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Fungi are of great functional significance in terrestrial ecosystems as the main decomposers. To better understand their decomposing process and population coexistence, we first describe and quantify the decomposition rate, focusing on three traits of interest selected by machine learning algorithm: moisture tolerance, hyper extension rate, and hyphal density and obtain, and use a Ternary Linear Regression Decomposition Model (TLRDM) to quantify the decomposition rate. Then, to incorporate the interactions, we build an Interactive Decomposition Model (IDM) and creatively employ a Three-player Logistic-based Competition Population Model (TPLCM). Based on logistic growth, we formulate a differential equation group, fit the curves of this unsolvable equation group to obtain a function of population density versus time and compare the decomposition rates of three populations under interactive and non-interactive conditions, followed by analyzing the impact of the communications on decomposing ability. We obtain the population combinations that can coexist in certain climates. Furthermore, we include environmental factors, conducting a sensitivity analysis to describe how short-term and long-term climate changes affect our models.