carbon fractions, one that is easily mineralizable (C 1 ) and the other, resistant (k 0 ). The Stanford and Smith and Juma models consider only a fraction of carbon that is potentially mineralizable (C 0 ). The half-life time (v) of the potentially mineralizable carbon for the Stanford and Smith model was estimated by the equation: The estimation of the parameters C 0 , C 1 , k, k 1 , k 0 and v of the models was done by the least squares method, through which the nonlinear normal equations system is obtained. In the case of nonlinear models, the system does not present a direct solution, requiring the use of iterative numerical algorithms to obtain the parameter estimates (DRAPER; SMITH, 2014). Several iterative processes are described in the literature, and the algorithm used in the present study was the Gauss-Newton one. This algorithm considers the Taylor series expansion to approximate the nonlinear regression model with linear terms and then apply the method of ordinary least squares to estimate the parameters (MUIANGA et al., 2016;MUNIZ et al., 2017;FERNANDES et al., 2017;RIBEIRO et al., 2018a;RIBEIRO et al., 2018b;SOUSA et al., 2014;SILVA et al, 2019a;OLIVEIRA et al., 2013;PEREIRA et al., 2005;PEREIRA et al., 2009). Calculations of estimates for the sample data, as well as the graphic adjustments and all the computational part involved in the elaboration of this study were obtained using the statistical software R (R DEVELOPMENT CORE TEAM, 2016).
Assuming the normality of residuals, the confidence intervals for parameter estimates were also obtained. According to Draper and Smith (2014), the 95% confidence interval for the βi parameter is defined as: at which: b i is the estimate for the parameter (β i ); S (b i ) is the standard error of the estimate; t(v;0;025) is the upper quantile of the Student's t distribution, considering α = 5% and the degree of freedom v = n -d, where is the number of parameters of the model.
The Durbin Watson test allowed to verify the presence of residual dependence between the measures, evaluating whether the residual of an observation can be associated with the residual of adjacent observations (HOFFMANN AND VIEIRA, 1998). The Breusch-Pagam test was applied to check the homogeneity of the residuals and the Shapiro-Wilk test, to check normality.
Models were compared as to the goodness of fit and it was indicated which model was the most appropriate to describe the mineralization curve as a function of time. The following criteria were used: i.
Coeficiente de determinação ajustado, R 2 aj : at which R 2 is the coefficient of determination; n is the number of observations; and d is the model number of parameters. One model should be preferred over the other if it has a higher R 2 aj.
ii. Akaike Information Criterion, AIC AIC = 2logL( ᶿ ) + 2p (7) at which L ( ᶿ ) is the maximum of the likelihood function; p is the number of parameters in the model; and log is the natural logarithm operator. Between two models, the lower the AIC value, the better the model fits the data.
iii. Residual standard deviation, RSD RSD=√MSE (8) at which MSE is the mean squared error. RSD is proportional to the mean squared error, so lower values indicate better fits.
Carbon mineralization of wheat straw was calculated based on the C 0 estimates of the Stanford and Smith and Juma models. Carbon mineralization for treatments using straw alone was calculated based on the equation: And for treatments with the use of straw combined with manure, based on the equation: at which MC is carbon mineralization of the straw (% added carbon); C 0 straw is the estimate of the potentially mineralizable carbon of the straw by the Stanford and Smith or Juma models. C 0 soil is the estimate of the potentially mineralizable carbon of the soil by the Stanford and Smith or Juma models. C 0 straw+manure is the estimate of the potentially mineralizable carbon of the treatments with straw + manure by the Stanford and Smith or Juma models. C 0 manure is the estimate of the potentially mineralizable carbon of manure by the Stanford and Smith or Juma models. C added is the added carbon (Mg kg -1 ) with the straw, which was 2,135 Mg kg -1 dry soil.

