![\"\"](\"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-content\/uploads\/sites\/2056\/2023\/10\/Ecotracer-1.png\")
<\/p>\r\n<\/p>\r\n
Ecotracer is a useful tool within the Ecopath with Ecosim (EwE) modelling approach to track radioisotopes, contaminants, persistent pollutants, or stable isotopes through a food web model.\u00a0 After achieving a mass\u2010balanced Ecopath model, Ecotracer can be used with the Ecosim (time dynamic) or Ecospace (spatial\u2010temporal dynamic) to track the flow of the pollutant through the modelled ecosystem.<\/p>\r\n
EwE uses a mass\u2010balance approach, and the flows of a contaminant due to predator\/prey interactions are tracked within the underlying Ecopath model. However, Ecotracer also needs parameters for groups based on a kinetic toxicology approach to estimate initial conditions. However, similar to Ecopath, Ecotracer can become dynamic through either the use of Ecosim or Ecospace to follow the changes of a contaminant that has different temporal inputs or to variations in temporal spatial concentrations in the water column.<\/p>\r\n
The purpose of this manual is to give a full description of the Ecotracer approach including the dynamic equations that describe the basis for the input parameters, and to familiarize users with the various interfaces for the inputs and outputs. Simulation scenarios are also given to allow users to become more familiar with Ecotracer, and instructions are given on how to navigate through the different interfaces used.<\/p>\r\n\r\n
Ecotracer is a sub\u2010routine in the Ecopath with Ecosim (EwE) modeling framework[footnote]Christensen, V., Walters, C.J., 2004. Ecopath with Ecosim: methods, capabilities and limitations. Ecological Modelling, Placing Fisheries in their Ecosystem Context 172, 109\u2013139. https:\/\/doi.org\/10.1016\/j.ecolmodel.2003.09.003<\/a>[\/footnote] [footnote]Walters, W.J., Christensen, V., 2018. Ecotracer: analyzing concentration of contaminants and radioisotopes in an aquatic spatial-dynamic food web model. Journal of Environmental Radioactivity 181, 118\u2013127. https:\/\/doi.org\/10.1016\/j.jenvrad.2017.11.008<\/a>[\/footnote] that allows the modeller to follow a contaminant or stable isotope in modelled functional groups and the environment in a balanced Ecopath model.<\/p>\r\n Many EwE models have been made that focus on fishery\u2010related questions, but here the focus is on how the Ecotracer routine is used within EwE to trace contaminants such as radionuclides through an aquatic ecosystem. EwE consists of three routines: Ecopath which is a mass balance interpretation of an ecosystem where, in essence, the production of a group in the model is equal to its consumption; Ecosim allows the user to build in time dynamics to the Ecopath model for events such as changes in contaminant loading to an ecosystem; and Ecospace which allows for the spatial\u2010temporal resolution for such events as the effects of change in loading on marine organisms that result from organisms inhabiting different spatial areas or habitat types that have different environmental concentrations through time.<\/p>\r\n Typical applications of Ecotracer have been for contaminants such as mercury[footnote]Booth, S., Zeller, D., 2005. Mercury, Food Webs, and Marine Mammals: Implications of Diet and Climate Change for Human Health. Environmental Health Perspectives 113, 521\u2013526. https:\/\/doi.org\/10.1289\/ehp.760<\/a>3[\/footnote], 14<\/sup>C[footnote]Sandberg, J., Kumblad, L., Kautsky, U., 2007. Can ECOPATH with ECOSIM enhance models of radionuclide flows in food webs? \u2013 an example for 14C in a coastal food web in the Baltic Sea. Journal of Environmental Radioactivity 92, 96\u2013111. https:\/\/doi.org\/10.1016\/j.jenvrad.2006.09.010<\/a>[\/footnote] [footnote]Tierney, K.M., Heymans, J.J., Muir, G.K.P., Cook, G.T., Buszowski, J., Steenbeek, J., Walters, W.J., Christensen, V., MacKinnon, G., Howe, J.A., Xu, S., 2018. Modelling marine trophic transfer of radiocarbon (14C) from a nuclear facility. Environmental Modelling & Software 102, 138\u2013154. https:\/\/doi.org\/10.1016\/j.envsoft.2018.01.013<\/a>[\/footnote], 137<\/sup>Cs[footnote]Walters & Christensen. 