Application of a Negative Multinomial Model Gives Insight into Rarity-Area Relationships

Youhua Chen,Yongbin Wu,Wenyan Zhang,Tian Zhao,Weihua Chen,Tsung-Jen Shen

doi:10.3390/f11050571

Abstract

The distribution of individuals of different species across different sampling units is typically non-random. This distributional non-independence can be interpreted and modelled as a correlated multivariate distribution. However, this correlation cannot be modelled using a totally independent and random distribution such as the Poisson distribution. In this study, we utilized the negative multinomial distribution to overcome the problem encountered by the commonly used Poisson distribution and used it to derive insight into the implications of field sampling for rare species’ distributions. Mathematically, we derived, from the negative multinomial distribution and sampling theory, contrasting relationships between sampling area, and the proportions of locally rare and regionally rare species in ecological assemblages presenting multi-species correlated distribution. With the suggested model, we explored the cross-scale relationships between the spatial extent, the population threshold for defining the rarity of species, and the multi-species correlated distribution pattern using data from two 50-ha tropical forest plots in Barro Colorado Island (Panama) and Heishiding Provincial Reserve (Guangdong Province, China). Notably, unseen species (species with zero abundance in the studied local sample) positively contributed to the distributional non-independence of species in a local sample. We empirically confirmed these findings using the plot data. These findings can help predict rare species–area relationships at various spatial scales, potentially informing biodiversity conservation and development of optimal field sampling strategies.

Highlights

For better conservation of biological diversity, ecologists have explored the spatial distribution patterns of rare species
Our empirical applications (Table 1) showed that the interspecific distribution of tree species in the HSD forest plot was less positively correlated (k = 0.16445), while the tree distributions were more correlated in the Barro Colorado Island (BCI) plot in Panama, which had a corresponding k value of 0.1003
By contrast, regarding the comparison of the two CVs, the BCI forest plot had a higher value than the HSD plot

Summary

Introduction

For better conservation of biological diversity, ecologists have explored the spatial distribution patterns of rare species. A variety of ecological mechanisms can contribute to species rarity; for example, habitat heterogeneity, dispersal limitation, and pest-pressure hypothesis [1,2,3]. Forests 2020, 11, 571 relationship between species rarity and non-independence of species distribution remains to be explored [3,4,5]. The definition of distributional non-independence or non-randomness can be multifaceted, some tangible forms of which can be aggregated distribution [6,7], regular distribution or correlated distribution [8]. For the multivariate framework that will be employed here, we interpret the term distributional non-independence as a correlated multivariate distribution. Distribution of individuals of different species across different quadrats presents some degree of correlation [8]

Methods

Results

Discussion

Conclusion