Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 5, No. 2, 2023 

 

187 

Quantitative Analysis of Plant Population Quantity and 
Species Adaptation to Drought Based on Differential 
Dynamics Model 
Qi Hua1, Bo Wang2, Shuoxing Zhang2 
1 School of Overseas Education, Nanjing Tech University, Nanjing, 211816, China 
2 School of Mathematical Sciences, Nanjing Tech University, Nanjing, 211816, China 

 
Abstract: To address the impact of drought on species changes in plant communities, first, based on the weather data obtained 
in Area A, a Markov weather prediction model was constructed to simulate the changes in irregular weather in that area, and the 
probability of drought was found to be 54.73%. Then, a differential dynamics model was established to simulate the changes in 
plant populations, and ultimately the population changes with weather were obtained. Secondly, an optimization model was 
constructed from the population number to the total number of plants, and the optimal population number was obtained through 
numerical simulation. Thirdly, under the condition that other factors remain unchanged, the species number charts with weather 
changes are simulated, and the impact of different species types on the environment is analyzed. Thirdly, based on the above 
weather change results, increase or decrease the probability of dry weather factors, and obtain a change map of the number of 
species to analyze the impact on the environment. The research shows that when the pollution is light, the plant community will 
not be greatly affected, while when the pollution is serious, the plant population will degenerate. When habitat decreases, the 
growth rate of plant communities slows down. 

Keywords: Plant community, Drought; Markov model, Differential dynamics, Simulated prediction. 
 

1. Introduction 
1.1. Problem Background 

Drought is a common weather condition in some areas. The 
viability and response of different plant communities vary. 
There are also many levels of drought, and different plant 
communities show different responses to different levels of 
drought. And as the number of plant species increased, they 
were better able to cope with higher levels of drought than 
communities with just one plant species. The city A we 
studied has a temperate continental climate. The average 
annual temperature is 10.3℃, and the average annual 
precipitation is 360-400 mm, mainly from June to September. 

1.2. Literature Review 
Liang-liang Zhang et al. (2018) conducted a study on the 

impact of garden plant communities on summer microclimate 
characteristics [1]. Cen Yang et al. (2022) took the park green 
space in HuaiHua City, Hunan Province as an example to 
analyze the ability of plant communities to regulate 
microclimate comfort and its impact factors [2]. Dong-dong 
Duan (2022) conducted a study on the impact of drought and 
its soil legacy effects on the growth of typical grassland plants 
on the Loess Plateau [3], while Yu-lin Huang et al. (2022) 
provided an analysis on the impact of plant community 
characteristics on the microclimate in summer park shade 
space [4]. In this paper, based on the weather data obtained in 
Area A, we understand the probability of drought occurrence, 
establish a differential dynamics model to simulate changes 
in plant populations. From the population number to the total 
number of plants, we obtain the optimal population number 
through numerical simulation, and analyze the impact of 
different species types on the environment, in order to study 
the impact of changes in the number of species on the 
environment. 

1.3. Restatement of the Problem 
Considering the background information and restricted 

conditions identified in the problem statement, we need to 
solve the following problems: Develop a mathematical 
model to address the changes of the same plant community in 
different weather conditions (sunny, cloudy, rainy, snowy and 
weather changes) and study their adaptation differences. 
To further study the number of species in plant communities 
and how species types change their adaptability to arid 
environments. For the first two problems, external factors, 
such as environmental pollution and habitat reduction, should 
be taken into account to analyze the impact on the plant 
community and provide methods to protect the long-term 
survival of the plant community. 

2. Sources and Assumptions of Data 
The data in this article is derived from Question A of the 

2023 American College Student Mathematical Modeling 
Competition. In order to facilitate problem solving, the 
following assumptions are proposed: The same plant has 
the same effect on other plants. In order to simplify the study 
of the model, the result of the problem is clearer. For example, 
let's assume that plant 1 has the same effect on plant 2 as plant 
1 has on other plants. Each plant has the same effect on the 
other plants, but let's think about different plants having the 
same effect on the other plants. For region A, the annual 
precipitation greater than 1200mm is not considered. The 
region A studied in this paper belongs to the temperate 
continental climate, with perennial drought and little rain. The 
main precipitation in Region A is only from June to September. 
Precipitation exceeding 1200mm is a small probability event, 
so we do not consider annual precipitation exceeding 
1200mm. 