2018, op. cit<\/em>.[\/footnote]\u00a0[footnote]Booth, S., Walters, W.J., Steenbeek, J., Christensen, V., Charmasson, S., 2020. An Ecopath with Ecosim model for the Pacific coast of eastern Japan: Describing the marine environment and its fisheries prior to the Great East Japan earthquake. Ecological Modelling 428, 109087. https:\/\/doi.org\/10.1016\/j.ecolmodel.2020.109087<\/a>[\/footnote], and PCBs[footnote]Booth, S., Cheung, W.W.L., Coombs-Wallace, A.P., Zeller, D., Christensen, V., Pauly, D., 2016. Pollutants in the seas around us, in: Pauly, D., Zeller, D. (Eds.), Global Atlas of Marine Fisheries: A Critical Appraisal of Catches and Ecosystem Impacts. pp. 152\u2013170.[\/footnote] that can have detrimental impacts on human and environmental health. The use of Ecotracer can help to estimate the amount of contaminant or concentration in a group\/species of interest, spatial differences in concentration within the same functional groups if Ecospace is used, the fluxes between groups due to trophic interactions, and the importance of diet versus direct environmental uptake. It can also help to estimate functional groups\u2019 concentrations when such data are lacking (i.e., have a starting value of zero) and make forward projections based on changing environmental concentrations. Concentration levels are an important aspect for environmental and human health as, in conjunction with consumption rates, they determine exposure levels that may have detrimental effects. Regulatory limits on the concentration in aquatic products destined for human consumption may also affect trade and fisheries opportunities.<\/p>\r\n Ecotracer requires a balanced Ecopath model to follow the contaminant, radioisotopes or stable isotopes in the model groups, and environment (e.g., water concentration). Ecotracer when used with Ecosim can provide estimates to important ecotoxicological questions such as,<\/p>\r\n\r\n Ecotracer when used with Ecospace can help to answer whether there are differences in the same species that occur over a large geographic area, and whether different environmental concentrations in different areas impact the resulting concentrations in organisms. In this case, a two\u2010dimensional representation of the model area is made which has a user defined spatial resolution (i.e., grid cells). Spatial environmental concentrations can be driven by effluents being released as a point source, or from atmospheric deposits that change over space and time. Effluents released from a point source would be affected by currents resulting in different spatial and temporal distributions, and atmospheric releases could be affected by different levels of releases due to industrial activity through time or accident scenarios as well as currents. In the case of large\u2010scale accidents, such as the Dai\u2010ichi nuclear accident at Fukushima, spatial differences can result from both point sources and differing atmospheric deposits both of which occurred through time.<\/p>\r\n\r\n Ecotracer simulates the contaminant fluxes and resulting amounts and concentrations using a modified transfer contaminant model (e.g.,[footnote]Landrum, P.F., Lydy, M.J., Lee, H., 1992. Toxicokinetics in aquatic systems: Model comparisons and use in hazard assessment. Environ Toxicol Chem 11, 1709\u20131725. https:\/\/doi.org\/10.1002\/etc.5620111205<\/a>[\/footnote] [footnote]Thomann, R.V., 1981. Equilibrium Model of Fate of Microcontaminants in Diverse Aquatic Food Chains. Can. J. Fish. Aquat. Sci. 38, 280\u2013296. https:\/\/doi.org\/10.1139\/f81-040<\/a>[\/footnote]), and applies it to both the environment and biota. Resulting changes at any time step are dependent upon the gains and losses in functional groups and are described in Walters and Christensen[footnote]Walters & Christensen, 2018, op. cit<\/em>.[\/footnote]\u00a0as,<\/p>\r\n [latex]\\frac{dA_i(t)}{dt} = \\alpha_i - \\beta_i A_i(t)\\tag{1}[\/latex]<\/p>\r\n where \u03b1i<\/sub><\/em>\u00a0represents the gains (Bq\u2219year\u20101<\/sup>) in each functional group i<\/em>, \u03b2i<\/em><\/sub> represents the rate losses (year\u20101<\/sup>) to each functional group, and Ai<\/sub><\/em>\u00a0represents the amount (e.g., Bq) in each functional group i.