- Aim: Explaining and formulating the pattern of the species-area relationship, SAR, that fits better the real data in a small area. - Location: Barro Colorado Island (BCI), Panama. - Time period: No specific time period. - Major taxa studied: tropical tree species - Methods: 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 , then we apply a translation of the well-studied problem of mixed salt-water in a tank to describe the formula of SAR. - Results: 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 of the 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 . - Main conclusions: The new formula of SAR better describes the pattern of SAR for a small area and for the large area it is equivalent to the well-known log-log linear pattern .
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 .
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