Species-specific growth adjustment - Nutrients

The nutrient stress growth reducer $NU{T}_{ts}$ [-] is defined as:

$$NU{T}_{ts}=max(NU{T}_{AMC,ts},NU{T}_{RSA,ts})$$

The growth reducers based on arbuscular mycorrhizal colonisation rate $NU{T}_{AMC,ts}$ and the root surface area $NU{T}_{RSA,ts}$ are described below. The maximum of both response curves is used for the nutrient reduction function. It is assumed that the plants needs either many fine roots per above ground biomass or have a strong symbiosis with mycorrhizal fungi. Both functions use the calculation of the plant available nutrients.

Growth reducers

• the nutrient stress growth reducer based on the arbuscular mycorrhizal colonisation rate $NU{T}_{AMC,ts}$ [-] is defined as:

$$\begin{array}{rl}NU{T}_{AMC,ts}& =\{\begin{array}{ll}0& \text{if }R=0\\ 1/(1+\exp (-{\beta }_{NUT,amc}\cdot (N_{p,ts}-x_{0,N,AMC})))& \text{if }0<R<1\\ 1& \text{if }R>=1\end{array}\\ x_{0,N,AMC}& =\frac{1}{{\beta }_{NUT,amc}}\cdot (-{\delta }_{NUT,amc}\cdot (TAM{C}_{ts}-(\frac{1}{{\delta }_{NUT,amc}}\cdot \log \left(\frac{1-{\alpha }_{NUT,amc,05}}{{\alpha }_{NUT,amc,05}}\right)+{\varphi }_{TAMC})))+0.5\\ TAM{C}_{ts}& =\frac{B_{B,ts}}{B_{ts}}\cdot am{c}_s\end{array}$$

• the nutrient stress growth reducer based on the root surface area $NU{T}_{RSA,ts}$ [-] is defined as:

$$\begin{array}{rl}NU{T}_{RSA,ts}& =\{\begin{array}{ll}0& \text{if }R=0\\ 1/(1+\exp (-{\beta }_{NUT,rsa}\cdot (N_{p,ts}-x_{0,N,RSA})))& \text{if }0<R<1\\ 1& \text{if }R>=1\end{array}\\ x_{0,N,RSA}& =\frac{1}{{\beta }_{NUT,rsa}}\cdot (-{\delta }_{NUT,rsa}\cdot (TRS{A}_{ts}-(\frac{1}{{\delta }_{NUT,rsa}}\cdot \log \left(\frac{1-{\alpha }_{NUT,rsa,05}}{{\alpha }_{NUT,rsa,05}}\right)+{\varphi }_{TRSA})))+0.5\\ TRS{A}_{ts}& =\frac{B_{B,ts}}{B_{ts}}\cdot rs{a}_s\end{array}$$

• ${\varphi }_{TAMC}$ reference trait value [-]

• ${\beta }_{NUT,amc}$ slope of response function [-]

• ${\alpha }_{NUT,amc,05}$ response at $N_{p,ts}=0.5$ for species with the reference trait value [-]

• ${\delta }_{NUT,amc}$ scales the difference in the growth reducer between species [-]

• ${\varphi }_{TRSA}$ reference trait value [m² g⁻¹]

• ${\beta }_{NUT,rsa}$ slope of response function [-]

• ${\alpha }_{NUT,rsa,05}$ response at $N_{p,ts}=0.5$ for species with the reference trait value [-]

• ${\delta }_{NUT,rsa}$ scales the difference in the growth reducer between species [g m⁻²]

Visualization

• growth reducer based on root surface area per total biomass:

response at Np = 0.5 for species with the reference trait value α_NUT_rsa_05 (strong to weak growth reduction)	0.9
difference between species δ_NUT_rsa (no to strong difference)	10
slope of response β_NUT_rsa	7
reference trait value ϕ_TRSA	0.15

• growth reducer based on arbuscular mycorrhizal colonisation rate per total biomass:

response at Np = 0.5 for species with the reference trait value α_NUT_amc_05 (strong to weak growth reduction)	0.9
difference between species δ_NUT_amc (no to strong difference)	10
slope of response β_NUT_amc	7
reference trait value ϕ_TAMC	0.2

API

GrasslandTraitSim.nutrient_reduction! Function

nutrient_reduction!(; container, nutrients, total_biomass)

Reduction of growth based on plant available nutrients and the traits arbuscular mycorrhizal colonisation and root surface area per belowground biomass.

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Plant available nutrients

The plant available nutrients $N_{p,ts}$ [-] are described by:

$$\begin{array}{rl}{N}_{p,ts}& =(1-\exp (-{\omega }_{NUT,N}\cdot N-{\omega }_{NUT,F}\cdot F))\cdot NU{T}_{adj,ts}\\ NU{T}_{adj,ts}& ={\alpha }_{NUT,maxadj}\cdot \exp \left(\frac{\log \left(\frac{1}{{\alpha }_{NUT,maxadj}}\right)\cdot \sum _{i=1}^{S}T{S}_{s,i}\cdot B_{ti}}{{\alpha }_{NUT,TSB}}\right)\\ \mathbf{TS}& =\left[\begin{array}{ccccc}1& T{S}_{1,2}& \dots & & T{S}_{1,S}\\ T{S}_{2,1}& 1& & \\ ⋮& & \ddots & & \\ T{S}_{S,1}& & & & 1\end{array}\right]\\ \mathbf{TS}& =1-\frac{\mathbf{TD}}{max(\mathbf{TD})}\\ T{D}_{s,i}& =\sqrt{{(RS{A}_{norm,s}-RS{A}_{norm,i})}^2+{(AM{C}_{norm,s}-AM{C}_{norm,i})}^2}\\ RS{A}_{\text{norm},s}& =\frac{rs{a}_s-\text{mean}(RSA)}{\text{sd}(RSA)}\\ AM{C}_{\text{norm},s}& =\frac{am{c}_s-\text{mean}(AMC)}{\text{sd}(AMC)}\end{array}$$

• ${\omega }_{NUT,N}$ controls the influence of the total soil nitrogen on the nutrient index [kg gN⁻¹]

• ${\omega }_{NUT,F}$ controls the influence of the fertilization rate on the nutrient index [kg N⁻¹]

• ${\alpha }_{NUT,maxadj}$ maximum nutrient adjustment factor [-]

• ${\alpha }_{NUT,TSB}$ reference value, at ${\alpha }_{NUT,TSB}=T{S}_{s,i}\cdot B_{ti}$ is the nutrient adjustment factor $NU{T}_{adj,ts}=1$ [kg ha⁻¹]

Visualization

maximum nutrient adjustment factor α_NUT_maxadj
reference value for ∑ TS ⋅ B α_NUT_TSB

API

GrasslandTraitSim.similarity_matrix! Function

similarity_matrix!(; container)

Calculates the similarity between plants concerning their investment in fine roots and collaboration with mycorrhiza.

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GrasslandTraitSim.nutrient_competition! Function

nutrient_competition!(; container, total_biomass)

Models the density-dependent competiton for nutrients between plants.

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GrasslandTraitSim.input_nutrients! Function

input_nutrients!(; container)

Calculates nutrient index based on total soil nitrogen and fertilization.

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