So I am going to share the principles of feeding. When it comes to aquaculture, Swingle was among the first to propose these principles but they are actually more deeply rooted in other forms of agriculture. So below you could substite cattle for fish or pigs for fish. These principles apply to any animal you may feed.
Paraphrased from Swingle:
Given no other source of food, feed must first supply the maintenance for the fish's metabolic needs. After the metabolic requirement is met additional feed will cause gain in proportion to the weight of feed. The maintenance requirement is the specific maintenance rate SMR(wgt of feed/wgt of fish). The feed rate to maintain an arbitrary total weight of fish is expressed by:
Wgt Feed for Maintenance = SMR * Wgt of fish
If the fish's metabolic requirement is met, the fish will convert some portion of feed into gain. The gain will be some proportion of the weight of feed fed but only to the extent the feeding rate exceeds the maintenance rate. The FCR describes how feed (that exceeds maintenance) converts into the wet weight of fish. To apply FCR we need to know the feed in excess of the maintenance requirement. This excess quantity of feed can be calculated by subtracting the SMR from the Specific Feed Rate, SFR (wgt feed fed/weight fish). If we know the SMR and FCR, we can calculate the Specific Growth Rate SGR (wgt gained/weight fish/day). This is expressed below:
SGR (gain/wgt fish) = (SFR - SMR)/FCR
If you multiply both sides by the weight of fish on the left side is "Weight gained" and the right side is the "weight fed above maintenance" divided by FCR.
Wgt Gain = (Feed above Maintenance)/FCR
But we don't know the two variables FCR and SMR. Even so, these are easily determined by feeding at different rates. So lets say you feed at 3% SFR (3% the weight of the fish daily) and at 6% SFR. You may plot your resultant SGR vs the SFR and the plot will look like this:
The SFR where the extrapolated line intersects zero SGR is the Specific Maintenance Rate (SMR) and represent the specific feeding rate you must exceed to get gain. The slope of the line _is_ (1/FCR). The FCR derived from this method is valid for both feed rates which is the beauty of this kind of solution.
One could calculate "an" FCR by dividing the amount fed by the weight gained but it isn't a very reliable metric. The problem is that you can't predict conversion with it unless you precisely feed at the same Specific Feed Rate (SFR) that you did in obtaining the metric. The FCR is invalid for all other feed rates. Furthermore, feeding at a invariant SFR is often impractical. For example ... fingerling CC will consume 10% of their weight a day but a second year 1.25 lb CC will only consume around 1.25% of its weight (IIRC). To feed a SFR > .0125 would waste feed. The point is the "Gross FCR" is like using a rock to drive a nail while understanding the true FCR and the SMR is like a fine tuned nail gun. One is the stone age ... the other modern aquaculture. Below is a graph depicting how variable "Gross FCR" is at different feeding rates where FCR is limited by the quantity of feed a fish can eat daily.
So this gives you a look under the hood of how people who grow fish understand FCR. From this you should come away with this awareness.
1. A "Gross FCR" is completely without context. One needs to understand the rate of feeding particularly. I will mention that the intrinsic FCR is better than any true measure of Gross FCR. So how much does your fish gain on feed? It depends in part on how much it needs the feed. In other words is the pond otherwise supporting all of its maintenance? If not, then part of the feed maintains the fish while the rest of it gains the fish are according to intrinsic FCR.
2. I have neglected the secondary effect where waste nutrient recycle in the food chain providing more gain/maintenance to the fish. So the example of above would apply in an indoor facility where wastes are clean from recirculated water or an outdoor facility where wastes are carried away by water exchange. Even so, in ponds ... nutrients continue to do their thing after the fish expel the waste. The FCR in ponds will (under normal circumstances) be lower where the exceptions would arise from water quality issues or impairment of first consumer populations..
3. FCRs are specific to Feed formulation and Fish species. The Gross FCR of one species is not same as that of another ... same applies for the intrinsic metrics of Specific Maintenance Rate and FCR. There isn't just a one number fits all.
4. We haven't considered how this knowledge applies in year after year feeding regimes to same fish. This is something I am interested in telling you more about. Only to endow you with additional knowledge and tools that you can use to make prudent decisions about your water.
I have attached a spreadsheet that you are welcome to use and ask questions about. The green cells are where you can enter data and the brown ones are output. On the first tab one can enter the SGR and SFR. The SS uses a regression to solve for the FCR and SMR. This first page is how an aquaculturist would solve for the FCR and SMR after recording SGR at two different SFRs. After doing this one can fine tune a feeding plan that produces predictable results in single season growouts and calculate inventory needs.
The second tab allows you to enter FCR, SMR, and SFR. It yields SGR. You can tell with the current data, the second page matches the first page (including graphs) . You could use this tab if you have access to valid FCR and SMR metrics for a Feed/Fish species combination. It could serve as means of inferring FCR and SMR under certain circumstances if you have a Gross FCR data point. Anyways, feel free to check scenarios and ask questions. (Note: the SS is updated in case you may have downloaded an earlier version. It now computes SGR on the second tab using the green SFR cells instead of the original fixed values of .03 & .06 SFR).
Thanks for the obvious hard work you put into this! I particularly liked your discussion about how feed needs change with fish size, lower as a percent of body mass as size increases even though higher (if I understand correctly) in absolute terms.