Results and discussion
The Shapiro-Wilk, Breusch-Pagan and Durbin-Watson tests were applied to analyze the experimental errors (Table 1). According to the results of the Shapiro-Wilk test, there was residual normality for all models and all treatments. Also, there was residual homogeneity in all models and treatments by the Breusch-Pagan test (p>0.05). In the Durbin-Watson test, there was a correlation in all models and treatments, except for the INCS, MSUR and INCM treatments in the Cabrera model, and for the S treatment in all models. In the treatments in which there was a correlation, fits with first order autoregressive errors AR (1) were used to elucidate the dependence of residuals of these treatments. Since these measurements were performed on the same plot over time, this correlation in errors was expected. Silveira et al. (2018) also reported a correlation in the errors in the fit of the nonlinear model of the cumulative biogas production from swine manure. Paula et al. (2020) also found a correlation in the fit of nonlinear models in data on carbon mineralization of swine manure in the soil. Tables 2, 3 and 4 list the estimates of the model parameters with their respective 95% confidence intervals. Table 2 -Estimates for the Stanford and Smith model parameters and their respective asymptotic 95% confidence intervals (LL -lower limit and UL -upper limit) in the fit of mineralized C, in mg of CO 2. kg -1 , of the analyzed treatments.    Considering the confidence intervals for the estimate of parameter (C 0 ) in the Stanford and Smith model, there was an overlap in the confidence intervals of the treatments SSUR, INCMSSUR, INCMINCS and SSURMSUR, indicating that all treatments had the same amount of potentially mineralizable carbon, which were higher than the amount in treatments S, INCS, MSUR and INCM. These results occur due to the increase in the carbon content from straw and/or manure available to microorganisms, thus stimulating the mineralization of the added carbon, as well as the degradation of soil organic matter (FERNANDES et al. 2011).

Stanford and Smith
In the Cabrera model, considering the confidence intervals for the estimation of parameter (C 1 ), the amount of easily mineralizable carbon followed the order: S<MSUR= INCM<SSUR=INCS=INCMSSUR=INCMINCS=SSURMSUR. Taking into account the parameter (k 0 ), there was an overlap between the confidence intervals of the MSUR and INCM treatments, thus, they had the same mineralization rate as the resistant carbon. The INCS, SSUR, INCMSSUR, INCMINCS and SSURMSUR treatments had the highest rate of resistant carbon mineralization in relation to the other treatments.
In the Juma model, considering parameter (C 0 ), the SSUR and INCS treatments had the same amount of potentially mineralizable carbon, as there was an overlap in the confidence intervals. The same occurred in the INCMSSUR and INCMINCS treatments, as well as in the MSUR and INCM treatments, that showed the same amount of potentially mineralizable carbon. According to Silva et al. (2019b) and Giacomini et al. (2008), the result presented shows that there is a fraction of C in the residues that is difficult to decompose, regardless of whether they are incorporated into the soil or on the surface, whether they are in greater contact with the microorganisms.
Considering the confidence intervals for the estimation of parameter (v), half-life, in the Stanford and Smith model, there was no difference between the time spent to mineralize half of the potentially mineralizable carbon between the SSURMSUR and INCMINCS treatments. The S treatment in relation to the SSUR, INCMSSUR, INCMINCS and SSURMSUR treatments took longer to mineralize half of the potentially mineralizable carbon (PMC), this happens because there were no nitrogen supplied by manure and straw to the soil and, consequently, the growth and development of microorganisms were not stimulated (SAVIOZZI et al. 1997).
In the Cabrera model, taking into account the confidence intervals for the estimation of the half-life, there was a difference between the INCM and MSUR treatments, in which manure on the surface spent less time compared to the incorporated residues for half of the (C 1 ) to be mineralized.
In the Juma model, considering the confidence intervals for the estimation of parameter (v), treatment S spent more time than the others to mineralize half of (PMC), due to the lack of nitrogen from manure and straw (SAVIOZZI et 1997).
All models had excellent fits in all treatments, since the values of the adjusted coefficient of determination (R 2 aj) were above 95%, as can be seen in Table 5. In addition, for each treatment, similar values were obtained for the residual standard deviation of the models (Table 5). In the fit of nonlinear models, Stanford and Smith and Cabrera, for carbon mineralization of swine manure and oat straw in soil, Silva et al. (2019b) obtained values of R 2 aj greater than 0.97, indicating that the models adequately describe the data.
For all treatments, the most suitable model was the Cabrera one, as it presented the lowest AIC values and the highest R 2 aj values compared to the Stanford and Smith and Juma models; thus, these treatments present mineralizable carbon fractions with exponential behavior and more resistant fractions, with constant mineralization. The fit of the Cabrera model to the treatments can be seen in Figures 1 and 2.