 

188 

3. Adaptation Differences of the Same 
Plant Community under Different 
Weather Conditions Based on 
Markov Chain Model 

3.1. Research Ideas 
For plant communities affected by drought, select 

precipitation, species type, species number, interplanting 
impact, environmental capacity, and pollution in dex. Firstly, 
Markov models are used to predict how the weather will 
change over time in the future. Precipitation is then used to 

reflect varying degrees of weather change. Finally, a 
differential dynamics model is used to consider the effects of 
species interactions and species numbers on the prediction 
results.  

3.2. Research Method 
Weather conditions can be divided into many kinds, can be 

divided into sunny, cloudy, light rain, heavy rain, light snow 
and heavy snow, this weather is classified into four categories, 
respectively: sunny, cloudy, light, heavy [5] Weather 
Classification Standard is shown in Table 1. 

 
Table 1. Weather Classification Standard

Number Weather Weather condition 
0 Sunny Clear, clear to cloudy 
1 Cloudy Cloudy, cloudy to sunny, cloudy to cloudy, cloudy to rain (snow) 

2 Light Light rain (snow), light rain (snow) to clear, light rain (snow) to cloudy, light 
rain (snow) to heavy rain 

3 Heavy Heavy rain (snow), heavy to torrential rain (snow), heavy rain (snow) 
 

We set the state 0 for those with annual precipitation less 
than 200mm as arid zone (which is shown in Figure 1). When 
the annual precipitation is between 200mm and 400mm, it is 
set as state 1, which is semi-arid zone. When the annual 
precipitation is 400mm to 800mm, it is set as state 2, which is 
subhumid area. When the annual precipitation ranges from 
800mm to 1200mm, it is set as state 3, which is a humid area 

[6]. 
 

 
Figure 1. Annual precipitation 0 to 1200mm color scale plot. 

 

 
Figure 2. Annual precipitation distribution map of City A in the country. 

 

The average annual precipitation of city A is shown in 
Figure 2. We study the typical Markov model of weather 
changes, and the conditions of a system at a given time in the 
future are only relevant to the present, not directly related to 
the past history. So we use Markov chain to predict the future 
weather, let { , 1,2,3, }nX n }  be a random sequence, state 
space E is a finite or column able set, for any positive integer 
m, n, if , , ( 1,2, , 1)ki j i E k n, 1),,  , where is as follow 

formula (1):  

1 1 1 1{ | , , , } { | } ( )n m n n n n m n ijP X j X i X i X i P X j X i p m1 111 111 11 11 (1) 
 
It's called a Markov chain. It has no aftereffect. 

3.3. Result Analysis.  
According to the table 2, the weather transfer data is shown 

in Figure 3. 
 



 

189 

 
Figure 3. Statistical chart of weather conversion probability for Region A from February 2020 to February 2022. 

 
The probability of obtaining the one-step transition matrix 

is as follow formula (2): 
 

(1)

0.639098 0.240602 0.097744 0.022556
0.453488 0.261628 0.191860 0.093024
0.452174 0.252174 0.234783 0.060869
0.325581 0.069767 0.348837 0.255815

P      (2) 

 
Using the C-K equation, we can get: 
 

( )n n

n

P P P P P
n

P PP P P              (3) 

 
Finally, the limit distribution of the transition probability 

matrix can be calculated as: 
 

( )lim 0.547319 0.237316 0.15633 0.05904n

n
P     (4) 

 
We conducted invariant measure test on the result: 
Suppose: 1 2 3 4( , , , )  
 

, 0, 1i ij j j i
i i

P           (5) 

 
Get the invariant measure for (0.547427, 0.238018, 

0.15603, 0.058352), because of the limitation of precise stable 
distribution and constant error has some error, but all in the 
range of allowable error. 

According to the above results, Markov chain, based on the 
previous weather in region A, concludes that the probability 
of precipitation in the future day is 54.743% in the interval (0, 
200] 23.8% in the interval (200, 400] 15.63% in the interval 
(400, 800] and 5.9% in the interval (800, 1200] (the units of 
precipitation above are mm). Because the region A we chose 
belongs to the temperate continental climate, which is dry and 
rarely rains all year round, it is very rare for the precipitation 
to be greater than 1200mm. This is a low probability event, so 
we're not going to think about it. 

