This model is concerned with simulating a tank containing Talapia. The main focus will be dynamic modelling of the oxygen content of the aquarium. A constant temperature throughout the tank is assumed.
The setup:
In this simulation we have one aquarium which receives water at a set rate and loses water via overflow at the same rate. At the starting conditions the water is assumed to be in equilibrium with the atmosphere with concern to oxygen. This aquarium can be occupied by any number of fish. All fish start at a average weight of 3.8g.
Fish respiration:
While these fish are in the tank they respire at a certain rate which is dependent on the temperature, the weight of the fish and the current concentration of oxygen. This rate will primarily be limited by physiological factors and by oxygen concentration. The rate of respiration when in oxygen saturated water is considered the maximum rate of respiration. At a certain level of oxygen saturation the fish will begin to down regulate their activity to compensate for the low oxygen content. This saturation level will be denoted as the oxygen threshold. A final threshold is the oxygen level of no excess activity, which is also temperature dependent and below which the fish will do nothing but what is needed the just survive. This respiration rate is set to be 0.1 times their maximum respiration. Both the respiration, the oxygen level of no excess activity and the oxygen threshold are calculated from data of Fry and Hart 1948 and are temperature dependent.
Km:
Since respiration can be discribed through Michaelis-Menten kinetics, a Km (concentration at which respiration is half the maximum rate) has to be estimated. This is done by finding the relationship between temperature and oxygen threshold and dividing this value by 2 and multiplying by the oxygen solubility.