Pond Boss
Posted By: jpsdad Feeding and Conversion - 05/18/22 12:41 AM
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:

[Linked Image]

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.

[Linked Image]

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).

Attached File
SGRvsSFR.jpg  (471 downloads)
Attached File
FCRvsSFR.jpg  (478 downloads)
Attached File
Feed Conversion Solver.xlsx  (30 downloads)
Posted By: anthropic Re: Feeding and Conversion - 05/18/22 02:42 AM
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.
Posted By: jpsdad Re: Feeding and Conversion - 05/18/22 02:55 AM
Yes Frank, I guess whatever spurs consumption is in overdrive for YOY but as fish get older their rates of consumption decrease. Now they eat as much as they ever did because they are bigger but the specific rates do fall until adulthood is reached. For every variable that is preceded by the word specific this means in relation to the weight of a fish at the start of a daily increment. FCR, SGR, SFR, SMR are all dimensionless entities (or ratios of the same units). Whether you work in metric or English units, the values of these variables are always the same. They are universal. To someone like me, reducing natural relationships to such intrinsic universal meaning is something of beauty. I appreciate that you liked it.

Frank, also I noticed you downloaded it. Do it again, I need to modify a formula on the second tab so changes of SFR would compute in the SGR calculation.
Posted By: anthropic Re: Feeding and Conversion - 05/19/22 04:09 AM
Posted By: jpsdad Re: Feeding and Conversion - 05/21/22 12:32 PM
So along the lines of maintenance and conversion I thought I would add some reference in order to provide context, pique your curiosity, and hopefully encourage your desire to study and learn. But mostly, I would like to encourage your curiosity and encourage you ask yourself questions that spur further discovery.

We may conclude that the principles of feeding tell us that maintenance inhibits the conversion of feed and so we come away with the understanding that there exists a goldilocks Specific Feeding Rate (SFR) that optimizes the Gross FCR for a fish at a given stage of development. Just a casual glance at the Gross FCR vs SFR Chart tells us that the intrinsic FCR is reached at an infinite SFR. But common sense tells us that our typical fish can't eat its own weight every day let alone an infinite weight of feed. So we know there are physical/natural limits. Further careful thought also tells us that retention in the gut could also be important to conversion and if too much were consumed on a daily basis that it is possible that the efficiency of assimilation could be compromised. This SRAC publication tells us that :

Under most circumstances, fish need to be fed less than they will eat. Overfeeding will cause the fish to use the feed less efficiently and will not increase growth rates signficantly

It includes an SFR table that out lines feeding rates at various stages of growth (fish size as expressed in number per pound). A table like this is specific to "a feed" and "a species" and can generally be obtained from the feed manufacture for the formulations designed for the farmed fish. Big producers sometimes develop their own tables and design and formulate their own feeds. To do so economically requires economy of scale.

[Linked Image]

The same publication mentions the rainbow trout Specific Maintenance Rate at temps below 38 F:

The minimum temperature for growth in trout is about 38 F. At this temperature and below, appetites are suppressed, digestive systems operate very slowly, and trout require only a maintenance diet (0.5 to 1.8 percent of body weight per day, depending upon fish size). Feeding more than this wastes feed.

Now I was very surprised to see a maintenance rate (SMR) as high as 1.8 percent of body weight but glancing at the left most SFR column in the table it made more sense. While this column "anticipates growth" we might reasonably infer that smaller fish could have greater metabolic requirements that require a higher maintenance rate.

Attached File
SFR Chart.jpg  (346 downloads)
Posted By: anthropic Re: Feeding and Conversion - 05/22/22 04:13 AM
Interesting stuff. My background is economics, so naturally thoughts go to how to utilize feed most efficiently. Particularly now with high inflation, probable recession ahead, and shrunken 401ks. Didn't think I'd see stagflation again after the Carter era, but here it is.

Along those lines, I wonder if a given amount of feed is best converted into fish flesh in several smaller amounts per day or all at once. And does it matter what time of day, or the interval between multiple feedings? As feed gets more & more expensive, we need the most bang for our bucks.
Posted By: jpsdad Re: Feeding and Conversion - 05/22/22 01:29 PM
I like where your curiosity is taking you. To be sure, the main reason to understand optimum feeding is to increase the bottom line. Anyways, I'll share with you some of my thoughts.

