Generally speaking, there are at least two methods to establish an ecological mathematical model: one is the compartment method, which is used to study the flow of matter and energy in each compartment in the ecosystem and give a quantitative expression. One is the experimental component method, which is mainly used to analyze the ecological processes of complex ecosystems (such as predation and competition). The following is the general flow diagram of ecological modeling: it can be summarized as follows: to prepare the model, we must first clearly study the problem, determine the modeling purpose, determine the system boundary, determine the components of the model (input and output variables, initial and driving variables, parameters, space-time scale), and establish the flow chart. Understand the actual background of the problem, clarify the purpose of modeling, and collect all kinds of information necessary for modeling, such as phenomena and data. And try to understand the characteristics of the object, so as to initially determine which model to use. In a word, we should make preparations for modeling. This step cannot be ignored. When encountering problems, we should humbly consult comrades engaged in practical work and try our best to master first-hand information. According to the characteristics of the object and the purpose of modeling, model hypothesis can be said to be a key step to simplify the problem and make assumptions in accurate language. Generally speaking, it is difficult to turn a practical problem into a mathematical problem without simplifying the hypothesis, and even if it is possible, it is difficult to solve it. Different simplified assumptions will lead to different models. Unreasonable or oversimplified assumptions will lead to model failure or partial failure, so the assumptions should be revised and supplemented. If the assumptions are too detailed, trying to take all the factors of complex objects into account may make it difficult or even impossible for you to continue your next work. Usually, the basis of making assumptions is based on the understanding of the inherent law of the problem, the analysis of data or phenomena, or the combination of the two. When making assumptions, we should not only use the knowledge of physics, chemistry, biology and economy related to the problem, but also give full play to our imagination, insight and judgment. We should be good at distinguishing the primary and secondary problems, firmly grasp the main factors, abandon the secondary factors, and linearize and homogenize the problems as much as possible. Experience often plays an important role here. When writing assumptions, the language should be accurate, just like writing known conditions when doing exercises. Model construction is based on the assumptions made, using the internal laws of the object and appropriate mathematical tools to analyze the causal relationship of the object. Construct equation (or inequality) relations or other mathematical structures between various quantities (constants, variables). In addition to the professional knowledge of some related disciplines, we often need more extensive application of mathematical knowledge to broaden our thinking. Of course, we can't ask to master mathematics subjects, but we should know what problems these subjects can solve and how to solve them generally. Similarity analogy method, that is, according to some similarities of different objects, borrows mathematical models in known fields, and is also a method of building models. One principle to follow in modeling is to use simple mathematical tools as much as possible, because the model you build always wants to be understood and used by more people, not just a few experts. Establish a quantitative model (or a quantitative conceptual model): select a model type and establish a model (determine the functional relationship between variables). Parameter estimation and calibration, writing computer program, model verification: carefully check the mathematical formula and computer program, and write model documents. Various traditional and modern mathematical methods can be used to solve the model, such as solving equations, drawing, proving theorems, logical operation, numerical calculation and so on. , especially computer technology. The mathematical analysis of model solution sometimes needs to analyze the dependence or stability of variables according to the nature of the problem, sometimes it needs to give a mathematical prediction according to the obtained results, and sometimes it may need to give a mathematical optimal decision or control. In any case, it is often necessary to analyze the error, stability or sensitivity of the model to data. Model checking converts the results of mathematical analysis back to practical problems, and compares them with actual phenomena and data to test the rationality and applicability of the model. This step is very important for the success or failure of modeling and should be taken seriously. Of course, some models, such as the nuclear war model, cannot pass the test of practice. If the results of model verification are not in line with the reality or partially, the problem usually lies in the model assumptions, which should be modified, supplemented and re-modeled. Some models have to be repeated several times until the test results are satisfactory to some extent. Spatio-temporal extension of the model: the application of the established model on the spatiotemporal scale: the application method naturally depends on the nature of the problem and the purpose of modeling. Model operation and evaluation Levins( 1966) once put forward three criteria for establishing a mathematical model: (1) authenticity, and the mathematical description of the model should conform to the reality of the ecosystem; (2) accuracy refers to the difference between the predicted value and the actual value of the model, and (3) universality, that is, the scope and breadth of application of the model. In practice, it is difficult for a model to meet these three criteria at the same time. Walters had an incisive exposition on this, and also introduced two indicators related to authenticity and universality, namely, resolution and integrity. These two concepts were put forward by Bledsoe and Jamieson( 1969) and Holling( 1966) respectively. In short, not all modeling processes have to go through these steps, and sometimes the boundaries between steps are not so clear. Don't stick to formal step-by-step modeling, you can use it flexibly in the actual modeling process.