Species Area Relationship (SAR): Pattern Description with Geometrical Approach

TL;DR

This paper introduces a geometric approach to modeling the species-area relationship (SAR), providing a new formula that better fits small-area data and relates to macroecological patterns, validated with tropical tree data from Panama.

Contribution

The paper presents a novel geometric formulation of SAR based on individual positions, improving small-area predictions and linking to macroecological patterns.

Findings

The new SAR formula fits empirical data well across different scales.

The parameter z relates to spatial aggregation and coverage.

Application to Panama data demonstrates model effectiveness.

Abstract

Several formulations are describing the pattern of species-area relationship, log-log linear, semi-log linear, among others. These patterns mainly explain the species-area relationship for large areas, and for the small area, they provide significant differences from real data. We consider the geometric position of individuals of species, and base on that, we find the probability of observing at least one individual of the species. We apply a translation of the well-studied problem of mixed salt-water in a tank to describe the formula of SAR. For a rectangular sample area the species-area relationship follows the pattern, with some simplification, $S=c|A^{\beta}+a|^z$, where $S$ is the number of species in the area of size $A$ and $a,c,z$, and $\beta$ are constants with $z<1$ and $\beta\leq1$. We also show how the constant $z$ relates to some macroecological patterns, namely spatial aggregation, percentage of area coverage, and the core-satellite model. We exemplify our method using data on tropical tree species from a 50ha plot in Barro Colorado Island (BCI), Panama, using all individuals.