[Jiangxi Postgraduate Mathematical Modeling Contest] Topic 3 Plant Diversity Modeling Scheme and References

[Jiangxi Postgraduate Mathematical Modeling Contest] Topic 3 Plant Diversity Modeling Scheme and References

1 topic

2023 Jiangxi Provincial Postgraduate Mathematics Competition Topic 3

plant diversity

As producers in the food chain, plants absorb carbon dioxide through photosynthesis to produce oxygen, and at the same time provide food and habitat for other organisms to support their survival. Plants also play a role in preventing soil erosion and alleviating the greenhouse effect in the ecosystem. Therefore, the diversity of plants helps to maintain the stability of the food chain, ecological balance and biological diversity.

There are many kinds of plants growing in a forest, and there are different relationships between different kinds of plants. Please build a mathematical model to solve the following problems:

Question 1 If there is a single relationship between various plants in the forest, try to study the law of the change in the number of various plants, and analyze how to maintain the diversity of plants in the forest.

Question 2 If there are several different relationships between various plants in the forest, try to study the law of the number changes of various plants, and analyze how to maintain the diversity of plants in the forest.

Question 3 Now it is found that an alien plant has invaded this forest, which has caused a sharp decrease in the number of certain plants in the forest and is in danger of extinction. In order to clean up this invasive plant, the forest management department intends to use some special measures (for example: use the method of burning). Please give the specific implementation plan of this special measure (for example: measure intensity, duration, etc.), so that within a certain period of time, the scale of the original plants in the forest will recover without the risk of extinction.

2 Modeling ideas

In addition to building a mathematical model, some visual pictures need to be added. Here are some examples of pictures, and refer to such pictures for drawing.

2.1 Question 1

For the situation that there is a single relationship between various plants in the forest, a competition model can be established, that is, the interdependence relationship between various plants can be described by competition. After comparing the ecological characteristics of each plant, a competition model can be selected, such as the environmental carrying capacity model, Lotka-Volterra model, Ricker model, etc., and combined with the actual situation to obtain the competition intensity among various plants in the forest. In order to maintain the diversity of plants in the forest, it is necessary to find a balance in competition, such as adding external disturbances and moderately cultivating certain species.

2.2 Question 2

Aiming at the situation that there are several different relationships among various plants in the forest, a multivariate ecological model can be established. After comparing the ecological characteristics of each plant, you can choose an appropriate multivariate solution model, such as a stability model, an interface model, etc., and consider multi-dimensional ecological factors at the same time. For the issue of forest diversity, you can try to find a balance point in space, such as strengthening the separation distance and considering human interference.

2.3 Question 3

For the situation where invasive plants lead to a sharp reduction in the number of certain plants in the forest, classification models can be established, including the original forest plant model and the invasive plant model. According to the characteristics of invasive plants, special means are designed to clean up invasive plants. During the cleaning process, it is necessary to plan and control the cleaning intensity and cleaning time of different plants to avoid damage to original plants. At the same time, consideration should be given to the protection and restoration of existing plants, and the use of invasive plants in the market to promote the restoration of forest diversity.

3 Mathematical models

3.1 Question 1

Assume that there are nn in the forest$There\; are\; n$ different plants, and the relationship between these plants is a single relationship. The following differential equation model can be established:
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3.2 Question 2

Assume that there are nn in the forest$n$ kinds of different plants, and there are many different relationships among these plants, a multi-relationship ecosystem dynamics model can be established. Taking R* theory as an example, for each plant, its corresponding resource utilization rate$R_i$. Assuming $The\; resource\; utilization\; rate\; of\; i$ plants is$R_i$, then the difference equation model of its quantity change is:
. . . . slightly, please download the full document

3.3 Question 3

For this situation, the forest management department can take some special clean-up measures, such as burning, mowing and so on. The specific plan needs to consider the following factors:
$$....slightly,\; please\; download\; the\; full\; document$$

4 Visualization example

Figure 1 Global map of plant form and function

Figure 2 Multi-scale research direction of biodiversity conservation decision support

Figure 3 GLOBIO freshwater ecosystem model structure

Figure 4 Structural equation modeling of biodiversity and ecosystem function

5 data

6 downloads

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