Is the Tea Bag Index (TBI) Useful for Comparing Decomposition Rates among Soils?

: The Bag Index (TBI) is a novel approach using standardized materials (i.e., commercial tea bags) to evaluate organic matter decomposition by determining two indexes: the early stage decomposition constant k ( k_TBI ) and litter stabilization factor S ( S_TBI ). k_TBI is deﬁned as the decomposition constant of an asymptote model describing the decomposition curve of rooibos tea, whereas S is the ratio of the stabilized to total hydrolysable fractions of green tea. However, it was recently revealed that both k_TBI and S_TBI deviate from the actual S and k values accurately determined by ﬁtting an asymptote model to the time series mass of green and rooibos teas remaining ( k_ﬁtting and S_ﬁtting , respectively). Nevertheless, k_TBI and S_TBI , which can be determined in a cost-and labor-effective manner, might indicate the relative values of k_ﬁtting and S_ﬁtting across different soils and be useful for comparative analyses. Therefore, this study investigated the positive correlations of k_TBI and S_TBI with k_ﬁtting and S_ﬁtting , respectively, in which case these indexes are useful for comparative analyses. However, the result showed that k_TBI was negatively correlated with k_ﬁtting . This study underscores the importance of obtaining time-series data for accurately determining the decomposition constant of an asymptote model describing the decomposition curve of rooibos tea. S_TBI was positively correlated with S_ﬁtting , implying that S_TBI can be used as an indicator of S .


Introduction
Decomposition is an essential ecological process with an important role in nutrient recycling and carbon dynamics. Accordingly, various studies have evaluated the impact of anthropogenic environmental changes, including climate change and eutrophication, on litter decomposition rates [1]. Because the impact on decomposition rates is largely influenced by the variability in litter chemistry, which regulates litter decomposition, standardized materials are essential for evaluating the global-scale impact of environmental changes on litter decomposition.
The Tea Bag Index (TBI) was proposed as a novel approach using standardized materials (i.e., commercial green and rooibos tea bags [2]) to evaluate organic matter decomposition. This approach was designed to determine two decomposition indexes, the decomposition constant k (hereafter k_TBI) and stabilization factor S (hereafter S_TBI), which indicate the early decomposition rate and litter stabilization, respectively [2] (see Figure 1). Originally, this approach was proposed for promoting citizen science [2], but researchers are increasingly using this approach for academic studies, including studies to clarify the precise decomposition mechanisms [3][4][5][6]. In the TBI approach, k_TBI is defined as the decomposition constant of an asymptote model describing the decomposition curve of rooibos tea (Figure 1b), while S_TBI is calculated as the ratio of the stabilized to hydrolysable fractions of green tea. The TBI approach enables determination of k_TBI and S_TBI using a single pair of mass loss values for the two types of tea during an approximately 90-day incubation ( Figure 1). Namely, time-series data are not required. This is possible because the TBI approach assumes that most of the unstabilized hydrolysable fraction of green tea is decomposed within 90 days (the first assumption), and the stabilization factor S (i.e., the ratio of the stabilized to total hydrolysable fractions) of rooibos tea equals that of green tea (second assumption). In the TBI approach, the hydrolysable fractions of green and rooibos teas were divided into unstabilized (i.e., ag and ar, respectively) and stabilized (i.e., 1 -ag and 1 -ar, respectively) fractions. Using the first assumption, ag can be approximated to the mass loss ratio of green tea at the end of the approximately 90-day incubation. Therefore, stabilization factor S (S_TBI) can be determined using the approximated ag and Hg (0.842, determined by Keuskamp et al. (2013) [2]) (i.e., 1 -ag / Hg, Figure 1). Using the second assumption, stabilized hydrolysable fraction of rooibos tea (i.e., Hr -ar) can be determined by multiplying Hr (0.552, determined by Keuskamp et al. (2013) [2]) by S_TBI, and therefore ar can be calculated as multiplication of Hr by (1 -S_TBI). k_TBI can be determined by fitting an asymptote model to the mass of rooibos tea remaining at the end of the approximately 90-day incubation (Figure 1, see also Section 2.2.).
