Context or problem: Plant-available soil phosphorus (P) is commonly assessed by chemical extractions with the purpose of diagnosing and advising fertilizer P application. However, for a given crop, this approach only poorly predicts yields obtained from several experimental sites. To solve this major drawback, a functional and mechanistic evaluation has been developed to mimic dominant processes involved in the absorption of phosphate ions. Objective or research question: In this study, we investigated the predictive ability of a mechanistic approach to diagnose maize (Zea mays L.) yields, in comparison to the common Olsen's method (0.5 M bicarbonate solution). Methods: The processes-based assessment consists of parameterizing relationships between amount of diffusible phosphate ions (P-r) at the solid-to-solution interface equilibrating the phosphate ions concentration in solution (C-P) with time (t). We parameterized [P-r vs. (C-P, t)] relationships for stored and archived soil samples (plough layer) of nine long-term field experiments (LTFEs) on increasing rates of P applications including the zero-P treatment (P0). LTFEs were located in different soils (Luvisol, Podzol, Arenosol, Calcosol) with large variations in physico-chemical properties. We also used LTFEs database of maize yields. Results: The C-P values ranged from 0.02 to 3.86 mg P L-1 for 40 (LTFExyear of maize cropping) combinations. The (P-r=vxC(P)(w)xt(p)) equation closely described the [P-r vs. (C-P, t)] datasets, with (v, w, p) parameters being soil specific. Maximum yields ranged from 5.5 to 14.7 t DM ha(-1) depending on LTFEs and years. Yields decreased significantly only in P0, and did not differ for other P rates. The relationship between the relative maize yield and C-P was sites-specific with C-P thresholds to obtain a relative yield of 0.95 ranged from 0.07 to 0.88 mg P L-1 solution. Taking into account amounts of phosphate ions which balance C-P by diffusion using (P-r=vxC(P)(w)xt(p)) equations, a single response curve is observed for the 9 LTFEs when the replenishment time is 1500 minutes (i.e. about one day). The critical C-P thresholds closely correlated to the ability of the soil solid phase to buffer phosphate ions in solution. Conclusions: For the 9 studied LTFEs on P fertilization, the [P-r vs. (C-P, t)] relationships were more able to account for maize response curves than P extracted by Olsen method, improving the precision and reliability of the multisite diagnosis of maize yield response. Implications or significance: As a result, P fertilization recommendations are more reliable regardless of soil type. Further progress could be gained by taking into account for the role of the soil layer beneath the plough layer.