Gompertz model describing co2 evolved from legumes in the soil: bayesian approach with maximum entropy prior

Abstract

For residues maintained on the soil surface, microbial colonization of the substrate is slower initially due to the microbial population's adaptation phase to the substrate. Subsequently, decomposition becomes more intense due to easily mineralizable matter, and as the process progresses, there is a predominance of more resistant materials that can reduce microbial attack. Thus, the maximum rate of CO₂ release occurs in the early days of decomposition, and this process is described by the Gompertz model, which is a nonlinear sigmoidal regression model. The theory for regression models is valid for sufficiently large samples, and generally, in research with carbon mineralization data, few observations are used, and parameter estimation should preferably be done using Bayesian methodology since prior information is incorporated, reducing the effect of having few observations. One way to determine objective priors is through maximum entropy prior distributions. This study aims to fit the Gompertz model to the release of carbon dioxide over time from leguminous species using a Bayesian approach with maximum entropy priors for the model parameters. The treatments (leguminous species) evaluated were Arachis pintoi, Calopogonium mucunoides, Stylosanthes guianensis, and Stizolobium aterrium. Eight observations of carbon released over time up to 480 hours from the start of incubation were made. In the soil with the addition of legumes, the abscissa of the inflection point was estimated between 4 and 5 days, meaning this was the time the microorganisms needed to reach the maximum decomposition rate. The species A. pintoi showed the average estimate of 481 mg CO₂ of potentially mineralizable carbon, being the species that released the most carbon.