Guide for the establishment of the decomposition model of the probability density function based on the hyphal extension rate of fungi

Abstract

The main purpose of this paper is to provide readers with a guide to mathematical modeling. The idea of establishing a model is roughly as follows: extract the probability factors of the research object, analyze the research object itself, observe the changes of the research object, and observe the effects of environmental changes on the research object. In this article, taking the 2021 American Mathematical Competition in Modeling (MCM) as an example, using the proposed modeling guidelines, a mathematical model was established to describe the decomposition of woody fiber by fungi, and the independent variable was set to hyphal extension rate, temperature conditions, climate conditions, etc. Set the dependent variable to decomposition rate, and fit a series of logarithmic expression and exponential expression according to the data provided by references[1][2]. Establish a community evolution model to realize the dynamic evolution of the interaction between different types of fungi, fungi with a higher competitive ranking will have a higher hyphal extension rate than the original without the interaction. As a result, fungi with a higher competitive ranking is in a dominant position in the colony, and fungi with a lower competitive ranking is in a subordinate or inferior position in the colony. In order to use the relative advantages and disadvantages of various fungi in different environments to predict the exact composition of fungi in the colony, considering the influence of initial climatic conditions on the evolution of the community, and bring about relative changes in the competitive ranking of different types of fungi. The model example in this article reflects the correctness of the modeling guidelines.