The contemporary scientific scene is characterized by an exponential growth in the publication of scientific articles, mainly in digital format (^{Rubio et al. 2018}). In this context, there are different types of classical approximations that make it possible to summarize, interpret, and assess information, such as narrative reviews, systematic reviews, and metaanalysis (^{Huedo and Johnson 2010}).
Authors such as ^{Botella and Zamora (2017)} describe the narratives as imprecise and subjective, since they are based on the particular opinion of the writer. However, the systematics complies with the standards of the scientific method for their elaboration (^{Mikolajewicz and Komorova 2019}). ^{Toledo et al. (2018)} state that metaanalysis techniques also use all the steps of a systematic review, but include the statistical combination of the study results, with the objective of identifying consistent patterns in the data and the variation sources between them.
According to ^{Sánchez et al. (2011)}, metaanalysis has its beginnings in the medical, social and behavioral sciences. However, at present this type of technique is also beginning to be applied in the context of agricultural sciences, since it makes possible to reach new conclusions without the need for any experimentation.
In the agricultural sphere, the forages conservation through silage production allows supplying food of nutritional quality to cattle during the dry period (^{Espinoza 2016}). Specifically, in the scientific literature there is extensive information about the use of this conservation method, in which energy additives with high levels of fermentable carbohydrates are used, such as molasses, grains and tubers (^{Rodríguez et al. 2017}) with the objective of to favor lactic acid activity, achieve pH values below 4.0 and, finally, guarantee adequate forage conservation (^{Espinoza 2016}). In some studies it is possible to verify the improvement of the ensiled product, while in others no significant results are reported with the use of additives.
The objective of this study was to apply metaanalysis techniques to estimate the average effect of energy additives on the fermentative indicator pH, when ensiling tropical forages as a case study.
Materials and Methods
To perform the metaanalysis, the following steps, described by ^{Shah et al. (2020)} were fulfilled:
1. Information search sources and established inclusion / exclusion criteria. To search for information from the scientific literature, the Cuban Journal of Agricultural Science (CJAS) and the electronic databases EBSCO, ScienceDirect, Scielo and ResearchGate were consulted, without defining a specific time period to cover as many publications as possible.
Articles in Spanish, English and Portuguese were selected and the search terms were defined as silage/silage/silagem and additive/additive, which were combined with the Boolean operator “AND” or “OR”. Titles and abstracts were screened to exclude irrelevant reports, duplicate studies were deleted, the full text was recovered for relevant studies, papers were reviewed in their entirety to verify the degree of compliance with the established inclusion criteria, and finally, the necessary statistical data were obtained from each article.
The experimental studies that had the objective of ensiling tropical forages; researches where energy additives (molasses, cereal grains or industrial byproducts: meal and citrus pulp) were used as treatment/s and studies in which the efficacy of the treatment was compared in the experimental groups were stated as inclusion criteria. The variable pH was taken as the resulting measure and the position (mean) and dispersion statistics (standard deviation, standard error or coefficient of variation) were reported.
2. Reliability between reviewers. In accordance with the methodology, two reviewers were selected to independently identify and select the titles and abstracts derived from the search sources based on the fulfillment of the inclusion criteria. The Kappa index (^{Cortés and Guerra 2020}) was used to measure the degree of agreement between the reviewers.
3. Evaluation of the methodological quality of the studies. For the methodological assessment of the selected studies, the specific quality scale on chemical composition and nutritional value of forage silages, proposed by ^{Torres et al. (2018)} was used.
4. Data extraction. Coded moderating variables of the studies. For each of the studies, the data reported for the pH variable, with its position and deviation statistics, were tabulated. In addition, moderating variables were extracted and coded, and grouped into three categories: substantive, methodological, and extrinsic. The type of tropical grass used for ensiling, the grass age, the type of energy additive, the inclusion level of the additive and the days the silo was opened were considered as substantive. As methodological, the sample size, the applied experimental design and the methodological quality of the study were considered. The publication year of the research was selected as an intrinsic variable.
