This is the appearance of the Food Web tab of the System Coefficients dialog:
The Food Web tab has coefficients which describe how bioaccumulated toxic chemicals pass through an aquatic ecosystem. There are three categories of coefficients in the drop down box at the top of the dialog: bioaccumulated constituents, invertebrates, and fish.
The Bioaccumulated Constituents category has the following coefficients for each toxic chemical:
Organic Carbon Kd is the adsorption isotherm for the chemical on organic carbon. (>=0 L/kg, varies by chemical)
Algae Kd is the adsorption isotherm for the chemical on algae. (>=0 L/kg, varies by chemical)
Detritus Kd is the adsorption isotherm for the chemical on detritus. (>=0 L/kg, varies by chemical)
Water Uptake Efficiency is the efficiency of uptake of the chemical from the water (0-1, unitless)
Food Uptake Efficiency is the efficiency of uptake of the chemical from food (0-1, unitless)
Clearance Rate is the rate at which an organism removes the chemical from the body ()
The Invertebrates category has the following coefficients for each toxic chemical:
Pollutant is the toxic chemical whose bioaccumulation in the invertebrate is being simulated
Uptake Rate is the rate at which the specified invertebrate takes up the toxic chemical from the water (0-20 L/g/d)
Ingestion Rate is the rate at which the specified invertebrate takes up the toxic chemical in food (0.1-0.5 g/g/d)
Elimination Rate is the rate at which the specified invertebrate removes the toxic chemical from its body (0.03-0.08/d)
Assimilation Efficiency is the fraction of consumed toxic chemical incorporated into the body (0-1, unitless)
The Food Sources spreadsheet at the bottom of the dialog has the food sources for each invertebrate. The total for each column should be 1.
The Fish category has the following coefficients for each toxic chemical:
Pollutant is the toxic chemical whose bioaccumulation in the invertebrate is being simulated
Food Conversion Efficiency is the fraction of food mass converted to fish mass (0 – 1, unitless)
Caloric Uptake Efficiency is the fraction of food calories consumed (0 – 1, unitless)
Oxygen Uptake Efficiency is the fraction of available oxygen used (0 – 1, unitless)
Assimilation Weight Exponent is the exponent which achieves proportionality between fish weight and assimilation rate (0 – 1, unitless)
Elimination Weight Exponent is the exponent which achieves proportionality between fish weight and elimination rate (-1 – 0, unitless)
Routine Metabolic Rate Constant is the mass units to the assimilation weight exponent (0.01 – 0.1 kcal/d/g)
Growth Rate is the growth rate of each fish (0.0001-0.01/d)
Weight is the weight of the specified age and species of fish (>0 g)
The Food Sources spreadsheet at the bottom of the dialog has the food sources for each fish. The total for each column should be 1.
Following is a detailed discussion of the food web algorithms as they have been applied in WARMF.
Introduction
The criterion of concern for mercury is concentration within fish rather than within water itself like most pollutants. Mercury concentration in fish is a function of the concentrations in water and biota the fish eat. To simulate fish mercury concentrations thus requires a simulation of mercury in the food eaten by the fish. The mercury concentration will be simulated in the phytoplankton and zooplankton that make up the trophic levels below fish. The food web is represented by three species of algae, zooplankton in the water column, benthic invertebrates in the river/lake bed sediments, and any number of fish species.
Approach
The implementation of algorithms to simulate mercury in the food web is designed so that it might be applied to other toxic chemicals in future WARMF applications. Within WARMF, a new type of chemical constituent has been created, a “toxic” chemical, which bioaccumulates in the food web. For mercury simulation, MeHg is the only constituent classified as “toxic”, which means it accumulates in biota. Because Hg2+ rapidly clears from biota, it does not accumulate like MeHg. For other projects, it will be possible to have different toxic chemicals, such as PCB’s, or even simulate multiple toxics in a single application.
The food web starts with algae and simulate its mercury concentration with an adsorption isotherm to directly relate the biotic concentration to water concentration. Then each toxic chemical needs associated zooplankton and fish established as WARMF parameters. For testing purposes, the food web components used were zooplankton-Hg, benthos-Hg, and fish-Hg. For simulation purposes, many food web components can be used to track mercury in greater detail throughout the food web.
