{"id":3981,"date":"2024-10-11T12:39:09","date_gmt":"2024-10-11T16:39:09","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/?post_type=chapter&p=3981"},"modified":"2026-02-18T18:23:30","modified_gmt":"2026-02-18T23:23:30","slug":"primary-production-and-nutrients","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/chapter\/primary-production-and-nutrients\/","title":{"raw":"Primary production and nutrients","rendered":"Primary production and nutrients"},"content":{"raw":"
\r\n\r\nFor primary producers the production is estimated as a function of the producers\u2019 biomass, Bi, from a simple saturating relationship\r\n\r\n<\/div>\r\n[latex]f(B_i)=\\frac{r_i \\cdot B_i}{1+B_i \\cdot h_i} \\tag{1}[\/latex]\r\n

where, r<\/em>i<\/sub> is the maximum production\/biomass ratio that can be realized (for low Bi<\/sub><\/em>\u2019s), and r<\/em>i<\/sub>\/h<\/em>i<\/sub> is the maximum net primary production when the biomass is not limiting to production (high Bi<\/sub><\/em>\u2019s). For parameterization it is only necessary to provide an estimate of r<\/em>i <\/em><\/sub>\/ (P<\/em>\/B<\/em>i<\/sub>),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<\/em> parameter in the equation above.<\/p>\r\n\r\n

Nutrient cycling and nutrient limitation<\/h2>\r\n

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<\/sub><\/em>, which is partitioned between nutrient \u2018bound\u2019 in biomass versus free in the environment (accessible to plants for nutrient uptake). That is, T<\/em> is represented as the sum NT <\/sub>= <\/em>\u2211i<\/em><\/sub>\u014bi<\/sub>Bi<\/sub> + Nf<\/sub><\/em>, where \u014bi <\/em><\/sub>is (fixed) nutrient content per unit of pool i<\/em> biomass, and Nf<\/em><\/sub> is free nutrient concentration. Then assuming that N<\/em>T <\/em><\/sub>varies as dN<\/em>T<\/sub>\/dt <\/em>= I - vN<\/em>T<\/em><\/sub>, where I <\/em>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 <\/em>is relatively large, N<\/em>T <\/em><\/sub>is approximated in Ecosim by the (possibly moving) equilibrium value N<\/em>T <\/em><\/sub>= \u00a0I\/v<\/em>.<\/p>\r\n

Changes in nutrient loading can be simulated by assigning a time forcing function to N<\/em>T<\/em>,<\/sub> in which case NT<\/sub> is calculated as NT<\/sub> = ft<\/sub> N<\/em>To <\/em><\/sub>where N<\/em>To <\/em><\/sub>is the Ecopath base estimate of NT<\/sub> (at the start of each simulation) and ft<\/sub><\/em> is a time multiplier (f<\/em>t <\/em><\/sub>= 1 implies Ecopath base value of N<\/em>T<\/em><\/sub>). Under the moving equilibrium assumption, changes in f<\/em>t<\/sub> can be viewed as caused by either changes in input rate I <\/em>or nutrient loss rate v<\/em>.<\/p>\r\n

The Ecopath base estimate N<\/em>To <\/em><\/sub>of total nutrient is entered by specifying the base free nutrient proportion pf<\/sub>\u00a0<\/em>= Nf<\/sub> \/ N<\/em>To <\/em><\/sub>(at: Time dynamic (Ecosim) >Input > Ecosim parameters<\/em>), from which the Ecosim initialization can calculate NTo<\/sub><\/em> as simply N<\/em>T<\/em><\/sub>o<\/sub> = <\/em>\u2211i <\/em><\/sub>\u014bi<\/sub> Bi<\/sub> \/ (1-<\/em>pf<\/sub>)<\/em>. The units of nutrient concentration are contained in the per-biomass relative nutrient concentrations \u014bi<\/sub>, and these need not be specified in any particular absolute units. During each simulation, N<\/em>f <\/em><\/sub>is varied dynamically by setting it equal at any time to N<\/em>T<\/sub> - <\/em>\u2211I <\/em><\/sub>\u014bi<\/sub> B<\/em>i<\/em><\/sub>, so that accumulation of nutrient in any functional group can reduce free nutrient available to promote primary production.<\/p>\r\n