<\/em> This general formulation allows different measurement units of substances (e.g., Bq or \u00b5g) to be tracked in the modelled environment, and the resulting concentrations\u00a0(e.g., Bq\u2219t\u20101<\/sup>) are computed separately using the biomass output in Ecopath and Ecosim.<\/p>\r\n The environmental compartment concentrations are also calculated by tracking the gains and losses in the cells representing the environment,<\/p>\r\n [latex]\\frac{dC_o(t)}{dt} = \\alpha_o - \\beta_o C_o(t)\\tag{2}[\/latex]<\/p>\r\n where Co<\/em><\/sub> represents the environmental concentration (e.g., Bq\u2219km\u20102<\/sup>), \u03b1o<\/sub>,<\/em> represents the gains and losses\u00a0in each environmental cell o<\/em>, and \u03b2o<\/em><\/sub> represents the rate losses (year\u20101<\/sup>) in each cell.<\/p>\r\n\r\n Gains in the environment originate from the release of contaminants into the environment as a base inflow rate, and from the excretion from organisms. Losses originate from the direct uptake from the environment by organisms, physical decay rates, and base volume exchange. In Ecospace, the environment can be represented by multiple grid cells and thus the gains and losses can be considered to be for each environmental compartment o<\/em>, such that,<\/p>\r\n [latex]\\alpha_o = BI_o + \\sum\\limits_{i=1}^{n}m_iA_i\\tag{3}[\/latex]<\/p>\r\n where BIo<\/sub><\/em> is the base inflow rate (Bq\u2219km\u20102<\/sup>\u2219year\u20101<\/sup>) to a grid cell, and mi<\/em><\/sub>Ai<\/em><\/sub> are the excretory products for each functional group within each grid cell.<\/p>\r\n Losses from the environment are due to biological, physical decay processes, environmental volume changes, and direct uptake by organisms, such that,<\/p>\r\n [latex]\\beta_o C_o=(d_i+V_i)C_o+\\sum\\limits_{i=1}^{n}u_iB_iC_o\\tag{4}[\/latex]<\/p>\r\n where di<\/sub><\/em> represents the physical decay rate (year\u20101<\/sup>), Vi<\/sub><\/em> represents the base volume exchange loss (year\u20101<\/sup>), and the second term (ui<\/sub>Bi<\/sub>Co<\/sub><\/em>) represents the total uptake rate by all functional groups (see below). Temporal changes to the environmental concentration (Co<\/sub><\/em>) can be made by applying a forcing function to the base inflow rate, through a contaminant concentration driver file (Table 1), or by current\/advection fields.<\/p>\r\n\r\n In biota, intake amounts (e.g., Bq\u2219year\u20101) result from direct uptake rates (i.e., respiration) the fraction retained from trophic interactions (i.e., diet), and immigration. i.e.,<\/p>\r\n [latex]\\alpha_i=u_iB_iC_o+AE_i \\sum\\limits_{i=1}Q_{ij} \\frac{A_j}{B_j}+c_iI_i\\tag{5}[\/latex]<\/p>\r\n where, Co<\/sub><\/em> represents the environmental concentration (Bq\u2219km\u20102<\/sup>), Bi<\/em> is the biomass (t<\/em>) of group i<\/em>, ui<\/sub><\/em> represent the intake\/biomass\/environmental concentration\/year (km2<\/sup>\u2219t\u20101<\/sup>\u2219year\u20101<\/sup>); AEi<\/sub><\/em> is the assimilation efficiency for each group, Qji<\/sub><\/em> is the consumption rate (t\u2219year\u20101<\/sup>) of group j<\/em> by group i<\/em>, Aj <\/sub><\/em>is the amount of substance in a group (e.g., Bq), Bj<\/sub><\/em> is the prey biomass of each prey item j<\/em> (Bq\u2219t\u20101<\/sup>); c<\/em>i<\/em><\/sub> is the group biomass concentration (Bq\u2219t\u20101<\/sup>) and Ii<\/sub><\/em> is the immigrating biomass (t\u2219year\u20101<\/sup>).<\/p>\r\n The losses from a group (\u03b2i<\/em><\/sub>Ci<\/em><\/sub>) are attributed to predation, fisheries, other mortality, excretion and decay, i.e.,<\/p>\r\n [latex]\\beta_iC_i=(\\sum\\limits_{j=pred}(\\frac{Q_{ij}}{B_i})+F_i+MO_i+E_i+m_i+d_i) C_i\\tag{6}[\/latex]<\/p>\r\n where Qij<\/sub><\/em> is the rate of consumption (t\u2219year\u20101<\/sup>) of group i<\/em> due to predation by j<\/em>, Fi<\/sub><\/em> is the fishing mortality rate (year\u20101<\/sub>), MOi<\/sub><\/em> (year\u20101<\/sup>) is other mortality rate (i.e., non\u2010predation mortality), Ei<\/sub><\/em> is the emigrating biomass rate (year\u20101<\/sup>), mi<\/sub><\/em> (year\u20101<\/sup>) is the excretion and\/or metabolic rate, and di<\/sub><\/em> (year\u20101<\/sup>) is the physical decay rate. These rates are multiplied by Ci<\/sub><\/em> the amount of contaminant (Bq) in each group i<\/em>. Excretory products that are released from tissues to the environment are added to the environmental concentration.