植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。

Nearest neighbor distance in spatial point patterns of plant species-probability distribution model and parameter estimation

In ecology, the spatial point pattern, which is obtained by mapping the locations of each individual as points in space, is a very important tool for describing the spatial distribution of species. There are three generally accepted types of spatial point patterns:regular, random, and aggregated. To detect spatial patterns, quadrat sampling is commonly applied, where quadrats are randomly thrown on the space and then the number of individuals in quadrats is used to fit Poisson model or NBD model, respectively. Distance sampling is an alternative method for spatial point pattern analysis, which is flexible and efficient, especially in highly dense plant communities, and in difficult terrain. Nearest neighbor method is one effective distance sampling method in spatial distribution pattern analysis. There are two kinds of nearest neighbor distances (NND):point-to-tree NND, distances from randomly selected points (sampling points) to the nearest individuals; and tree-to-tree NND, distances from selected individuals to their nearest neighbors. In this paper, we show a probability distribution model of higher order nearest neighbor distance (tree-to-tree). As we see the expression of this model is complicated; therefore, parameter estimation using conventional method is not a trivial task. In statistics, there are many numerical methods for estimating the parameters of complicated probability distribution model such as moment method, empirical method, graphical method, and maximum likelihood method. In previous literature, maximum likelihood method has been applied for parameter estimation and the optimized estimates on the log-likelihood surface were searched by Nelder-Mead algorithm. However, maximum likelihood estimation was fraught with nontrivial numerical issues when the samples of tree-to-tree distance were rare. In this paper, we use an alternative method, genetic algorithm, to estimate the two model parameters. The computation can be further simplified by defining a suitable objective function based on the expectation and variance. The probability distribution model is then used to fit spatial distribution data of three tree species on southern Vancouver Island, western coast of Canada. It is found that the proposed probability distribution model can fit nearest neighbor distance samples well for Douglas-fir (Pseudotsuga menziesii) and western hemlock (Tsuga heterophylla). For tree species western red cedar (Thuja plicata), the fitting is not so satisfied because individuals of western red cedar are usually distributed as small clusters. As Douglas-fir is almost randomly distributed in space, the estimated parameter representing spatial aggregation nearly does not change. However, the estimated parameter increases when spatial scale increases for the other two tree species, western hemlock and western red cedar. A short discussion about the advantages and limitations of the probability model and its parameter estimation methods is also presented. Theoretically, the probability distribution model presented in this study is applicable to all kinds of spatial point patterns ranging from highly aggregated to complete random. However, as the actual point patterns of tree species usually deviate from theoretical assumptions, the probability distribution model has a few shortcomings such as scale dependence. To gain a better fitting, higher orders of nearest neighbor distances are needed. A balance between field work burden and performance of model fitting should be considered. We suggest that ideal orders of nearest neighbor distances are from 2 to 6. Another potential that can improve the fitting performance is using mixed probability distributions.