The "plants" of the Great Barrier Reef
There aren't very many actual plants there, but there are many plant like organisms that are widely accepted as autothrophs.
Seagrass
Seagrass is mostly found in the shallower parts of the sea. They are the only type of true plant that can successfully colonize within the subtidal sea. These plants can form meadows in the right conditions. These meadows become home and play key roles in the lives of many animals. Some of the largest marine animals use seea grass as a food source.
Mangroves *KEYSTONE*
Mangroves grow in groups of thick, complex forest like groups and tend to line the shores and shallow areas of the sea. It is one of the few terretrial plants that can be derictly immersed in sea water. The can do this because of their salt filtering roots and salt excreting leaves. Their complex "prop root" system is a nursery habitat for many reef fishes as well as a substrate for man algae, sponges an other invertabrate animals. They also help build shorelines by creating a place for sediments to settle and later form land.
Green algae
Green algae are most common in the shallow reef areas. These ar mostly found on rocky like reef surfaces, but can be found on sand. The most abundant types of green algae are "sea lettuce" and "sea grapes".
Red Algae
Red Algae is a close relative of the Green Algae. Red Algae can be found in the shallowest parts of the coral reefs to the deepest parts exceeding 150 ft. At these depths they use their photosynthetic pigments that can still extract the blue part of sunlight since at that depth that is all that is left. There are many types of red algae but the most common by far is the "crustose coralline algae" or CCA. Much like coral they produce calcium carbonate and are a huge contributor towards coral reef formation.
Brown "algae"
Brown algae are as different from red and green algae as they are from animals. They are not not uncommon in the coral reef, but not nearly as common or have as much variety as green or red algea. They are most abundant at around 30-70 ft. deep. They can sometimes become very common depending on the season.