. 2012 Aug 3;7(8):e42045. doi: 10.1371/journal.pone.0042045

Table 2. Parameter assumptions for analytical simplifications.

Assumption	Reasons/references	Exceptions
δ_i, δ_i(1– ε_i) >> h_i	Recycling exceeds losses¹	Heavy soil disturbance
Bν_i >>k_i	Recycling exceeds losses¹	Low B (after disturbance)
m_i >> φ_i	Recycling exceeds losses¹	Heavy soil disturbance
φ_i >> ψ	Weathering is very slow²	Rapid weathering rate
ω_P>> ω_N	Biological stoichiometry³
ε_P> ε_N	Litter biochemistry⁴	Common ground fires
m_P> m_N	SOM biochemistry⁴	Common ground fires
δ_P ≈ δ_N	Parameter definition⁵
h_P ≈ h_N	Same material⁶	Common ground fires
φ_P ≈ φ_N	Same material⁶	Common intense fires
m_iD_i >> \|I_i – k_iA_i,i\|	Recycling exceedsinputs/losses¹	Heavy pollution, Low D

Table notes and references: The subscript i refers to nitrogen (N) and phosphorus (P).

In non-agricultural systems, internal recycling of both N and P (between plants and soils) typically exceeds total inputs and losses (to or from the atmosphere or waterways) many fold, both globally [44], [101] and at individual sites [102]. Consequently, litter decomposition is much greater than litter loss (δ_iL_i >> h_iL_i), plant uptake is much greater than losses of plant-available nutrients (Bν_iA_i >> k_iA_i), SOM mineralization is much greater than SOM loss (m_iD_i >> φ_iD_i), and SOM mineralization is much greater than the balance of abiotic inputs and plant-available losses (m_iD_i >> |I_i – k_iA_i,i|). Exceptions to this pattern will occur where losses are very high (e.g., when ground fires or heavy erosion frequently remove substantial amounts of litter, it is unlikely that δ_i >> h_i), where plant or SOM pools are very small (e.g., at the beginning of primary succession, it is unlikely that m_iD_i >> |I_i – k_iA_i,i|; see text and analysis), or in heavily polluted regions.

See ref [51].

Plants typically have an order of magnitude higher N content than P content [44], [103].

⁴

P is more readily cleaved from organic matter than N (see text).

⁵

For decomposition, we have defined the parameters such that ε controls the relative mineralization of N versus P and δ is the overall litter decomposition rate.

⁶

N and P loss rates via leaching and erosion should be similar because they come from the same organic material. In ecosystems where fire is important, organic N loss rates may be relatively higher than P.