4. Study on the Adaptability of Species 
Quantity and Type of Plant 
Communities to Drought Based on 
Differential Dynamics 

4.1. Research Ideas. 
Here we look for twelve plants that are typical of dry 

regions (see in Table 2), numbered 1 to 12. We categorize the 
plants into herbaceous plants from 1 to 6, bush plants from 7 
and 9, and arbors from 10 and 12. The initial density of plant 
No. 1 was 120 plants /hm2, No. 2 was 200 plants /hm2, No. 3 
was 160 plants /hm2, No. 4 was 150 plants /hm2, No. 5 was 
165 plants /hm2 and No. 6 was 135 plants /hm2. The initial 
density of plants from 7 to 12 can also be seen from the table 
above. The area density of herbaceous plants is higher than 
that of bush plants, and bush plants are higher than that of 
arbors. 

 
Table 3. Plant data sample 

Number Botanical name Plant classification Initial density (plant /hm2)
1 Eurya nitida Korthals Herb 120 
2 Artemisia argyi Levl. et Van Herb 200 
3 Astragalus membranaceus (Fisch.) Bunge Herb 160 
4 Medicago L. Herb 150 
5 Pennisetum sinese Roxb Herb 165 
6 Trifolium repens L. Herb 135 
7 Rhododendron ovatum (Lindl.) Planch. ex Maxim Bush 16 
8 Albizia kalkora (Roxb.) Prain Bush 8 
9 Calligonum rubicundum Bge. Bush 10 

10 Pistacia chinensis Bunge Arbor 7 
11 Pinus thunbergii Parl. Arbor 5 
12 Liquidambar formosana Hance Arbor 8 

 

34.98%

13.17%
5.35%

1.23%

10.70%

6.17%

4.53%
2.19%

7.13%

3.98%
3.70%

0.96% 1.92% 0.41% 2.06%
1.51% 0-0

0-1
0-2
0-3
1-0
1-1
1-2
1-3
2-0
2-1
2-2
2-3
3-0
3-1
3-2
3-3



 

190 

 
4.2. Research Method 

Differential dynamics models are suitable for solving 
dynamic mathematical models. The result is simple and clear, 
and the result is clearer when combined with the image. This 
model plays an important role in this paper. When we think 
about the development of plant communities, we consider the 
interspecific relationships between them. According to the 
literature, the influencing factors, maximum growth rate and 
environmental capacity among different species all have 
certain effects on the number of plant communities. We model 
the differential equation as follows formula (6)-(8). 

 
( ) ( ) ( )( ) ( )(1 )i i k

i i k
ii k

dx t x t x tr t x t a
dt N N       (6) 

 

( ( ) )

( ) ( )( )
21

i i
i h t h

L t L tr t
e

              (7) 

 
( ) ( )i

i
N t x t                  (8) 

 
Where ( )ix t   represents the number of species i; ( )ir t  

represents the growth rate of species i; ( )iL t  represents the 
maximum growth rate of species i; The above variables all 
take t as the independent variable. iN   represents the 
environmental capacity of species i; ka   represents the 
influence factor of species k on species i; ( )h t  represents the 
precipitation at time t; h  represents the average precipitation 
in the study area; ( )N t  represents the total number of plant 
community species at time t. 

4.3. Result Analysis 
(1) Analysis of Impact Factors. Impact Factor Analysis for 

System (6): 
First: ( )ix t  
Under the condition that other factors remain unchanged, 

the right side of the equation of system (6) forms a quadratic 
function of one variable, which becomes 

2 ( ) ( )( ) (1 )i k
i k

ii t

x t x tr t a
N N   after derivative, and the 

extreme point is found to be * ( )(1 ) / 2k
i i k

i k

x tx N a
N  . 

When *
i ix x  , ( )idx t

dt
  also increases with the increase of 

ix  ; At *
i ix x  , as ix   goes up, ( )idx t

dt
  goes up. This is 

realistic logic. When the initial number of species is small, 
there is no great limit to species growth under the existing 
resources. When the number of species is large enough, there 
are fewer resources and the growth rate is slow. 

Second: ( )ir t  

As ( )ir t  increases, ( )idx t
dt

 also increases, assuming other 

factors remain constant. As the growth rate increases, so does 
the number of plants. 

Third: iN  

If other factors remain unchanged, ( )idx t
dt

 increases with 

the increase of iN  . Conversely, ( )idx t
dt

  goes down. The 

growth rate increases as environmental capacity increases and 
material resources become more abundant. 

Fourth: ka  

If other factors are kept constant, ( )idx t
dt

 decreases with 

the increase of ka  ; Conversely, ( )idx t
dt

  increases. The 

increase of plant influence factor will inhibit other plants, 
resulting in a decrease in their growth rate. 

Fifth: ( )kx t  

If other factors remain unchanged, ( )idx t
dt

  decreases as 

( )kx t  increases; Conversely, ( )idx t
dt

 increases. The number 

of other species increases, resulting in less space for this 
species. 

