Abstract:

Aim: Spatial distribution of species represents a core issue in population biology and macroecology. Commonly used metrics for quantifying species aggregation include the negative binomial distribution parameter k for quadrat data and neighborhood density indices (such as Ω proposed by Condit et al, 2000 and k_ff proposed by Wiegand et al, 2025) for point pattern data. However, how the choice of index and its estimation uncertainty jointly affect the inference of the aggregation–abundance relationship remains unclear. 

Methods: We use a spatially explicit neutral model to simulate community data, then computed the aforementioned aggregation indices along with their standard errors. Finally, we analyzed how the index selection and its estimation error influence the power-law relationship between aggregation and species abundance. 

Results: (1) The three aggregation indices are strongly correlated under high aggregation intensity. Under weak aggregation, however, k remains effective in discriminating interspecific differences in aggregation, whereas the two point-pattern indices lack such discriminative power. (2) Estimation errors of different indices are weakly positively correlated. The standard error of k for rare and weakly aggregated species estimated by maximum likelihood is large, consistent with simulation results. In contrast, standard errors of point pattern indices based on resampling methods are generally smaller. (3) The aggregation–abundance relationship varies depending on the chosen index and whether weighted regression is applied. For 1/k, weighted regression consistently recovers the theoretical exponent of –1 predicted by neutral theory, whereas unweighted regression yields shallower slopes, especially in communities with weak aggregation. The exponents for the two point-pattern indices vary with the mean aggregation intensity of the community. 

Main conclusions: Ignoring the uncertainty in aggregation estimates can significantly bias inferences of the aggregation–abundance relationship, potentially leading to the incorrect rejection of the neutral null hypothesis (i.e., an increased risk of Type I error). The relationships derived from the two point-pattern-based indices reflect mean community aggregation but are not suitable for directly testing neutral assembly mechanisms. We recommend using the maximum likelihood estimate of the negative binomial parameter k and its standard error to measure species aggregation from quadrat data and incorporating uncertainty into subsequent analyses. For other aggregation indices, there is a need to develop predictions of their relation with species abundance from theories such as the simple neutral case.

Key words: spatial pattern, aggregation-abundance relationship, negative binomial distribution, point pattern analysis, neutral theory