Nutritional Geometry: From Insects to Ruminants

The factors driving food selection, feeding and nutrition-related performance are multiple and complex. These complexities arise from the fact that the many nutrients obtained from foods usually cannot be considered in isolation, but interact in complex ways in their effects on animals. Most models of nutrition have ignored this complexity, rather opting for the simplifying assumption that the effects of nutrients can be understood in isolation.

Over the past two decades we have developed an integrative framework for nutrition, called the Geometric Framework (GF), which is designed to detect and measure the interactive effects of nutrients on animals (Simpson and Raubenheimer 2012). GF enables multiple food components and animal attributes to be distinguished, and the relationships among components and attributes disentangled and then linked to individual performance, ecological outcomes and evolutionary consequences. This approach has been used to describe how an ecologically and taxonomically diverse range of animals regulate their intake of multiple nutrients, both in tightly controlled laboratory experiments and in un-manipulative studies of animals in the wild. The framework has also been used to address problems in applied nutrition, including the design of diets for domestic animals, diet and habitat needs of endangered species, and the nutritional causes of human obesity. Here we present the foundation of the basic models and refer to a literature illustrating their use in a range of contexts. 

A distinguishing feature of GF is that it models animal nutrition in terms of more than one nutrient simultaneously, enabling both the individual and interactive effects of nutrition to be measured. The device used for this is a Cartesian space, called a nutrient space, in which each axis represents a nutrient in the model. The nutrient space provides a context in which the various components of the animal?s nutritional ecology can be represented in common units (e.g. mass, molar or energy equivalents of the various nutrients in the model) and interrelated. Components might, for example, include the animal?s current nutritional state, its optimal state, body composition, food compositions, and the trajectory over which its current nutritional state changes as it eats one or more foods [see Simpson and Raubenheimer (2012) for a comprehensive review].

The animal's current and optimal nutritional states (the latter termed the intake target) are represented by dynamic points in the nutrient space (see for example Raubenheimer et al 2007). Current nutritional state changes as the animal feeds, and the optimal state changes with nutrient requirements, for example with increased levels of activity, and as the animal grows, reproduces etc. Foods are represented as vectors at angles determined by the balance of the component nutrients they contain (these vectors are called nutritional rails). As the animal eats, its nutritional state changes along the rail for the chosen food. The challenge for animal is to select foods and eat them in appropriate amounts to direct them to the intake target.

An animal can reach its intake target by eating a single food that is nutritionally balanced with respect to the nutrients in the model. Because, by definition, a balanced food has the same ratio of nutrients as is required by the animal, such a food is represented by a nutritional rail that intersects the intake target, and thus provides a direct route to the target. An imbalanced food, by contrast, constrains the animal to a trajectory that does not enable it to reach the target. If, however, it had access to two nutritionally imbalanced foods with rails that fall on opposite sides of the target, it could combine these in the diet through complementary feeding to reach the target.

When an animal is restricted to a nutritionally imbalanced food, without access to a complementary food, it must reach a compromise between over-ingesting some food components and under-ingesting others, and bear the associated performance consequences. Such compromises, called rules of compromise, represent an important context in which nutrients interact in their effects on animals. It has, for example, been postulated that a dominant protein appetite in humans has interacted with a reduction over recent decades in dietary protein concentration, resulting in the excessive intake of carbohydrates and fats and hence the rise in obesity (Simpson and Raubenheimer 2005, Gosby et al 2011, Gosby et al 2013).

Performance consequences are incorporated into geometric models by superimposing a response surface onto the nutrient space, which represents the variable of interest. This approach was taken by Lee et al (2008) and Jensen et al (2012) to examine the consequences of dietary selection and constraint for lifespan and fecundity in flies (Drosophila melanogaster), and fecundity in beetles (Anchomenus dorsalis), respectively. 

