Foraging in space, data and mind

Optimal foraging theory has always fascinated me. It is an attempt to formalise and explain how animals allocate time and energy to best exploit the resources within their environment. Thus an animal judges how to offset the energy it loses whilst searching for and handling food against the energy it gains from consuming food. The basic assumption, as with all optimality models, is that the animal makes perfect decisions based on the information available. This assumption, along with the extreme simplicity of many attempts to model foraging behaviour, has led some to dismiss the theory as irrelevant. In terms of predictive power, it’s difficult to argue with this position: foraging is hard to quantify in anything other than the most simplistic and contrived of scenarios. For me, however, the beauty of the theory is not in its predictive power, but in the rich vocabulary it offers for describing behaviour and the breadth of its application. Foraging is not just about food, but about the exploitation of any resource within any ‘space’ and the vocabulary that has developed alongside optimal foraging theory offers fascinating new perspectives on the fields of human memory and data search.

Charnov (1976)1 made an influential early contribution to foraging theory when he considered how a predator should behave when foraging for prey items that occur in patches. Charnov suggested that there are two main concerns: how long to spend in a patch and how long to spend looking for the next patch. On the face of it there’s no choice at all: the predator should spend all of its time within patches as no food is available when travelling from one patch of prey to another. However, Charnov assumed that the rate of return decreases with time spent in a patch due to prey items being consumed. As a consequence, the predatory animal spends progressively more time searching for the next prey item. Clearly, there comes a point when search time within the current patch is so long that the patch should be abandoned in favour of a fresh one. Charnov modelled behaviour and derived a rule to determine the optimum point at which the current patch should be abandoned: the Marginal Value Theorem. In his words it occurs when, “… the marginal capture rate in the patch … drops to the average capture rate for the habitat” (p. 132). In other words, a predator should leave a patch when the rate of return of prey items falls to the average rate for all patches available to the animal. Following this rule ensures that the costly business of travelling between patches, for no immediate return, is offset by ensuring that the animal always forages in prey-rich patches.

Charnov’s work highlighted the fact that foraging isn’t a continuous process and that an animal must monitor the current rate of return to ensure it best exploits the available resources. But what if that resource is not food, but information? There are two important differences between physical resources and information. The first lies in how resource acquisition is measured. It is relatively easy for economists and ecologists to find out how much money or food has been collected either by measuring what has been acquired or inferring this from what is left over. Information, by contrast, does not build up in the same way and certainly doesn’t leave any leftovers. The second difference manifests itself when it comes to choosing a suitable currency, i.e. the value of the resource. In the case of food the currency is the nutritional content; food has intrinsic value and there is generally no dispute over currency assumptions. In the case of money the question of currency disappears entirely. Information, on the other hand, is fundamentally different because its value is based on the ever-changing qualities we ascribe to it. Choosing an information currency is therefore a major hurdle if we want to apply an optimality model of acquisition to information gathering. Happily, lots of people have found clever ways around these problems.

 Information foraging

Sandstrom (1994)2 provided an early description of what is now called information foraging (to my knowledge, predated only by a Russell, Stefik, Pirolli and Card’s 1993 conference paper3). In the article, she describes similarities between hunter-gatherers and scholars and suggests that the mathematical models developed to describe and predict behaviour in foraging animals could be adapted to the purposes of understanding how scholars gather information. She chose ‘novelty of citation’ as the currency for an optimality model of scholarly information foraging, the goal being to maximise novelty. Sandstrom assumed that finding and exploiting novel information is highly desirable because it demonstrates the scholar’s experience and expertise with the literature.

Sandstrom’s use of novelty as a currency is interesting because it also solves the problem of measuring resource acquisition. As mentioned above, food and information differ in that food is used up during the act of foraging, an important constraint assumption in models. Sandstrom suggested that the use of novelty as a currency provides a similar constraint assumption because a scholarly citation loses its novelty the more it is cited, thus Sandstrom’s approach can be mapped more closely onto readymade models from behavioural ecology. Sandstrom was therefore able to create a plausible theoretical framework for investigating the topic of information gathering by scholars from a completely new perspective.

The scope of Sandstrom’s application of the theory is relatively narrow. However, Pirolli and Card (1999)4 demonstrated that the foraging analogy could be applied to a much broader range of information-search scenarios. They termed this approach ‘information foraging theory’ and used a new currency assumption: the maximisation of the quality of the information gathered. In my opinion, the most interesting outcome from their work is the concept of patch enrichment. Information is fundamentally different to food in terms of how we manipulate and extract what we need from it. They pointed out that, like food, information can be thought of as occurring in patches, but, unlike food, we can modify these patches to better suit our needs. The examples they use are of situations in which information is collected in order to research a particular topic. The process is one of refinement. People don’t typically read all available information; rather, they look for relevant sources and highlight potentially informative items. These items might themselves be sorted into sub-topics and therefore undergo further refinement. The point is that the initial patches are transformed into new patches with higher rates of return and therefore lower search times which helps the forager to reduce the chances of investing time in poor quality sources of information.

