i am confused, are you proving my point, or some other point? the same reasons why the P level increases as you go deeper is the same reason why in a substrate the P level also increases. even water has layers and equilibrium can only happen so fast across distances.
again, there is no difference between how a lagoon and the deep see behave compared to the settling of P, or any organic material. the differences come with access to tidal flushing or major disturbing events. these events affect a substrate deeper, than even our "deepest" substrates.
No, the reason P decreases as you go deeper is because there's nothing photosynthesizing to take it up. The closer you get to the surface, the more light, the more dissolved P gets immediately consumed by living organisms. A coral reef has low dissolved nutrients because it's the most efficient ecosystem on earth, not because the compounds aren't present. It's not about diffusion gradients. By mass, there's mountains of P and N on a coral reef, you just don't find it in the water column. That's the whole point of a deep sand bed - recycle the inputs as much as is conceivably possible while providing as many opportunities for the export of any ions or molecules that are not otherwise being used as possible. Nitrogen eventually gets off-gassed, and phosphate gets recycled until it ends up getting skimmed out in organic matter, bound to a phosphate absorbing resin, incorporated in to the tissue of corals, or locked up forever in the crystal matrix of aragonite. In some cases that might mean a long term net accumulation of P in the system, in some cases it might not, and even if it does, that does not necessarily mean that from a coral keeping point of view you will ever have a problem so long as the accumulated P is in desirable tank biomass and not in the water column or problem algae. It depends on the system and how it's set up. It may be the case that P accumulates until it reaches equilibrium with the exports, it may be the case that it doesn't. It's system dependent, which is why you can't make universal statements about deep sand beds being an eternal sink of P.
And yes, there is a drastic difference between a deep sand bed, the sand at the bottom of a lagoon, and muck at the bottom of a deep ocean trench, and further there's even differences within those specific substrates depending on the time scale you are considering. The graph you keep referencing is a hyper simplified chart describing a global process that is measured in terms of eons. Scale is critical when talking about earth system processes. A couple quotes from the geography literature because they say it way better than me:
"œas the dimensions of time and space change, cause-effect relationships may be obscured or even reversed, and the system itself may be described differently" (Schumm and Lichty, 1965 from Time, space, and causality in geomorphology. in the American Journal of Science)
and
"œmany earth-surface systems are inherently dynamically unstable and deterministically chaotic. This indicates that fundamental system-level behaviors vary with scale or resolution, dictating different approaches." (Phillip, 1999 from Methodology, scale, and the field of dreams in Annals of the Association of American Geographers)
The model you are using does not describe things that happen on a micro scale, which is what our tanks are relative to the system you're comparing them to. The processes that result in the deep sea bed being a net sink of P as measured in geologic time are not good analogies for an aquarium. At the micro scale, there is far more exchange of phosphate in a high energy, biologically active system than the diagram you reference can account for. There are no zones in aquariums that replicate kilometres of cold, pitch black water with little to no life of any kind that decomposing material can sink through. The sand beds people keep in their tanks have an order of magnitude more biological activity in them than an equivalent volume of sediment in a frigid deep ocean sea bed that relies 100% on falling material for energy. The chemistry in our aquariums is significantly different from the ocean, in which many of the ions are never in equilibrium driving permanent precipitation reactions. calcium and carbonate are not in equilibrium in the ocean, and in the deep ocean the equilibrium states of phosphate and calcium are far more favourable for the spontaneous precipitation of calcium phosphate minerals, which in geologic time eventually get sequestered because they get buried by material from above. It's true that on the sea bed there might be some exchange and recycling of P when you look at it on the micro scale, but on a macro scale at that depth the net effect, across millions of years, is a sink. That is nothing like a deep sand bed, where our 'net' effects are measured in terms of months and years and are subject to totally different physical, biotic, and chemical conditions.
you would be correct if we only had to worry about chemistry in our systems. bacteria are the biggest consumer of P in our systems. it is they that are pulling the P off of the calcium carbonate and not the pH or the equilibrium. it is the bacteria that are driving the P cycle and it is them that we rely on for providing P for other organisms in our system. if P were not doing this, then life on Earth would not exist. the bacteria are driving the equilibrium reaction towards the substrate and not away.
think about the bacteria. this is why the bacteria are driving the equilibrium reaction towards the substrate and not into the water column. the bacteria are creating new binding sites on the aragonite. throwing the equilibrium action towards the aragonite.
You are confusing bacterial metabolism with a chemical reaction. The bacteria do not 'create new binding sites'. If they are scavenging phosphate that has been bound to aragonite, all they're doing is opening up an existing binding site, not creating a new one. Once that Phosphate is inside the tissue of the bacteria it is a) now bound up in organic molecules that can eventually be skimmed out or consumed by corals (which you want) and b) no longer an inorganic nutrient that can diffuse back in to the water column, which you also want. Further, to say you know for sure that bacteria scavenging phosphate that is bound to aragonite crystals is a significant component of the micro-scale phosphate cycle in aquarium really should be backed up with some sort of a reference. There's plenty of forms of organic and inorganic phosphate, and they're in constant transition from one state to another with differing levels of bioavailability to different kinds of organisms, both on land and in the sea, how do you know for certain that that specific bacterial pathway for that form of orthophosphate is possible, significant, or favoured?
if it gets taken up by something else, then that something else will poo it back out. isn't that the whole point of keeping the ecosystem? to always feed something else? a growing population of any organism is proof of a growing supply of food. the entire ecosystem is powered by the ability of bacteria to access P from inorganic sources. a bed "working" like is should is just binding more P. that is how beds work. it is only those in the aquarium hobby that think otherwise.
Yes exactly. It gets pooped out. That's why we have skimmers. You can have lots of life in a tank, fed by a complex food web that keeps inorganic nutrients locked up in the tissues of living things for the entire time that it's in your system and still have something that resembles a 'low nutrient' system, because the nutrients aren't in the water. That's the point. Having bacteria take up inorganic phosphate means that at some point, it will either be eaten by things you are trying to grow, or get permanently exported by a skimmer.
stop thinking chemically, think bacterial.

our systems are bacterial driven. they need to be. we use the bacteria for everything. we need to understand what they are doing in order to get a better understanding of what is going on in our systems. looking at the chemistry is only going to give us a partial picture of what is going on in our systems. the nitrate cycle is not chemistry, but bacterial. ammonia is not just going to be converted to nitrate because. the bacteria do it. what do the bacteria need to do this?
G~
On this last point I completely agree with you, where I disagree is that that a priori means that a DSB is by default going to result in a perpetual accumulation of problematic P. There are too many biotic and chemical ways for the inorganic P that winds up in a sand bed to either become liberated as soluble inorganic P and removed by phosphate binding media, get permanently sequestered in the tank itself (as in the case of growing aragonite crystals), or consumed and turned in to organic P and either eventually get skimmed out, or removed through trimming of macro algae. I am not saying that it can't become a problem, and the possibility of things going wrong that I can't see and have no control over is one of the reasons why I've never run a DSB, but what I am saying is that a blanket statement about the nature of DSBs made based on an analogy to a process that operates on a completely different spatial and temporal scale is not appropriate, and does not assist in understanding what's going on in your tank.
Having no sand bed and vacuuming up detritus also works, it just works on a different principle. You'll note that November's TOTM on RC, which is spectacular, has a DSB and has been running it for 2 or 3 years. Lots of ways to skin a cat.