The intake target is a fundamental reference point in nutritional geometry; it provides a basis for making predictions about the animal?s physiological, behavioural and performance responses to the nutritional environment (Raubenheimer et al 2012). For many purposes, an important starting point in building GF models is to measure the position in nutrient space of the target. One approach to this is to offer the animal complementary food combinations and measure the composition of the selected diet - this shows the nutritional target towards which the homeostatic regulatory systems aim within the conditions of the experiment. However, additional information is required to establishing definitively that the selected diet represents a homeostatic target rather than an outcome of some other process such as random food selection.

One way to do this is to compare the intakes of more than one experimental group of animals that differ in their starting nutritional state (i.e., following different nutritional pre-loadings). An example of this is the experiment of Raubenheimer and Jones (2006). In a first phase of the experiment, cockroaches (Blatella germanica) were preloaded for 48h with foods of high, intermediate or low protein:carbohydrate ratio. In the second phase the three groups were given access to all three foods from which they could compose a diet ad- libitum. Preloading in phase 1 resulted in the cockroaches in the respective groups initially eating very different combinations of the three foods in phase 2, until 48 h into the phase when they converged on a point in nutrient space (i.e. had compensated for their respective prior nutritional states). Thereafter, the proportions of the three foods eaten did not differ between experimental groups, and consequently all cockroaches moved along the same nutritional rail until the experiment ended 120h into phase 2. This result demonstrates unequivocally that feeding was governed by homeostatic systems regulating the balance of protein and carbohydrate in the diet, and identifies the common trajectory followed from 48 ? 120 hour in the phase 2 as the target rail.

Another way to demonstrate homeostatic target selection is to expose animals that are in the same nutritional state to different combinations of nutritionally complementary foods. In this design, the animals would need to eat different combinations of their respective food pairings to achieve the same nutrient intake. If this is the case, as was demonstrated by Chambers et al (1995) for locusts (Locusta migratoria), then it again provides evidence that the selected intake point is a homeostatic regulatory target. 

The most powerful geometric models are those that integrate within a single analysis the intake target, rules of compromise, and performance consequences. Lee et al (2008), for example, exposed female fruit flies to one of 28 diets differing in the protein:carbohydrate ratio, and measured lifespan, egg production rate and lifetime fecundity (the product of lifespan and egg production rate). Lifespan peaked on a diet with protein:carbohydrate ratio 1:16, egg production rate peaked at 1:2, and lifetime fecundity (the product of egg production rate and reproductive lifespan) peaked the intermediate value of 1:4. To test which diet, and hence which outcome (maximum longevity, egg production rate or lifetime egg production) was prioritised by the flies, an additional three treatments were established, each of which was provided with a different combination of complementary foods (as in the locust experiment mentioned above). All three groups of self-selecting flies selected a diet with protein:carbohydrate ratio of 1:4, and hence prioritised lifetime reproduction over longevity or high egg production rate, as would be predicted by evolutionary theory. Similar experiments have been conducted on caterpillars (Simpson et al. 2004) and predatory beetles (Jensen et al 2012).

Equivalent experiments have been performed on mammals. In a recent study, GF was used to measure interactive effects of dietary energy, protein, fat and carbohydrate on food intake, cardiometabolic phenotype and longevity in mice fed one of 25 diets (Solon et al 2014). Food intake was regulated primarily by protein and carbohydrate content. As in flies (Lee et al 2008), longevity was greatest on low protein, high carbohydrate diets, and multiple measures of cardio metabolic health mirrored this effect. These consequences were shown to be associated with hepatic mTOR activation and mitochondrial function, which in turn were related to circulating branched chain amino acids and glucose. 

Nutritional geometry has been developed and most extensively applied in laboratory experiments, where variables of interest can be systematically manipulated and others controlled. This has enabled us to elucidate with confidence the ways that nutrients and their interactions influence the behaviour, physiology, and performance of animals. However, many interesting questions concern the roles that these interactions play in free-ranging animals outside of the laboratory, in the complex environments that they normally inhabit. To investigate such questions, observational studies in situ are needed that record food choice, measure amounts eaten and food compositions, and model nutrient gains of undisturbed animals in the wild.

