2023年美赛特等奖论文-A-2300336-解密.pdf
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Problem Chosen
A
2023
MCM/ICM
Summary Sheet
Team Control Number
2300336
Community Succession Simulation: Surviving Drought
Summary
The species richness of plant communities has a significant influence on their ability to withstand
drought. From an ecological niche perspective, we simulate plant community succession under
drought conditions and analyze the effects of various factors.
First, we develop the Plant Community Succession Model based on niche theory to simulate
community succession under drought conditions. The model applies changes in niche width as
the indicator to simulate community succession and utilizes competition matrix to describe in-
teractions between species, including competition and facilitation. Then, the Niche Width Model
is established, comprehensively considering the effects of reproduction, mortality, and uncer-
tainties. Among them, reproduction depends on the degree of drought, niche width, interspecific
relationships, and environmental capacity, while mortality depends on the degree of drought and
the niche width. Uncertainties are measured with Gaussian white noise.
A niche width differential equation model is built based on the Beverton-Holt and the Lotka-
Volterra equations. To account for various irregular weather cycles, we utilize random variables
obeying normal distribution to simulate the extent and duration of drought. As a case study, we
simulate the evolution of a three-species community and draw the conclusion that the total niche
width of the community increases, suggesting long-term survival.
To investigate the influence of species number on community dynamics, we utilize the Plant
Community Evolution Model to simulate communities containing one to four species separately.
The results demonstrate that three species are necessary for the community to benefit. Additionally,
as the number of species increases, the drought resistance improves and then stabilizes.
Based on the competition matrix, we set up three distinct communities and discuss their drought
resistance through simulations. It can be concluded that facilitation-dominated relationships en-
hance drought resistance and increase the community’s survival time. Moreover, we vary the
frequency and intensity of drought and then conclude that species extinction is more likely to occur
during severe droughts.
Pollution and habitat shrinkage affect plant communities’ niche width and competitive rela-
tionships. Therefore, we adjust the niche width and competition matrix accordingly. The results
indicate that pollution and habitat shrinkage may cause the extinction of certain species.
Finally, based on the impact of various factors, we recommend some measures to ensure
the long-term viability of a plant community. Additionally, we also analyze the significance of
protecting vulnerable communities for the overall health of ecosystems.
Keywords: Community succession; Drought resistance; Niche width; Population interactions;
Beverton-Holt equation
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