According to our preview post, in this post we are going to approach the problem mathematically and adjust mathematically each factor of our Causal Loop Diagram.
Based on our preview analysis, the human behavior implies on changes in a global scale. This changes consists on the variation of the global temperature, such as the level of green gases on the atmosphere. According to this and taking into account the litterature we are going to stipulate the maximum temperature level that Turtles can survive in the environment.
Besides that, we will analyse the human behavior according to climate changes and its capacity to mitigate this problem. The more anthropological actions, more the Turtle population will decrease, signaling that the some action should be taken in order to minimize the problem.
Modelling:
Temperature: The temperature tends to grow according to human activity, so the Temperature variables is set in our project as:
T = 20 + kt
Gas Solubility: The gas solubility on water is inversely proportional to the temperature. Assuming that the source of food for turtles depends on the fotosintesis of the ecossistem and it depends on the amount of CO2 on the water, the less CO2, the less food and consequently less turtles.
According to our analysis, we have the following equation for gas solubility:
GS = 0.032275 + 3.2841325*e^(-t/28.3120)
Food Availability: The marine ecossistem depends on the fotosintesis of phytoplankton to make O2 available for fish breathing and for energy flux on the system. In our mathematical analysis we are going to addopt the food availability as:
FA = GS*0.6357 - 0.1142
Tortoise: The main study of this document is to analyse the behavior of the turtles population according to climate changes. The derivative of the turtle population must include the variables that affects its population.
X` = (FA*2 - 0.5*Y )*X
Fishing/Anthropological Factors: The act of fishing turtles depends on the amount of turtles on the environment and the amount of fishermans. As more turtles, more they will be fished and its devivative tends to decay as the number of fishing practice grows. The human behavior leads to the rising temperature of the planet. According to the human ecological consciousness, this temperature can grow fast or slow. So, this must be counted in our model. The function that describes this factor is:
Y` = ( -1 + 0.5*X )*Y
On the next post we are going to show the results of the analysis generated by Software.
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