Regime Shift Of Marine Ecosystem By Copula And Regression Tree Estimation Of Lyapunov Exponent

Marine, covered 72 percent surface of the earth, is the key part of the globalecosystem. In the past ten years, more attention has been paid to marine ecosystemresearch and great progress was achieved. Many famous international organizations,like The United Nations, GBP, SCOR, IOC, UNEP and UNDP, are emphasizing theimportance of marine ecosystem function study. Major programs about marine science,such as national 973 plan, foundation projects and national special fund, were carriedout in China. Our scientist noticed and took part in the development and began to seekcross-disciplinary and integration about marine system. This paper originally calcu-lated regime shift probability by statistical method-Copula, proposed regression treeestimation of Lyapunov exponent from time series and unified several statistical tests tochoose forecast model. Original work is listed as below:Taking bifurcation parameter of ecological model like total nitrogen and fishingintensity as stochastic variable, their probability distribution were estimated by Copulabased on yearly data. State transfer was modeled by homogeneous Markov chain ifevery traditional bifurcation region was regarded as a state. Transfer probability matrixwas calculated by Monte Carlo. Stable probability was clear sequently. The adjustmentof bifurcation parameter was suggested to make ideal state probability maximization,which provided theory evidence for marine ecosystem manager.Based on phase space reconstruction, largest Lyapunov exponent of time series wascomputed from linear combination of regression tree using stochastic gradient boosting.Our method, without using Jacobin matrix, inherit many virtues of stochastic gradientboosting like perfect prediction precision and easily dealing with higher dimension.Simulation showed that the method got very close to the true value, had smaller standarderror and was robust to noise and embedding dimension, so it is convenient in practice.Dependence was tested in Bohai COD from 1995 to 2005 by BDS, Box-pierceand Ljunng-Box independence test. Considering surrogate data test IAAFT for nonlin-earity, White's and Teravirta's artificial neuron network test for neglected nonlinearity,Hinich's bispectrum test and a test without Fourier transfer, no nonlinearity was madeout. The statistic was Lyapunov exponent from regression tree. The mean error andstandard error of linear ARMA model were the minimum comparing local linear, ruleensemble, random forest, stochastic gradient boosting, support vector, artificial neuron network and multivariate adaptive regression splines. So linear ARMA model fittedbetter, which testified former tests result.