 
Impact factor analysis for system (7) : 
First: ( )iL t  
Other factors remain unchanged. ( )ir t  increases with the 

increase of ( )iL t , and system (7) has an upper limit, that is, 
it does not increase infinitely with the increase of ( )iL t , but 
keeps ( )ir t  close to ( )iL t . 

Second: ( )h t  
As ( )h t   keeps increasing, ( ( ) )h t he   keeps decreasing 

until it goes down to 0. And ( )ir t  keeps increasing until it 
reaches the upper limit. 

(2) Pseudocode Flowchart.  
Combining the previous model with the model of this 

differential equation, we get the process of species number 
change over time as Table 4. 

 
Table 4. Algorithms of the process of species number change over time. 

Input Ni, Li(t), ka (i, k=1,…,n), h  
Output: xi(t) 
for t = 1 to 100 do 

According to equation (4), we get h(t)  
According to h(t) and equation (7), we get ri(t)  
The number of species at time t can be calculated according to ri(t)   

end 
 
 



 

191 

 
(3) Solution to Precipitation and the Number of Plants 

Change over Time 
To describe the good and bad of a plant community, we 

need to look at the growth of its species. The selected plant 
community contains six species, namely three herbs, two 
bushes and one arbor, and the initial value given is (54, 42, 45, 
17, 16, 4). Forecast the future growth trend under irregular 
weather changes on an annual cycle. By studying the weather 
data for Region A from February 2020 to February 2022, we 
use Markov chain to predict the future precipitation. The 
results of (4) are used to simulate random precipitation in the 
next few years, as shown in Figure 4. With the change of time, 
the number of different plants is also changing with time as 
shown in Figure 5. 

 Double y axes are used in the diagram. Only the right y 

axis is used for arbors, and the left y axis is used for other 
plants. This is true for all of the following cases with double 
y axes. Based on the above two figures, it can be seen that 
plant changes are affected by precipitation and have a certain 
after-effect. Further study showed that when the precipitation 
changed, the trend of herbs changed obviously, followed by 
bushes and arbors. This reflects the drought resistance: arbors> 
bushes> herbs. The influence factors between species are also 
considered in the differential equation. Most plants compete 
with each other in the natural environment. By analyzing the 
data, we calculated the impact factor and reflected it on the 
image. According to the image, it can also be concluded that 
the plant community can survive and finally reach A steady 
state under the irregular weather in region A. 

 

 
Figure 4. Plot of future precipitation over time. 

 

 
Figure 5. The number of future plant species over time. 

 



 

192 

 
Figure 6. A plot of the number of species over time under extreme drought conditions. 

 
(4) Solution to Extreme Drought Conditions. 
The differential dynamics model considers the influence 

factors between plants and environmental capacity. Simply 
changing the amount of precipitation can simulate the weather 
and draw the desired conclusions. In order to simulate a more 
arid environment, we will calculate the probability of 
precipitation in the interval (0, 200] as 68%, the probability 
of precipitation in the interval (200, 400] as 23%, the 
probability of precipitation in the interval (400, 800] as 6%, 
and the probability of precipitation in the interval (800, 1000] 
as 3% (all the above precipitation units are mm) according to 
the existing conclusions to get Figure 6. 

As can be seen from Figure 6, under extreme drought 
conditions, plant communities gradually die over time. Soil in 
ecological environments can dry out and crack due to lack of 

water. The land will desert. In order to protect the 
environment, human intervention is needed, such as artificial 
rainfall and afforestation to restore the activity of plant 
community. 

(5) Optimal Number of Species. 
The number of species also affects the rate of species 

growth in a plant community. A single species population, 
disturbed by small environmental factors, will degrade. When 
the complex plant community meets the interference of 
environmental factors, it can self-regulate and achieve 
stability again. Therefore, we discussed the relationship 
between the total number of plant communities with different 
species and changes over time, and drew the cases of 3,4, and 
5 species respectively, as shown in Figure 7. 

 

 
Figure 7. Bubble map of number of plant species 

 

According to Figure 7, when the number of species is 3, the 
number of plant community will first increase, then decrease, 
and finally disappear gradually. When the number of species 
is 4 or 5, the number of plant communities gradually increases 
and becomes stable. So it's reasonable to assume that plant 
populations benefit when the number of species is at least four. 

