The paper
The derivation of chemical prediction equations for monitoring energy declarations
- Author
- C. Fisher
- Published
- 1983
- In
- Recent Advances in Animal Nutrition in Australia
- Collection
- RAAN proceedings
- Listed on the old library
- 1 February 2012
We know of no online copy of this paper today. A university or state library that holds the Recent Advances in Animal Nutrition in Australia is the place to ask.

In this summary
- Why energy declarations became a live issue
- Building and testing the chemical prediction equations
- What the figures actually showed
- Correlation, bias and the age-of-bird problem
- Weighing accuracy against practicality
- Known weak points in the underlying chemistry
- Alternatives considered and the paper's own verdict
- Sources and further reading
- Questions
Why energy declarations became a live issue#
Trade in compound animal feeds across most countries is governed by regulations setting out what information sellers must provide and how it can be checked. In the UK at the time this paper was written, those regulations required declarations of oil, crude protein, fibre and ash levels, along with vitamin contents and various other additives, but not energy or amino acid values, even though these are the factors that most determine a feed's economic worth.
Some farmers argued the existing declarations did not tell them enough about unusual ingredients, particularly industrial by-products. Farmers Unions pushed government for open declarations, meaning a full listing of each formula. That specific demand was not granted, but authorities agreed to expand the nutritionally useful information provided, starting with energy declarations, a decision that was moving in parallel with similar discussions in Europe.
Once the principle of declaring energy was accepted, the practical question became how to define, monitor and verify those values. The paper describes this as having been debated mainly around chemical prediction equations, since this was judged the method most likely to be adopted for legislation, with rapid bioassays and in vitro digestion methods considered as alternatives but not expected to form the legal basis of control. Readers comparing this with the broader collection of RAAN Conference Proceedings will notice feed evaluation and monitoring methods are a recurring theme across those meetings.
Building and testing the chemical prediction equations#
The core experimental work, reported by Fisher in an earlier publication, used 56 estimates of metabolisable energy from feeds tested both as mash and pelleted, since pelleting had little effect on the results. Chemical variables on every feed were measured at a minimum of three separate laboratories, which allowed the researchers to estimate how reproducible the chemical analyses themselves were, not just how well the equations predicted energy.
Metabolisable energy was measured using adult cockerels given 30 grams of each feed, delivered directly into the crop following a starvation period of 40 hours, with excreta collected over the following 48 hours. Endogenous energy losses, the losses that occur regardless of food intake, were measured separately and found to be very consistent across experiments, allowing the researchers to adjust results to a common intake of 80 grams using a technique built on Sibbald's true metabolisable energy assay.
Several thousand equations were computed from the chemical and energy data, though only a handful are discussed in detail. The best of these accounted for almost all of the observed variation in apparent metabolisable energy, 98.5%, and combined fat, starch and protein terms with a negative effect of neutral detergent fibre, which the paper treats as an index of digestibility rather than an energy source in its own right.
What the figures actually showed#
The best-performing equation from the UK work had a residual standard deviation of 0.24 megajoules per kilogram, rising to 0.33 megajoules per kilogram once the variability of the chemical analytical methods was factored in. By comparison, a mean metabolisable energy value based on six replicate bird determinations had a standard error of 0.15 megajoules per kilogram, meaning direct measurement was still somewhat more precise but prediction came reasonably close.
A separate equation, built by pooling data from several European laboratories and based on fat, crude protein, starch and sugar, was adopted provisionally as the basis for European Economic Community legislation. This equation was taken forward into a ring-test, in which four feeds were circulated to 21 laboratories across Europe for analysis.
That ring-test found within-laboratory repeatability was good, with a standard deviation of 0.40% of the mean, but between-laboratory reproducibility was far weaker, at 4.48% of the mean. Translated into practical terms, duplicate analyses of the same feed at two randomly chosen laboratories could be expected to produce mean predicted energy values differing by as much as 1.65 megajoules per kilogram, or 12.7% of the mean, at the 95% confidence level, though the average difference across many such comparisons was smaller, at 0.56 megajoules per kilogram.

