【免费】2021年美国大学生数学建模竞赛A题M奖论文1资源-CSDN文库

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Problem Chosen

2021

MCM/ICM

Summary Sheet

Team Control Number

2113656

Fungus: Who Moved My Woody Fibers

Summary

The carbon cycle includes the decomposition of plant material and woody fibers. In nature,

fungi are the main decomposers. The decomposition rate of fungi is determined by two traits: the

growth rate of the fungus and their tolerance to moisture. In this paper, our goal is to model the

decomposition of woody fibers and analyze the interactions between different species.

In view of a single type of fungus living in America, firstly, we use the exponential decay

model to describe the decomposition process. Then we fit the experimental data related to growth

rate and moisture resistance to obtain the function between the decomposition rate and these two

traits. Finally, we establish the decomposition model of a single species of fungus. Taking five

types of fungi as examples, we get their decomposition processes respectively shown in Figure 6.

In view of various types of fungi living in America, we analyzed the short-term and

long-term trends respectively. In a short period of time, various species grow independently.

The total average decomposition rate is the sum of each. Then we establish the decomposition

model of various species in short-term. The simulated decomposition process is shown in Figure

7. In a long period of time, the species will influence on each other. We improved the Logistics

differential equation model and established a competition model of various species. After using

the Runge-Kutta method, we get their succession and decomposition process with interactions

shown in Figures 8 and 9.

Based on the above two models, we consider the impact of global warming and climate

conditions changes on the model. First, according to the time series ARIMA (0,1,1), we predict

the future annual average temperature in America. Compared with 2020, temperature conditions

in 2060 will cause the extinction of three species (Figure 13). Next, we bring the environmental

conditions of five representative climates into the competition model. Results show different

climates lead to different endings of competition (Figure 15).

Using the above two models, we find that as the number of fungal species increases, the

overall decomposition efficiency of ground litter continues to increase. And we analyze that

biodiversity plays a huge role in maintaining system stability.

Keywords: Fungus The carbon cycle Biodiversity of fungi The decomposition model

The Competition model of various species Differential equation

Team#2113656    Page  2  of 25   
Contents 
  Introduction ............................................................................................................................... 3 
1    Background ..................................................................................................................... 3 
2    Restatement of the Problem ............................................................................................ 3 
  Analysis of the Problem ............................................................................................................ 4 
  Assumptions .............................................................................................................................. 5 
  Symbols..................................................................................................................................... 6 
  The Decomposition Process of Fungi ....................................................................................... 6 
1    The Decomposition Model of Single Species ................................................................. 7 
2    The Decomposition Model of Various Species ............................................................... 9 
3    Simulations Based on The Decomposition Model ........................................................ 10 
  The Interactions Between the Various Species of Fungi..........................................................11 
1    The Competition Model of Various Species ..................................................................11 
2    Solutions of The Competition Model ........................................................................... 13 
3    Sensitivity to Environmental Fluctuations .................................................................... 15 
  The Impact of Biodiversity ..................................................................................................... 18 
1    The Impact on Decomposition Efficiency .................................................................... 18 
2      The Importance and Role of Biodiversity ................................................................... 19 
  Model Test............................................................................................................................... 20 
1    Analysis of Sensitivity .................................................................................................. 20 
2      Analysis of Robustness ............................................................................................... 20 
  Strengths and Weaknesses ...................................................................................................... 21 
1    Strengths ....................................................................................................................... 21 
2    Weaknesses ................................................................................................................... 22 
  An Article for Fungi .............................................................................................................. 23 
  References ............................................................................................................................. 25 
 
 
 
 
 
 
 
 
 
 

Team#2113656 Page 4 of 25

between different types of fungi, and the different performance of the dynamic

characteristics of the interaction in short-term and long-term trends should be characterized

and described. When the environment fluctuates rapidly, we need to test the sensitivity of the

model and determine the overall impact of changing atmospheric trends, so as to assess the

impact of local weather changes on the model.

⚫ We need to predict the relative advantages and disadvantages for each species and

combinations of species that may last for a period of time, and do so for the different

environments of arid, semi-arid, temperate, arbor, and tropical rainforest.

⚫ Analyze how the diversity of fungal communities of a system affects the overall efficiency

of ground waste decomposition. When there are varying degrees of changes in the local

environment, predict the importance and role of biodiversity.

⚫ By establishing and solving above models, we need to write a two-page article to discuss the

latest progress in our understanding of the role of fungi play in ecosystems.

2 Analysis of the Problem

⚫ Based on the Mitscherlich equation, we build a litter attenuation model conforming to the

negative exponential form. From the figures of the paper, we believe that the average

decomposition rate of the plant material and woody fibers is affected by the growth rate and

moisture resistance of the fungus (fungi). We fit this set of experimental data with a power

function and an exponential function, and found the equivalence relation between the growth

rate, the moisture resistance and average decomposition rate. Based on this, we show the

change of remaining proportion over time (single species) (Figure 6).

⚫ When a variety of fungi gather together, there is interactions between them, which is mainly

competition. We divide the decomposition process of various species into short-term and

long-term. In a short period of time, we believe that each fungus decomposes litter

independently, when the decomposition of litter by multiple groups can be considered as the

sum of individual’s. Taking five groups as an example, we show the change of remaining

proportion (various species, short-term trends) (Figure 7).

⚫ Over a long period of time, the result of fungal competition can be measured by the steady

state of the extension length of the hyphae. Based on the Logistics model and the

Lotka-Volterr model, we establish a competition model of various species, and measure the

contribution of different fungi in decomposition with the steady-state dominant

species-inferior species (Figure 8), and show the above five the change of remaining

proportion with competitions (various species, long-term trends) (Figure 9).

Team#2113656 Page 5 of 25

⚫ Since the external environment will determine the succession of the community, we

separately consider the impact of global warming and climate change on the model.

According to the time series ARIMA(0,1,1), we predict the annual average temperature of

North America in 2060 (Figure 12), which is 1.2℃ higher than 2020. We find that such a

small temperature change will cause three of the five species perish (Figure 13). Under the

different environments including arid, semi-arid, temperate, arboreal, and tropical rain

forests, the competition results of populations vary (Figure 15).

⚫ Considering the fungus and different combinations of fungi, we find that when the extension

length increases, the overall efficiency of ground garbage decomposition continues to

increase (Table 4). As for single fungus, environment change may cause the growth rate

greatly reduced, which hinder decomposition. But as for multiple groups, even if

environment change result in different results in the steady state of competition, the

decomposition rate is impacted little.

Figure 2: Problem solving ideas

3 Assumptions

⚫ In a short period of time, there is no interaction between different species of fungi

living in the same environment. In the early stages of growth, for all kinds of species,

resources such as nutrients, space, and dissolved oxygen are sufficient. Therefore, in the

short term, the adverse effects from other species on the growth of fungi can be ignored.

⚫ The interaction between different species of fungi is only equal to the competitive

relationship. When different types of fungi live in the same environment, there are complex

interrelationships between them, such as competition, cooperation, symbiosis and so on, but

competition is the most important and common relationship, so we can ignore other types of

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