I would suggest looking at abundance and diversity seperately. Coral cover will enhance biodiversity by its nieches for small, cryptic fish species and prey items for other species, abundance might be lower though. Live coral cover also greatly enhances habitat complexity, so analysing them separately might be fruitless?

Of course there will always be exceptions.

How do you measure your complexity?

Leon Green @ Thanks for the response. Recently I surveyed an Island at 2 different depths. The shallow part comprises rocky substratum with low live coral cover and high fish abundance. Whereas the deeper one comprises sandy substratum interspersed with small rocks and have high live coral cover and low fish abundance. I measure the complexity by calculating the mean substratum (rocks) cover and by counting the number of holes and crevices present on the substratum. Live coral cover enhancing the habitat complexity may be true with the branching form of corals. But how the massive forms and encrusting forms contribute to the habitat complexity?

You are welcome! Encrusting coral can contribute to habitat complexity through their symbiotic/competing organisms burrowing in them such as hermit crabs from the genus Paguritta and polychates (such as Spirobranchus), the holes these organisms construct later become homes for blennies, hawkfishes and gobies.

If you are looking at comparing encrusting coral to rock, you might however be right that the rock will hold a higher abundance of fish, possibly also biodiversity.

Best Regards,

L

My findings also same like yours Manikandan. In many cases that I found in Indonesia, some places have the inverse correlation between the live coral cover and fish abundance. But in the case of fish diversity, I think it should be calculate separately because in several cases in my observations, the fish diversity positively correlated with the coral diversity. It because some corals have their own association with specific reef fish. But generally, the rocky substrate will provide more abundant fish than in high coral coverage area.

Try Papers By Wilson et al

Here's a start

Wilson SK, Depczynski M, Fisher R, et al. (2010) Habitat Associations of Juvenile Fish at Ningaloo Reef, Western Australia: The Importance of Coral and Algae. PLoS ONE 5:e15185. doi: 10.1371/journal.pone.0015185

Wilson SK, Dolman AM, Cheal AJ, et al. (2009) Maintenance of fish diversity on disturbed coral reefs. Coral Reefs 28:3–14.

Wilson SK, Fisher R, Pratchett MS, et al. (2008) Exploitation and habitat degradation as agents of change within coral reef fish communities. Global Change Biology 14:2796–2809.

Wilson SK, Graham N a. J, Pratchett MS, et al. (2006) Multiple disturbances and the global degradation of coral reefs: are reef fishes at risk or resilient? Global Change Biology 12:2220–2234. doi: 10.1111/j.1365-2486.2006.01252.x

Wilson SK, Graham N a. j., Polunin N v. c. (2007) Appraisal of visual assessments of habitat complexity and benthic composition on coral reefs. Marine Biology 151:1069–1076. doi: 10.1007/s00227-006-0538-3

Essentially as long as habitat complexity remains fishes are somewhat resilient to loss of live coral cover as long as habitat (structure and complexity) remains intact.

I worked with modules covered by any kind of fouling, but anyway, take a look, perhaps it could be useful:  

Article The effect of artificial reef structural complexity and bent...

one more

Article Structural complexity of substrata and antifouling paint eff...

This may strongly depend on the fish and the coral species. Small fish can hide inbetween coral branches. Some small associated fish species (crypto-ichthyofauna) are host specific, like small gobies in  Acropora corals. If the reef architecture is less complex, there will be more space for large fish. Then, it depends on whether these fishes are just temporary or territorial.