2023年美赛特等奖论文-A-2303950-解密.pdf

A Methodology to Simulate Drought-Stricken Plant Communities

Summary

The study of plant communities in arid areas is an indispensable part of environmental

protection. In these regions, annual plants are important components of vegetation, by virtue

of their unique characteristics. This paper presents a method of simulation for the growth,

competition, and facilitation of annual plants, which can be applied to various circumstances.

To begin with, we establish the Growth Model of annual plants. At first, we determine

simulate their root competition. For the competition coefficient in Lotka-Volterra Model, we

innovatively determine its relationship with root growth and water-utilizing capacity of plants.

Considering the structure of root system, we estimate the parameters in the model reasonably.

Based on the Competition Model, we further establish the Facilitation Model of shrub

plants to herbaceous plants. Given the water-lifting action of shrub plants, we modify the water

absorption rate in the Competition Model. So far, our models have been elaborated and the

parameters have been estimated properly.

After that, we use the fourth order Runge-Kutta algorithm to give numerical solutions

to the differential equations. And the problems in the Requirement have been solved as follows:

⚫ Based on the results from our TOPSIS model, at least eight plant species are required

community will be decreased by over 67% and the fluctuation of the evolution will be

enlarged by over 36%. But these indexes still follow the similar trend in Section 5.2 as

the number of species grows regardless of different weather cycles.

⚫ The effects of two typical types of pollutants are compared. The results show that

pollutants such as acid rain are more dangerous because it can decrease the scale by 14.6%

and increase the fluctuation by 14.4% at the same time. Also, the diminishment of habitat

by 50% will cause the system to lose 22.9% of its scale but reduce 8.7% of its fluctuation.

⚫ Based on our model and analysis, our strategies are expressed from two main aspects：

the Preservation and Modification of the ecosystem.

Finally, the sensitivity and stability of the model are fully analyzed.

1 Introduction ...................................................................................................... 3

1.1 Background ...................................................................................................................... 3

1.2 Restatement of the Problem ............................................................................................. 3

1.3 Our Work .......................................................................................................................... 4

2 Assumptions and Justifications ....................................................................... 4

3 Notations ........................................................................................................... 5

4 Model Establishment ....................................................................................... 6

4.1 The Growth Model of One Species in Drought Circumstances....................................... 6

4.2 The Competition Model of Multiple Species ................................................................... 9

4.3 The Facilitation Model of Shrub Plants to Herbaceous Plants ...................................... 12

5.5 The Impact of Other Factors on Plant Community ........................................................ 19

5.6 Measures Needed for Long-Term Viability ................................................................... 20

6 Sensitivity Analysis and Stability Analysis .................................................. 21

6.1 Sensitivity Analysis ........................................................................................................ 21

6.2 Stability Analysis ........................................................................................................... 22

7 Strengths and Weaknesses ............................................................................. 24

7.1 Strengths ........................................................................................................................ 24

7.2 Weaknesses .................................................................................................................... 24

References .......................................................................................................... 25

changeable frequencies and wide range of severity. To be specific, plants are better adapted to

drought conditions in communities with several species, rather than in those with only one

species. Therefore, this phenomenon, which is a consequence of localized biodiversity, is of

great research value.

Considering the background information and limiting conditions identified in the problem

statement, we are supposed to address the following issues:

⚫ Build a mathematical model to describe drought adaptability with regard to the number of

species in a plant community. Notably, we need to predict what changes will take place

when a plant community is exposed to variable weather cycles. And our model should

the occurrence of droughts has fluctuant frequency and greater variation. Meanwhile, we

should also take other factors such as pollution and habitat reduction into consideration.

⚫ Illustrate what measures should be taken to ensure the long-term viability of a plant

community. Conclude the impacts of this phenomenon on the larger environment.

In this paper, we establish three mathematical models progressively and address six

problems, which are listed below:

To simplify the problems, we make the following assumptions, each of which is justified.

⚫ Assumption 1: The research object of this paper is mainly summer-type annual plants,

additional water supply between two rains.

⚫ Assumption 3: Water evaporation is directly proportional to the total water amount in the

soil in arid areas.

⚫ Assumption 4: Annual plants have a regular period of flowering and fruiting, and the

duration of flowering is short.

⚫ Assumption 6: In the experimental area, the plants distribute evenly.

⚫ Assumption 7: In the process of plant growth (between germination and flowering), the

death of the whole plant is not considered.

resource availability (soil water content)

the upper limit of water absorption rage

controls the variation trend of the uptake curve