Using Nutritional Geometry in Food Animal Production

In GF models, individual animals, foods and their interactions are represented graphically in a geometric space defined by two or more food components (for a comprehensive review see Simpson and Raubenheimer, 2012). Foods are represented as vectors through nutrient space at angles determined by the balance of the component nutrients they contain (nutritional rails), and the animal's nutritional state as a point that changes over time. As the animal eats, its nutritional state changes along the vector of the rail for the chosen food. The challenge for animals is to select foods and eat them in appropriate amounts to direct them to their optimal nutritional state (the intake target). Knowing the position in nutrient space of an individual's intake target provides a basis for making predictions about its physiological, behavioural and performance responses to the nutritional environment. An animal can reach its intake target by eating a single nutritionally balanced food, or by mixing its intake from two or more nutritionally complementary foods. If the individual is restricted to a nutritionally imbalanced food, however, it must reach a compromise between over-ingesting some food components and under-ingesting others (termed its rule of compromise), and bear the associated performance consequences. 

Much of our research has concerned fundamental biology, but a wide range of applied nutritional problems demand scientifically designed management solutions. There are many examples, but among the most important is the need to feed production animals (Raubenheimer and Simpson 2007).

The intake targets of animals and rules of compromise they adopt when constrained from reaching their intake target are sculpted over evolutionary time to produce favourable outcomes within the particular ecological circumstances of the animal. In the process of domestication, humans have altered both the characteristics of the animal (through artificial selection) and the environment, thereby disrupting the ancestrally evolved match between the nutritional biology of the animal and its nutritional environment. An important challenge of managing domesticated animals is to ensure that they are provided with foods that enable them to meet their nutritional needs: but how to decide what the optimal requirements of a domesticated animal are?

A major complication concerns the question of which factors we wish the diet to optimise. For domesticated animals, the concept of 'evolutionary fitness' in the normal sense no longer applies. Other criteria that come into play when designing diets for food animals include the health and welfare of the animal, economics, logistics, environmental and ethical concerns – and in many cases these conflict. The fact that multiple, conflicting optimisation criteria need to be taken into account is not unique to domestic animals, however. The geometric framework can be used to model these processes.

An experiment that illustrates the above issues, and could serve as a reference for experiments in the poultry industry was performed by Ruohonen et al. (2007) on a salmonid fish species, the European whitefish (Coregonus lavaretus). The aim of this work was to use the GF to define the optimal macronutrient composition in the diet of the whitefish, to quantify the behavioural responses of fish to diets that depart from this composition, and to optimize multiple performance criteria, taking account of economic, environmental and animal welfare concerns.

The protocol for the analysis involved four main stages. The first step was to plot the pair-wise relationships between the three macronutrients separately (fat vs. protein, carbohydrate vs. protein and fat vs. carbohydrate). This showed that, as long as carbohydrate levels were below a damaging threshold (whitefish suffered when carbohydrate was above a relatively low level), the fish regarded lipid and carbohydrate as interchangeable sources of energy. Nutrients that the animal regards as interchangeable can for practical purposes be regarded as a single resource, enabling us to collapse two axes into one (non-protein energy) and plot it against protein. The second step was to construct nutrient intake and growth arrays, according to the usual procedures in the GF. Relative to an estimate for the intake target (derived from self-selection studies in other salmonids), whitefish overconsumed non-protein energy to gain limiting protein when restricted to diets low in % protein. They did this to a greater extent than they overconsumed protein to gain limiting non-protein energy on diets containing a high % protein, probably reflecting the toxic limits to voiding excess protein as ammonium via the gills. Protein growth was more tightly regulated than lipid growth. Thus, fattiness of the flesh was a result of overeating carbohydrate and lipid to gain limiting protein on diets containing a low % protein, while diets high in % protein resulted in low levels of body fat as a result of fish refusing substantially to overconsume protein.

In the third step, we superimposed measures of performance and other response variables onto the intake array. Wet weight growth of fish was consistent across the intake array, but this growth was composed of differing amounts of protein and fat, with flesh protein content rising as dietary % protein increased. Feed efficiency and energy retention efficiency showed little change across the intake array, but nitrogen waste rose with % protein in the food. Commonly-used welfare indicators, such as plasma glucose, plasma cortisol, liver glycogen, and liver somatic index, fell as % dietary protein rose, although the interpretation of these 'welfare measures' is problematic.

The final step was to choose a set of performance responses to be considered in diet optimisation, and to normalise and scale these relative to each other. This involved making a priori judgements about which variables were relevant, what each was 'worth' and, for each variable, whether high or low values were the more desirable. Fish and fish feed have a market price, and there is a price premium for high quality flesh. Environmental and welfare costs are harder to measure, but can be the target for taxes and licensing restrictions which have a measurable cost. We did not conduct a full economic analysis, but for illustration chose four scenarios, in which production costs, flesh quality, environmental impact and animal welfare were prioritised (Ruohonen et al. 2007). 

This study illustrates a major advantage of using the Geometric Framework in applied nutrition: that it places not just foods, but the interaction of the animal with those foods, at the centre of diet optimisation decisions. Taking account of the pre- and post-ingestive regulatory responses of the animal simplifies the problem of identifying optimal diet formulations, while multi-criterion optimisation is a matter of deciding how to select and weight normalised response surfaces and then summing these to arrive at the decision function. 

Raubenheimer, D. and Simpson, S.J. (2007) Geometric analysis: from nutritional ecology to livestock production. Recent Advances in Animal Nutrition in Australia 16, 51-63.

Ruohonen, K., Simpson, S.J., and Raubenheimer, D. (2007) A new approach to diet optimisation: a reanalysis using European whitefish (Coregonus lavaretus). Aquaculture 267, 147-156.

Simpson, S.J. and Raubenheimer, D. (2012) The Nature of Nutrition: A unifying framework from animal adaptation to human obesity. Princeton: Princeton University Press.