5. Statistical analysis of the metaanalysis. Effect size. The statistic effect size (ES) was calculated in all the studies and for each experimental group individually, using the equations proposed by ^{Sánchez et al. (2011)}:
Where:
d  
ES index that is used for the difference of standardized means 
Y_{e}  
mean value of the dependent variable in the experimental group 
Y_{c}  
mean in the control group 
S  
standard deviation of both groups 
c(m)  
correction factor for small samples 
The variances for treatment and control are defined as S_{e} ^{2} and S_{c} ^{2}, respectively. Similarly, the acronyms ne and nc show the sample sizes in the experimental and control groups, respectively.
Then, with all the individual indices of the ES, an average ES was estimated using a random effects model to obtain a summary result of the treatments efficacy, as well as its 95 % confidence interval to inform the precision of the effect (^{Borenstein et al. 2010}).
Where:
ES_{j}  
estimates around the parametric ES (θ) for each study (j = 1, 2…, k) 
e_{j}  
error given by intrastudy variability, which normally and independently distributes with zero mean and variance σ_{j}2; 
ξ_{j} 
product of the interstudy variability and normally and independently distributed with zero mean and variance U_{j}2. 
Heterogeneity analysis. According to ^{Rubio et al. (2018)}, to verify the presence of heterogeneity between studies, the Cochrane Q test was performed, whose result was complemented with the inconsistency (I^{2}) statistic. In case of showing interstudy variability, the subgroup analysis technique was used to analyze the qualitative moderating variables (^{Borenstein et al. 2010}), and for the quantitative variables, the regression model (metaregression), proposed by ^{Huedo and Johnson (2010)} was applied. The linear model was estimated using the weighted least squares method, where the selected moderating acts as independent variables and the ES as the dependent variable, according to the expression:
Publication bias. To verify the presence of publication bias, the rank correlation methods, described by ^{Begg and Mazumdar (1994)}, and linear regression analysis, proposed by ^{Egger et al. (1997)} were performed. Finally, to correct the bias, the trim & fill method (^{Duval and Tweedie 2000}) was implemented.
Statistical packages used. Data from studies for metaanalysis were tabulated in ^{Excel (2010)} in matrix form. Each row corresponds to a study and the columns to the moderating variables that characterize them. To determine the agreement between the reviewers, the information was processed in the statistical package ^{IBMSPSS version 22 (2013)}. The calculation of the individual ES, the estimation using a random effects model, the heterogeneity inter studies, the specific analyzes of the moderating variables and of the publication bias were carried out using the statistical package Comprehensive MetaAnalysis version 3.0 (^{Borenstein et al. 2014}).
Results and Discussion
The search by the information sources allowed locating a total of 197 studies. Once the inclusion criteria were verified in the full texts, a total of 16 studies were selected that were derived from 44 researchers and 194 observations, since sometimes the same study evaluated different energy sources with different inclusion levels. For the metaanalysis, the researchers were analyzed independently and each treatment was compared vs. the control. It is important to note that the minimum possible number of studies for metaanalysis is 10, since the methods for detecting publication bias are unreliable for lower values.
The values of the Kappa statistic for each information source were: 0.64; 0.68; 0.82; 0.80; 0.79, for Scielo, ResearchGate, EBSCO, ScienceDirect and CJAS, respectively. These results were higher than 0.60 in all cases, so the concordance is classified between adequate and excellent agreement, according to the scale proposed by ^{Huedo and Johnson (2010)}.
In the evaluation of the methodological quality of the studies, it was observed that the researchers selected to carry out the metaanalysis fulfilled 9 or more of the 12 total criteria of the scale proposed by ^{Torres et al. (2018)}, so the evaluation was considered of good methodological quality.
In the analysis of the average ES for the pH variable, it was observed (figure 1) that the weighted mean was d=3.077, with a confidence interval between 2.365 and 3.789, which shows that the mean ES was statistically significant, as it did not contain the null value in the interval (^{Huedo and Johnson 2010}). In figure 1 it is important to show that most of the studies showed significant results in favor of the treatment (addition of the energy additive) compared to the control, since the individual ES values were positive (right part of the graph). In this sense, it is corroborated that the addition of energy additives in the silage favors the decrease in pH (^{Rodríguez et al. 2017}).