With regard to trout, according to the reference noted in my previous post:

When fed nearly to satiation, trout will consume roughly 1 to 2 percent of their body weight in dry feed at each feeding.

I would think that most any fish has a similar Specific Satiation Rate (SSR). I say it that way because this is a legitimate scientific metric of consumption even though I have never given this metric enough thought. So one of the great things about interaction with others is the sharing of questions and the sharing of ideas. Regrouping and rereading to spot information that earlier didn't pop out. So in this spirit let's compare this range of SSRs (1 to 2 %) to the optimum SFRs in the table recommended by an arbitrary feed manufacture of its arbitrary feed. For a fish that will satiate at 2 %. For SFRs > 2, this would require more than 1 feeding. If optimum efficiency of any given feeding is below the SSR then even SFRs less than 2 could benefit by splitting the ration into two feedings ... in terms of efficiency.

I don't know if you noticed, but the table displays the entire life cycle beginning with free swimming sac fry. I know this because I am familiar with counts per pound but the confirmation is that the feed rate increases in the second row. You see in the first row, the fry is still assimilating its yolk. Without the yolk you will notice feeding rates decline thereafter. Indeed, in hatcheries, fry feeding is separated into periodic feeding spreading out the ration to consumable chunks that are within the limits of satiation.

Now let's consider your pond. We have natural foods to deal with that are not in a hatchery building or its feeding raceways. The situation is clear as mud. If we could depend that all of the maintenance being provided by pond organisms, then any consumption which did not take fish into inefficient consumption would be assimilated optimally. This a rather difficult question, IMWOT, where contributions of feed have the potential to achieve the SFR of maximum efficiency and to exceed the SFR of maximum efficiency. But back to your question. If one is feeding 1 lb per day ... the efficiency could be improved by dividing into 4 1/4 lb feedings. Here I am assuming that dominant fish are not getting the less efficient satiation ration at the expense of consumption by other fish.

So its complicated in a pond with natural foods. It's not just that one has to balance the predators and prey ... one must also balance the feed to natural consumption in order to use feed at optimum efficiency. Yet even if some nutrients are wasted through efficiency, there remains opportunity for the nutrients to reassert in the food chain which provides food as demanded/supplied (in the spirit of economy) by predators.
Posted By: jpsdad Re: Feeding and Conversion - 05/23/22 11:07 AM
Along the lines of economics ... although FCRs increase as fish get bigger the value of the fish can more than compensate the extra feed. This web article describes how producers can increase profits by growing larger fish. The article has some interesting information on how they use the maintenance/conversion relationships to their best advantage.

Here they mention how the FCR is best below satiation:

While most of the previous studies were completed by feeding fish to satiation, Cleveland and her team had observed that optimum feeding satiation doesn’t occur at 100 percent of satiation but at 75 percent. Specific growth rate, however, is achieved at 100 percent of satiation.

So SGR is the weight gained daily and they found it is best not to maximize growth because it is not as efficient. (The Gross FCR is not as good). So if you will imagine the Gross FCR versus SFR chart .... the Gross FCR curve would stop approaching the intrinsic FCR limit at the SFR corresponding to 75% satiation. Beyond that feeding rate, the Gross FCR would worsen (increase) indicating the efficiency of assimilation is declining at the increased feed rate. So maximizing SGR doesn't lead to most efficient use of feed.

Another takeaway from the article. Maintenance matters. When delivery must occur at a specific time the best path on feeding may not be minimizing daily FCR in the early going:

“For example, if a fish needs to get at 3 kg at a specific time, it is more beneficial to feed a fish to a small level of moderate feed restriction during this time because this will result in improved feeding procedure,” she said. This is a better approach compared to feeding the fish through satiation, reaching market weight too early and then feeding maintenance ration through the remainder of the period.

Four percent less feed was consumed in this method, saving the producer $50,000 in feed cost.

To illustrate ... look at the Individual Weight versus Time(days) chart below. The area below each curve is the Maintenance Weight Days of an individual fish growing to 3kg from .5 kg in 180 days. If this metric is multiplied by the SMR it will quantify the weight of feed required to maintain the fish throughout the grow out. The Gross FCR is modestly advantages at 135 days but will be less advantageous by the end of the grow out due to the costs of maintenance. This does not include cost savings of water treatment and oxygenation costs which are part of maintenance and would also contribute to the bottom line.

