2024年美赛35篇特等奖O奖论文-A-2405424.pdf资源-CSDN文库

版权申诉

167 浏览量 2024-05-06 11:41:10 上传评论收藏 2.94MB PDF 举报

### 2024年美国大学生数学建模竞赛（MCM/ICM）特等奖O奖论文解析 #### 概述本论文聚焦于“Lamprey: a Vivid Example of the Doctrine of the Mean”，主要探讨了海鳗作为地球上最古老生物之一，在资源可获得性变化时调整其性别比例的能力及其生态意义。研究采用经典的Lotka-Volterra捕食者-猎物模型以及Nicholson-Bailey宿主-寄生虫模型为基础，并构建了理想参考模型、恒定性别比例模型以及变动性别比例模型。 #### 任务一：生态系统中资源总量与物种多样性我们通过模型分析发现，当引入海鳗或其它寄生生物后，生态系统中的总资源量会下降。然而，在包含海鳗的模型中，能够存活的物种数量最多。这一结果表明，相比普通的寄生物种，海鳗通过改变性别比例的方式对其他生物的压力较小，有助于增加生态系统的多样性。 #### 任务二：环境资源变化对种群的影响为了进一步探究不同模型下环境资源的变化如何影响海鳗种群数量，我们人为地降低了环境资源条件，并绘制了恒定性别比例模型与变动性别比例模型中海鳗种群数量的变化曲线。结果显示，传统寄生物种的数量受环境影响较大，而能够调整性别比例的海鳗种群则表现出更高的稳定性，这是海鳗种群最大的优势之一。然而，这种高度适应性的代价是种群规模相对较小。 #### 任务三：生态系统的稳定性分析我们收集了大量的数据，并运用熵权法评估了三种模型下生态系统最终的稳定性。通过分析得出，海鳗种群能够通过改变性别比例来适应环境变化，从而维持生态系统的稳定性和多样性。虽然这可能导致种群规模较小，但总体上对生态系统的长期健康是有利的。 #### 结论与启示本研究揭示了海鳗在面对资源变化时通过调整性别比例来适应环境的独特策略。这种策略不仅有利于海鳗种群自身的生存和发展，也对维护生态系统的多样性和稳定性具有重要意义。此外，研究还提示我们在设计生态保护策略时，应考虑物种自身适应环境变化的能力，以促进生态平衡的维持。 #### 扩展讨论 - **生态系统的复杂性**：生态系统是由多种因素相互作用构成的复杂系统。本研究中的模型简化了许多现实世界的复杂性，但在理解和预测生态系统的行为方面仍然具有一定的指导意义。 - **性别比例调控机制**：海鳗通过何种生物学机制实现性别比例的调节仍需进一步探索。了解这一机制对于理解生物多样性的维持机制以及开发新的生物保护策略具有重要意义。 - **模型局限性**：虽然Lotka-Volterra和Nicholson-Bailey模型为研究提供了基础框架，但它们在描述更复杂的生态系统动态方面存在局限性。未来的研究可以考虑结合更多现实世界的数据，以提高模型的准确性和实用性。 - **跨学科合作**：解决生态环境问题往往需要跨学科的合作。本研究的成功案例展示了数学模型在生物学、生态学等领域的应用潜力，鼓励更多的跨领域合作以解决复杂问题。该篇论文通过对海鳗种群性别比例调节的研究，不仅为我们提供了一种新的视角来看待生物适应环境变化的能力，也为生态保护策略的设计提供了重要的理论支持。

资源推荐

资源详情

资源评论

Problem Chosen

2024

MCM/ICM

Summary Sheet

Team Control Number

2405424

Lamprey: a Vivid Example of the Doctrine of the Mean

The survival mechanism of the lamprey, one of the oldest organisms on earth, has

always been a topic of interest for researchers. When it comes to lampreys and resource

availability, the phenomenon that their populations can change their sex ratio has

become an inescapable topic. Studies have found that resource availability affects the

sex ratio of lamprey populations.

In order to study the ability of species to change their sex ratios according to resource

availability, we adopted the Lotka-Volterra predator-prey model and the Nicholson-

Bailey host-parasite model as modeling bases, and then constructed the Ideal Reference

Model, the Constant Sex Ratio Model, and the Models of Changing Sex Ratios, and

successfully solved the problem.

For Task 1,we ﬁrst found that the total amount of resources in the ecosystem de-

clined with the introduction of lamprey or other parasites, while the number of species

surviving was highest in the model with lamprey. Therefore, we conclude that lamprey

with altered sex ratios are less stressful to other organisms than ordinary parasites,

which is conducive to increasing the diversity of the ecosystem.

