dtθ dtC = + dChldt dC dθ dt = V − L Q dP

1 Appendix

The rates of change are defined by the following set of equations:

dDIN

dt =−V^N_phy+X_zoo^N (1)

dDIP

dt =−V^P_phy+X_zoo^P (2)

d C_phy

dt =V^C_phy−L^C_phy (3)

d N_phy

dt =V^N_phy−L^C_phyQ_phy^N (4) d P_phy

dt =V^P_phy−L^C_phyQ_phy^P (5)

dChl

dt =d C_phy

dt θ_phy+d θ_phy

dt C_phy (6)

d C_zoo

dt =V_zoo^C −L^C_zoo (7)

where DIN and DIP are dissolved inorganic nitrogen and phosphorus, C is carbon biomass (POC), N is particulate nitrogen (PON), P is particulate phosphorus (POP) and Chl is chlorophyll of the respective model compartments, V is net acquisition by the model compartment in the subscript of the element in the superscript, ^Xzoo is excretion by all zooplankton compartments present, L is predation loss of the compartment in the subscript, Q^N_phy and Q^P_phy are phytoplankton N:C and P:C ratios, and ^θphy is the whole-cell phytoplankton Chl:C ratio. The NNP configuration is obtained by setting all zooplankton-related terms to 0 in Equations (1)-(6).

The change of the whole-cell Chl:C ratio over time is given by d θ_phy

dt =θ_phy ζ^Chl

d V^C_phy

d θ_phy+d Q^N_phy dt

∂ θ_phy

∂ Q^N_phy (8)

The first term in Eq. (8), ^θphy ζ^Chl

d V^C_phy

d θ_phy , represents the light dependence of chlorophyll driven by the chloroplast, where θ_phy is the whole cell Chl:C. The second term, d Q_phy^N

dt

∂ θ_phy

∂ Q_phy^N , describes the nutrient-driven change of the whole-cell Chl:C ratio ( ^θphy ) as a consequence of

changes in the N:P ratio ( Q^N_phy ). The whole-cell Chl:C ratio is a function of the chloroplast Chl:C ratio ( θ^_phy ) and the N:C ratio:

θ_phy=^θ_phy

(

)

where the optimal allocation factor for nutrient acquisition ( fv ) maximises net balanced growth rate:

f_v= 1 2Q

0 N

QphyN −ζ^Chl

(

N −Q₀^N

)

The predation loss terms are defined by:

L_x^C=I_x^C , x∈{phy , zoo} (11) where I is ingestion of the compartment x by zooplankton.

The excretion terms for N and P are defined by:

X_zoo^N =L^C_phyQ^N_phy+(L^C_zoo−V_zoo^C )Q_zoo^N (12) X_zoo^P =L^C_phyQ^P_phy+(L^C_zoo−V_zoo^C )Q_zoo^P (13) The summed root mean square errors (RMSE) of the NNPZ simulations for 4 state variables (DIN, DIP, phytoplankton POC (phyto POC) and zooplankton POC (zoo POC)) of the PU1 and PU2 model simulations are defined by:

RMSE=

√ ^∑

^∑

⁽

⁽

⁾

⁾

where o represents the mesocosm observations, n the number of days of the experiments and r_i the number of replicates per treatment. mtx

is either the model simulation (PU1) or the mean of the 3 ensemble model simulations per treatment (PU2), calculated for the state variable (x) in consideration (see above).

We then normalised the RMSE with the mean of mesocosm observations ( o ) of the PU1 and PU2 experiments, respectively, to obtain the coefficient of variation (CV) of the RMSE:

CV(RMSE)=RMSE o