The use of microbial metabolic limitation techniques has the potential to provide insights into carbon and nutrient cycling in an ecosystem under the influence of climate change. This study aimed to determine the characteristics and potential mechanisms of microbial metabolic limitation at the different growth stages of winter wheat (Triticum aestivum L.) in response to elevated CO2 concentrations, warming and drought. Winter wheat plants were grown in artificial climate chambers, and a set of treatments were employed, including two levels of CO2 concentration (400 and 800 μmol·mol−1), a temperature regime (the current ambient temperature and a temperature increase of 4 °C) and water conditions (80% and 60% of the field water capacity). The results showed that the soil microbes were mainly limited by C and P. Microbial C limitation significantly decreased by 26.7% and 36.9% at the jointing stage and significantly increased by 47.6% and 42.6% at the grain filling stage in response to elevated CO2 and warming, respectively. The microbial P limitation significantly decreased by 10.9–13.0% under elevated CO2 at the anthesis and grain filling stages, while it was not affected by warming. Both microbial C and P limitations were unaffected by drought. The growth stage, soil dissolved organic carbon (DOC) and available phosphorus (AP) were the key factors affecting microbial C limitation, and microbial P limitation was mainly affected by the soil microbial biomass carbon (MBC), phosphorus (MBP) and microbial C:P ratio. Thus, the soil microbial C and P limitations differed with growth stages and were primarily indirectly affected by the available nutrients in the soil and the properties of the microbial biomass, respectively. These findings are important for understanding the mechanisms underlying microbe-mediated C and nutrient cycles. Overall, this study provides guidance for soil nutrient management in an agroecosystem experiencing climate change.
A nonlinear second-order ordinary differential equation with four cases of three-point boundary value conditions is studied by investigating the existence and approximation of solutions. First, the integration method is proposed to transform the considered boundary value problems into Hammerstein integral equations. Second, the existence of solutions for the obtained Hammerstein integral equations is analyzed by using the Schauder fixed point theorem. The contraction mapping theorem in Banach spaces is further used to address the uniqueness of solutions. Third, the approximate solution of Hammerstein integral equations is constructed by using a new numerical method, and its convergence and error estimate are analyzed. Finally, some numerical examples are addressed to verify the given theorems and methods.
MSC: 34B10; 45B05
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