Inferring single- and multi-species distributional aggregation using quadrat sampling

Abstract

Ecologists often employ cost-effective strategies such as quadrat sampling for field-based biodiversity assessments. While the negative binomial distribution (NBD) is widely used to characterize quadrat sampling-derived biodiversity data in single-species settings, an equivalent model for accurately modeling community-level distributional aggregation levels, especially for quadrat sampling data, is still lacking. Here, we recommend the application of symmetric Dirichlet-multinomial (SDM) distribution to characterize aggregation patterns for single- or multi-species. Theoretically, we proved that the likelihood formulae for the SDM and NBD models were nearly equivalent, and consequently, the shape parameters of both models were almost identical. Numerical simulations demonstrated that the SDM model consistently outperformed the NBD model except for cases with large numbers of small-sized quadrats. Empirical tests using the SDM model showed that trees of the forest plot on the Barro Colorado Island shifted from aggregated to even and then back to aggregated again from 1982 to 2015 because of stand competition dynamics driven by tree mortality and recruitment balance. Functionally, the aggregation parameter of the SDM model reflects more purely this biological mechanism-driven aggregation trend, whereas classical nonparametric aggregation metrics failed. In summary, the proposed SDM can be an indispensable tool for inferring species- and community-level distributional aggregation patterns.