<\/p>\r\n The solution for finding the equilibrium amount of contaminant in a primary producer with the resulting concentration only being due to direct uptake, losses to due predation, other mortality, metabolism, and decay is given as,<\/p>\r\n [latex]C_{i,eq}=\\frac{u_iB_iC_o}{\\sum\\limits_{j=pred}(\\frac{Q_{ij}}{B_i}) +MO_i+m_i+d_i}\\tag{7}[\/latex]<\/p>\r\n whereas for other groups an additional term must be accounted for due to the group\u2019s prey items; in these cases the equilibrium solution can be defined as,<\/p>\r\n [latex]C_{i,eq}=\\frac{u_iB_iC_o+AE_i \\frac{Q_{ji}}{B_i}}{\\sum\\limits_{j=pred}(\\frac{Q_{ij}}{B_i}) +MO_i+m_i+d_i}\\tag{8}[\/latex]<\/p>\r\n The Ecotracer approach is dynamic and extends the basic concentration ratio (CR) approach, but the CR approach is contained within it as,<\/p>\r\n [latex]CR_i=\\frac{(A_i\/B_i)}{C_o}=\\frac{u_i+AE_i\\frac{Q_{}ji}{B_i}CR_j}{Z_i+m_i}\\tag{9}[\/latex]<\/p>\r\nThe amount of contaminant in the detritus compartment originates from the unassimilated consumption resulting from predation, as well as non\u2010predation mortality. Thus, groups feeding on detritus will have exposure levels associated with the contributions from the fraction of unassimilated consumption from all groups. Initial concentrations in the biota and environment are also input parameters that can be used if data is available. For groups lacking contaminant data from field studies or literature data, the model is able to estimate concentration or burdens in the groups, leading to the ability to estimate risk through time and make comparisons to regulatory limits.\r\n Ecotracer is a useful tool within the Ecopath with Ecosim (EwE) modelling approach to track radioisotopes, contaminants, persistent pollutants, or stable isotopes through a food web model.\u00a0 After achieving a mass\u2010balanced Ecopath model, Ecotracer can be used with the Ecosim (time dynamic) or Ecospace (spatial\u2010temporal dynamic) to track the flow of the pollutant through the modelled ecosystem.<\/p>\n EwE uses a mass\u2010balance approach, and the flows of a contaminant due to predator\/prey interactions are tracked within the underlying Ecopath model. However, Ecotracer also needs parameters for groups based on a kinetic toxicology approach to estimate initial conditions. However, similar to Ecopath, Ecotracer can become dynamic through either the use of Ecosim or Ecospace to follow the changes of a contaminant that has different temporal inputs or to variations in temporal spatial concentrations in the water column.<\/p>\n The purpose of this manual is to give a full description of the Ecotracer approach including the dynamic equations that describe the basis for the input parameters, and to familiarize users with the various interfaces for the inputs and outputs. Simulation scenarios are also given to allow users to become more familiar with Ecotracer, and instructions are given on how to navigate through the different interfaces used.<\/p>\n Ecotracer is a sub\u2010routine in the Ecopath with Ecosim (EwE) modeling framework[1]<\/sup><\/a> [2]<\/sup><\/a> that allows the modeller to follow a contaminant or stable isotope in modelled functional groups and the environment in a balanced Ecopath model.<\/p>\n Many EwE models have been made that focus on fishery\u2010related questions, but here the focus is on how the Ecotracer routine is used within EwE to trace contaminants such as radionuclides through an aquatic ecosystem. EwE consists of three routines: Ecopath which is a mass balance interpretation of an ecosystem where, in essence, the production of a group in the model is equal to its consumption; Ecosim allows the user to build in time dynamics to the Ecopath model for events such as changes in contaminant loading to an ecosystem; and Ecospace which allows for the spatial\u2010temporal resolution for such events as the effects of change in loading on marine organisms that result from organisms inhabiting different spatial areas or habitat types that have different environmental concentrations through time.