118 林业科学 49卷 and the initial state as a random pattern of a Poisson Gibbs models.Three example plots were selected to process). illustrate that the patterns of the simulated tree In this study,the Gibbs point process models locations were very similar to the observed ones. were applied to all spatial distributions of trees.It has The spatial structures of a forest stand include its the advantage of being flexible to fit various spatial horizontal and vertical structures.The horizontal point patterns.This is extremely useful if the spatial structure can be characterized by the relative locations pattern of the data is not certain.Because of this of trees over space and the distributions of tree general property,its performance varies among diameters.The vertical structure can be represented by different spatial patterns.For example,in this study,the height distribution and diameter-height it did not fit the clustered pattern as well as it fitted the relationships.The spatial models developed in this CSR or regular patterns.In addition,the empirical study can provide useful information on the horizontal regression models for predicting the two parameters of structures of forest stands,whereas the information on the Gibbs models worked best for the CSR pattern,the vertical structures of forest stands can be obtained followed by the regular pattern,and worst for the from a bivariate distribution model of tree diameter and clustered pattern.This was consistent with the height.The combination of these models will offer goodness-of-fit of the Gibbs point process models for much more information on the three dimensional profile the spatial patterns.Therefore,it would be interesting and dynamics of forest stands to forest managers and to compare the model fitting and prediction,especially researchers. for the clustered plots,using the Gibbs point process 参考文献 model against other spatial models such as Cox process model or Poisson cluster process model Matern, Cressie N A C.1993.Statistics for spatial data:revised edition.John 1971;Cressie,1993)in a future study. Wiley Sons,New York,900. Diggle P J.1983.Statistical analysis of spatial point patterns.Academic 5 Conclusion Press,New York,148. Diggle P J.Fiksel T,Grabarnik P,et al.1994.On parameter estimation The Gibbs point process model with three pair for pairwise interaction point process.Interational Statistical potential functions were used to model the spatial point Review.62(1):99-117. patterns of trees in the 50 spruce-fir plots in the Dovciak M,Frelich L E,Reich P B.2001.Discordance in spatial Northeast,USA.The results indicated that the three patterns of white pine (Pinus strobus)size-classes in a patchy near- pair potential functions fitted 82%-84%of the plots boreal forest.Joumal of Ecology,89(2):280-291. Fox J C,Ades P K,Bi H.2001.Stochastic strueture and individual-tree well.The Diggle's pair potential function performed growth models.Forest Ecology and Management,154(1/2):261- slightly better than the other two pair potential 276. functions (i.e.,VSC and Ogata and Tanemura's).In Friedman S K,Reich P B,Frelich L E.2001.Multiple scale general,the plots of CSR and regular patterns were composition and spatial distribution patterns of the north-eastem Minnesota presettlement forest.Journal of Ecology,89 (4 ) modeled better than the clustered plots by all three pair 538-554. potential functions.Further,empirical regression Gill P E,Murray W,Wright M.1981.Practical optimization.Academic models were developed to predict the two parameters Press,New York. (and)of the Gibbs point process model with the Haase P.1995.Spatial pattern analysis in ecology based on Ripley's K- function:Introduction and methods of edge correction.Journal of Diggle's pair potential function using the available Vegetation Science,6(4):575-582. stand variables as predictors (i.e.,stand density, Hara T.1992.Effects of the mode of competition on stationary size basal area,mean diameter,mean tree height,mean distribution in plant populations.Annals of Botany,69(6): crown length,and mean crown width).The simulation 509-513. results showed that 81%of the 50 plots were predicted Jensen J L,Moller J.1991.Pseudolikelihood for exponential family models of spatial point processes.Annals of Applied Probability,1 satisfactorily by these models,in which 100%of the (3):445-461. CSR plots,71%of the regular plots,and 56%of the Kenkel N C.1988.Pattern of self-thinning in jack pine:testing the clustered plots were predicted satisfactorily by the random mortality hypothesis.Ecology,69(4):1017-1024. 