## 2 Model Structure and Description
### Soil P Pools, Fluxes and Mineralization
Three main soil P pools (labile, absorbed and strong absorbed) were modeled using the equations  
\[\frac{\text{dP}_{\text{lab}}}{\text{dt}}=\frac{\text{F}_{\text{pnet}}+\text{F }_{\text{pdep}}+\text{F}_{\text{pfert}}+\text{F}_{\text{Pwea}}+\text{F}_{ \text{Fbase}}-\text{F}_{\text{pup}}-\text{F}_{\text{ploss}}-\text{t}_{\text{ sob}}\cdot\frac{\text{psorbmax}\cdot\text{P}_{\text{lab}}}{\text{P}_{\text{lab}}+ \text{k}_{\text{pulsor}}}}{1+\frac{\text{psorbmax}\cdot\text{k}_{\text{plab}}}{ \left(\text{P}_{\text{lab}}+\text{k}_{\text{pulsor}}\right)^{2}}} \tag{8}\]  
\[\frac{\text{dP}_{\text{sorb}}}{\text{dt}}=\frac{\text{k}_{\text{plabor}}\cdot \text{psorbmax}}{\left(\text{k}_{\text{plab}}\cdot\text{P}_{\text{lab}} \right)^{2}}\cdot\text{P}_{\text{lab}} \tag{9}\]  
\[\frac{\text{dP}_{\text{ssb}}}{\text{dt}}=\text{t}_{\text{sob}}\cdot\text{P}_{ \text{sorb}}-\text{t}_{\text{ssb}}\cdot\text{P}_{\text{ssb}} \tag{10}\]  
where P\({}_{\text{lab}}\) is the labile phosphorus pool (g P\(\cdot\)m\({}^{-2}\)); F\({}_{\text{pnet}}\) is the mineralization rate (g P\(\cdot\)m\({}^{-2}\)-day\({}^{-1}\)); F\({}_{\text{pdep}}\), F\({}_{\text{pfert}}\), F\({}_{\text{pwea}}\), and F\({}_{\text{P}\text{t}\text{n}\text{e}}\) are P inputs into the ecosystem due to deposition, fertilization, weather and biological mineralization (g P\(\cdot\)m\({}^{-2}\)-day\({}^{-1}\)); t\({}_{\text{sob}}\) is the turnover time constant rate for absorbed pool (day\({}^{-1}\)); P\({}_{\text{sorbmax}}\) is the maximum amount of absorbed phosphorus (644.0 g P\(\cdot\)m\({}^{-2}\)); and k\({}_{\text{plabor}}\) is an empirical parameter for describing the equilibrium between labile and absorbed phosphorus, which was defined to be 55.0 [53]. F\({}_{\text{pup}}\) and F\({}_{\text{ploss}}\) refer to two pathways out of the labile pool due to P uptake by plants and leaching from the ecosystem (g P\(\cdot\)m\({}^{-2}\)-day\({}^{-1}\)), the loss rate is 0.04 yr\({}^{-1}\)[70]. We focused on labile P pools, which P for mineralization. The net biological phosphorus mineralization rate (prnetminer) and biochemical phosphorus mineralization rate (prbiochemimer) can both be used to describe P mineralization, but due to the long turnover of this process, we simplified it using the equations  
\[\frac{\text{dprnetminer}}{\text{dt}}=\text{Plittermin}+\text{P}\text{S}\text{ min}+\text{P}\text{S}\text{imm} \tag{11}\]  
\[\frac{\text{dprbiochemimer}}{\text{dt}}=\text{u}_{\text{mvmax}}\cdot\text{M4} \cdot\left(\text{t}_{\text{slo}}\text{P}_{\text{slo}}+\text{t}_{\text{pass}} \text{P}_{\text{pass}}\right) \tag{12}\]  
where Plittermin is the minimum value in the litter pool; Psim is gross immobilization from litter; Psim is immobilization from other soil pools; M4 is \(\frac{\text{u}_{\text{mvmax}}\cdot\left(\text{nsstpup}-\text{nsstppro}\right)}{ \text{nsstpup}-\text{nsstppro}+\text{k}_{\text{pibochem}}}\), where u\({}_{\text{mvmax}}\) is the maximum specific biochemical phosphorus mineralization rate; nsct-pup is N cost for P uptake; and kpbiochem is the Michaelis-Menten constant for biochemical P mineralization. Each of the 12 PFTs featured different values of u\({}_{\text{mvmax}}\) and nsctpup. In our model, all P pool sizes were cumulative at each time step, and all the constants used in the algorithms of fluxes and pools are listed in Table S1. The P pool size at a specific time step, P\({}_{\text{tot}}\), was calculated as  
\[\text{P}_{\text{tot}}=\sum_{\text{t}}\text{P}_{\text{it}} \tag{13}\]  
where t represents the time step, and P\({}_{\text{it}}\) is the amount of P in different pools.