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Several theoretical frameworks have been proposed to explain observedbiodiversity patterns, ranging from the classical niche-based theories, mainlyemploying a continuous formalism, to neutral theories, based on statisticalmechanics of discrete communities. Differences in the descriptions ofbiodiversity can arise due to the discrete or continuous nature of theunderlying models and the way internal or external perturbations appear intheir formulations. Here, we trace the effects of stochastic populationdynamics on biodiversity, from the scale of the individuals to the communityand based on both discrete and continuous representations of the system, byconsistently using measures of community diversity like the species abundancedistribution and the rank abundance curve and applying them to both discreteand continuous populations. A novel measure, the community abundancedistribution, is introduced to facilitate the comparison across differentlevels of description, from microscopic to macroscopic. Using a simple birthand death process and an interacting population model, we highlightdiscrepancies in their discrete and continuous distributions and discussrelevant implications for the analysis of rare species and extinction dynamics.Quantitative consideration of these issues is useful for better understandingof the contributions of non-neutral processes and the mathematicalapproximations to various measures of biodiversity.

Bridging discrete and continuous formalisms for biodiversity quantification