The model describes the setting of the experiment and uses data acquired in the study by Fry & Hart, 1948. The aim of the study was to explore the relationship between the ambient temperature and a standard and a maximum level of metabolism of a golden fish.
To a tank with a constant water flow, they put golden fish and measured the oxygen content in the water in order to determine the metabolic rate. Oxygen saturation is temperature dependant, thus the amount of oxygen in tank as well as in the supplied water varies in different settings.
In oxygen optimal conditions the weight specific respiration rate is constant, but varies with the temperature. In the range of interest it well follows power function (see below) dependent on temperature. Physiological threshold under which the oxygen uptake decrease in a linear fashion is considered constant - 1.8 cc/L - to simplify the model, however in reality it is dependent on temperature as well. Finally, the amount of oxygen used by the fish is determined as a product of fish mass and oxygen compensated respiration rate.
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.
Flow rate per hour [L] - amount of water going through the tank every hour
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.
Inflow [cc] -the amount of oxygen entering the tank every hour.
Outflow[cc] - the amount of oxygen leaving the tank every hour (dependent on Oxygen concentration)
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 when oxygen concentration is less than optimal (below the threshold)
Threshold [cc/L]- oxygen concentration above which it doesn't affect the respiration rate. Based on data from Fry & Hart and derived using Unisense Seawater and Gas tables (Ramsing & Gundersen)
Fish mass [kg] - self explenatory
Respiration [cc] - the amount the oxygen used by the fish every hour
Example
After running the model @ 5 oC and 60 time steps, we observe decreasing concentration of oxygen from 8.5 cc until it reaches stable point at ca. 8.35 cc. As the concentration is above the physiological threshold, oxygen compensated respiration rate stays constant.
After running the model @ 30 oC and 60 time steps, we observe decreasing concentration of oxygen from 4.93 to 1.69 cc. However around 12th time step the oxygen concentration reaches the threshold, therefore the oxygen compensated respiration rate starts to decrease as well, until the system reaches equilibrium again.