Table 1 List of model state variables and parameters, with relative description, units, and values (initial value for the state variables). The asterisks indicate that these two parameters vary depending on the considered hypothesis. [0.1–0.5] is for the coupled hypothesis (both), 0 for the hydrophobicity hypothesis and [0.9–1.3] for the phytotoxicity hypothesis.

State variables

F

Fungus

g dm⁻²

0.01 (initial value)

I

Fungus self-inhibitor

g dm⁻²

0 (initial value)

T

Phytotoxicity

g dm⁻²

0 (initial value)

P

Plant

g dm⁻²

1 (initial value)

S

Phytostimulants

g dm⁻²

0 (initial value)

N

Nutrients

g dm⁻²

0 (initial value)

Parameters

\({g}_{F}\)

Fungus growth rate

d⁻¹

[0.01–0.05]

\({s}_{I}\)

Sensitivity of F growth to I

dm² g⁻¹

1

\({k}_{W}\)

Michaelis–Menten constant for W

–

0.3

\({d}_{F}\)

Fungus death rate

dm² d⁻¹ g⁻¹

0.005

\({s}_{F}\)

Sensitivity of F death to I

dm² d⁻¹ g⁻¹

2

\({c}_{I}\)

Accumulation of I due to F death

–

0.05

\({k}_{I}\)

Degradation rate of I

d⁻¹

0.001

\({l}_{I}\)

Leaching rate of I

d⁻¹

0.001

\({c}_{T}\)

Accumulation rate of T due to F

d⁻¹

0.07

\({k}_{T}\)

Degradation rate of T

d⁻¹

0.07

\({l}_{T}\)

Leaching rate of T

d⁻¹

0.01

a

Soil water parameter

dm² g⁻¹

0/2*

b

Soil water parameter

–

9

\({g}_{P}\)

Plants growth rate

dm² d⁻¹ g⁻¹

0.9

\({q}_{P}\)

Baseline P biomass

g dm⁻²

1

\({s}_{T}\)

Sensitivity of P death to T

dm² d⁻¹ g⁻¹

[0.1–0.5]/0/[0.9–1.3]*

\({c}_{S}\)

S accumulation rate

d⁻¹

0.07

\({k}_{S}\)

S degradation rate

d⁻¹

0.07

\({g}_{N}\)

N accumulation due to plant death

–

0.08

\({u}_{N}\)

N plant uptake rate

–

0.3

\({l}_{N}\)

N leaching rate

d⁻¹

0.1

W

Soil water

–

[0.1–2]

\({D}_{F}\)

Fungus diffusion rate

dm² d⁻¹

0.01

\({D}_{P}\)

Plants diffusion rate

dm² d⁻¹

0.01