27 Primary production and nutrients
For primary producers the production is estimated as a function of the producers’ biomass, Bi, from a simple saturating relationship
[latex]f(B_i)=\frac{r_i \cdot B_i}{1+B_i \cdot h_i} \tag{1}[/latex]
where, ri is the maximum production/biomass ratio that can be realized (for low Bi’s), and ri/hi is the maximum net primary production when the biomass is not limiting to production (high Bi’s). For parameterization it is only necessary to provide an estimate of ri / (P/Bi),i.e., a factor expressing how much primary production can be increased compared to the base model state. If a Forcing function is applied to primary production, it multiplies the r parameter in the equation above.
Nutrient cycling and nutrient limitation
Ecosim uses a very simple strategy to represent nutrient cycling and potential nutrient limitation of primary production rates. It is assumed that at any instant in time the system has a total nutrient concentration NT, which is partitioned between nutrient ‘bound’ in biomass versus free in the environment (accessible to plants for nutrient uptake). That is, T is represented as the sum NT = ∑iŋiBi + Nf, where ŋi is (fixed) nutrient content per unit of pool i biomass, and Nf is free nutrient concentration. Then assuming that NT varies as dNT/dt = I – vNT, where I is total inflow rate to the system from all nutrient loading sources and v is total loss rate from the system due to all loss agents (volume exchange, sedimentation, export in harvests, etc.), and that v is relatively large, NT is approximated in Ecosim by the (possibly moving) equilibrium value NT = I/v.
Changes in nutrient loading can be simulated by assigning a time forcing function to NT, in which case NT is calculated as NT = ft NTo where NTo is the Ecopath base estimate of NT (at the start of each simulation) and ft is a time multiplier (ft = 1 implies Ecopath base value of NT). Under the moving equilibrium assumption, changes in ft can be viewed as caused by either changes in input rate I or nutrient loss rate v.
The Ecopath base estimate NTo of total nutrient is entered by specifying the base free nutrient proportion pf = Nf / NTo (at: Time dynamic (Ecosim) >Input > Ecosim parameters), from which the Ecosim initialization can calculate NTo as simply NTo = ∑i ŋi Bi / (1-pf). The units of nutrient concentration are contained in the per-biomass relative nutrient concentrations ŋi, and these need not be specified in any particular absolute units. During each simulation, Nf is varied dynamically by setting it equal at any time to NT – ∑I ŋi Bi, so that accumulation of nutrient in any functional group can reduce free nutrient available to promote primary production.
Primary production rates for producer functional groups j are linked to free nutrient concentration during each simulation through assumed Michaelis-Menten uptake relationships of the form P/Bj = P/Bmax,j Nf/(Kj+Nf), where the parameters P/Bmax,j and Kj are calculated as part of the Ecosim initialization using input estimates of the ratios P/Bmax,j / P/BEcopath,j (Ecosim > Input > Group info form). The Michaelis constant Kj is set so that P/Bj = P/BEcopath,j when Nf is at the initial concentration determined by NT – ∑I ŋi Bi when all Bi are at Ecopath base values). The sensitivity to changes in nutrient concentration can be increased by increasing the input P/Bmax,j / P/BEcopath,j ratio. This will make P/Bj more variable with changes in NT and Nf.
The default free nutrient proportion pf is set at unity, which causes Nf to be virtually constant over time (and hence P/Bj’s to be virtually independent of nutrient concentration changes). To “turn on” nutrient limitation effects, pf must be set to a lower value, (e.g., 0.3 at Ecosim > Input > Ecosim parameters).
Be aware that this simple approach to accounting for nutrient limitation can interact with the numerical method used to simulate very fast phytoplankton dynamics over time, to cause numerical instability or “chattering” in the values of phytoplankton biomass. This happens mainly in cases where pf is low, so that Nf is initially small. Then any biomass decline in the system, (e.g., due to decline in zooplankton biomass) results in a relatively large increase in Nf, which can cause an over-response in the calculated phytoplankton biomass(es) Bj, which then drives Nf to near zero, which in turn causes too large a decrease in calculated Bj for the next monthly Ecosim time step.
The single free nutrient concentration Nf is linked to all primary producer groups in the model (through the uptake kinetics-P/B relationships), implying competition among all plant types in the model for free nutrients. This can cause major shifts in primary production structure over time, e.g. between benthic and pelagic primary production and between grazeable and non-grazeable algal types.