For Task 2, we artiﬁcially worsened the environmental resources, and plotted the

change curves of the number of lamprey in Constant Sex Ratio Model and Models

of Changing Sex Ratios, respectively. Obviously, the population size of conventional

parasitic species is severely affected by the environment, while lamprey, which is able

to change its sex ratio, is very stable, which is the greatest population advantage

of lamprey.However, win some, lose some.With higher resilience to environmental

risk comes lower population size, which is the disadvantages to the population of

lampreys.

For Task 3, we collected a large amount of data and analyzed the ﬁnal ecosystem

stability of the three models through the entropy weighting method, and concluded that

the introduction of parasites led to a decrease in ecosystem stability, but the property

of lamprey that can change the sex ratio signiﬁcantly mitigated this phenomenon.

For Task 4,we then integrated these three models to explore the effects of introduc-

ing lamprey on other conventional parasites in the ecosystem. Under deteriorated

conditions, we found that the parasite was less able to resist the external environ-

ment in ecosystems lacking lamprey. However, after the introduction of lamprey, their

population size showed stable periodic ﬂuctuations. This ampliﬁed the negative feed-

back regulation of the ecosystem, and also led to a signiﬁcant strengthening of the

resistance of the original parasite to the adverse environment.

After that, in order to test the model, we ﬁrstly discussed the rationality of the

experimental results from various aspects. Then we analyzed the sensitivity of the model

from two perspectives: the disturbance of human activities and the change of the initial

value of the population, and found that the model is more resistant to the uncertainty

factors, and it is applicable to different initial values of the population, which

just shows the reliability and universality of the model. Finally, we analyzed the

advantages and disadvantages of the model and proposed a corresponding optimization

scheme.

Keywords:Changing Sex Ratios,Ideal Reference Model,Constant Sex Ratio Model

, Model of Changing Sex Ratios, Entropy Weighting Method.

Team # 2405424 Page 3 of 25

1 Introduction

1.1 Research Background[1]

1.The Living Habits of Lampreys.

The entire life cycle of the lamprey, from fertilized egg to adult, typically takes 5-8

years. Fertilized eggs hatch into worm-like larvae that reside in small burrows on the

bottom of sandy streams. The larvae feed on detritus and small plant algae, and after

three to six years become parasitic adults. Adults migrate to lakes and seas where they

feed on ﬁsh.As a typical migratory organism, the lamprey lives part of the time in the

sea. They enter large rivers in the fall, overwinter in the lower reaches of the rivers, and

return to the upper reaches to spawn when the water temperature reaches about 15

degrees Celsius in May to June of the following year. Both parents die after spawning.

Figure 1: Lamprey[2]

Parasitism is the main way of survival

for the lamprey. Adult lampreys attach

themselves to a host ﬁsh through their

toothed sucker mouths and feed on its

blood. This parasitic behavior not only

causes damage to the health of the host

ﬁsh and reduces its ability to survive and

reproduce, but also affects the number

and structure of ﬁsh populations, thus af-

fecting the balance of the aquatic ecosys-

tem.

2.Population Dynamics of Lampreys.

Since the lamprey is regarded as a delicacy in some cultures, heavy human ﬁshing in

recent years has led to a decline in its population. While considering the predator, prey

and parasitic relationships of lampreys, changes in sex ratio may also have a signiﬁcant

impact on their ecological roles. For example, if an increase in the proportion of males

leads to a decrease in reproduction rates, then the impact of lamprey on their host ﬁsh

may be reduced, thus affecting the associated food chain. In addition, changes in sex

ratios may also affect the genetic diversity and adaptive capacity of lampreys, which in

turn may affect their long-term viability.

1.2 Restatement of the Problem

•

For Task 1, we need to build a mathematical model based on the basic property

of lampreys that can change the sex ratio, which can reﬂect the impact of the

sex-changing property of lampreys on the ecosystem, and draw the corresponding

conclusions based on the built model.

•

For Task 2,we need to utilize and improve the above model and derive the

strengths and weaknesses of lampreys population from the model results.

•

For Task 3,e need to establish an evaluation criterion on ecosystem stability, and

determine and validate the effect of the characteristic of lampreys that can change

the sex ratio on the stability of the ecosystem by comparing the change of this

indicator before and after the introduction of lampreys.