However, Mori (2022) [7] recently reported that these essential premises for determining k_TBI and S_TBI are not always satisfied by demonstrating that both k_TBI and S_TBI deviated from k and S, respectively, which were determined accurately by fitting an asymptote model to the time-series mass of the remaining green and rooibos teas (k_fitting and S_fitting). Nevertheless, k_TBI and S_TBI, which can be determined in a cost-and labor-effective way, might be useful for comparative analyses, indicating the relative values of k and S across different soils. Therefore, this study investigated the correlations of k_TBI and S_TBI with k_fitting and S_fitting, respectively, to examine if they are positively correlated with each other, in which case these indexes are useful for comparative analyses. Data for the analysis were collected from literature on the time-series mass of both  [7]. The (a) left and (b) right figures are the decomposition curves of green and rooibos teas, respectively. a g and a r are the unstabilized hydrolysable fractions of green and rooibos teas, respectively. H g (0.842) and H r (0.552) are the hydrolysable fractions of green and rooibos teas, respectively. The S in the figure indicates S_TBI. The decomposition constant k (k_TBI) can be determined by fitting an asymptote model (Mass of rooibos tea remaining = a r × e -k×t + (1 − a r ), see Equation (4)), to the mass of rooibos tea remaining at the end of the approximately 90-day incubation.
In the TBI approach, k_TBI is defined as the decomposition constant of an asymptote model describing the decomposition curve of rooibos tea (Figure 1b), while S_TBI is calculated as the ratio of the stabilized to hydrolysable fractions of green tea. The TBI approach enables determination of k_TBI and S_TBI using a single pair of mass loss values for the two types of tea during an approximately 90-day incubation ( Figure 1). Namely, time-series data are not required. This is possible because the TBI approach assumes that most of the unstabilized hydrolysable fraction of green tea is decomposed within 90 days (the first assumption), and the stabilization factor S (i.e., the ratio of the stabilized to total hydrolysable fractions) of rooibos tea equals that of green tea (second assumption). In the TBI approach, the hydrolysable fractions of green and rooibos teas were divided into unstabilized (i.e., a g and a r , respectively) and stabilized (i.e., 1 − a g and 1 − a r , respectively) fractions. Using the first assumption, a g can be approximated to the mass loss ratio of green tea at the end of the approximately 90-day incubation. Therefore, stabilization factor S (S_TBI) can be determined using the approximated a g and H g (0.842, determined by Keuskamp et al. (2013) [2]) (i.e., 1 − a g /H g , Figure 1). Using the second assumption, stabilized hydrolysable fraction of rooibos tea (i.e., H r − a r ) can be determined by multiplying H r (0.552, determined by Keuskamp et al. (2013) [2]) by S_TBI, and therefore a r can be calculated as multiplication of H r by (1 − S_TBI). k_TBI can be determined by fitting an asymptote model to the mass of rooibos tea remaining at the end of the approximately 90-day incubation (Figure 1, see also Section 2.2.).
However, Mori (2022) [7] recently reported that these essential premises for determining k_TBI and S_TBI are not always satisfied by demonstrating that both k_TBI and S_TBI deviated from k and S, respectively, which were determined accurately by fitting an asymptote model to the time-series mass of the remaining green and rooibos teas (k_fitting and S_fitting). Nevertheless, k_TBI and S_TBI, which can be determined in a cost-and labor-effective way, might be useful for comparative analyses, indicating the relative values of k and S across different soils. Therefore, this study investigated the correlations of k_TBI and S_TBI with k_fitting and S_fitting, respectively, to examine if they are positively correlated with each other, in which case these indexes are useful for comparative analyses. Data for the analysis were collected from literature on the time-series mass of both green and rooibos teas remaining. An incubation study was performed to obtain time-series tea decomposition data under relatively dry conditions.

Incubation Study
An incubation study was performed to investigate the correlations of k_TBI and S_TBI with k_fitting and S_fitting, respectively, under relatively dry conditions. A surface soil sample (0-10 cm) collected in a Japanese cedar (Cryptomeria japonica [L. f.] D. Don) plantation at the Tatsudayama research site in Kumamoto, Japan (32.82 • N, 130.73 • E) was used for the incubation. The average annual temperature in the study area is 17.1 • C, and the annual precipitation is 1951 mm (Agro-Meteorological Grid Square Data of the National Agriculture and Food Research Organization). The soil sample was sieved through a 4 mm sieve. Large pieces of organic matter were removed from the soil sample. Because the incubation study aimed to obtain data under relatively dry conditions, the soil was pre-incubated to decrease the soil water content. The initial soil water content of 0.39 (w/w) decreased to 0.31 (w/w) during the 25 h drying process. After pre-incubation, green (EAN: 8714100770542; Lipton, London, UK) and rooibos (EAN: 8722700188438; Lipton, London, UK) tea bags were buried in 100 g of fresh soil in a polyethylene terephthalate bottle. Although Lipton has changed the bag material from 0.25 mm woven mesh to nonwoven mesh, the tea materials inside were unchanged (see Teatime 4 Science; https://www.teatime4science.org/ (accessed on 1 December 2021)). Therefore, I reproduced woven tea bags using the tea inside the nonwoven tea bags and 0.25 mm of mesh (For detailed information, see Mori et al. (2021) [8]). The teas were oven-dried at 70 • C for >72 h, and the initial mass was recorded before the start of incubation. Five bottles were placed in an incubator at 25 • C for 5, 13, 23, 58, and 90 days. The bottles were covered with polyethylene sheets to prevent water evaporation [9]. At the end of the incubation, the tea bags were immediately placed in an oven and dried at <70 • C to prevent further decomposition. Then, after cleaning the surface soil and removing the bags, the teas were oven dried at 70 • C for >72 h and weighed.