Correlation, bias and the age-of-bird problem#
Comparing predicted against measured energy values from the ring-test gave a high correlation, with a correlation coefficient of 0.98. But the paper is clear that a strong correlation masked a considerable bias. Values for cockerels were underestimated by 0.57 megajoules per kilogram, while values for young chicks were overestimated by 2.24 megajoules per kilogram.
This divergence between age classes is described as expected, since the equation had been derived only from data on adult birds. The practical implication is that an equation can rank feeds correctly relative to one another while still being systematically wrong in absolute terms for a class of animal it was never built to describe.
The paper treats this as a genuine limitation rather than a minor technical wrinkle. It notes that variation in metabolisable energy values between different classes of poultry remains unresolved, since most development work had involved adult fowls, and it is left uncertain whether the equations can be carried across to younger birds or to different species without further testing.
Weighing accuracy against practicality#
The paper proposes judging equations in three ways: by the conventional residual standard deviation, which measures how well an equation fits the observed energy data; by a second measure combining that unexplained variation with the reproducibility of the chemical analyses; and by a third measure reflecting analytical variability alone. It argues that equation selection should rest mainly on the first two, since once an equation is fixed, its practical reproducibility depends only on how repeatable the underlying chemical analyses are.
Simpler equations based only on the standard proximate components, those already required under existing feed labelling rules, accounted for about 95% of the variation in the UK data without needing any extra analyses. More complex equations incorporating fatty acid ratios or separate starch and sugar determinations improved fit only modestly, at the cost of additional analytical expense.
This is where the paper's own argument becomes most useful to a reader weighing up feed labelling systems generally: better statistical fit is not free, and a scheme intended for routine commercial use has to balance predictive accuracy against the reproducibility and cost of the chemistry behind it. We would treat the headline correlation of 0.98 as describing how well the equation ranks feeds against each other, rather than as a guarantee of absolute accuracy for any single declared value, given the bias the ring-test also uncovered.
Known weak points in the underlying chemistry#
The paper flags several specific sources of error that chemical prediction equations cannot fully resolve. Sugar is a clear example: the adopted equation used a coefficient implying an energy digestibility for sugar of 0.71, yet feeds containing sucrose, with a digestibility of 0.99, would tend to be underestimated, while feeds relying on milk sugars, with a lower digestibility, would be overestimated.
Fat presented a related problem, since its usable energy value depends on its fatty acid composition, something an expensive analysis could capture but which most routine schemes would want to avoid measuring. The paper also notes that the energy value of fat can decline with the level included in a feed, an effect that was sometimes significant for pelleted feeds in the original experiments, though not detectable in the four datasets combined for the European equation.
Differences between analytical methods added further uncertainty. Three laboratories in the ring-test found that acid hydrolysis before fat extraction gave higher fat readings than standard ether extraction, by amounts ranging up to around 0.91%, and starch determined by polarimetry differed from an enzymic method by several percentage points in different datasets. The paper treats better standardisation of these methods as a priority for making any declaration scheme workable.

Alternatives considered and the paper's own verdict#
Bioassays and in vitro digestion methods were both considered as alternatives to chemical prediction equations. An in vitro energy digestibility method, tested on 28 of the same feeds used in the energy experiments, gave a mean value of 14.69 megajoules per kilogram against an observed value of 14.20 megajoules per kilogram, with a correlation of 0.87 and a residual standard deviation of 1.00 megajoules per kilogram once regressed against the observed values, a clearly weaker performance than the better chemical equations.
Rapid bioassays were acknowledged as potentially competitive on cost, but the paper argues that building an entire declaration scheme around routine bioassay testing would carry heavy organisational costs, and suggests a bioassay might instead serve as a final check in disputed cases rather than as the everyday basis for verification.
The paper's own conclusion is measured rather than triumphant: chemical prediction equations can deliver a workable, reasonably accurate basis for energy declarations within the constraints of a legal and commercial system, but they remain imperfect tools whose limitations, in sugar digestibility, fat variation, age effects and analytical reproducibility, are unlikely to be solved by further equation development alone. Only a direct bioassay, the paper notes, could remove these sources of error entirely, and even that option came with practical costs regulators would have to weigh. This paper sits within the wider Recent Advances in Animal Nutrition community, alongside other contributions now held in the Livestock Library research index.
Sources and further reading#
- Trove library search: find a library that holds the paper
- Animal Genetics and Breeding Unit
- Feedipedia animal feed database: an open-access database of animal feeds
- Poultry Hub Australia: poultry science information
Questions#
What is a chemical prediction equation for feed energy?
It is a formula that estimates the metabolisable energy value of a compound feed from its measured chemical components, such as fat, crude protein, starch, sugar and fibre, instead of measuring energy directly in live animals. The paper describes how such equations were derived from feeding trials and then tested for how well they predicted energy values of feeds with varying composition.
How accurate were the equations compared with direct measurement?
The best equation in the UK experiments had a residual standard deviation of 0.24 megajoules per kilogram, rising to 0.33 megajoules per kilogram once analytical variability was included, compared with a standard error of 0.15 megajoules per kilogram for a mean value from six replicate bird measurements. Prediction was described as nearly as good as direct measurement, though not quite as precise.
Why did the equation work differently for young chicks than for adult cockerels?
The equation adopted provisionally for European legislation was derived only from data on adult birds. When tested in a ring-test against measurements made on young chicks, the predicted values overestimated chick energy by 2.24 megajoules per kilogram while underestimating cockerel values by 0.57 megajoules per kilogram, a bias the paper attributes to the equation's adult-only origin.
Were there cheaper alternatives to the full set of chemical analyses?
Yes. Equations based only on the standard proximate components already required for existing feed labelling accounted for about 95% of the variation in energy values in the UK dataset, without needing extra analyses such as fatty acid ratios. More complex equations improved the fit only slightly while adding analytical cost.
Written by the Livestock Library team from the published paper by C. Fisher (1983), and released on 9 October 2026. It is our account of the research in our own words, not the paper itself. For anything you plan to act on, read the original.
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