Primary production rates for producer functional groups j <\/em>are linked to free nutrient concentration during each simulation through assumed Michaelis-Menten uptake relationships of the form P\/B<\/em>j <\/sub>= P\/B<\/em>max,j<\/sub> N<\/em>f<\/sub>\/(K<\/em>j<\/sub>+N<\/em>f<\/sub>)<\/em>, where the parameters P\/B<\/em>max,j <\/em><\/sub>and K<\/em>j <\/em><\/sub>are calculated as part of the Ecosim initialization using input estimates of the ratios P\/B<\/em>max,j<\/sub> \/ P\/B<\/em>Ecopath,j <\/em><\/sub>(Ecosim > Input > Group info <\/em>form). The Michaelis constant K<\/em>j <\/em><\/sub>is set so that P\/B<\/em>j = P\/B<\/em>Ecopath,j <\/em><\/sub>when N<\/em>f<\/sub> is at the initial concentration determined by N<\/em>T<\/sub> - <\/em>\u2211I <\/em><\/sub>\u014bi<\/sub> B<\/em>i <\/em><\/sub>when all B<\/em>i <\/em><\/sub>are at Ecopath base values). The sensitivity to changes in nutrient concentration can be increased by increasing the input P\/B<\/em>max,j<\/sub> \/ P\/B<\/em>Ecopath,j <\/em><\/sub>ratio. This will make P\/B<\/em>j <\/em><\/sub>more variable with changes in N<\/em>T <\/em><\/sub>and N<\/em>f<\/em><\/sub>.<\/em><\/p>\r\nThe default free nutrient proportion pf<\/sub><\/em> is set at unity, which causes N<\/em>f <\/em><\/sub>to be virtually constant over time (and hence P\/B<\/em>j<\/em><\/sub>\u2019s to be virtually independent of nutrient concentration changes). To \u201cturn on\u201d nutrient limitation effects, pf<\/sub><\/em> must be set to a lower value, (e.g., 0.3 at Ecosim > Input > Ecosim parameters<\/em>).\r\n

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 \u201cchattering\u201d in the values of phytoplankton biomass. This happens mainly in cases where p<\/em>f <\/em><\/sub>is low, so that N<\/em>f <\/em><\/sub>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 N<\/em>f<\/em><\/sub>, which can cause an over-response in the calculated\u00a0phytoplankton biomass(es) B<\/em>j<\/em><\/sub>, which then drives N<\/em>f <\/em><\/sub>to near zero, which in turn causes too large a decrease in calculated B<\/em>j <\/em><\/sub>for the next monthly Ecosim time step.<\/p>\r\n

The single free nutrient concentration Nf<\/sub> is linked to all primary producer groups in the model (through the uptake kinetics-P\/B<\/em> 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.<\/p>","rendered":"

\n

For primary producers the production is estimated as a function of the producers\u2019 biomass, Bi, from a simple saturating relationship<\/p>\n<\/div>\n

[latex]f(B_i)=\\frac{r_i \\cdot B_i}{1+B_i \\cdot h_i} \\tag{1}[\/latex]<\/p>\n

where, r<\/em>i<\/sub> is the maximum production\/biomass ratio that can be realized (for low Bi<\/sub><\/em>\u2019s), and r<\/em>i<\/sub>\/h<\/em>i<\/sub> is the maximum net primary production when the biomass is not limiting to production (high Bi<\/sub><\/em>\u2019s). For parameterization it is only necessary to provide an estimate of r<\/em>i <\/em><\/sub>\/ (P<\/em>\/B<\/em>i<\/sub>),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<\/em> parameter in the equation above.<\/p>\n

Nutrient cycling and nutrient limitation<\/h2>\n

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<\/sub><\/em>, which is partitioned between nutrient \u2018bound\u2019 in biomass versus free in the environment (accessible to plants for nutrient uptake). That is, T<\/em> is represented as the sum NT <\/sub>= <\/em>\u2211i<\/em><\/sub>\u014bi<\/sub>Bi<\/sub> + Nf<\/sub><\/em>, where \u014bi <\/em><\/sub>is (fixed) nutrient content per unit of pool i<\/em> biomass, and Nf<\/em><\/sub> is free nutrient concentration. Then assuming that N<\/em>T <\/em><\/sub>varies as dN<\/em>T<\/sub>\/dt <\/em>= I – vN<\/em>T<\/em><\/sub>, where I <\/em>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 <\/em>is relatively large, N<\/em>T <\/em><\/sub>is approximated in Ecosim by the (possibly moving) equilibrium value N<\/em>T <\/em><\/sub>= \u00a0I\/v<\/em>.<\/p>\n

Changes in nutrient loading can be simulated by assigning a time forcing function to N<\/em>T<\/em>,<\/sub> in which case NT<\/sub> is calculated as NT<\/sub> = ft<\/sub> N<\/em>To <\/em><\/sub>where N<\/em>To <\/em><\/sub>is the Ecopath base estimate of NT<\/sub> (at the start of each simulation) and ft<\/sub><\/em> is a time multiplier (f<\/em>t <\/em><\/sub>= 1 implies Ecopath base value of N<\/em>T<\/em><\/sub>). Under the moving equilibrium assumption, changes in f<\/em>t<\/sub> can be viewed as caused by either changes in input rate I <\/em>or nutrient loss rate v<\/em>.<\/p>\n

