Ajuste de modelo de regressão linear múltipla em dados de δ15N do solo para o Bioma Cerrado

Abstract

Nitrogen plays a fundamental role in primary productivity and the structure of terrestrial ecosystems. In some biomes, such as the Cerrado, nitrogen is a limiting nutrient for productivity. Therefore, it is essential to understand the processes that affect its availability and transformations. Stable nitrogen isotopes (δ15N) provide an integrated measure of these processes, allowing for the assessment of the relative contribution of different nitrogen sources to the environment, such as atmospheric deposition and biological fixation. Understanding the variation of δ15N in soil provides a comprehensive understanding of the nitrogen cycle and its effects on terrestrial ecosystems. In this context, the objective of this study was to propose a predictive and explanatory model for soil δ15N in the Cerrado biome. A total of 97 soil samples were collected from various locations within the biome. Values of climatic and biophysical predictor variables were extracted from secondary spatial data for each location, and soil variables were obtained from laboratory analyses. In total, 46 predictor variables of δ15N were included in the database. A multiple linear regression model was fitted including all predictive variables with some significant correlation with the dependent variable. Subsequently, regression models were adjusted following the assumptions of regression analysis. Correlation matrices were used to eliminate correlated predictor variables, avoiding multicollinearity. The final model was adjusted after selecting the best variables using the stepwise AIC method. The residuals of the final model were tested for normality, homoscedasticity, autocorrelation, and spatial autocorrelation. Leave-One-Out cross-validation was applied to assess predictive performance. The first model (Model 1), adjusted with all variables, achieved an R2adj of 0,66 and an R2 of 0,81 after cross-validation. Despite its high predictive power, Model 1 did not meet the assumptions of multiple linear regression, which hinders the interpretation of the model coefficients. The final model followed all assumptions of multiple linear regression and achieved an R2adj of 0,57 and an R2 of 0,59 after cross-validation. Despite its lower predictive power, the coefficients of the model can be interpreted. The variables that contributed to the adjustment of the final model were Ca2+ concentration, soil δ13C, temperature seasonality, annual temperature range, and precipitation in the wettest quarter. All these variables were significant for the final model and exhibited coefficients consistent with their expected contribution to the variation of soil δ15N. The adjusted model brings advancements in the study of the nitrogen biogeochemical cycle for the Cerrado biome, as it incorporates soil data and indicates a positive and yet underexplored influence of Ca2+ on soil δ15N. Despite the progress, the final model may have excluded important predictor variables in explaining the phenomenon due to variable selection criteria and the method used. Future studies should apply methods that identify non-linear relationships among variables.