摘 要 ：本文以油松毛虫(Dendrolimus tabulaeformis Tsai et Liu)幼虫为材料,采用频次分布X~2检验法和分布型指数法测定种群空间格局,并提出了研究种群空间格局的新模型和新的拟合方法:(1)m*-m幂的法则(另文发表);(2)用刀切法估计种群分布型指数;(3)用麦夸方法最优拟合Taylor幂的法则和新的模型。通过频次分布X2检验法和分布型指数法测定结果表明:油松毛虫幼虫的静态空间格局为负二项分布;其空间格局的基本成份为疏松个体群;个体群的分布是聚集型,但在低密度时呈现为均匀型;个体群内个体的分布为随机型;个体群的平均大小介于40—60之间。通过新模型m*-m幂的法则拟合结果表明:当Iwao m*—m迥归模型中的α<0,β>1时,新模型测定油松毛虫幼虫种群的静态空间格局为聚集型,其聚集度则随着密度的升高而增加。用刀切法估计种群分布型指数,可以减小估计的偏离度,并给出近似的区间估计值。用麦夸方法拟合Taylor幂的法则和新模型,可以求得原变量的最小残差解,使其幂函数得到最优参数的估计值。
Abstract:Spatial patterns of Chinese-pine caterpillar(Dendrolimus tabulaeformis Tsai et Liu)were measured by Chi square test of frequency distribution and distribution indies.And also new mathematical model and a few of new fit methods on the research of spatial pattern are presented, its includes:(1)m*—m power law;(2)Jackknifing method is introduced for estimating the population distribution indices;(3)Marquardt‘s algorithm is applied to the fitting Taylor‘s power law and the new model. By the Chi square test of frequeucy distribution and distribution indices,the result have shown that follow:The spatial pattern of chinesepine caterpillar larve obeys the negative Binomial distribution;The basic component of spatial pattern is loose colony;The distribution of loose colony is aggregated but is uniform at lower density;The intra-colony distribution is random;The mean size of colony is between 40—60. By testing of the new model,m*—m power law,it concludes that: When α<0.β>1 in Iwao‘s reg ression model,the statically spatial pattern of Chinese-pine caterpillar is aggregated,and its aggregation increases as density increase. Estimating the distribution indices with jackknifing method can reduce the bias of estimation give the approximatively fiducial interual.Therefore it may overcome the defaults of common used method. Fitting Taylor‘s power law and the new model with Marquardt‘s algorithm is better than the usual logarithm linear transform fitting method.