2.2. Determination of k_TBI, S_TBI, k_Fitting, and S_Fitting k_TBI was calculated following Keuskamp et al. (2013) [2] as follows: where Mloss_R is the mass loss ratio of rooibos tea during an incubation period of t days (generally t = 90), and a r is the unstabilized hydrolysable fraction of rooibos tea determined as follows (because it is assumed that the stabilization factor S of rooibos tea equals that of green tea): where H r (0.552) is the hydrolysable fraction of rooibos tea [2], and S_TBI is determined as follows: where H g (0.842) is the hydrolysable fraction of rooibos tea [2], and a g is the unstabilized hydrolysable fraction of green tea. In the framework of the TBI approach, a g equals the mass loss ratio of green tea during a 90-day incubation because it is assumed that most of the unstabilized hydrolysable fraction of green tea is decomposed within 90 days. k_fitting and S_fitting were calculated following Mori (2022) [7]. k_fitting was calculated by fitting the asymptote model to the mass of rooibos tea remaining as follows: Mass of rooibos tea remaining = a r _fitting × e −k_fitting×t + (1 − a r _fitting) where t is the number of days after the start of incubation. The asymptote (1 − a r _fitting) and k_fitting of the model were determined by nonlinear regression ("nls" library). The mass of green tea remaining was fitted by the asymptote model: Mass of green tea remaining = a g _fitting × e −k_fitting_G×t + (1 − a g _fitting) where the asymptote (1 − a g _fitting) and k_fitting_G of the model were determined by nonlinear regression in the same manner. S_fitting was determined by the following equation:

Data Collection from the Literature
Data were collected from published reports of k_TBI, S_TBI, and the time-series mass of green and rooibos teas remaining [2,7,10,11]. Data for aquatic ecosystems [12][13][14] were not included in this analysis, because the initial leaching of the soluble fraction would change the decomposition curves [13]. Data taken from field experiments [15] were also excluded because environmental conditions such as temperature and moisture were not constant during the incubation. Data using tea bags with nonwoven mesh were included. Different mesh sizes can affect the decomposition pattern of teas by changing the water content inside the tea bags or community composition of decomposers [11]. However, these changes are not problematic in this analysis because those changes influence the k_TBI, S_TBI, and time-series mass loss of green and rooibos teas similarly. To extract data from figures, DataThief 3.0 was used [16]. k_TBI, S_TBI, k_fitting, and S_fitting were calculated as described in Section 2.2. If the mass loss data of the teas were not reported on day 90 of an incubation study, the data were estimated using the fitted asymptote model (data from Keuskamp et al. (2013) [2]), or the data from day 91 were used instead (data from Duddigan et al. (2020) [10]). In the present analysis, data collected from the same study area but different subplots or from different incubation studies under different environmental conditions were treated as independent. A linear mixed-effects model with method (TBI vs fitting) as a fixed effect and incubation condition (such as soil type and incubated temperature) as a random effect was used to examine the differences between parameters (S, k, and asymptote) obtained by the TBI approach and those obtained by fitting the asymptote model to the time series data. R ver. 4.0.2 [17] was used for the statistical analysis.

