Epiphytic ferns grow on trees, but not parasitic --- they do not feed the tree, only use it as a growing support. The ones you are likely to spot are the large Bird’s Nest Fern (Asplenium nidus).
Tree-ferns (cyathea) can be found within the Reserve and can be recognized from their large fronds borne on a distinct trunk which can be about 3 m tall.
Resam (dicranopteris linearis and dicranopteris curranii) proliferates in sunny clearings and along the open edge of the Reserve. These ferns grow in poor clay soils and, with their ever-growing fronds which keep on branching for long periods, may totally cover any open area with a resam “carpet”, through which no other plants can grow. Together with Resam, you can find the sun-loving Climbing Ferns (Lygodium), which also have perpetually growing fronds and wiry “feelers” which twine around supports and give off leaflets.