Dependencies

As figure 3.3 shows, there are now two parameters $POP$ and $ChR$ arranged along different time points. It is known that the change of the parameter $POP$ between two successive time points (t, t+1) is depending from the values of the parameter $ChR$. Therefore one can hypothesize a dependency between these two parameters as follows (cf. figure 3.4):

Figure 3.3: Looking for dependencies between parameters

Figure 3.4: Establish a simple dependency between parameters

One connects the parameter $POP$ and the parameter $ChR$ with their values at time $t$ with a new box. The attached label (name, ID) $f1$ is arbitrary. The box shall represent the assumed connection. From the box leads another arrow again into the parameter $POP$, but now this is the parameter $POP$ with the value at time point $t+1$. In mathematics one can translate this drawing of a simple dependency into the expression of a mapping (function) as follows:

$$\textbf{f1} : POP \times ChR \longmapsto POP$$ (3.2)