 Cognitive foraging

Hills (2006)5 gives an account of the evolution of goal-directed cognition from its ancient behavioural precursors. The account moves from area restricted search in invertebrates to more abstract learning such as operant conditioning and finally to the kind of highly abstracted internal search that humans engage in when accessing memory for episodes and concepts. He further suggests that dopamine could be a common driving force behind these behaviours. The following is Hills’ own summary of the central idea:

Molecular machinery that initially evolved for the control of foraging and goal-directed behavior was co-opted over evolutionary time to modulate the control of goal-directed cognition. What was once foraging in a physical space for tangible resources became, over evolutionary time, foraging in cognitive space for information related to those resources (2006, p.4).

Hills reminds us that successful behavioural strategies tend not to undergo abrupt and wholesale changes over evolutionary time and, consequently, there is much that we can learn about ourselves from the behaviour of even the simplest organisms. He also clearly sets out how his ideas can be tested empirically. Hills, Todd and Goldstone (2008)6 reasoned that if cognitive and spatial foraging both rely on the same underlying neural architecture then it should be possible to find behavioural similarities between the two. For example, if an individual has a foraging style that is peculiar to them, such as the tendency to perseverate, we would expect this to be the same whether they are doing cognitive or spatial foraging. Furthermore, because animals often adapt their behaviour to whatever resource distribution they are faced with, we might expect that engaging in one kind of foraging would result in a behavioural after-effect when engaging in the other kind of foraging.

They investigated this by asking participants to complete a computer based spatial search for resources that were either patchily or evenly distributed. This acted as a priming condition for the subsequent cognitive foraging task in which participants were required to make as many words as possible from a set of letters in a scrabble-like game (based on a game developed by Wilke, 20067). Each set of letters represented a patch and a between-patch delay was imposed when requesting a fresh set of letters, analogous to the between-patch travel time in food foraging. The letter sets are a clever solution to adapting foraging theory to cognitive search: they allowed for a simple currency (number of correct words generated); they are depletable; and they can be delivered in patches. The researchers found that participants who had searched in the patchy spatial environment persisted with letter sets for longer. These people also showed longer giving-up times; in other words, they waited longer following their last correct word submission before requesting a new set. In addition to this, they found that the foraging habits of individuals were consistent between the tasks so, irrespective of whether they had experienced the patchy or even-spread spatial task, an individual’s tendency to explore more in spatial search was mirrored by a tendency to explore more in the scrabble task.

Whilst this experiment doesn’t prove that different types of search mechanism have a common evolutionary origin, it offers tantalising support and their explanation is, to me at least, reasonably persuasive:

We believe that the general search process produces priming across domains because it operates on expectations regarding environment structure that develop during performance of a task, not simply because the individual perseverates on the behavioral strategies that were used to solve the first task (p.807).

Whatever the ultimate truth of the matter, it is at least refreshing to see new approaches to psychology and neuroscience that move beyond the computer metaphor of the brain. Cognitive foraging and other approaches such as embodied cognition are exciting because they take into account the long evolutionary history of organisms. Even if we don’t have models with high predictive accuracy, it is at least promising that researchers are attempting to describe the brain and animal behaviour in terms that do not treat the agent as a finished product.


  1. Charnov, E. L. (1976). Optimal Foraging, the Marginal Value Theorem. Theoretical Population Biology, 9, 129-136. 

  2. Sandstrom, P. E. (1994). An optimal foraging approach to information seeking and use. Library Quarterly, 64, 414-449. 

  3. Russell, D.M., Stefik, M.J., Pirolli, P., & Card, S.K. (1993). The cost structure of sensemaking. Proceedings of the InterCHI Conference on Human Factors in Computing Systems, 269-276. New York: Association for Computing Machinery Press. 

  4. Pirolli, P. & Card, S. (1999). Information Foraging. Psychological Review, 106, 643-675. 

  5. Hills, T. (2006). Animal foraging and the evolution of goal-directed cognition. Cognitive Science, 30, 3-41. 

  6. Hills, T., Todd, P.M., Goldstone, R.L. (2008). Search in external and internal spaces: evidence for generalized cognitive search processes. Psychological Science, 19, 676-682. 

  7. Wilke, A. (2006). Evolved responses to an uncertain world. PhD Thesis, Department of Education and Psychology, the Free University of Berlin. 

 
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