Fig. 5

Structural equation model (SEM) illustrating the effects of nitrogen fertilizers, soil physicochemical properties, and bacterial and fungal community on alpha diversity (faith_pd index) of the protist community in the black (a) and red soil (b) in summer, and in the fluvo-aquic (c) and red soil (d) in autumn in which protist diversity was significantly reduced. Continuous and dashed arrows represent significant and nonsignificant relationships, respectively. Adjacent numbers that are labeled in the same direction as the arrow are path coefficients, and the width of the arrow is in proportion with the degree of path coefficients. Green and red arrows indicate positive and negative relationships, respectively. r² values indicate the proportion of variance explained for each variable. Significant levels are denoted *P < 0.05, **P < 0.01, ***P < 0.001. Standardized total effects (direct plus indirect effects) calculated by the SEMs (a, b, c, d) are displayed in e, f, g, h, respectively. The low chi-square (χ²), nonsignificant probability level (P > 0.05), high goodness-of-fit index (GFI > 0.90), low Akaike information criteria (AIC), and low root-mean-square errors of approximation (RMSEA < 0.05) listed below the SEMs indicate that our data matches the hypothetical models