As per what Gonzo says above - you should do some careful initial exploring by cutting out a section (eg a simple rectangular shape, with boundaries on the 'long' sides in way of the joints in the planks) of deck in way of one of the damaged areas.
Try to just cut away the timber layer on top, without damaging (too much) the fibreglass underneath.
You should hopefully then be able to determine what type of wood was used.
And as the deck was painted, if it is teak then you wouldn't necessarily have to replace the damaged section with new teak - you could use another type of good quality hardwood. of the same section dimensions as the existing strips.
I wouldn't be surprised though if you find more rot damages, hitherto unseen, when you start exploring and digging out the rotten wood.
The odds are very good that the core in the fibreglass deck underneath the timber is also in poor condition in many areas, if not all over.