An exactly solvable coarse-grained model for species diversity

TL;DR

This paper introduces an exactly solvable coarse-grained neutral model for ecosystem species diversity, providing analytical solutions for species distribution, correlations, and extinction times, validated with empirical data.

Contribution

It offers a novel analytical framework for neutral biodiversity models based solely on species persistence time distributions, bridging theory and empirical evidence.

Findings

Analytical solutions for species number distribution in ecosystems.

Robustness of ecosystem properties across different model details.

Empirical validation with estuarine fish data.

Abstract

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results of ecological neutral theory and empirical evidence on species diversity preservation. Neutral model of biodiversity deals with ecosystems in the same trophic level where per-capita vital rates are assumed to be species-independent. Close-form analytical solutions for neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain: the probability distribution function of the number of species in the ecosystem both in transient and stationary states; the n-points connected time correlation function; and the survival probability, definned as the distribution of time-spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from a estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications on biodiversity and conservation biology.