Generality Of Power-law Model In The Study Of Spatial Heterogeneity In Abandoned Grassland Community

This research was conducted on the long-term abandoned grassland communities in Yangling District of Shaanxi Province.The number of occurrences and individuals,cover and above-ground biomass as four investigation methods and index values were used to investigate all plant species in the plant communities.We analyzed the spatial heterogeneity of the whole community and each plant species based on the survey data from 2016 and 2017by using the power law model,and comparative researched the power-law models of the four index values with other analytic models such as the binomial distribution model,the negative binomial distribution model,the?-distribution model,and the?-distribution model.And further explore whether the power-law model can be used to analyze spatial pattern of grassland plant cover,above-ground biomass,occurrence and individual number,namely whether power-law model has generality,which can provide a new analytical method for the research of spatial pattern of grassland.It will provide a simple,intuitive and comprehensive analytical method for the study of the spatial heterogeneity in grassland plant communities.The main results are as follows:?1?In the line graph of power law model for all species in four index values,R²?coefficients determinant?of the regression line>0.85.Therefore,the power-law models are highly fit well to the spatial pattern of number of occurrence and individuals,coverage and above-ground biomass of all plant species composing this abandoned grassland community.Absolute value of power law model regression linear regression residual<1;?2?“Ii”refer to the spatial heterogeneity index of occurrence frequency,individual number,coverage,and above-ground biomass of plant species calculated using?-binomial distribution model,negative binomial distribution model,?-distribution model,and?-distribution model respectively.“?i”refer to the spatial heterogeneity index of four index values calculated using the power-law model.The results show that,in 2016,the correlation between I_i and?_i of the number of occurrences is significant?P<0.05?,while there was no correlation between I_i and?_i of the individuals number?P>0.05?;In 2017,there was a significant correlation between the Ii and?i of number of occurrences and individuals?P<0.01?;In 2016 and 2017,there was a complete positive logarithmic correlation between Ii and?_i of plant coverage,above-ground biomass?P<0.01 and R²=1?.?3?“mi”refer to the mean of four index values.In 2016,there was a highly significant positive correlation between m_i and?_i of the number occurrences and the number of individuals?P<0.01?.Although there was no significant correlation in 2017,there was still a positive correlation trend?P>0.05?.There is no correlation between m_i and I_i of the number of occurrences and individuals.As for the coverage and above-ground biomass of plant species,there was a significant negative logarithmic correlation between m_i and?_i,and a significant negative power function relationship between m_i and I_i.?P<0.05?.And the correlation coefficient R² between the two correlation of the coverage and above-ground biomass are equal.Therefore,the power-law model analysis method is not only simple and intuitive,but also universal in the analysis of spatial heterogeneity of this abandoned grassland community.There was a very significant positive correlation between the heterogeneity index?Ii?calculated using the?-distribution model and the?-distribution model and the heterogeneity index??_i?calculated using the power exponent model,and R²=1,so that the power-law models can completely replace?-distribution model and?-distribution model.