•

For Task 4,we need to further reﬁne the model to ﬁnd out if there are species (e.g.,

Team # 2405424 Page 5 of 25

1.4 Our Work

Based on the Nicholson-Bailey host-parasite model and the Lotka-Volterra predator-

prey model, we will build the Ideal Reference Model , Constant Sex Ratio Model ,

and Models of Changing Sex Ratios .

By adjusting the ecosystem parameters in each model, we will simulate the sur-

vival of different species in different climates as well as changes in total resources.

We will analyze the resulting data and compare the three models above to discuss

the advantages and disadvantages of the ability of lamprey to alter sex ratios on

lamprey’s own populations, as well as the effects on factors such as the number of

ecosystem species surviving, total resources, and ecosystem stability.

Combining the three models, we will discuss the impact of lamprey on conven-

tional parasitizers with a sex ratio of 1:1 by making reasonable improvements to

Constant Sex Ratio Model and Models of Changing Sex Ratios.

Finally, we will perform a sensitivity analysis of the model by varying the initial

value of the population size of each species, and by adding the disturbance of

anthropogenic ﬁshing factors both.

2 Model Preparation

2.1 Assumptions

•

Assumption 1: Natural enemies of parasitic species other than humans are not

considered. That is, the relationship between species and parasitic organisms

in the community is mostly parasitism and interspeciﬁc competition.

Justiﬁcation: According to references [5], parasitic species such as the lampreys

are invasive in the Great Lakes of North America, suggesting that they have very

few natural enemies and can be ignored.

•

Assumption 2: The survivability of male and female lampreys in the population

is approximately the same.

Justiﬁcation: From the references [6], it can be seen that there is little difference in

the survival ability of male and female lampreys, and this assumption can avoid

the extreme situation of a larger death in this party due to the lack of survival abil-

ity of either females or males, which ensures the reliability of the model prediction

results.

•

Assumption 3: All species in an ecosystem can obtain energy directly from

environmental resources.

Justiﬁcation: A simple analysis shows that when this hypothesis is valid, it is more

effective to use Model 1 to reﬂect the competitive relationship between different

species, and it also simpliﬁes the model to some extent.

These are the main assumptions, and other assumptions will be given at appropriate

places in the article.

剩余24页未读，继续阅读

评论收藏

内容反馈

版权申诉

阿拉伯梳子

粉丝: 2681
资源: 5734

2024年美赛35篇特等奖O奖论文-A-2405424.pdf

2024年美赛35篇特等奖O奖论文-C-2409404.pdf

2024年美赛35篇特等奖O奖论文-C-2401445.pdf

2024年美赛35篇特等奖O奖论文-A-2424371.pdf

2024年美赛35篇特等奖O奖论文-A-2407093.pdf

2024年美赛35篇特等奖O奖论文-A-2425397.pdf

2024年美赛35篇特等奖O奖论文-F-2422054.pdf

2024年美赛35篇特等奖O奖论文-D-2419588.pdf

2024年美赛35篇特等奖O奖论文-A-2400996.pdf

2024年美赛35篇特等奖O奖论文-E-2407414.pdf

2024年美赛35篇特等奖O奖论文-F-2426941.pdf

2024年美赛35篇特等奖O奖论文-E-2400860.pdf

2024年美赛35篇特等奖O奖论文-E-2410889.pdf

2024年美赛35篇特等奖O奖论文-F-2417340.pdf

2024年美赛35篇特等奖O奖论文-E-2410578.pdf

2024年美赛35篇特等奖O奖论文-C-2401298.pdf

2024年美赛35篇特等奖O奖论文-E-2413552.pdf

2024年美赛35篇特等奖O奖论文-C-2406176.pdf

2024年美赛35篇特等奖O奖论文-B-2411570.pdf

2024年美赛35篇特等奖O奖论文-B-2407038.pdf

2024年美赛35篇特等奖O奖论文-F-2413565.pdf

2024年美赛35篇特等奖O奖论文-D-2417831.pdf

2024年美赛35篇特等奖O奖论文-C-2406324.pdf

2024年美赛35篇特等奖O奖论文-D-2417004.pdf

2024年美赛35篇特等奖O奖论文-D-2429211.pdf

2024年美赛35篇特等奖O奖论文-C-2418251.pdf

2024年美赛35篇特等奖O奖论文-B-2419984.pdf

2024年美赛35篇特等奖O奖论文-F-2409949.pdf

最新美赛案例分析2024年美国大学生数学建模竞赛特等奖论文概览.docx

2024年美赛试题中英文完整版（附文档与附件下载链接）.pdf

2022A题一篇美赛O奖论文

最新资源