The Ecopath base estimate N<\/em>To <\/em><\/sub>of total nutrient is entered by specifying the base free nutrient proportion pf<\/sub>\u00a0<\/em>= Nf<\/sub> \/ N<\/em>To <\/em><\/sub>(at: Time dynamic (Ecosim) >Input > Ecosim parameters<\/em>), from which the Ecosim initialization can calculate NTo<\/sub><\/em> as simply N<\/em>T<\/em><\/sub>o<\/sub> = <\/em>\u2211i <\/em><\/sub>\u014bi<\/sub> Bi<\/sub> \/ (1-<\/em>pf<\/sub>)<\/em>. The units of nutrient concentration are contained in the per-biomass relative nutrient concentrations \u014bi<\/sub>, and these need not be specified in any particular absolute units. During each simulation, N<\/em>f <\/em><\/sub>is varied dynamically by setting it equal at any time to N<\/em>T<\/sub> – <\/em>\u2211I <\/em><\/sub>\u014bi<\/sub> B<\/em>i<\/em><\/sub>, so that accumulation of nutrient in any functional group can reduce free nutrient available to promote primary production.<\/p>\n

Primary production rates for producer functional groups j <\/em>are linked to free nutrient concentration during each simulation through assumed Michaelis-Menten uptake relationships of the form P\/B<\/em>j <\/sub>= P\/B<\/em>max,j<\/sub> N<\/em>f<\/sub>\/(K<\/em>j<\/sub>+N<\/em>f<\/sub>)<\/em>, where the parameters P\/B<\/em>max,j <\/em><\/sub>and K<\/em>j <\/em><\/sub>are calculated as part of the Ecosim initialization using input estimates of the ratios P\/B<\/em>max,j<\/sub> \/ P\/B<\/em>Ecopath,j <\/em><\/sub>(Ecosim > Input > Group info <\/em>form). The Michaelis constant K<\/em>j <\/em><\/sub>is set so that P\/B<\/em>j = P\/B<\/em>Ecopath,j <\/em><\/sub>when N<\/em>f<\/sub> is at the initial concentration determined by N<\/em>T<\/sub> – <\/em>\u2211I <\/em><\/sub>\u014bi<\/sub> B<\/em>i <\/em><\/sub>when all B<\/em>i <\/em><\/sub>are at Ecopath base values). The sensitivity to changes in nutrient concentration can be increased by increasing the input P\/B<\/em>max,j<\/sub> \/ P\/B<\/em>Ecopath,j <\/em><\/sub>ratio. This will make P\/B<\/em>j <\/em><\/sub>more variable with changes in N<\/em>T <\/em><\/sub>and N<\/em>f<\/em><\/sub>.<\/em><\/p>\n

The default free nutrient proportion pf<\/sub><\/em> is set at unity, which causes N<\/em>f <\/em><\/sub>to be virtually constant over time (and hence P\/B<\/em>j<\/em><\/sub>\u2019s to be virtually independent of nutrient concentration changes). To \u201cturn on\u201d nutrient limitation effects, pf<\/sub><\/em> must be set to a lower value, (e.g., 0.3 at Ecosim > Input > Ecosim parameters<\/em>).<\/p>\n

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 \u201cchattering\u201d in the values of phytoplankton biomass. This happens mainly in cases where p<\/em>f <\/em><\/sub>is low, so that N<\/em>f <\/em><\/sub>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 N<\/em>f<\/em><\/sub>, which can cause an over-response in the calculated\u00a0phytoplankton biomass(es) B<\/em>j<\/em><\/sub>, which then drives N<\/em>f <\/em><\/sub>to near zero, which in turn causes too large a decrease in calculated B<\/em>j <\/em><\/sub>for the next monthly Ecosim time step.<\/p>\n

The single free nutrient concentration Nf<\/sub> is linked to all primary producer groups in the model (through the uptake kinetics-P\/B<\/em> 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.<\/p>\n","protected":false},"author":1909,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3981","chapter","type-chapter","status-publish","hentry"],"part":987,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/3981","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/users\/1909"}],"version-history":[{"count":5,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/3981\/revisions"}],"predecessor-version":[{"id":4449,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/3981\/revisions\/4449"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/parts\/987"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/3981\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/media?parent=3981"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapter-type?post=3981"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/contributor?post=3981"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/license?post=3981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}