Abstract presented at the 41st University of Nottingham Feed Conference. Our deep appreciation to the authors and the kindly cooperation of Prof. Julian Wiseman, Professor of Animal Production / Head of Division, Division of Agricultural & Environmental Sciences, School of Biosciences at the University of Nottingham.
The fact that feedstuffs used in animal diets have variable composition is well recognized and it is also accepted that this variability will lead to uncertainty in final diet composition. The current paper will discuss sources of variation that lead to uncertainty in diet specification, examine the effects of variability in feed components in diet formulation and propose that a Bayesian, decision-theoretic framework may be useful in working with the variability that inevitably occurs, to improve on-farm decision-making. The objective is to stimulate thought and discussion on how to deal practically with uncertainty in the nutritional value of feed components. A crucial aspect of understanding the relevance of variability in feedstuffs is the question “How does variability in feedstuff affect the decisions we make in formulating rations?” and it is intended to address this question.
The nutritional value of any particular raw material or forage is not the same for all batches used in animal feeds. For example, the ruminant energy concentration for rolled wheat used in a particular mill over a six month period may have a mean value of 13.5 MJ ME/kg DM but, for any given diet formulation during that six month period, there will be some variation around this mean value. Another way to look at variability is that there is uncertainty associated with the compositional value of a particular sample. The degree of uncertainty may be expressed as a credibility interval (an interval within which there is a specified probability that the true value lies) or, assuming a normal distribution, as a standard deviation (SD) or variance (SD2).
Variability in feedstuff composition can arise from two general sources; random variation (often termed ‘error’) or systematic variation (‘bias’). Random variation may arise from (for example) natural variation in a product or random measurement error in laboratory methods. Systematic variation may arise from (for example) analytical equipment that always reads ‘low’ or ‘high’ for a particular nutrient, decomposition of feeds in certain storage conditions, or poor sampling technique.
It is essential to minimise random and systematic variation as far as possible and methods for this are suggested. Having accomplished this, there are some pragmatic principles to reduce the impact of uncertainty in feed components in a final diet specification; do not use highly variable feedstuffs, reduce the proportion of variable products used in a diet, increase the number of dietary components (this has the effect of ‘averaging’ feeds that may be higher or lower than their expected mean value, an example is provided), consider adjusting a feedstuff by a proportion of the SD to allow for the probability of the feed being above a specified nutrient level.
The problem with individual feed adjustments is that it is difficult to assess the final output probabilities for the overall diet (combinations of distributions are needed for this). Rations that use individual component ‘safety margins’ have been shown to be less cost effective than full probability based models.
Methods to calculate diets to incorporate feedstuff probability distributions (uncertainty in feed component nutrients) will be presented and this will include a detailed farm example. The effects of uncertainty in feed components as well as variability farm management on productivity, diet costs and production decisions, will be assessed in the context of a dairy farm. The effects of different magnitudes of variability in forages and feedstuffs on the probability distribution of dietary energy supply will be illustrated. The impact of variability of feeds on the cost of a diet is discussed and the importance of using such information for transparent individual farm decision-making is illustrated.
Modelling of sources of variability is extended by combining prior beliefs (current knowledge) alongside new data to present a fully Bayesian framework. The resulting ‘posterior’ distribution can be used for subsequent ration prediction and may be thought of as a weighted mean of established knowledge and new data from current samples. This may work well for forage analysis, when a prior distribution for a specific silage cut (e.g. mid May, new grass variety, good making conditions) could be combined with a relatively small number of analyses from a silage clamp and the influence of one or two very unusual sample results would be limited.
This concept can be extended to all feed components for which there is reasonable prior knowledge from literature, laboratory data or expert advice, and used to formulate diets with outputs in the form of probability distributions. These models can also incorporate knowledge of farm feed practices and produce outputs to aid farm decisions (such as the probabilities of achieving different levels of production or costs per unit output for example) and this will be illustrated.
Thus, variation in feed components used to produce animal diets is unavoidable and this leads to uncertainty in the final diet suggested. Important steps in handling this uncertainty are:
Minimise variation by:
- Reducing random and systematic variation wherever possible.
- Using a variety of different feeds to make a diet
- Limiting the use of highly variable feeds
Allow for uncertainty in feed components:
- A decision-based approach can be used to model uncertainty with decisions set in the context of each farm situation.
- A Bayesian approach can incorporate prior knowledge of feed component characteristics as well as results of recent farm samples and may provide improved estimates for decision-making.
Expect formulation to be an iterative process:
- Monitor cow performance and farm outputs regularly and carefully as a guide for possible errors in dietary assumptions. It should not be assumed a diet is correct just because it is ‘right’ on paper and vice versa.
Martin Green, School of Mathematics and School of Veterinary Medicine and Science, University of Nottingham.
James Husband, Richard Vecqueray, Evidence Based Veterinary Consultancy, 68 Arthur Street, Penrith.
Laura Green, Ecology and Epidemiology Group, Department of Biological Sciences, University of Warwick.