Let \(T\) be a time scale and \(X\) a metric space. A mapping \(\varphi:\{(t,\tau)\in T^2:\,\tau\leq t\}\times X\to X\) is said to be a \(2\)-parameter semiflow on \(X\) (or evolutionary process), if the mappings \(\varphi(t,\tau,\cdot)=\varphi(t,\tau) : X \to X\), \(\tau\leq t\), satisfy the following properties: (i) \(\varphi(\tau,\tau)x=x\) for all \(\tau\in T\), \(x\in X\), (ii) \(\varphi(t,s)\varphi(s,\tau)=\varphi(t,\tau)\) for all \(\tau,s,t\in T\), \(\tau\leq s\leq t\), (iii) \(\varphi(\,\cdot,\cdot)x:\{(t,\tau)\in T^2:\,\tau\leq t\} \to X\) is continuous for all \(x\in X\). The authors consider such systems that are also order preserving in normal cones of strongly ordered Banach spaces. Then, it appears that there are only three possible asymptotic behaviors and they are analyzed in the paper. This, in particular, generalizes an old theorem of Müller and is applied to a specific model from population dynamics.