Such studies have already begun. Felton et al (2009) used nutritional geometry to analyse patterns of nutrient gain by wild spider monkey (Ateles chamek) in Bolivian rainforest. The composition of available foods differed across the annual cycle, providing a natural equivalent of the no-choice protocol used to measure rules of compromise in laboratory studies (above). Results showed that spider monkeys prioritise protein and consequently will over- or under-eat non-protein energy while maintaining daily protein intakes within tight limits, the same regulatory pattern that has been measured in humans (see above). Rothman et al (2011) performed a similar analysis on mountain gorillas (Gorilla beringei beringei) in Bwindi Impenetrable National Park, Uganda, and found that these apes showed the opposite pattern of spider monkeys and humans: they over- ate protein to maintain the intake of non-protein energy within narrow limits. Johnson et al (2013) obtained continuous record over 30 days of feeding for a single free-ranging chacma baboon (Papio hamadryas ursinus) in the Cape Peninsula, South Africa. Although there was substantial variation in daily energy intakes, the ratio of protein:non-protein energy eaten (1:5) was remarkably constant across days. Given the breadth of the diet ? the baboon was observed to feed on 85 different foods during the study ? this suggests complementary feeding, similar to the insect examples discussed above.

It is no coincidence that all of the above field studies involve primates: they are relatively easy to habituate and observe at close quarters. Most wild animals cannot, however, be habituated and observed for prolonged periods in situ, and this poses considerable challenges for the field of nutritional ecology. To deal with these, we have developed miniaturized data loggers that can be attached to free-ranging animals and collect global positional data, patterns of movement (via accelerometers) and digital video recordings of food choice and food intake. 

Much of our research, including the examples cited above, has concerned fundamental biology conducted within the framework of nutritional ecology (Raubenheimer et al 2009). We have, however, also used this framework to address applied problems, including the causes of human obesity (discussed above), companion animal nutrition and the formulation of diets for production animals.

The common theme across the research programme is the focus on how nutrient interactions mediate between the animal?s environment and its behavioural, physiological and performance responses. In the case of animal conservation, the important goal is to manage the environment so as to provide foods from which the animal can compose a diet that optimises stable population sizes and appropriate genetic diversity (Raubenheimer et al 2012). This is closely aligned with our basic studies, which are aimed at understanding how evolution by natural selection has moulded animals to maximise fitness within the evolutionary environment (Simpson and Raubenheimer 2012).

In some respects the situation is comparable for human nutrition. In this case the challenge is to understand and manage the consequences of evolved regulatory mechanisms operating in nutritionally altered environments, in much the same way as habitat degradation is a concern for the conservation of endangered species (Raubenheimer et al 2014). Unlike endangered species, however, the management goal for modern humans is not to maximise, or even stabilise, population levels, but to optimise different outcomes such as health and longevity.

The situation for domesticated animals is different in several respects. In the process of domestication, humans have altered both the characteristics of the animal (through artificial selection and training) and the environment, thereby disrupting the match between the nutritional biology of the animal and its evolutionary environment. Domesticated dogs (Canis lupus familiaris), for example, select an intake target comprising 30% protein, which is considerably lower than expected based on the diets of their wolf ancestors (Canis lupus) (Hewson-Hughes et al 2013a); domesticated cats (Felis catus), in contrast, have retained the dietary signature of obligate carnivores (Hewson-Hughes et al 2011, 2013b). Additionally, the optimisation criteria for domesticated animals are diverse. For some, including breeding animals and layer hens, nutritional management is still tightly linked to reproduction, but in others (companion animals, meat animals and working animals) nutrition is designed to optimise other outcomes.