Results and Discussion
All of the time-series data on the masses of both green and rooibos tea remaining after decomposition, including the data obtained in the present incubation study (Figures 2a and 3a), were well fitted by the asymptote model (Figures 2 and 3). The fittings of the asymptote model were much better than those of the single exponential model (Figures 2 and 3), which justified the use of the asymptote model rather than the single exponential model for describing the decomposition of teas in the TBI approach. The decomposition curves of rooibos tea were well described by the TBI-based asymptote model in some, but not all, of the incubation studies (Figure 2a,b,j,k,m-o). As Mori (2022) suggested, the TBI-based asymptote model did not well describe the decomposition curve in some soils (Figure 2d-g,i,r), most likely because the essential premise of the TBI approach, i.e., the stabilization factors of rooibos and green teas are equal, was not satisfied [7]. Indeed, the asymptote obtained by the fitting differed significantly from that calculated based on the TBI approach (p < 0.01, Figure 4c). The asymptote (i.e., 1 − a r ) was underestimated by the TBI approach because unstabilized hydrolisable fraction in rooibos tea (i.e., a r ) was overestimated by the TBI approach in most cases (Figure 5a). This unsatisfied assumption of the TBI approach resulted in significant differences between k_TBI and k_fitting (p < 0.01, Figure 4a). These results underscore the importance of obtaining time-series mass loss data of teas for accurately determining the early stage decomposition rate k of the asymptote model, as suggested previously [7,18]. of teas for accurately determining the early stage decomposition rate k of the asymptote model, as suggested previously [7,18].      The purpose of this study was to test if S_TBI and k_TBI are indicative of the relative values of S_fitting and k_fitting across different soils. If S_TBI and k_TBI are positively correlated with S_fitting and k_fitting, respectively, they can be used as an indicator of the relative decomposition rate across different soils, which would be useful for comparative analyses, although they do not determine k and S accurately. However, the results showed that k_TBI and k_fitting were not positively correlated but were significantly negatively correlated (Figure 6a). This indicates that k_TBI is not indicative of the asymptote modelbased decomposition constant k and is therefore not useful for comparative analysis of the decomposition rates of rooibos tea among soils. The negative correlation between k_TBI and k_fitting was observed probably because of the following mechanism. The overestimation of ar_TBI became greater as ar_fitting decreased (Figure 5a). Because smaller ar_fitting was associated with larger k_fitting (Figure 5b), greater overestimation of ar_TBI was associated with larger k_fitting. Because overestimation of ar_TBI causes underestimation of k_TBI [19], underestimation of k_TBI became greater as k_fitting became larger, which caused negative correlations between k_TBI as k_fitting. On the other hand, S_TBI and S_fitting were significantly positively correlated (Figure 5b), indicating that S_TBI can be used as an indicator of S. Furthermore, the regression line was close to the 1:1 line, and  The purpose of this study was to test if S_TBI and k_TBI are indicative of the relative values of S_fitting and k_fitting across different soils. If S_TBI and k_TBI are positively correlated with S_fitting and k_fitting, respectively, they can be used as an indicator of the relative decomposition rate across different soils, which would be useful for comparative analyses, although they do not determine k and S accurately. However, the results showed that k_TBI and k_fitting were not positively correlated but were significantly negatively correlated (Figure 6a). This indicates that k_TBI is not indicative of the asymptote modelbased decomposition constant k and is therefore not useful for comparative analysis of the decomposition rates of rooibos tea among soils. The negative correlation between k_TBI and k_fitting was observed probably because of the following mechanism. The overestimation of ar_TBI became greater as ar_fitting decreased (Figure 5a). Because smaller ar_fitting was associated with larger k_fitting (Figure 5b), greater overestimation of ar_TBI was associated with larger k_fitting. Because overestimation of ar_TBI causes underestimation of k_TBI [19], underestimation of k_TBI became greater as k_fitting became larger, which caused negative correlations between k_TBI as k_fitting. On the other hand, S_TBI and S_fitting were significantly positively correlated (Figure 5b), indicating that S_TBI can be used as an indicator of S. Furthermore, the regression line was close to the 1:1 line, and The purpose of this study was to test if S_TBI and k_TBI are indicative of the relative values of S_fitting and k_fitting across different soils. If S_TBI and k_TBI are positively correlated with S_fitting and k_fitting, respectively, they can be used as an indicator of the relative decomposition rate across different soils, which would be useful for comparative analyses, although they do not determine k and S accurately. However, the results showed that k_TBI and k_fitting were not positively correlated but were significantly negatively correlated (Figure 6a). This indicates that k_TBI is not indicative of the asymptote modelbased decomposition constant k and is therefore not useful for comparative analysis of the decomposition rates of rooibos tea among soils. The negative correlation between k_TBI and k_fitting was observed probably because of the following mechanism. The overestimation of a r _TBI became greater as a r _fitting decreased (Figure 5a). Because smaller a r _fitting was associated with larger k_fitting (Figure 5b), greater overestimation of a r _TBI was associated with larger k_fitting. Because overestimation of a r _TBI causes underestimation of k_TBI [19], underestimation of k_TBI became greater as k_fitting became larger, which caused negative correlations between k_TBI as k_fitting. On the other hand, S_TBI and S_fitting were significantly positively correlated (Figure 5b), indicating that S_TBI can be used as an indicator of S. Furthermore, the regression line was close to the 1:1 line, and the difference between S_TBI and S_fitting was not significant (p = 0.49, Figure 4b). Although a previous study reported that S_TBI and S_fitting were slightly but significantly different [7], the difference might be negligible. More data are required to examine this. the difference between S_TBI and S_fitting was not significant (p = 0.49, Figure 4b). Although a previous study reported that S_TBI and S_fitting were slightly but significantly different [7], the difference might be negligible. More data are required to examine this. The finding that the k_TBI does not indicate the asymptote model-based decomposition constant k does not reduce the value of the TBI approach. The tea bags provide effective standardized materials for evaluating organic matter decomposition; the method is cost-effective and reduces the effort needed to prepare litter bags. Because of these advantages, obtaining time-series data is not difficult using the TBI approach, and I recommend obtaining time-series data to determine the early-stage decomposition constant k of rooibos tea. Alternatively, to reduce the effort in obtaining decomposition data as much as possible, I recommend using the raw mass loss data of rooibos tea, rather than k_TBI, as suggested previously [19], because k_TBI is biased by an unsatisfactory assumption of the TBI approach: the stabilization factors of rooibos and green teas are equal.
This study demonstrated that k_TBI does not indicate the relative decomposition rate across different soils and is not useful for comparative analyses. However, it might be possible to overcome the unsatisfactory assumption of the TBI approach to improve the k_TBI calculation if the asymptote of the rooibos tea decomposition curve can be predicted by the mass loss data of green tea (Figure 5a, note that ar_TBI is the constant factor of ag_TBI). Because the currently obtained data are insufficient to test this, more time-series data need to be obtained from various soil types.

Conclusions
The present study examined if k_TBI and S_TBI, which can be determined in a costand labor-effective manner, indicates the relative values of k_fitting and S_fitting across different soils and be useful for comparative analyses. The correlations of k_TBI and S_TBI with k_fitting and S_fitting, respectively, were examined, because if they are positively correlated with each other, these indexes are useful for comparative analyses. However, the result showed that k_TBI was negatively correlated with k_fitting, indicating that k_TBI is not indicative of the asymptote model-based decomposition constant k and is therefore not useful for comparative analysis of the decomposition rates of rooibos tea among soils. This study underscores the importance of obtaining time-series data for accurately determining the decomposition constant of an asymptote model describing the decomposition The finding that the k_TBI does not indicate the asymptote model-based decomposition constant k does not reduce the value of the TBI approach. The tea bags provide effective standardized materials for evaluating organic matter decomposition; the method is cost-effective and reduces the effort needed to prepare litter bags. Because of these advantages, obtaining time-series data is not difficult using the TBI approach, and I recommend obtaining time-series data to determine the early-stage decomposition constant k of rooibos tea. Alternatively, to reduce the effort in obtaining decomposition data as much as possible, I recommend using the raw mass loss data of rooibos tea, rather than k_TBI, as suggested previously [19], because k_TBI is biased by an unsatisfactory assumption of the TBI approach: the stabilization factors of rooibos and green teas are equal.
This study demonstrated that k_TBI does not indicate the relative decomposition rate across different soils and is not useful for comparative analyses. However, it might be possible to overcome the unsatisfactory assumption of the TBI approach to improve the k_TBI calculation if the asymptote of the rooibos tea decomposition curve can be predicted by the mass loss data of green tea (Figure 5a, note that a r _TBI is the constant factor of a g _TBI). Because the currently obtained data are insufficient to test this, more time-series data need to be obtained from various soil types.

Conclusions
The present study examined if k_TBI and S_TBI, which can be determined in a costand labor-effective manner, indicates the relative values of k_fitting and S_fitting across different soils and be useful for comparative analyses. The correlations of k_TBI and S_TBI with k_fitting and S_fitting, respectively, were examined, because if they are positively correlated with each other, these indexes are useful for comparative analyses. However, the result showed that k_TBI was negatively correlated with k_fitting, indicating that k_TBI is not indicative of the asymptote model-based decomposition constant k and is therefore not useful for comparative analysis of the decomposition rates of rooibos tea among soils. This study underscores the importance of obtaining time-series data for accurately determining the decomposition constant of an asymptote model describing the decomposition curve of rooibos tea. Nevertheless, S_TBI was positively correlated with S_fitting, indicating that S_TBI can be used as an indicator of S.