The heterogeneity analysis showed variability in the data with respect to pH, since the Q statistic showed significant differences with P = 0.000. The value of I^{2} = 82.8 % quantified the existing variability. In accordance with what was stated by ^{Zimmermann et al. (2016)}, when this value is above 75 %, heterogeneity is classified as high. In addition, ^{Rubio et al. (2018)} suggest that when this index exceeds 50 %, it is necessary to analyze the moderating variables and determine how much they influence on the variability.
The subgroup analysis was carried out for the three qualitative moderating variables selected (type of additive, type of grass and experimental design) with their respective levels found in the literature. These levels correspond to rice meal, cassava meal, molasses and citrus pulp for the type of additive. The type of grass was fragmented into: Cynodon nlemfuensis, Brachiaria decumbens, Manihot esculenta (Leaves), Panicum maximum and Cenchrus purpureus. The experimental design was divided into: random block design (RBD), completely random design (CRD) and completely randomized with factorial arrangement. For the heterogeneity test of this type of analysis, the Q statistic was represented as Qbetween (QB), and tested the homogeneity between the levels of each qualitative moderating variable analyzed (^{Villasís et al. 2020}).
Table 1 shows how each moderating influences on the variability of the pH results. For each level of the variables, the mean ES, confidence intervals, amount of variability that it contributes in percentage (I^{2}), Q test and its significance were determined.
Moderating variables  Leves of moderating variables  Number of studies  d_{+}  95 % CI  I^{2}  Q test and its significance  

D_{lower}  D_{upper}  
Type of additive  Rice meal  6  5.118 ± 0.619  3.905  6.331  30 % 

Cassava meal  12  1.212 ± 0.224  0.773  1.650  24 %  
Molasses  12  4.003 ± 0.433  3.153  4.852  15 %  
Citrus pulp  8  0.589 ± 0.264  0.072  1.106  13 %  
Type of grass  C. nlemfuensis  6  3.318 ± 1.052  1.256  5.380  80 % 

B. decumbens  4  7.138 ± 0.871  5.431  8.846  80 %  
M. esculenta (leaves)  7  4.332 ± 1.247  1.888  6.777  79 %  
P. maximum  4  5.863 ± 0.621  4.646  7.080  86 %  
C. purpureus  20  1.115 ± 0.245  0.636  1.594  45 %  
Experimental design  RBD  5  0.596 ± 0.325  0.040  1.232  0 % 

CRD  28  2.059 ± 0.187  1.693  2.425  85 %  
CRD with factorial arrangement  9  1.903 ± 0.337  1.243  2.564  76 % 
The results of table 1 showed that for the three moderating variables there are significant differences (P = 0.000) between the different levels, which allows us to analyze each one separately. In the case of type of additive variable, there was not substantial heterogeneity, since at all of the additive levels the values of the I^{2} statistic are less than 50 % (^{Borenstein et al. 2010}), so that the moderating variable type of additive did not influence on the all variability of the metaanalytic analysis.
For the type of grass variable, it was observed that C. purpureus showed more homogeneous results between the studies, since the I^{2} index was less than 50 % (^{Borenstein et al. 2010}). However, the rest of the grass showed high variability, with index higher than 75 % (^{Zimmermann et al. 2016}), which could be related to the sample size. ^{Alvarado and Butanero (2008)} state that when the sample size is large enough, the distribution of means approximately follows a normal distribution with zero mean and constant variance (central limit theorem).
In the analysis of the moderating variable experimental design, there were significant differences between the designs used in the research, the CRD with the greatest application with 28 studies. In addition, this simple classification design, as well as the factorial arrangement, showed high variabilities in the analysis, which could be associated with the differences between the experimental conditions of each of the studies. However, the RBD was only applied in five studies, and did not contribute to the variability of analysis (I^{2} = 0 %) (^{Borenstein et al. 2010}).
For the metaregression analysis, a multiple linear regression was used, which allowed estimating the ES of the pH as a function of the quantitative variables. In the analysis, only the moderating that were significant in the model (P <0.05) were taken into account (table 2).
