Species spatial distribution analysis using nearest neighbor methods: aggregation and self-similarity

Spatial aggregation and self-similarity are two important properties in species spatial distribution analysis and modeling. The aggregation parameter k in the negative binomial distribution model and fractal dimension are two widely used measures of spatial aggregation and self-similarity, respectively. In this paper, we attempt to describe spatial aggregation and self-similarity using nearest neighbor methods. Specifically, nearest neighbor methods are used to calculate k and box-counting fractal dimension of species spatial distribution. First, five scaling patterns of k are identified for tree species in a tropical rainforest on Barro Colorado Island (BCI), Panama. Based on the scaling patterns and the means of the nth nearest neighbor distance (NND), the mean NND of higher ranks can be accurately predicted. Second, we describe how to use the theoretical probability distribution model of the nth NND for a homogeneous Poisson process on regular fractals to estimate the fractal dimension. The results indicate that the fractal dimensions estimated using the nearest neighbor method are consistent with those estimated using the scale-area method for 85 tree species on BCI (abundance a parts per thousand yen 100 individuals and a parts per thousand currency sign 5000 individuals). For other tree species, the breakdown of self-similarity in estimates of fractal dimension causes these two methods to be inconsistent. The applicability of the nearest neighbor method is also discussed.