5. Analysis of the Species of Plants 
5.1. Proportional Combination of Different 

Plant Species 
Based on the above analysis, we first control 6 different 

N
um

be
r o

f s
pe

ci
es



 

193 

species, and respectively adjust the different ratios of herbs, 
bushes and arbors as (herbs, bushes, arbors). Using biological 
knowledge, six different combinations of (6,0,0), (4,2,0), 
(3,2,1), (3,3,0), (3,0,3) and (2,3,1) are selected. When other 
conditions are suitable, the relationship between the number 
of plants over time is drawn respectively, which provides a 
reference for the development of subsequent plant 
communities. 

5.2. Adaptation of Different Plant Species 
Below is a graph of trends in six plant communities over 

time, ranked from largest to smallest in terms of the number 
of herbs. The Figure 8 analyzes the similarities and 
differences in the future due to the differences in plant 
populations. 

For (a): The six herbaceous plants were generally 
competitive in their growth over time. At the beginning, the 
living environment is favorable and the competition for 
resources is not fierce. With the increase of time, the 
environmental capacity gradually reached saturation, and the 
growth curve of various plants became "S" shape, and the 
"inferior" plants gradually died. Although the number of 
plants has been at a high level, but the ability to tolerate 
drought is weak. 

For (b): Four herbs and two bushes, according to the image 
analysis, the growth rate of herbs is obviously higher than that 
of bushes, which is obviously caused by different families. 
Since bushes have taller plants than herbs, the influence on 
herbs is great. Compared with figure (a), it can also be seen 
that the growth rate of herbs is slower. In the long growth 
cycle, it is difficult to form a strong drought tolerance system. 

For (c): The combination of three herbs, two bushes and 
one arbor, the double Y-axis is adopted in the image, so that 
the trend changes can be more clearly seen. Because 
compared to herbs, the growth rate of arbors is very small. 
This combination is more common in nature and also 

represents the vertical community of plant communities. With 
the change of time, the whole plant community tends to be 
more balanced and has strong tolerance to drought, which is 
an ideal species combination. 

For (d): The combination of three herbs and three bushes 
generally reflects the changes in the initial stage of the plant 
community, and bushes have more influence on herbs. 
Because bushes are relatively dense and abundant, they are 
more effective in inhibiting herbs. When there is a small 
increase in the number of bushes, the trend of herb growth is 
curbed. The growth cycle of bushes is much smaller than that 
of herbs, but it can also be seen that the growth rate is 
gradually increasing. After long-term development, it is not 
conducive to the formation of stable plant communities, and 
the adaptability to drought is relatively weak. 

For (e): A combination of three herbs and three arbors does 
not easily form this type of community in a normal plant 
community. With the increase of time, herbaceous plants 
declined significantly. However, the growth rate of arbors is 
very low, unable to reach a stable equilibrium state, the ability 
to adapt to drought is not strong, if there is a big drought will 
become barren. 

For (f): A combination of two herbs, three bushes, and one 
arbor, this community corresponds to the distribution of 
plants in nature. As you can see from the image, the growth 
rate of herbs is very fast at the beginning. When the number 
of bushes and arbors came up, there was a phenomenon of 
decreasing first and then leveling off, reaching a relatively 
stable state, with strong drought tolerance. Over time, this 
plant community is better able to evolve into a plant 
community with higher species richness. 

To sum up: we believe that the top three drought tolerance 
are figure(c)>figure(f)> figure(d). Suitable species types have 
better resistance to drought and can form relatively stable 
plant communities. 

 

   

(a) (6,0,0) (b) (4,2,0) (c) (3,2,1) 

   

(d) (3,3,0) (e) (3,0,3) (f) (2,3,1) 
Figure 8. The combination of different plant species 

 

6. Sensitivity Analysis 
In plant communities, there are many other factors that 

affect plant growth in addition to those we have already 
discussed. The effect of pollution on plants in real life cannot 
be ignored. In recent years, many plant communities have 



 

194 

been seriously degraded due to environmental pollution [8]. 
Therefore, we further expand the original differential 
equation and add pollution disturbance factor v to get: 

 
( ) ( ) ( )( ) ( )(1 ) ( )i i k

i i k i
ii k

dx t x t x tr t x t a vx t
dt N N   (9) 

 

We still chose a combination of three herbs, two bushes and 
one arbor. According to the above analysis, this combination 
is the best drought resistance combination. This combination 
was selected for sensitivity analysis, and the disturbance 
factors of environmental pollution were selected as 
0,0.1,0.2,0.3,0.4, and 0.5, respectively, to obtain the changes 
of the number of different species over time as shown in 
Figure 9. 

