While we can only rtest for phospahte aka orthophosphate aka disolved inorganic phosphate (DIP) there is also particulate organic phosphate (POP) and disolved orgainc phosphate (DIP). while corals can genreally use all three their prefference is DIP.
The same is true for nitrogen with particualate, organic anc inorganic forms which are being used by corals and algae. Additioanlly corals have diazotrophs or nitrogen fixing microbes in their holobiont.
If corals can't get enough phosphorus it creates a deficiency which seriously affects their photobiology which reduces the amount of food they're getting from thier zooxanthellae and affects their immune systems. One consequence is they are not able to compete with other algae as well which typically results in nuisance algae thriving even under low nutrient conditions. I would advise feeding your fish more.
I would recommend reading Forest Rohwer's "Coral Reefs in the Microbial Seas".
And here's some more stuff :
"When I see the colors of some of these low nutrient tanks, I can't help but be reminded of bleached coral reefs. It should therefore not come as a surprise that feeding corals in such systems becomes a very important component in these systems. Though reefs are often catagorized as nutrient "deserts" the influx of nutrients in the form of particulates and plankton is quite high when the total volume of water passing over a reef is taken into consideration.
Our crystal-clear aquaria do not come close to the nutrient loads that swirl around natural reefs. And so when we create low-nutrient water conditions, we still have to deal with the rest of a much more complex puzzle. Much like those who run their aquarium water temperature close to the thermal maximums of corals walk a narrow tight rope, I can't help but think that low-nutrient aquariums may be headed down a similar path." Charles Delbeck, Coral Nov/Dec 2010, pg 127
"Imported nutrients are usually transported to reefs from rivers; but if there are no rivers, as with reefs remote from land masses, nutrients can only come from surface ocean circulation. Often this supply is poor, and thus the vast ocean expanses have been refered to as "nutrient deserts". The Indo-Pacific has many huge atolls in these supposed deserts which testify to the resilience of reefs, but the corals themselves may lack the lush appearance of those of more fertile waters. Many reefs have another major supply of inorganic nutrients as, under certain conditions, surface currents moving against a reef face may cause deep ocean water to be drawn to the surface. This "upwelled" water is often rich in phosphorus (.2 mg/l) and other essential chemicals." J. E. N. Veron "Corals of Austrailia and the Indo-Pacific" pg 30
Ammonium Uptake by Symbiotic and Aposymbiotic Reef Corals
http://www.ingentaconnect.com/content/umrsmas/bullmar/1979/00000029/00000004/art00011
https://www.cambridge.org/core/jour...reef-corals/AFB1CF4CB68823BD13AD254623FD3C7C#
An Experimental Mesocosm for Longterm Studies of Reef Corals
Phosphate Deficiency:
Nutrient enrichment can increase the susceptibility of reef corals to bleaching:
https://www.nature.com/articles/nclimate1661
Ultrastructural Biomarkers in Symbiotic Algae Reflect the Availability of Dissolved Inorganic Nutrients and Particulate Food to the Reef Coral Holobiont:
https://www.frontiersin.org/articles/10.3389/fmars.2015.00103/full
Phosphate deficiency promotes coral bleaching and is reflected by the ultrastructure of symbiotic dinoflagellates
https://www.sciencedirect.com/science/article/pii/S0025326X17301601?via=ihub
Effects of phosphate on growth and skeletal density in the scleractinian coral Acropora muricata: A controlled experimental approach
https://www.sciencedirect.com/science/article/pii/S0022098111004588
High phosphate uptake requirements of the scleractinian coral Stylophora pistillata
http://jeb.biologists.org/content/214/16/2749.full
Phosphorus metabolism of reef organisms with algal symbionts
https://esajournals.onlinelibrary.w...98e60zfBEvx5IcIVGhmlpUYmzIJuqUNVm0sG8_0vth6lq
https://therichross.com/skeptical-reefkeeping-ix-test-kits-chasing-numbers-and-phosphate/
Coral and macroalgal exudates vary in neutral sugar composition and differentially enrich reef bacterioplankton lineages.
https://www.ncbi.nlm.nih.gov/pubmed/23303369
Sugar enrichment provides evidence for a role of nitrogen fixation in coral bleaching
https://onlinelibrary.wiley.com/doi/full/10.1111/gcb.13695