The model was designed in order to parametrize the half saturation constant, which is needed to fully formulate Michaelis‐Menten equation
V = Vmax * C/(C+km)
in another model. V is the oxygen consumption rate, V max is the maximum oxygen consumption rate, C is the oxygen concentration and km is the half‐saturation constant.
The final result is achieved by iterative simulation with manual adjustments of focal value, based on the fit with the experimental data.
Model Description
The model is a modified version of Fish Respiration Model (Zieliński P. see for more details)
The model uses set-up of the experiment and data acquired in the study by Fry & Hart, 1948 (Figure 3.). The aim of the experiment was to explore the relation of temperature and oxygen tension to the maximum rate of oxygen uptake.
They used 20 fish (80 g in total) in a rotating chamber filled with 4 litters of water @ 15 oC. There was no water flow during the experiment. The oxygen content was measured until depletion.
The starting oxygen content was not consistent with the expected saturation for given temperature, thus the oxygen content was forced to be 7.13 cc during the simulation.
Data
Data comes from Fry & Hart, 1948.
Variables [units] - description
Oxygen content [cc/L] - oxygen content in the water in the tank. Compensated for temperature.
Temperature [C] - temperature of the water. Influence the oxygen content and the respiration rate.
Oxygen saturation [cc/L] - the amount of oxygen soluble in the water. Data from Fry & Hart.
Volume of a tank [L] - Volume of the rank
Oxygen concentration [cc/L] - oxygen concentration in the water inside the tank
Weight specific respiration rate per hour [cc/kg] - the amount of oxygen used by fish in oxygen concentration above threshold in one hour standardized for mass of 1 kg. Equation acquired by fitting power function in Excel.
Oxygen compensated respiration rate per hour [cc/kg] - corrected respiration rate with Michaelis‐Menten kinetics
Half-saturation constant (cc/L) - parameter to find
Fish mass [kg] - self explanatory
Respiration [cc] - the amount the oxygen used by the fish every hour
Results
After every simulation the data were saved as a table and inspected for the fit with the experimental data in RStudio. Visual fit was satisfactory.