1 agricultural experiment statistics
In mathematical agricultural experiment statistics, when studying the correlation of protein content between parents and children, the related analysis theory was put forward. When studying the effect of fertilizer on potato yield, a new theory was put forward, and the new concepts of variance analysis and interaction were produced. In the analysis and comparison of potato yield in different varieties, different regions and different years, the interaction among various factors was further verified. This proves that mathematical statistics, which was widely used later, was produced on the basis of studying agricultural scientific experimental methods, and also laid a solid theoretical foundation for agricultural experimental statistics.
Because crops are easily influenced by external factors in the process of growth and development, there are many factors in the experiment, so the results produced by the experiment are also dominated by external factors, and uncontrollable factors such as interaction effect and error are easy to appear among various factors. Because crops are easily influenced by external natural factors in the production process, there are many influencing factors in the test process, and there are a lot of factor effects in the test results, as well as uncertainties such as interaction and errors among factors. In addition, there will be some abnormal data and lost data during the test. These will bring many problems to our statistical work, so we must adopt scientific and reasonable experimental design and statistical inference modeling methods. In agricultural production, a large number of experimental statistical methods and statistical analysis methods have been applied to agricultural scientific planting. In addition, agricultural experiments are different from other production fields, and there are many problems such as long test period and many influencing factors. In practical application, the experimental statistical method can effectively improve work efficiency, facilitate the collection of agricultural data and make the analysis results more accurate.
Mathematical statistical model has strong explanatory power, which is convenient for analysis and processing in experimental design and statistical inference theory and method. In agricultural applications, in addition to the traditional orthogonal test, rotation design and corresponding statistical methods, some new methods are constantly emerging. For example, the uniform design produced by number theory method and its corresponding scientific achievements, and some nonlinear results processed by differential geometry method have been gradually applied to agricultural scientific experiments and statistical inference methods. Many mathematicians abroad have conducted in-depth research on agricultural statistics, and some professional magazines have also published many related articles. Domestic researchers also have many scientific research achievements in the fields of agriculture and biology, which have a positive role in promoting the teaching and academic research of agriculture and biostatistics in China.
Mathematical genetics and quantitative genetics
Mathematical genetics and quantitative genetics, strictly speaking, are marginal disciplines produced by the organic combination of mathematics and genetics. It can be regarded as a branch of genetics and a branch of biological number. As the basic theory of genetics-the law of genetic balance, the analysis of biological characters by genetics can be roughly divided into two categories. First, quality traits are generally discrete variations. Quality traits are mainly controlled by major genes and less influenced by environment. In the study of quality traits, the expression or genotype in the population is often classified, and the method of population genetic analysis is used in agricultural science research to estimate different genes and gene frequencies of different plant varieties and study the changes of gene frequencies. The other is quantitative trait, which mainly shows continuous variation. Quantitative traits are usually controlled by many micro-gene sequences and are greatly influenced by the external environment. Therefore, we can't use classical genetic analysis methods to analyze quantitative traits in groups, but only choose statistical analysis methods, and at the same time carry out genetic analysis on quantitative traits in specific plant recombinant inbred lines to distinguish genetic variation from environmental variation. Statistical analysis is often used in quantitative genetic research of plants to estimate the statistical parameters of recombinant inbred lines, such as mean, covariance and variance. Because plants have the characteristics of gene linkage and multiple effects. There are also different correlations between different quantitative traits of plants. The population average is the average performance of all individuals, and the variance and covariance of the population exist in individual variation. In agricultural production, China's quantitative inheritance has been gradually applied to all aspects of agricultural production. In the process of rice planting, studying the main quantitative characters of hybrid rice has played a positive role in improving its rice quality. The research on crop transgene and gene recombination has also been further developed, and related scientific and technological achievements have been gradually transformed into productive forces. At the same time, the research of bioinformatics statistics is also rising. Through the statistical analysis of agricultural planting process information, the scientific application of crops suitable for local growth and crop fertilization was analyzed.
3 mathematical epidemiology of plants and plant diseases
Since the development of agricultural technology in the 20th century, it has entered the stage of quantitative research on epidemic diseases and insect pests. From a disciplinary point of view, plant disease epidemiology is a comprehensive subject combining theory with practical application, which is closely related to mathematics, bioinformatics and ecology. Mathematics is widely used in the field of plant disease epidemiology. Judging from the current research results, mathematics is mainly reflected in the following aspects: First, a dynamic mathematical model describing the epidemic time of plant diseases in detail. The second is the mathematical space model to describe the epidemic areas of pests and diseases. Thirdly, the process of plant diseases is systematically analyzed and simulated by mathematical methods or statistical analysis methods. Fourthly, using mathematical statistics to predict the epidemic situation of pests and diseases and calculate the estimated losses. Fifth, using operational research and advanced computer technology, the comprehensive rule of law and field management of pests and diseases are studied.
4 the relationship between agricultural ecology and mathematics
As ecologist Pielou EC said, ecology is actually a mathematics. With the deepening of ecological research, this statement is gradually recognized by people. Quantification and modeling in ecology are the theoretical basis and academic knowledge of modern ecology. In China, ecological research has been incorporated into the national discipline system. In ecology, whether it is population dynamics, spatial pattern or stochastic theory of community food web, a large number of mathematical methods and operations are needed to draw corresponding conclusions. In the study of resources and environment related to ecology, mathematics also has in-depth research, such as water pollution, pesticide residues and so on. Through a large number of mathematical experiments and agricultural experiments, researchers in the field of agricultural ecology have summed up more than 1000 mathematical models related to the agricultural field, providing strong theoretical support for agricultural researchers and mathematicians. At the same time, it also proves that Chinese researchers have achieved fruitful scientific research results in this field.