 

(a) v=0 (b) v=0.1 (c) v=0.2 

(d) v=0.3 (e) v=0.4 (f) v=0.5 
Figure 9. Graphs of the number of different species over time under disturbed conditions. 

 
 

With the continuous increase of v, that is, the increasing of 
environmental pollution, the first two kinds of bushes showed 
a downward trend, followed by arbors and herbs. The result 
is food for thought. In this plant community, due to the initial 
number of herbs, so when the pollution is not serious, it can 
be increased to a certain extent. But as the number of bushes 
and arbors dwindled, the herbs began to suffer, too, 
diminishing. When v=0.4, two of the three herbs declined 
from the beginning, indicating that Herb I had significantly 
stronger pollution resistance than the other two herbs. When 
environmental pollution is already very severe, the result is 

that all plants begin to die. From the above analysis, we can 
see that environmental protection should be strengthened. As 
can be seen from the above picture, as long as the 
environment is polluted, the plant community will definitely 
be affected. If the pollution is severe, then the plant 
community will be seriously degraded. In addition to 
establishing changes in the number of species at different 
levels of pollution, the total number of species in a plant 
community is often a good indicator of plant community 
transformation. 

 

 
Figure 10. Area stacking diagram of the total number of species over time under disturbed conditions. 



 

195 

 

According to the figure 10, when the environment is 
pollution-free, the total number of plant communities 
increases first and then decreases, which conforms to the rule. 
However, when the pollution degree increases, the number of 
species in the plant community decreases sharply to 0, which 
is the same as the above analysis result. 

7. Conclusion 
In nature, plant community is the carrier of species and 

brings together all kinds of biological resources. It is the main 
body that provides the function of ecosystem and the 
comprehensive index of the basic property of land. It provides 
a favorable environment for human existence. In this paper, 
we established two models for region A, Markov chain and 
differential dynamics model, which were used to solve the 
future weather prediction and species number change 
respectively. Because have no aftereffect of Markov chain, 
has inherent advantages in forecasting the weather, finally the 
limiting distribution of transition probability matrix is 
(0.547427, 0.238018, 0.15603, 0.058352), for the further 
study of plant community succession process played an 
important role in guiding. Through the establishment of 
differential dynamics model, we simulated the changes of 
plant community over time, and obtained the relationship 
between the changes of plant community and precipitation, 
environmental capacity, maximum growth rate and 
influencing factors. Figure 6 is also drawn to intuitively show 
the changing trend of the number of species. Further analysis 
showed that under the more extensive drought conditions, 
even though the plant community reached the optimal 
combination, it could not reach equilibrium and finally 
degraded. Through the analysis of the number of species, we 
obtained that the number of species in the plant community 
should not be less than 4 to have a positive effect. Plant 
communities of less than 4 species will gradually degrade 
when disturbed by nature. 

We also studied the combination of different species and 
analyzed the drought resistance of plant communities. Six 
common combinations in nature were selected, which showed 
different development trends over time under the same 
conditions, and three herbs, two shrubs and one tree had 
stronger drought resistance. This suggests that species 
diversity affects resistance. When considering environmental 
pollution, the disturbance factor is introduced to get the 
change of species number. When the environmental pollution 
is light, it has little impact on the environment, and the plant 
community can purify itself through recycling. However, 
when the pollution is very serious, the plant community will 
become dysfunctional and degenerate as a whole. 

The evolution of plant community is the historical 
evolution process of plant community, which is the change of 
geological time and corresponding climate change. The 
evolution of plant community is mutually restricted with the 
evolution of plant species and is also carried out in 
conjunction with the evolution of animal kingdom. The type 

of modern plant community is the product of the development 
of nature history, and is unique to the development of nature 
at present stage. In order to protect the plant community 
through the study of this paper, we should: Regulate the 
type and number of species in the plant community to form a 
stable plant community. Control precipitation to meet the 
needs of plant community, not too little or too much. Set 
up nature reserves to prevent man-made destruction of plant 
communities. 

8. Data Availability 
The data in this paper come from Question A of the 2023 

American College Students Mathematical Modeling 
Competition. 

9. Conflicts of Interest 
The author declares that there are no conflicts of interest 

regarding the publication of this paper. 

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[2] Dongdong Du. “An Effects of drought and its soil residual 
effects on the growth of typical grassland plants on the Loess 
Plateau”. Lanzhou University, 2022. 

[3] Yulin Huang, Weicong Fu, Jingru Chen. “Study on the impact 
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