The 'Geometric Framework'

What is it?

The 'Geometric Framework' (GF) is a state-space modelling approach that explores how an animal solves the problem of balancing multiple and changing nutrient needs in a multidimensional and variable nutritional environment. It was originally developed by David Raubenheimer and Steve Simpson (in the early 1990's) and has much in common with MacFarland & Sibly's state-space models of motivation and shares features with Tilman's resource allocation models (RAM) and with ecological stoichiometry (ES). It differs from RAM and ES models in that it places more weight on the physiology and behaviour of individuals.

How does it work?

The GF treats an animal, in my case insects, as living within a multidimensional nutrient space where there are as many axes as there are functionally relevant (fitness-affecting) nutrients. There is a mixture and blend of these nutrients that is optimal, which the GF calls a nutritional target, and it is likely that most animals have evolved a suite of behavioural and physiological mechanisms that enable them to approach this point. The position of nutritional target is dynamic, however, and it can change over the course of the animal’s life depending on its stage of development and the environmental circumstances. The GF has two additional targets, and both can be measured empirically. The first is the intake target, which represents the amount of nutrients that an animal needs to ingest in order to reach its nutritional target. In all instances, the value of the intake target will exceed that of the nutritional target because not all ingested nutrients are absorbed. Animals also have a growth target, which reflects the level of nutrients incorporated into growth and storage tissues. The GF calculates the growth target as the nutritional target minus metabolic requirements.

Examples...

Scenario 1. The simplest example is where our test animal has access to a single food that contains our two nutrients, A and B, in a 1:1 ratio. Foods in the GF are represented as trajectories, or 'rails’, running through a defined nutrient space, and nutrient space can have as main axes as there are functional nutrients (in all the examples presented here nutrient space is always two-dimensional). In this first case our food is represented by the red dashed line, and if we assume that the distribution of nutrients in our hypothetical food is homogenous, then for every bite our animal takes, equal amounts of nutrients A and B are ingested. Our test animal always begins at the origin, and as it consumes the two nutrients it moves along the rail (the red arrow represents consumption). Here our test animal is able to reach its intake target because it lies on the available food rail.

Scenario 2. An animal cannot reach its intake target if it is restricted to a nutritionally unbalanced food (e.g. nutrients A and B are in a 1:2 ratio; the orange dashed line), and it must make one of three nutritional compromises. It can (i) eat until it reaches the target for nutrient B, but suffer a shortfall in nutrient A, (ii) eat until the requirement for A is reached, while ingesting an excess amount of nutrient B, or (iii) feed to some intermediate point between these extremes. In this last case the animal will experience a simultaneous deficit with respect to nutrient A, and an excess with respect to nutrient B. The key point is that when foods are nutritionally imbalanced, conflicts may arise between the mechanisms regulating the intake of the nutrients. In this case our animal must employ some ’decision rule’. In so far as these rules have evolved through natural selection, they should represent points of best compromise (functionally optimal compromise).

Scenario 3. A more typical situation for an animal is that it will have the opportunity to choose among foods with different nutritional profiles. If the choice is between a nutritionally balanced and imbalanced food, the animal should always eat the former. When no nutritionally balanced food is available, an animal can still reach its intake target if nutritionally complementary foods are available and the animal eats from these foods in the correct proportions. This is the finer-grained problem of nutritional homeostasis. In this last example, our animal has two nutritionally imbalanced foods available: one food contains nutrients A and B in a 1:2 ratio (the orange dashed line; as in scenario 2), while the other imbalanced food has the same nutrients in a 2:1 ratio (the blue dashed line). Under these conditions our animal can reach the intake target by moving between the two foods (always parallel to the rail on which it is feeding), but it cannot reach any point outside the area bounded by the two food rails. Switching between different food items can occur at any time-scale, ranging from bites to days, and the rate at which switching occurs will be determined by the costs associated with such behaviours (i.e., lots of switching leads to dithering, while infrequent switching can result in wildly fluctuating nutritional imbalances).

Key Publications using the 'Geometric Framework':

Behmer, S.T. and Joern, A. (2008) Coexisting generalist herbivores occupy unique
     nutritional feeding niches. Proceedings of the National Academy of Sciences,
     USA 105, 1977-1982 [pdf].

Warbrick-Smith, J., Behmer, S.T., Lee, K.P., Raubenheimer, D. and Simpson, S.J. (2006) 
     Evolving resistance to obesity in an insect. Proceedings of the National Academy
     of Sciences, USA 103, 14045-14049. [pdf]

Lee, K.W., Behmer, S.T. and Simpson, S.J. (2006) Nutrient regulation in
     relation to diet breadth: a comparison of Heliothis sister species and a hybrid.
     Journal of Experimental Biology 209, 2076-2084. [pdf]

Simpson, S.J., Sibly, R.M., Lee, K., Behmer, S.T. and Raubenheimer, D. (2004)
     Optimal foraging with multiple nutrient requirements. Animal Behaviour 68, 1299-1311.
     [pdf]

Behmer, S.T., Raubenheimer, D. and Simpson, S.J. (2003) The effects of distance between
     foods on nutrient regulation in a highly mobile insect herbivore. Animal Behaviour
     66, 665-675. [pdf]

Lee, K.P., Raubenheimer, D, Behmer, S.T. and Simpson, S.J. (2003) A correlation
     between macronutrient balancing and insect host-plant range: evidence from the
     specialist caterpillar Spodoptera exempta (Walker). Journal of Insect
     Physiology 49, 1161-1171. [pdf]

Behmer, S.T., Simpson, S.J. and Raubenheimer, D. (2002) Herbivore foraging in
     chemically heterogeneous environments: nutrients and secondary metabolites.
     Ecology 83, 2489-2501. [pdf]

van der Zee, B., Behmer, S.T. and Simpson, S.J. (2002) Food mixing strategies in the
     desert locust: effects of phase, distance between foods and food nutrient
     content. Entomologia Experimentalis et Applicata 103, 227-237. [pdf]

Lee, K.W., Behmer, S.T., Raubenheimer, D. and Simpson, S.J. (2002) A geometric analysis
     of nutrient regulation in the generalist caterpillar Spodoptera littoralis (Boisduval).
     Journal of Insect Physiology 48, 655-665. [pdf]

Simpson, S.J., Raubenheimer, D., Behmer, S.T., Whitworth, A. and Wright, G.A. (2002)
     A comparison of nutritional regulation in solitarious and gregarious phase nymphs
     of the desert locust, Schistocerca gregaria. Journal of Experimental Biology 205, 121-129.
     [pdf]

Behmer, S.T., Raubenheimer, D. and Simpson, S.J. (2001) Frequency-dependent food
     selection in locusts: a geometric analysis of the role of nutrient balancing. Animal
     Behaviour 61, 995-1005. [pdf]

For detailed discussion on the methodology and uses of the 'Geometric Framework' see:

Simpson, S.J. and Raubenheimer, D. (1995) The geometric analysis of feeding and nutrition:
     a user's guide. Journal of Insect Physiology 41, 545-553.

Simpson, S.J. and Raubenheimer, D. (1993) A multilevel analysis of feeding behaviour:
     the geometry of nutritional decisions. Philosophical Transactions of the Royal Society
     of London, Series B-Biological Sciences 342, 381-402.