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Microbes associated with phosphorus (P) cycling are intrinsic to soil P transformation and availability for plant use but are also influenced by the application of P fertilizer. Nevertheless, the variability in soil P in the field means that integrative analyses of soil P cycling, microbial composition, and microbial functional genes related to P cycling remain very challenging. In the present study in the North China Plain, we subjected the bacterial and fungal communities to amplicon sequencing analysis and characterized the alkaline phosphatase gene (phoD) encoding bacterial alkaline phosphatase in a long-term field experiment (10 years) with six mineral P fertilization rates up to 200 kg P ha–1. Long-term P fertilization increased soil available P, inorganic P, and total P, while soil organic P increased until the applied P rate reached 25 kg ha–1 and then decreased. The fungal alpha-diversity decreased as P rate increased, while there were no significant effects on bacterial alpha-diversity. Community compositions of bacteria and fungi were significantly affected by P rates at order and family levels. The number of keystone taxa decreased from 10 to 3 OTUs under increasing P rates from 0 to 200 kg ha–1. The gene copy numbers of the biomarker of the alkaline phosphatase phoD was higher at moderate P rates (25 and 50 kg ha–1) than at low (0 and 12.5 kg ha–1) and high (100 and 200 kg ha–1) rates of P fertilization, and was positively correlated with soil organic P concentration. One of the keystone taxa named BacOTU3771 belonging to Xanthomonadales was positively correlated with potential functional genes encoding enzymes such as glycerophosphoryl diester phosphodiesterase, acid phosphatase and negatively correlated with guinoprotein glucose dehydrogenase. Altogether, the results show the systematic effect of P gradient fertilization on P forms, the microbial community structure, keystone taxa, and functional genes associated with P cycling and highlight the potential of moderate rates of P fertilization to maintain microbial community composition, specific taxa, and levels of functional genes to achieve and sustain soil health.

Surface potential is an important parameter related to the physical and chemical properties of charged particles. A simple analytical model for the estimation of surface potential is established based on the Poisson-Boltzmann theory with the consideration of the dielectric decrement in mixed electrolyte. The analytical relationships between surface potential and charge density are derived in different mixed electrolytes with monovalent and bivalent ions. The dielectric decrease on the charged surface strongly affects the surface potential at a high charge density with different ion strengths and concentration ratios of counter-ions. The surface potential based on the Gouy-Chapman model is underestimated because of the dielectric decrement on the surface. The diffuse layer can be regarded as a continuous uniform medium only when the surface charge density is lower than 0.3 C•m −2 . However, the surface charge densities of many materials in practical applications are higher than 0.3 C•m −2 . The new model for the estimation of surface potential can return to the results obtained based on the Gouy-Chapman model at a low charge density. Therefore, it is implied that the established model that considers the dielectric decrement is valid and widely applicable.

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