万方数据118 林业科学 49卷 and the initial state as a random pattern o{a Poisson process)． In this study，the Gibbs point process models were applied to all spatial distributions of trees．It has the advantage of being flexible to fit various spatial point patterns．This is extremely useful if the spatial pattern of the data is not certain．Because of this general property， its performance varies among different spatial patterns．For example，in this study， it did not fit the clustered pattern as well as it fitted the CSR or regular patterns．In addition，the empirical regression models for predicting the two parameters of the Gibbs models worked best for the CSR pattern， followed by the regular pattern，and worst for the clustered pattern．This was consistent with the goodness—of-fit of the Gibbs point process models for the spatial patterns．Therefore，it would be interesting to compare the model fitting and prediction，especially for the clustered plots，using the Gibbs point process model against other spatial models such as Cox process model or Poisson cluster process model(Matern， 1971；Cressie，1993)in a future study． 5 Conclusion The Gibbs point process model with three pair potential functions were used to model the spatial point patterns of trees in the 50 spruce—fir plots in the Northeast，USA．The resuhs indicated that the three pair potential functions fitted 82％一84％of the plots well．The Diggle’s pair potential function performed slightly better than the other two pair potential functions(i．e．，VSC and Ogata and Tanemura’s)．In general，the plots of CSR and regular patterns were modeled better than the clustered plots by all three pair potential functions． Further， empirical regression models were developed to predict the two parameters (6 and&)of the Gibbs point process model with the Diggle’s pair potential function using the available stand variables as predictors(i．e．，stand density， basal area，mean diameter，mean tree height，mean crown length，and mean crown width)．The simulation results showed that 8 1％of the 50 plots were predicted satisfactorily by these models，in which 100％of the CSR plots，71％of the regular plots，and 56％of the clustered plots were predicted satisfactorily by the Gibbs models．Three example plots were selected to illustrate that the patterns of the simulated tree locations were very similar to the observed ones． The spatial structures of a forest stand include its horizontal and vertical structures．The horizontal structure can be characterized by the relative locations of trees over space and the distributions of tree diameters．The vertical structure can be represented by the height distribution and diameter—height relationships．The spatial models developed in this study can provide useful information on the horizontal structures of forest stands，whereas the information on the vertical structures of forest stands can be obtained from a bivariate distribution model of tree diameter and height．The combination of these models will offer much more information oil the three dimensional profile and dynamics of forest stands to forest managers and researchers 参 考 文 献 Crcssie N A C．1993．Statistics for Wiley＆Sons．New York．900． Diggle P J．1983．Statistical analysis Press，New York，148． spatial data：revised edition．John of spatial point patterns．Academic Diggle P J，Fiksel T，Grabarnik P，et a1．1 994 On parameter estimation for pairwise interaction point process．International Statistical Review，62(1)：99—117． Dovciak M，Frelich L E，Reich P B．2001．Discordance in spatial patterns of white pine(Pinus strobus)size—classes in a patchy near— boreal forest．Journal of Ecology，89(2)：280—291． Fox J C，Ades P K，Bi H．2001．Stochastic structure and individual—tree growth models．Forest Ecology and Management，154(1／2)：26 1— 276． Friedman S K，Reich P B，Frelich L E．2001．Multiple scale composition and spatial distribution patterns of the noah-eastern Minnesota presettlement forest．Journal of Ecology，89(4)： 538—554． Gill P E，Murray W．Wright M．1981．Practical optimization．Academic Press，New York． Haase P．1995 Spatial pattern analysis in ecology based on Ripley’s K· function：Introduction and methods of edge correction．Journal of Vegetation Science，6(4)：575—582． Hara T．1992．Effects of the mode of competition on stationary size distribution in plant populations．Annals of Botany，69(6)： 509—513． Jensen J L，Moiler J．1991．Pseudolikelihood for exponential family models of spatial point processes．Annals of Applied Probability，1 (3)：445—461． Kenkel N C．1988．Pattern of random mortality hypothesis self-thinning in jack pine：testing the Ecology，69(4)：1017—1024． 万方数据