<\/p>\n Typical applications of Ecotracer have been for contaminants such as mercury[3]<\/sup><\/a>, 14<\/sup>C[4]<\/sup><\/a> [5]<\/sup><\/a>, 137<\/sup>Cs[6]<\/sup><\/a>\u00a0[7]<\/sup><\/a>, and PCBs[8]<\/sup><\/a> that can have detrimental impacts on human and environmental health. The use of Ecotracer can help to estimate the amount of contaminant or concentration in a group\/species of interest, spatial differences in concentration within the same functional groups if Ecospace is used, the fluxes between groups due to trophic interactions, and the importance of diet versus direct environmental uptake. It can also help to estimate functional groups\u2019 concentrations when such data are lacking (i.e., have a starting value of zero) and make forward projections based on changing environmental concentrations. Concentration levels are an important aspect for environmental and human health as, in conjunction with consumption rates, they determine exposure levels that may have detrimental effects. Regulatory limits on the concentration in aquatic products destined for human consumption may also affect trade and fisheries opportunities.<\/p>\n Ecotracer requires a balanced Ecopath model to follow the contaminant, radioisotopes or stable isotopes in the model groups, and environment (e.g., water concentration). Ecotracer when used with Ecosim can provide estimates to important ecotoxicological questions such as,<\/p>\n The first question is useful if many functional groups in the model lack concentration data. The second question can be important to estimate resulting concentrations in biota if the input into the environment changes. The third can help to understand contaminant flows as a result of changes in the dynamics of the underlying structure of an ecosystem.<\/p>\n Ecotracer when used with Ecospace can help to answer whether there are differences in the same species that occur over a large geographic area, and whether different environmental concentrations in different areas impact the resulting concentrations in organisms. In this case, a two\u2010dimensional representation of the model area is made which has a user defined spatial resolution (i.e., grid cells). Spatial environmental concentrations can be driven by effluents being released as a point source, or from atmospheric deposits that change over space and time. Effluents released from a point source would be affected by currents resulting in different spatial and temporal distributions, and atmospheric releases could be affected by different levels of releases due to industrial activity through time or accident scenarios as well as currents. In the case of large\u2010scale accidents, such as the Dai\u2010ichi nuclear accident at Fukushima, spatial differences can result from both point sources and differing atmospheric deposits both of which occurred through time.<\/p>\n Ecotracer simulates the contaminant fluxes and resulting amounts and concentrations using a modified transfer contaminant model (e.g.,[9]<\/sup><\/a> [10]<\/sup><\/a>), and applies it to both the environment and biota. Resulting changes at any time step are dependent upon the gains and losses in functional groups and are described in Walters and Christensen[11]<\/sup><\/a>\u00a0as,<\/p>\n [latex]\\frac{dA_i(t)}{dt} = \\alpha_i - \\beta_i A_i(t)\\tag{1}[\/latex]<\/p>\n where \u03b1i<\/sub><\/em>\u00a0represents the gains (Bq\u2219year\u20101<\/sup>) in each functional group i<\/em>, \u03b2i<\/em><\/sub> represents the rate losses (year\u20101<\/sup>) to each functional group, and Ai<\/sub><\/em>\u00a0represents the amount (e.g., Bq) in each functional group i.<\/em> This general formulation allows different measurement units of substances (e.g., Bq or \u00b5g) to be tracked in the modelled environment, and the resulting concentrations\u00a0(e.g., Bq\u2219t\u20101<\/sup>) are computed separately using the biomass output in Ecopath and Ecosim.