In the literature, the Stanford and Smith model is widely used to describe the carbon mineralization in soil (FERNANDES et al., 2011;BARRETO et al., 2010;MARTINES et al., 2006). However, in the present study, this model did not obtain a better fit in the treatments under study, in relation to the Juma and Cabrera models. Table 5 -Estimates of the selection criteria: adjusted coefficient of determination (R²aj), Akaike Information criterion (AIC) and residual standard deviation (RSD) for the models fit in the description of mineralized carbon, in mg CO 2 kg -1 ,, of the treatments analyzed.     Table 6 lists the percentages of carbon mineralization (CM) of wheat straw alone and combined with swine manure. Based on the Stanford and Smith model, the carbon percentage of straw on the surface was approximately 39.0 %, and straw incorporated into the soil was approximately 53.0 %. Adding manure, straw mineralized approximately 60.0 %, indicating that the manure favored mineralization of the carbon of the straw, regardless of whether the straw is incorporated or on the soil surface. This increase in mineralization of straw incorporated in relation to straw on the surface may be related to the fact that microorganisms have a greater facility to decompose the materials incorporated into the soil (FERNANDES et al. 2011). In cases where the farmer decides to perform straw management and maintain this carbon stock as a soil cover in the area, it is interesting that the straw is not easily decomposed, and according to the results presented, in this case it is more feasible to use straw on the surface of the soil without using manure, as it would increase carbon mineralization of the straw, which could hinder management and leave the soil more exposed because of the consumption of carbon stock. On the other hand, the addition of manure to wheat straw can benefit the crop present in the area, as pig manure contains several nutrients in its composition, in addition to a large amount of nitrogen, that is quite required by most agricultural crops. Based on the Juma model, straw on the surface mineralized approximately 43.0 % added carbon; and the incorporated straw, approximately 67.0 %, which was expected, as the incorporation may have stimulated microorganisms to decompose the straw. With the addition of manure to the straw, carbon mineralization of straw was on average 77.0 %, regardless of whether the manure was incorporated or on the surface. This shows once again that the addition of manure to the straw increases carbon mineralization and the release of nutrients and, consequently, decreases the carbon stock that could be used as soil protection against weathering and invasive plants. Another noteworthy point is that the mineralization of straw in these treatments, with an average of 77%, obtained high rates of mineralization, and from an environmental point of view this is not good, as it causes an environmental impact due to the amount of CO 2 released into the atmosphere. On the other hand, with manure and straw incorporated into the soil, the percentage of mineralization was approximately 67.0 %.
In general, the treatments in which the straw was incorporated into the soil showed a higher percentage of mineralized carbon than the straw on the surface, thus leaving a smaller amount of carbon stock in soil. When pig manure was added to wheat straw, the percentage of mineralized carbon of the straw increased further, so the carbon stock of the straw decreased considerably because of mineralization. This is an interesting point for the farmer to consider in relation to the management of these residues, as the choice of whether or not to add manure to the straw will depend a lot on the production and management system the farmer wants to implant, because with the addition of manure, the soil becomes richer in nutrients over time; however, on the other hand, straw decomposition increased by the addition of manure may not be beneficial to the producer, as there may be an increase in the release of CO 2 into the environment, resulting in environmental impact. Moreover, straw on the soil has functions that are most often beneficial for soil conservation and crop production, such as controlling soil temperature, retaining water, increasing organic matter and controlling weeds.

Conclusions
The description of carbon mineralization of wheat straw and swine manure by nonlinear models was satisfactory.
The Cabrera model was the most suitable to describe the carbon mineralization of all treatments, since these treatments present mineralizable carbon fractions with exponential behavior and more resistant fractions, with constant mineralization.
The Stanford and Smith model, despite being widely used in the literature, did not achieve better results compared to the other nonlinear models evaluated in this study.
The treatments in which the straw was incorporated into the soil showed a higher percentage of mineralized carbon than the ones in which the straw was on the surface, thus leaving a smaller amount of carbon stock in soil. When swine manure was added to wheat straw, the percentage of mineralized carbon of the straw increased even further, so carbon stock of the straw decreased considerably because of mineralization.