# Are nutrition values always additive?

(Edited to clarify question, I am a math professor not a biologist so I appreciate help clarifying the language to match the knowledge base present here.)

As I understanding nutrition labels, if a label claims a product P (e.g. an orange) has 50% of a recommended daily diet of some nutrient N (e.g. Vit. C), it is simply saying that an idealized diet recommends twice as much as of the nutrient (Vit. C) found in that product (Orange). This is different from saying that by eating the orange you body will receive 50% of that nutrient for several reason, including:

1. Most digestion is not idealized so the comparison is at best an attempt at an average normalized to a specific capacity (2000 cal diet).
2. Just because the product contains 50% of the nutrient does not mean the body will absorb all of that nutrient in digestion.

Setting aside the effects on individuals, I am interested in the behavior of 2. Are their products and nutrients where (on average) eating larger servings leads to decreased (or increased) absorption of a fixed nutrient? If so how much can the the amount absorbed differ from the naive multiple of the listed nutrition quantity.

In mathematical language, if A(p) represents the percent of recommended daily diet typically absorbed from consuming p units of a product, is the the derivative A'(p) generally considered to be constant (which we call "additive" or "linear")?

So in a sense, if A(p) was plotted as a graph then the nutrient label is like a tangent line locally approximating the graph at A(1). I want to understand how well the actual nutrition absorption compares to this tangent line approximation in real life examples. Are they generally good approximations, within the significant figures of the displayed data, or are they sometimes very far from average absorption as p varies.

Though possibly not relevant, USDA literature here documents various conversions between different units, raw and cooked food (p. 11-12), how much of a product is refuse (p. 5), and each appears to be additive. Though I did not read every page, this seems to suggest that any non-linear behavior is in fact owed to biological/chemical reasons and not a reflection of how the data is reported in labels.

• Possible duplicate: medicalsciences.stackexchange.com/questions/27447/… It mostly seems like you are not understanding what these numbers mean. I would strongly recommend understanding measurements you're working with before trying to understand any resulting implications of those numbers, and certainly before you try to include them in a mathematical model. Commented Jun 24, 2022 at 16:26
• I'm suggesting that this isn't really subject matter expert stuff, these are consumer guidelines meant for consumers, so they're supposed to be easy to understand and there are resources designed for non-experts to understand them. It might be that you have a separate biochemical question, but haven't formulated it in that way and from that perspective it's certainly not reasonable to consider all nutrients equally which makes it a very broad topic. Commented Jun 24, 2022 at 17:40
• I've synthesized a prior comment discussion into a community wiki answer. Please feel free to edit the answer with any nuance I missed. Commented Jun 24, 2022 at 22:19
• * Setting aside the effects on individuals, I am interested in the behavior of 2. Are their products and nutrients where (on average) eating larger servings leads to decreased (or increased) absorption of a fixed nutrient?* Yes, trivially so. All absorption process are mediated with transporter/channels, and all of them can get saturated. As a case in point, the maximum fructose absorption is somewhere around 50mg, and larger uptake will just lead to osmotic diarrhoea. But I would bet my money that these sub-linear absorption rates due to saturation of transporters matter less than the Commented Jun 24, 2022 at 23:41
• [cont‘d] range/inaccuracy of the recommended daily uptake values, and inaccuracies in food labelling / batch differences (don‘t have a source for that, just a feeling) Commented Jun 24, 2022 at 23:43

As Bryan Krause notes in the comments:

The nutrition guidelines are based on some recommended intake of each nutrient, measured in mass. So if 100 mg of a substance is 20% of the recommendation, then 200 mg is 40%, etc.

Another key piece of information that you may be missing is that recommended daily allowances are determined while taking into account the age, and sex specific absorption of the individual nutrient.

For example, if the RDA for calcium for a 1 year old male is 700mg, that is taking into account the calcium absorption rate of a typical 1 year old male.

As Bryan Krause mentioned:

From a medical perspective it's rare that anything beyond [the RDA] matters. No one is achieving exactly 100% of every recommended nutrient every day, and until recently, human life has gotten on just fine without any such precision in diet - biology is quite flexible. The important medical cases are specific conditions and diets that are drastically outside the norm, and they're usually identified by symptoms, not by measuring uptake of particular nutrients.

I would add to the existing answer that this really boils down to which factors of nutrient uptake you want to ignore.

You mention already that you don't want to be concerned with variation of the human digestive system.

I guessed that meal size could be a factor too (a large meal being more likely to saturate uptake pathways), but apparently at least in laboratory dogs, it seems saturation is the norm regardless of meal size. I couldn't find any more evidence on this topic, but I could imagine that this only holds for macronutrients. Though it's just as possible that micronutrient uptake pathways' capacities are scaled accordingly and are also saturated as soon as a meal contains any appreciable fraction of the nutrient's RDA.

What about the influence of one compound contained in the meal on the uptake of another? E.g. Calcium reduces iron absorption, while vitamin C increases it. Zinc and iron compete for absorption. Indigestible dietary fibre also affects the uptake of nutrients (carbohydrates shown e.g. here, but as far as I am aware it's not just carbs).

Of course, you can decide to simplify and just assume a linear intake/uptake relationship. Around the scale of the RDA, that's not an unreasonable simplification to make, and for consumer purposes we do make that assumption all the time. Other purposes will require more careful research and study conditions appropriate for specific nutrients.

• These are excellent references, greatly appreciated. I simplified to get my question out better (I fumbled quite a lot at the start). Advanced math books in my field since the 1950's have been pushing nutrition tables that seem highly unrealistic and much better tools exist today. So it is time revisit the origin and validity of these older models and update these intended applications. Commented Jun 26, 2022 at 4:53