Growth Curves and Accuracy?
I have been working on some formulas to approximate the biological needs/impact of a fish as it grows. It is obvious to me that a growing fish is going to have a greater impact on its environment than an adult fish of equal length. What is not obvious is just how much more of an impact it will have. To that end I have created a few differential equations that all account for the endpoints of a fish's growth, but I am not sure about the middle. Any thoughts would be appreciated. I have made an image so that you guys can see what each one looks like (see attachment).
It is important to keep in mind that size of the tank, type of filtration, filter media, maintenance, and even the type and amount of food will all impact waste levels in an aquarium. To isolate just the waste passed by a specific fish would be impractical and less than accurate to say the least. Different fish also pass waste in different ways, and the amounts vary. There is ammonia that is expelled from the gills, but then there is also solid waste expelled from the anus. Again, this all is dependent on size of the tank, feeding, and maintenance habits.
This all said, then you have to work with growth rates, which differ not just from species to species, but individually from fish to fish. A fish that has come from a bad situation where growth was stunted can suddenly start growing again when put into proper conditions... changes in diet, tank space, hormone levels, and genetics have to be taken into account as well.
How would you propose to factor in all of those things to make for even a semi accurate chart?
Sorry I forgot to mention that this is part of a much larger project. You can check it out at this link: HMF Home (MOA's: How Many Fish?, Stocking Freshwater Aquariums)
I've been dealing with multiple factors for a while :)
So which curve, holding all other factors as constant, do you think is the best representation?
While I understand what you are attempting to do (and yes, I have been to your link and read through a few pages of information there) I cannot agree with or endorse such a thing. I find it to be very confusing, especially to a newbie in the fish hobby.
There is no defined constant in the aquarium hobby. There is no one specific way to keep any aquarium healthy. There are many methods at fish keeping that are tried and true, and a person should begin by studying and researching these various methods to find what works best for them and their situation. To try to define a constant would be a huge mistake, as nothing is ever constant in an aquatic habitat.
2 tanks that sit side by side and are set up identical to each other are going to be vastly different from each other. What applies to one aquarium will not always apply to another. This where experienced hobbyists and professionals in the aquatic industry come into play. Forums such as this are wide spread on the internet, some better than others, some providing more useful and accurate information than others... but all are similar in that they have experienced people to help weigh information to guide a newbie through the steps of a healthy aquarium.
I'm sorry, but I cannot contribute to what you are requesting because what you are trying to define simply can't be put down as an exact or constant due to the many factors I mentioned in my last post. I would feel as if I were contributing to misinformation if I contributed further.
(btw, there was some misinformation and misleading information on the web page I read entirely from your link...)
I am sorry you feel that way, but the fact is that the damage has already been done, sort to speak. People rely on oversimplifications every day, and the aquarium hobby is no exception. Even experienced aquarists will read a post by a newbie and make suggestions based on just a few factors (namely, ammonia, nitrite, nitrate, the number of fish, and type of fish). Whether or not you like to admit it, you have probably dealt in generalities yourself--have you ever told someone that tetras are mostly peaceful or that two male bettas should not be kept together? Such simplifications are how we understand our world: People build from generalities to eventually include the exceptionalities. No less, whenever people encounter new situations, they almost always fall back on the simple relationships they have come to trust.
Philosophy aside, my research serves a more important purpose than just offering the world an alternative look at stocking theories. Quite the contrary, it helps me learn more about the exceptions and how they fit into the more standardized assumptions. Exploring detailed explanations and a myriad of factors is an incredible way to grow as an individual aquarist. I want to figure out how things work. This means I need to be able to put relationships down in a tangible way. What I am attempting is difficult, but at least I am addressing the issue. Hiding behind the assumption that things are too difficult to quantify is what led Europe into the dark ages. If I do not believe that all stocking dynamics can be understood, then there is no point in even attempting to keep fish. After all, if aquarium husbandry is so complex that it cannot be explained in a rigorous fashion, then doesn't that imply that aquarists are more likely to make mistakes than succeed?
In keeping with my above statement that I want to learn, I would very much like to hear (read) what misinformation was present on the pages you read. I am not interested in intentionally leading people astray, so please tell me what the issues were. While I am unwilling to believe I have wasted the past few years of research, I am willing to retract statements that are absolutely harmful. I really do want to hear what the problems were. otherwise, how can I become better?
I am a little surprised that you (bettababy) have not responded with a list of problems on the website. I really did want to know what the problems were. Perhaps it is simply a very long list that you are preparing or you are looking for sources to support your claims. I understand. When you finish just send me a pm or email me (email address is on my site). I would be happy to look over your complaints.
I would probably choose something similar to the second degree, although I think something a bit less symmetrical would be more accurate. Because fish growth slows down with time, I think the effective biomass (if I understand you correctly in that effective biomass is measuring the food intake/waste production of the fish) of a fish at, say, 25% fully grown is going to be pretty similar to a fish that is 50% grown, despite the fish at 50% being much larger in IFU's. I don't think modeling the metabolic factor is as simple as something like A/C, which is hinted at on the IFU page, but I suppose that's what you're getting at in this thread in the first place. I think the most accurate way to get a factor for metabolism would just be to take lab measurements.
Yes, my old spreadsheets did use A/C to account for metabolism and that is what resulted in the linear approximation. You have an interesting point about expecting the biomass of a fish at 25% of its adult size to have an impact similar to a fish at 50% of its adult size in that it does indicate either of the single zero derivative models.
As to lab measurements, I heartily agree--I just don't know anyone with the money to undertake such a research endeavor. That is why I ask questions like this; I post questions to see how things act in the real world as not even lab test are absolute when you introduce the variables that exist in uncontrolled environments. I'm not trying to be precise, just close enough so that modifying the curve for various species is not too hard. :)
Thanks Loads 'n Loads,
I looked at your site and find it far to complex to hold my interest. However, I appreciate fully what you are trying to accomplish. My degree is in actuarial science, so I certainly appreciate that all things can be explained with an input and a predictable output. I am sure you will arrive at an outcome that is helpful to the new fishkeeper.
My big question is why are you doing this? Do you see a market for your research? In other words, do you intend to make money on this?
For the record, I feel this project is akin to trying to create a formula that will correctly predict which 2 people in a group of 1000 will fall in love. Good luck!
I am doing this because I love mathematics and I love fish, no other reason. I want to put my math skills to use and I want to learn more about aquarium husbandry. It has been my experience that the best way to learn a subject is to teach it, to try to explain it to someone else. Doing such forces me to try to present stuff in an understandable fashion, which in turn forces me to consider interconnected relationships. I do it because thinking it through is fun :).
Restropsective modification: the answer to the 2 in 1000 problem. Aquarium dynamics and real-world problems can be adjusted for once a significant event occurs. This adjustment can then be applied to the next situation to occur. It is not precise, but it generally becomes more accurate as time progresses. When you can't be precise, use a limit. This is what I am doing with my spreadsheets: I put a version out there and everyone tells me what went wrong. Then I begin again, correcting the errors in the first one, and send out the next version for "peer review." My spreadsheets are not perfectly accurate, but they have come a long way from their origins.
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