Toxic Chemicals
The simulation of a toxic chemical (like MeHg) is the same as other chemical constituents in WARMF. A toxic chemical has additional parameters specific to the pollutant used throughout the food web (Norstrom et. al. 1976). These are:
- the adsorption isotherms of the toxic chemical on organic carbon, algae, and detritus kd (L/mg)
- efficiency of pollutant uptake from water epw (unitless)
- efficiency of pollutant uptake from food epf (unitless)
- pollutant clearance rate kcl (empirical units)Algae
Algae adsorb toxic chemicals, which are then consumed by herbivores grazing on the algae. Three types of algae are simulated in WARMF. For the sake of simplicity, it is assumed that each type is equally likely to adsorb MeHg and each is equally likely to be eaten by higher trophic levels in the food web. Thus, the algae can be combined together to get a single mercury concentration for phytoplankton:
[algae-Hg] = [water-MeHg] * algae-kd
where [algae-Hg] is the mercury concentration in algae (mg Hg/mg algae), [water-MeHg] is the MeHg concentration in water (mg/l), and algae-Kd is the adsorption isotherm for MeHg on algae (L/mg). The concentration of mercury in algae is not maintained as a separate parameter in WARMF. It is calculated as needed to determine mercury concentrations in the food of higher trophic levels in the food web.
Invertebrates
The concentration of mercury in invertebrates is simulated as a new type of physical constituent. Both zooplankton (in the water column) and benthic organisms are simulated as invertebrates in the model. This trophic level is intended for organisms consuming algae and/or detritus, although the food sources are flexible and can include other types of invertebrates. Note that the invertebrates themselves are not simulated, only the concentration of the toxic chemical within them. These parameters do not flow by advection from one model segment to another, and only exist in terms of a concentration, not a mass. Following are the coefficients applying to invertebrates (Tsui & Wang 2004):
- the pollutant whose bioaccumulation in the invertebrate is simulated
- the uptake rate ku (L/g-d)
- the ingestion rate ki (g/g-d)
- the elimination rate ke (1/d)
- the assimilation efficiency AE (unitless)
The change of concentration of mercury in each invertebrate is calculated at each timestep as the sum of water uptake and food uptake minus clearance:
[invertebrate-Hg] and [food-Hg] are the respective concentrations of mercury in mg Hg / mg biomass wet weight. The initial mercury concentration in each invertebrate is established by using a steady-state solution:
Fish
The concentration of mercury in fish is an additional type of physical parameter in WARMF. There can be any number of parameters to represent different fish types. Like invertebrate toxic concentrations, fish toxic concentrations do not undergo advection and are only a concentration, not representing a mass of mercury. The abundance of the fish themselves is not simulated. Fish can be set to eat a variety of foods, including algae, zooplankton, and other fish. Fish concentrations are controlled by the following coefficients (Norstrom 1976):
- the pollutant whose bioaccumulation is simulated
- the food conversion efficiency for growth b (unitless)
- the efficiency of caloric uptake from food ef (unitless)
- the efficiency of oxygen uptake eox (unitless)
- the exponent of weight when calculating assimilation g (unitless)
- the exponent of weight when calculating elimination z (unitless)
- the initial weight W (g)
- the growth rate dW/dt (g/d or kcal/d, assuming caloric value of 1 kcal/g)
- the routine metabolic rate constant alr (kcal/d/gg)
As in invertebrates, the change in fish mercury concentration with time is the difference between food and water uptake and clearance:
Where Uw is uptake from the water, Uf is uptake from food, and C is clearance (all in mg Hg / mg biomass wet weight / d). Each term is calculated as follows:
Cpw is the concentration of the pollutant (MeHg) in water (mg/l), Cpw is the concentration of the pollutant (MeHg) in food (mg Hg/mg biomass wet weight), Cox is the concentration of dissolved oxygen in the water (mg/l), and qox is the caloric content of oxygen (3.42 kcal/g). q is a temperature correction for metabolism, estimated at 1.09 based on Figure 4 of Norstrom et. al. (1976). The same theta is used to seasonally prorate the average annual growth rate.
References
- Norstrom, R.J., A.E. McKinnon, A.S.W. deFreitas. A Bioenergetics-Based Model for Pollutant Accumulation by Fish. Simulation of PCB and Methylmercury Residue Levels in Ottawa River Yellow Perch (Perca flavescens). J. Fish. Res. Board Can. 33: 248-267
- Tsui, M.T.K., W.X.Wang. Uptake and Elimination Routes of Inorganic Mercury and Methylmercury in Daphnia magna. Environ. Sci. Technol. 2004 38: 808-816