Ripley's K(d)函数分析种群空间分布格局的边缘校正

Edge correction of Ripley's K(d) function on population spatial pattern analysis

Ripley's K( d)函数是分析种群空间分布格局最常用的方法 ,边缘校正是此方法的关键问题。传统的边缘校正包括 3种情形 :( i)圆完全包含在样地内 ;( ii)圆与样地的一条边相交 ;( iii)圆与样地的两条边相交 ,并有 2个或 3个交点。实际上 ,还存在第 ( iv)种情形 ,即圆与样地两条边相交有 4个交点的情形。本文从数学上证明 ,传统边缘校正中 ,当边缘校正属于第 ( iv)种情形时 ,仍按第 ( iii)种情形进行校正 ,必然导致权重估计偏大 ,L( d)值偏高 ,从而影响结果分析。采用我国东北长白山天然云冷杉林样地资料验证了此结论。结果表明 ,天然云冷杉林中 ,3个优势种群林木分布格局特点是 :鱼鳞云杉和臭冷杉的分布格局曲线非常相近 ,而与椴木的差异较大。原因是鱼鳞云杉和臭冷杉具有相似的生态学特性。椴木在小尺度显著聚集 ,因为椴木常在林隙更新。相比较而言 ,建群种云冷杉分布的均匀程度要比椴木高。

Ripley's K(d) function is an important analysis tool for study of population spatial pattern, and method of edge correction is a key part of the tool. Traditionally, there are three cases which the edge correction need to be done: (i) the circle is entirely contained in the plot; (ii) the circle intersects the plot on one side; (iii) the circle intersects two boundaries of the plot with two or three points. However, there exits still another case that the circle intersects two boundaries of the plot with four intersection points. It is proved mathematically in this paper, when the relationship between circle and plot belongs to the fourth case, but edge correction is still conducted on the regulation of the third case, the correction weight will certainly uprise, lead to an enlarged K(d) estimation, and the reliability of analysis will be reduced. This is an unsolved theoretical weakness. An improved method of edge correction that overcomes this weakness is tested in this paper. A sampling plot of 50×40 m2 has been established in unmanaged spruce-fir forest in Changbei Mountain of Northeast China since 1986, and rectangular grids of 10×10 m2 were set in 2002. Coordinates of all trees over 5 cm DBH and other parameters were measured. These data are used to test the improved method of edge correction. Spatial pattern characteristics of three dominant tree species, Picea jezoensis, Abies nephrolepis and Tilla amurensis, are analysed. As results, spatial patterns of Picea jezoensis and Abies nephrolepis are similar, and significantly different from Tilla amurensis. The reason is that Picea jezoensis and Abies nephrolepis have similar ecological characteristics. The spatial pattern of Tilla amurensis is significantly clustered at small scales due to the species habit of regenerating in forest gap. In comparison with Tilla amurensis, the spatial patterns of Picea jezoensis and Abies nephrolepis tend to be more regular.