Concept:
Evolutionary biology describes different mechanisms through which species evolve and diversify over time.
Step 1: Evaluating Statement I.
Anagenesis refers to evolutionary change occurring within a single lineage without branching.
One species gradually transforms into another over time.
Therefore Statement I is true.
Step 2: Evaluating Statement II.
Allopatric speciation occurs when populations become geographically separated by mountains, rivers, oceans, or other barriers.
This isolation eventually leads to formation of new species.
Therefore Statement II is also true.
Step 3: Final conclusion.
Since both statements are scientifically correct, the correct option is:
\[
\boxed{\text{Both Statement I and Statement II are true}}
\]