When considering equation 5, the parameters that were significant are substituted (table 2) and the expression to estimate the ES of the dependent variable pH was as follows:
Equation 6 shows the linear relation between pH and the independent variables. In this way, to achieve adequate pH values in the silage, the grass age used for ensiling, the amount of additive that is added, as well as the days on which the silo is opened for use, must be taken into account. The sample size had a positive influence on the estimate.
Regarding the dependence between the pH and the grass age, it is suggested that the most common thing in tropical grasses is that as it ages, its content of structural carbohydrates increases and the CHS decreases. The latter constitute the fundamental substrate for the silage fermentation process, from which lactic acid is obtained, which then contributes to decrease the pH for the conservation of the material (^{Espinoza 2016}).
Respect to the additive inclusion, it is important to point out that if the amount of fermentable substrate, necessary for adequate lactic fermentation, decreases, not enough lactic acid bacteria capable of producing the required lactic acid will develop and, therefore, the pH of the ensiled product increases (^{Valencia 2016}).
For the days of silo opening, it must be taken into account that the stabilization process of the fermentative processes in the silage is achieved between 15 and 21 d, moment in which the microbial processes are attenuated and the accumulation of necessary lactic acid occur, able of obtaining a pH with optimal values for the conservation of the product with its nutritional properties (^{Espinoza 2016}).
According to ^{Rodríguez et al. (2017)}, for practical purposes, it must wait a month to proceed to its opening, although for experimental purposes it is recommended to wait between 45 and 60 d to evaluate the quality of the ensiled product. That is why, if the days required to open the silo decrease, an ensiled material that does not have the necessary quality could be obtained. In the studies for the metaanalysis, the average opening values were approximately 58 d, which are in the interval suggested by the literature.
Table 3 shows the statistical criteria of the multiple linear regression analysis for the variable pH. According to ^{Sánchez et al. (2011)}, the Q statistic was represented as Q_{Regression} (Q_{R}) and Q_{Error} (Q_{E}).
Table 3 shows that the Q_{R} statistic was significant (P = 0.000), which showed that the estimated variable with its predictor variables had a correct linear relation. The Q_{E} statistic was also significant (p = 0.000), which showed that there must be other moderating variables in addition to those analyzed, which influence on the variability of the estimated ES, results that coincide with what was reported by ^{Sánchez et al. (2011)}.
In the analysis, a determination coefficient (R^{2}=11 %) was obtained, which corroborated the existence of other sources not studied, which may explain part of the variability of the data. Regarding this statistic, ^{Huedo and Johnson (2010)} report that these values will always be low or lower than the expected and it may even seem that the model does not have a good fit, but this type of result is something common in metaanalyzes, due to the great source of variability associated with the different studies that were selected.
Fernández et al. (2019) consider that publication bias represents a risk for the validity of any metaanalysis due to the selective publication of articles, so it should always be assessed. Egger and Begg tests showed significance values with p = 0.000, which indicated the presence of bias. Subsequently, the trim and fill method allow to identify the number of missing studies and estimated a new fitted ES (table 4).
Dependent variable  Number ofmissing studies to eliminate bias  d+  95 % CI  

D_{lower}  D_{higher}  
pH  8  2.379  1.631  3.126 
Table 4 shows the result of the new estimated value of the ES fitted for bias (d+ = 2.379). The difference between the estimate of the original ES and its value corrected for significance was examined and it was analyzed if the original estimate remained within the confidence limits of the corrected ES. According to ^{van Driel et al. (2009)}, the most important thing at this stage of the metaanalysis is not only knowing the existence of publication bias, but also its true impact on the conclusions of the study, so that its initial meaning does not change. Finally, the fitted result corroborates the effectiveness of the use of energy additives with respect to the control.
Conclusions
Despite the high variability found in the literature that was consulted (I^{2}>75 %), the metaanalysis techniques confirmed in a nonexperimental way the favorable effect of using energy additives to benefit the fermentative process of silage, since these additives make possible to reduce the pH to suitable values for the conservation of the final product. These results had an impact on two important elements in the research process, saving time and material and human resources. In this study, the description of each step of the methodology can be use as a guide to extrapolate and apply the metaanalysis to other spheres from the agricultural sector.