During the Hellenistic Age, Archimedes made advancements in "mathematics"--specifically in the realm of geometry, since he developed innovative ways to calculate volume, area, etc.
the term seizure is by force and arrest is more of a stop
If possible I'd say all of them except the fourth one down (parts of ecosystems are independant) but if not I'd say the most valid one is the second one down (healthy ecosystems help animals)