Estimating Forest Plant-diversity Based On Generalized Linear Models

Based on systematic analysis of the development of theory of biodiversity in internal and external, this paper summed up biodiversity measurement models and estimating models which are representative, discussed the concept of biodiversity and the application of several biodiversity indices, also, discussed the basic principle of the Generalized Linear Models (GLM) and the implementing method,. In the end, through combing the theory with the situation of northeast forest area of China, the simultaneous equation models for forest biodiversity were designed and constructed based on GLM. The main idea and conclusions were as follow.Firstly, Searching for abundance and diversity of species has been in the heart of ecology for decades, and the problem of biodiversity measurement still continues to be a core area of biodiversity research. If one wants to measure "biodiversity" there are no less than 12 different definitions to choose from, all of them different. The major problem with biodiversity in general is that most people interpret the concept differently. It is far too vague and generalized to be of any practical use in a situation and needs to be better defined. From a practical viewpoint, the definitions of biodiversity should involve a formula that includes not only the number of species in a place, but the abundances (absolute or relative) of those species, as well. Increasing this understanding is important, because it is necessary for biological diversity measurement in the distribution, abundance and diversity of forest species before biodiversity measurement can be rigorously estimated.Secondly, I put forward a critical review on a set of biodiversity and biodiversity measurement. The main conclusion is that biodiversity is generally recognized on four levels: (a) Genetic diversity; (b) Species diversity; (c) Ecosystem diversity and (d) landscape diversity; The measurement of biodiversity on scale involves three aspects: alpha diversity, beta diversity and gamma diversity, this paper focuses on the Alpha diversity and Species diversity, Alpha diversity (a-diversity) is species richness within a particular area, community or ecosystem, and is measured by counting the number of species. Species diversity is usually used as an index of community, and is incorporated by species richness, evenness, dominance, species rarity, relative species abundance, etc. Species richness is a fundamental measurement of forest community and regional diversity, underlies many ecological modelsThirdly, Forest community-level survey data is analyzed in this paper in different ways, which focus on biodiversity index modeling. The data is derived from at several forest bureaus in the Northeast forest area of China (Heilongjiang province and Jilin province). In order to validate the models and the initial analysis, this paper adopts the Cross-validation method, which is the statistical practice of partitioning a sample of data into subsets such that the analysis is initially performed on a single subset, while the other subset(s) are retained for subsequent use in confirming and validating the initial analysis. The initial subset of data is called the training set (205 field plots); the other subset(s) are called validation or testing sets (98 plus 64 field plots), totally 367 field plots.In each field plot, The dominant stands (or dominant tree species groups), the age class, the DBH, the height of tree, and the number of trees were measured, also in each field plot, there are one sample plot (5m×5m) for shrub investigation, and four small sample plots (2m×2m) for herb investigation. I have calculated the species diversity for 3 layers (i.e. tree layer, shrub layer and herb layer) by means of various biodiversity index formulas and analyzed the relative species abundance using 9 models of the probability density distribution functions, such as, (3 Distribution (or Beta Distribution), Weibull Distribution, Lognormal Distribution, Poisson Distribution, Binomial Distribution, Negative Binomial Distribution ,Geometric Distribution, etc.. chi-square analyses were conducted on species distribution by using the chi-square test formulated by Pearson to test which distribution function is better, the result of chi square test made it possible to reject the other 8 distribution functions, theβdistribution function performs better than other probability density functions, it has a very close approximation, which can be used for the description of relative abundances of species in forest communities in this data set.Fourthly, this paper defined the concept of the quasi maximum number of species. Estimating species richness (i.e., the actual number of species present in a given area) is a basic objective of biodiversity studies field. Because the species richness is a kind of sensitive index for biodiversity and usually systematic underestimation (bias) for the number of species in a population, the index of biodiversity is a biased data set. The basic problem is that from a limited sample, how to estimate the maximum number of species that would be found in a complete survey, but that have not yet been observed. Of the available methods, the Jackknife and Bootstrap estimation can be used to compensate for the underestimation associated with simple richness estimation (or the sum of species counted in a sample). The reason is that in general Jackknife and Bootstrap estimation methods will provide estimators with less bias and variance at maximum than the other estimation methods. These methods through using the estimators with simulation and resampling technique can provide a maximum number of species, which is close to the population, in measurement of biodiversity.Finally, this paper primarily focuses on the model-building of generalized linear models in biodiversity index. Regression analyses and Predictive models are increasingly used in biodiversity measurement. However, systematic applications of novel statistical techniques are still limited. The modern regression approaches are particularly useful for the modeling of the biodiversity of species and communities. The procedure is as follows.Generalized Linear Models (GLM) are an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the Normal distribution, such as the Poisson, Binomial, Multinomial, and etc.. Generalized Linear Models also relax the requirement of equality or constancy of variances that is required for hypothesis tests in traditional linear models. Hypothesis tests applied to the Generalized Linear Model do not require normality of the response variable, nor do they require homogeneity of variances. Hence, Generalized Linear Models can be used when response variables follow distributions other than the Normal distribution, and when variances are not constant. For example, the count data can often be poorly represented by classical Gaussian distributions (i.e. Normal distribution) but the data would be appropriately analyzed as a poisson random variable within the context of the Generalized Linear Model.This paper demonstrates the GLM model-building procedures step-by-step for the biodiversity of forest community in the northeast of china. Based on seemingly unrelated model, this paper analyzed the equation's relationship among forest plant-diversity index models, and introduced 3 endogenous variables: Y₁ (Shannon' biodiversity index of tree layer), Y₂ (Shannon' biodiversity index of shrub layer), Y₃ (Shannon' biodiversity index of herb layer), also 3 exogenous variables, X₁ (dominant stands); X₂ (Origin of forest) and X₃ (age class group or cohort). The linear simultaneous equation model can be represented by the matrix equation, which is described as follow YB + xΓ=ε(where B andΓare two structural parameter matrices,εis a matrix of unobserved residuals). Y₁, Y₂, and Y₃ as the independent variables can be put to another equation to construct simultaneous equation models, according to the latent relation between structural parameter matrices, the linear constrained equation HA = L is need This is very important and necessary constraint condition for obtaining estimates of the parameters of the structural equation. Generally, ordinary least squares method (OLS) is widely used for estimating a single equation, if estimating the parameters of the simultaneous equation model was done separately by OLS, it would be ignored the relationship between the equations, and should be yield biased and inconsistent estimates. In most cases, the species diversity index models are interdependent simultaneous-equation models, i.e., models which incorporate mutual causation, and there is dependence between the errors of the structural equations. Appropriate estimation techniques are usually required in this situation. The other techniques which can be used include generalized least squares (GLS), 2-stage least squares (2SLS) and 3-stage least squares (3SLS), 3SLS (combining constrained factor analysis and structural equation estimation) may be very useful. In the end, The final form of simultaneous equation models for forest plant-diversity was as follows,According to the results of variance analysis, there are significant effects among dominant stands, origin of forest and age class group.