The Freundlich isotherm equation best represents phosphate sorption across soil orders and land use types in tropical soils of Puerto Rico

Biomass production in the lowland wet tropical forest is greater than in any other biome, and it is typically limited by soil phosphorus (P) availability. However, the mechanisms involved in the P cycle remain poorly represented in Earth System Models (ESMs). Soil P sorption processes are key in the P cycle and for understanding the extent of P limitation for plant productivity. Currently, a few ESMs include isotherm equations to model these processes. Although the Langmuir equation is widely cited, other isotherm equations may better describe sorption in tropical soils. Here, we use a diverse range of soil samples from Puerto Rico to test the validity of the Langmuir, Freundlich, and Temkin equation. We found that across four soil orders (Inceptisols, Mollisols, Oxisols, Ultisols), and forested and cultivated land use types, the Freundlich equation best represented soil P sorption. Furthermore, the Langmuir and the Temkin equations poorly represent soil P adsorption, especially at low P concentrations. Specifically, the Langmuir equation underestimated soil P adsorption by 40% and the Temkin equation overestimated adsorption by 76%. We also found, as expected, that soil clay content and pH were the most important parameters explaining the variability of the Freundlich (K_f) constant. Greater clay content and lower pH, common in highly weathered Ultisols and Oxisols which are abundant in the tropics, led to greater K_f values. Overall, our results suggest that a diversity of soils can prompt underestimation of P sorption when using the Langmuir isotherm, which leads to an overestimation of available P that can have repercussions on ESM predictions of the P cycle and tropical forest productivity.