<\/p>\n The environmental compartment concentrations are also calculated by tracking the gains and losses in the cells representing the environment,<\/p>\n [latex]\\frac{dC_o(t)}{dt} = \\alpha_o - \\beta_o C_o(t)\\tag{2}[\/latex]<\/p>\n where Co<\/em><\/sub> represents the environmental concentration (e.g., Bq\u2219km\u20102<\/sup>), \u03b1o<\/sub>,<\/em> represents the gains and losses\u00a0in each environmental cell o<\/em>, and \u03b2o<\/em><\/sub> represents the rate losses (year\u20101<\/sup>) in each cell.<\/p>\n Gains in the environment originate from the release of contaminants into the environment as a base inflow rate, and from the excretion from organisms. Losses originate from the direct uptake from the environment by organisms, physical decay rates, and base volume exchange. In Ecospace, the environment can be represented by multiple grid cells and thus the gains and losses can be considered to be for each environmental compartment o<\/em>, such that,<\/p>\n [latex]\\alpha_o = BI_o + \\sum\\limits_{i=1}^{n}m_iA_i\\tag{3}[\/latex]<\/p>\n where BIo<\/sub><\/em> is the base inflow rate (Bq\u2219km\u20102<\/sup>\u2219year\u20101<\/sup>) to a grid cell, and mi<\/em><\/sub>Ai<\/em><\/sub> are the excretory products for each functional group within each grid cell.<\/p>\n Losses from the environment are due to biological, physical decay processes, environmental volume changes, and direct uptake by organisms, such that,<\/p>\n [latex]\\beta_o C_o=(d_i+V_i)C_o+\\sum\\limits_{i=1}^{n}u_iB_iC_o\\tag{4}[\/latex]<\/p>\n where di<\/sub><\/em> represents the physical decay rate (year\u20101<\/sup>), Vi<\/sub><\/em> represents the base volume exchange loss (year\u20101<\/sup>), and the second term (ui<\/sub>Bi<\/sub>Co<\/sub><\/em>) represents the total uptake rate by all functional groups (see below). Temporal changes to the environmental concentration (Co<\/sub><\/em>) can be made by applying a forcing function to the base inflow rate, through a contaminant concentration driver file (Table 1), or by current\/advection fields.<\/p>\n In biota, intake amounts (e.g., Bq\u2219year\u20101) result from direct uptake rates (i.e., respiration) the fraction retained from trophic interactions (i.e., diet), and immigration. i.e.,<\/p>\n [latex]\\alpha_i=u_iB_iC_o+AE_i \\sum\\limits_{i=1}Q_{ij} \\frac{A_j}{B_j}+c_iI_i\\tag{5}[\/latex]<\/p>\n where, Co<\/sub><\/em> represents the environmental concentration (Bq\u2219km\u20102<\/sup>), Bi<\/em> is the biomass (t<\/em>) of group i<\/em>, ui<\/sub><\/em> represent the intake\/biomass\/environmental concentration\/year (km2<\/sup>\u2219t\u20101<\/sup>\u2219year\u20101<\/sup>); AEi<\/sub><\/em> is the assimilation efficiency for each group, Qji<\/sub><\/em> is the consumption rate (t\u2219year\u20101<\/sup>) of group j<\/em> by group i<\/em>, Aj <\/sub><\/em>is the amount of substance in a group (e.g., Bq), Bj<\/sub><\/em> is the prey biomass of each prey item j<\/em> (Bq\u2219t\u20101<\/sup>); c<\/em>i<\/em><\/sub> is the group biomass concentration (Bq\u2219t\u20101<\/sup>) and Ii<\/sub><\/em> is the immigrating biomass (t\u2219year\u20101<\/sup>).<\/p>\n The losses from a group (\u03b2i<\/em><\/sub>Ci<\/em><\/sub>) are attributed to predation, fisheries, other mortality, excretion and decay, i.e.,<\/p>\n [latex]\\beta_iC_i=(\\sum\\limits_{j=pred}(\\frac{Q_{ij}}{B_i})+F_i+MO_i+E_i+m_i+d_i) C_i\\tag{6}[\/latex]<\/p>\n where Qij<\/sub><\/em> is the rate of consumption (t\u2219year\u20101<\/sup>) of group i<\/em> due to predation by j<\/em>, Fi<\/sub><\/em> is the fishing mortality rate (year\u20101<\/sub>), MOi<\/sub><\/em> (year\u20101<\/sup>) is other mortality rate (i.e., non\u2010predation mortality), Ei<\/sub><\/em> is the emigrating biomass rate (year\u20101<\/sup>), mi<\/sub><\/em> (year\u20101<\/sup>) is the excretion and\/or metabolic rate, and \r\n \t
Ecotracer dynamics<\/h2>\r\n
Environment<\/h3>\r\n
Biota<\/h3>\r\n
Attribution\r\n<\/strong>\r\nThis work was funded by the Institut de Radioprotection et de S\u00fbret\u00e9 Nucl\u00e9aire (IRSN) and the French program Investissement d\u2019Avenir run by the National Research Agency (AMORAD project, grant ANR\u201011\u2010RSNR\u20100002, 2013\u20102022)\r\n<\/strong><\/div>\r\n.","rendered":"<\/p>\nIntroduction<\/h2>\n
\n
Ecotracer dynamics<\/h2>\n
Environment<\/h3>\n
Biota<\/h3>\n