[Linked Image]

Attached File
IND WGT VS TIME.jpg  (210 downloads)
Posted By: DrLuke Re: Feeding and Conversion - 05/23/22 05:55 PM
So after reading through the above, I'm thinking that my tendency to feed my fish markedly less than they would seem to be able to consume could potentially be benefiting their growth in ways I didn't realize. Interesting.
Posted By: ewest Re: Feeding and Conversion - 05/23/22 07:57 PM
The article is an aquaculture application in an RAS and is different than what one would expect in a supplemental feeding program in a pond. In addition, it deals with a cool water species (RT and Steelhead) which changes feeding a bit as they are closer to HSB in feeing and aquaculture applications. Max growth and max feeding rate at temperature are often different. If interested, you might look into compensatory feeding as a theory. The article is a very good (straight-forward explanation) as it relates to basic bioenergetics in a recirculating aquaculture system. Look for upcoming articles on LMB and BG growth, metabolism and temperature in PB mag.
Posted By: jpsdad Re: Feeding and Conversion - 05/24/22 09:07 AM
So after reading through the above, I'm thinking that my tendency to feed my fish markedly less than they would seem to be able to consume could potentially be benefiting their growth in ways I didn't realize. Interesting.

Imagine we were partners in a feeding operation. We would measure satiation according to a defined method. It would involve feeding the fish more feed than they would consume in a given span of time. We would collect the uneaten feed and count the pellets and by knowing the count per pound we could then estimate the weight of feed consumed. This weight divided by they weight of the fish before eating is the specific satiation rate. To the one interviewed, this metric means 100% satiation.

Eric, rightly mentions that there are differences between a fish feeding operation and one's pond where the feed often represents a supplement that may or may not grow fish on any particular day. Fish benefit from feed whether they are being maintained (prevented from losing weight), growing at most optimum conversion, or growing maximally. So my sense is that pond fish do experience all of these possibilities throughout the year. Natural foods come and go in a progression with peaks of abundance. Fish grow into whatever foods (whether natural or supplemented) are available and/or provided. According to Swingle, growth will cease when the food supply can only maintain their biomass. But in the practical sense ... day by day ... fish growth and condition varies throughout the year in recreational pond.

When feeding at a constant daily weight, the specific rate of feed cannot keep pace with the SFR that is required to optimize FCR. The more a fish gains, the more it needs for maintenance and so the ongoing feed rates must compensate for the increased maintenance or growth will less than optimal as the limit of maintenance feed is approached.

If we are partners in a feeding operation, mortality would make its way into our figures of Gross FCR. The Gross FCR tells the story of how much feed it took grow a marketable crop and it will worsen due to mortality. If a particular formulation reduces mortality, we are going to use that feed if it helps the bottom line. In a pond there is always mortality each year. I recall reading an article by Dave Willis referencing a student's work in Northern Missouri where the winter mortality was estimated at 30% of the biomass. There was another paper where FCR was measured by fishermen's take and the standing weight at the end of a multi-year experiment. The FCR of that experiment was over 4. The standing weight of fish was ~ 1000 lbs/acre and the fish harvest was similar. The feed given was over 8000 lbs/acre for the course of the study. Few ponds could support 1000 lbs/acre of LMB/BG biomass on natural foods so these fish did depend on feed both for maintenance and growth. Fish that birds ate or that succumbed to sickness were not counted in the FCR calculation. The level of support that the pond food chain provided was also neglected. Both are uncertain metrics where measurement is difficult.

Feed provides nutrition that benefits a fish either by reducing loss of condition or by growth. It is possible that the most efficient use of feed is maintenance. IOWs the loss of weight prevented could be greater in magnitude than conversion at the intrinsic FCR. The equations still work with an SFR of zero ... predicting fish weight decline. It would be interesting to understand if the equations work when the fish is not eating for an extended time. But my sense is that fish adapt by slowing down metabolism (and maintenance required) during hunger periods ... quite possibly something like this is at play with compensatory feeding.
© Pond Boss Forum