Indeed, with the control that agriculturalists and animal breeders have both over the animal and its environment, the question of which criteria to optimise through management can be complex. Ruohonen et al (2007) demonstrated the set of trade-offs that are encountered in the design of aquaculture feeds for European whitefish (Coregonus lavaretus), and used nutritional geometry to design a protocol for deciding on the diet composition needed to produce a particular outcome. For example, plasma cortisol (an indicator of stress) was minimised on high protein diets (a favourable outcome for animal welfare concerns), but nitrogen waste was maximised on the same diet (an unfavourable outcome for environmental impacts). Body protein:fat ratio, an important determinant of flesh quality, varied in proportion to the protein:fat content of the diet. The protocol recommended by Ruohonen et al (2007) enables managers of domesticated species to select a weighted combination of desired outcomes, and design the feed most suited to providing the desired combination of outcomes. 

A group about which we know very little in the context of nutritional geometry are the ruminants. Given their global importance - including their role in natural ecosystems, human food production, and their contribution to greenhouse gases - this is an important omission. Ruminants are, furthermore, of special interest in the comparative context, because of the complexities introduced by the rumen microbiota. Nutritional homeostasis is achieved through a series of feedbacks linking the animal?s nutritional state to the composition of foods and mediated through behavioural and physiological responses (Simpson and Raubenheimer 2012). It remains to be seen what the consequences are for the geometric patterns of nutritional regulation of having a community of commensal organisms intervene between the animal and its foods, as is the case with ruminants.

To date, there is only one study of which we are aware that has applied nutritional geometry to a ruminant. Felton et al (under review) studied macronutrient selection and the rules of compromise in captive moose (Alces alces). Moose are particularly interesting in this respect, because despite a long history of diet selection studies on this species the nutritional factors that underpin their foraging decisions remain unresolved. The geometric studies showed that in free choice experiments the moose combined the two nutritionally complementary foods to obtain a diet with a protein (% available protein of total dry matter intake):non-protein (% Total non-structural carbohydrate +% fat + %NDF) of 14:46 (adult females), 14:45 (adult males) or 17:43 (calves). These ratios were derived by combining the foods in significantly non-random proportions, suggesting active selection of an intake target. When the moose were restricted to foods that differed in their macronutrient composition from the selected diet, they regulated intake to maintain non-protein macronutrient constant, while over-ingesting or under-ingesting protein on high and low-protein diets respectively. Moose therefore resemble mountain gorillas in their pattern of macronutrient regulation, and differ from spider monkeys and humans (see above). It remains to be seen whether this is characteristic of ruminants in general, whether it is characteristic of ruminant browsers like the moose and differs for ruminant grazers, or whether among ruminants it is more specific to the moose. Overall, however, the study showed that regulation of food intake by moose is based not on energy maximisation, as has been previously suggested, but on a more sophisticated macro-nutrient specific strategy. 

Nutritional geometry provides a means of integrating the various facets that comprise the nutritional interactions of animals with their environments, within the context of multiple nutrients. Key facets include foods, nutrient requirements, feeding, post-ingestive nutrient processing, signalling pathways and other mechanistic components, as well as performance (e.g. longevity and reproduction) and applied outcomes (e.g. growth rates and body composition of production animals). To date the majority of studies have involved macronutrients, but other nutrients and non-nutrient food components (e.g. fibre and allelochemicals) have also been the focus of geometric studies when biologically appropriate (Raubenheimer and Simpson 2006, Simpson and Raubenheimer 2012, Nie et al 2014). The challenge ahead is to continue to extend this type of study to diverse animals and contexts. This would enable comparative analyses to be performed for elucidating the ecological and evolutionary factors that drive different patterns of nutrient regulation. Despite their theoretical and applied significance, only one study has applied nutritional geometry to a ruminant, the moose. That study showed that like many other non-ruminants, moose use elaborate macronutrient specific strategies in the regulation of food intake. Further studies are needed to establish the theoretical, practical and comparative significance of this. 

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