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As the key medium for decomposing wood fibers, fungi play a vital role in promoting the carbon cycle. The purpose of this paper is to establish mathematic models describing the process of fungi decomposing litter and wood fiber. The paper comprehensively consider the effects of temperature, moisture, location and other factors on fungal traits, and introduced the experimental data of the US Forest Service Center for Forest Mycology Research (CFMR).Based on the model of competition among populations and the modern coexistence theory, this paper establishes the competitive model between two fungi, then generalizes it to a variety of fungi and predicts the short-term and long-term effects.