Bridging discrete and continuous formalisms for biodiversity quantification

TL;DR

This paper explores how stochastic population dynamics influence biodiversity patterns across discrete and continuous models, introducing a new measure to compare these frameworks and highlighting implications for rare species and extinction.

Contribution

It introduces the community abundance distribution to compare discrete and continuous biodiversity models and analyzes discrepancies using simple population processes.

Findings

Discrepancies exist between discrete and continuous biodiversity distributions.

The new community abundance distribution facilitates cross-level comparisons.

Implications for understanding rare species and extinction dynamics are discussed.

Abstract

Several theoretical frameworks have been proposed to explain observed biodiversity patterns, ranging from the classical niche-based theories, mainly employing a continuous formalism, to neutral theories, based on statistical mechanics of discrete communities. Differences in the descriptions of biodiversity can arise due to the discrete or continuous nature of the underlying models and the way internal or external perturbations appear in their formulations. Here, we trace the effects of stochastic population dynamics on biodiversity, from the scale of the individuals to the community and based on both discrete and continuous representations of the system, by consistently using measures of community diversity like the species abundance distribution and the rank abundance curve and applying them to both discrete and continuous populations. A novel measure, the community abundance distribution, is introduced to facilitate the comparison across different levels of description, from microscopic to macroscopic. Using a simple birth and death process and an interacting population model, we highlight discrepancies in their discrete and continuous distributions and discuss relevant implications for the analysis of rare species and extinction dynamics. Quantitative consideration of these issues is useful for better understanding of the contributions of non-neutral processes and the mathematical approximations to various measures of biodiversity.