Optimal Foraging

Update: the birth of information foraging studies

2010-01-05T00:04:00.002Z

In a previous post I wrote that Sandstrom (1994) was, to my knowledge, the first paper to explicitly link foraging theory with information search. Since that post was published, Pamela Sandstrom has written to me to point out that she isn't the only person to have a claim to being the first: a conference paper by Russell, Stefik, Pirolli and Card (1993) predates her own journal article. From what she tells me, it seems that Peter Pirolli and she probably hit on the idea at about the same time; a nice resolution in my opinion. Many thanks to Pamela for pointing this out and, of course, for reading!

References

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

- 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.

Prey discrimination and information scent

2010-01-03T01:49:00.003Z

All animals have limits as to what they are prepared to include in their diet (see diet-width); however, being picky brings with it the need to discriminate. Animals must choose between different food items and patches in order to make best use of the time they spend foraging. Whilst prey and patch choice behaviour are of interest to ecologists (for an accessible review of decision making see Chittka, Skorupski & Raine, 2009), they are of central importance to the study of information foraging because there is so much to gain from encouraging people to choose particular sources of information. Pirolli and Card (1999) recognised that information foragers base their choices on short quality indicators that are easy to process and that provide clues as to whether a particular source of information is worth investing time in: these indicators provide what Pirolli and Card call 'information scent'. If you want to see a good example of information scent, look no further than a set of Google search results.

References

- Chittka, L., Skorupski, P. & Raine, N. E. (2009). Speed–accuracy tradeoffs in animal decision making. Trends in Ecology & Evolution, 24(7), 400-407.

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

Dollar auctions and giving-up time

2009-11-09T20:29:00.002Z

The economist Martin Shubnik (1971) is responsible for a fiendish yet rather entertaining game called the dollar auction. I recommend trying the game next time you're out with friends, so here are some brief instructions and a couple of things to look out for:

Put a pound up for auction and invite some friends to bid for it (two works best)
They may bid any amount and could technically buy the pound for just one penny but, unlike in traditional auctions, the agreement is that both winner and loser must pay
Because the eventual loser must pay money in return for nothing, there is a large incentive for all parties to keep bidding once they have made their first bid
The moment someone bids fifty pence you are guaranteed to earn your pound back on the next bid; any further bids represent pure profit
If there is a bid of one pound, any further bid will commit the bidders to pay more than one hundred pence in order to win the pound! Whilst this is clearly irrational, on a bid-by-bid basis it is a more attractive option than paying a similar amount on a losing bid.

I was first introduced to this game when reading William Poundstone's excellent book, Prisoner's Dilemma (1993). Poundstone points out that we encounter similar scenarios all the time, such as when a company puts our phone call on hold or we wait in a queue for a ride at a theme park. In fact, examples are so exasperatingly common that I have found the term 'dollar auction' to be a depressingly useful bit of shorthand for explaining some of life's most irritating encounters. However, it occurred to me recently that dollar auctions aren't just a frustrating aspect of modern life, they are a frequent problem for foraging animals as they address the question: when to give up?

Giving-up time refers to the period between the last successful capture of a prey item and the time at which an animal decides to leave a foraging patch (McNair, 1982). Optimising giving-up time is an interesting alternative strategy to optimising within-patch time (also known as residence time). In both cases the animal must develop some idea of the distribution of resources within a patch and act accordingly but in the case of giving-up time the animal need only then keep track of the time since finding its last prey item when deciding whether to continue foraging in the current patch. This decision bears a striking resemblance to decisions in dollar auctions. For example, if a bird has been successfully foraging for ripe fruit in a tree but found nothing over the past couple of minutes, it has two options. It could leave the tree, accept that it has wasted time foraging for no return and incur the cost of travelling to the next tree in the hope of finding fruit more easily. Alternatively it could remain in the current tree in the hope that the recent difficulties don't represent a severe overall decline in resources.

References

- McNair, J. N. (1982). Optimal giving-up times and the marginal value theorem. The American Naturalist, 119, 511-529.

- Poundstone, W. (1993). Prisoner's dilemma: John von Neumann, game theory, and the puzzle of the bomb. Oxford University Press.

- Shubik, M. (1971). The dollar auction game: a paradox in noncooperative behavior and escalation. The Journal of Conflict Resolution, 15, 109-111.

Support for cognitive foraging

2009-10-29T01:28:00.011Z

Hills, Todd and Goldstone (2008) 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.

Their experiment required 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. 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. They found that those 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.

When I first read Hills’s (2006) paper about the origins of goal directed behaviour, I was not optimistic about the possibility of any experimental verification. Whilst this experiment doesn’t prove that different types of search mechanism in the brain have a common evolutionary origin, it offers some serious support and their explanation for the results is not unreasonable:

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 (Hills, Todd & Goldstone, 2008, p.807).

For me, however, the best thing is the beautiful application of Andreas Wilke’s (2006) clever choice of an information foraging resource; the letter sets allow for a simple currency (number of correct words generated), are depletable, can be delivered in patches and are easy for participants to use.

References

- 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.

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

Cognitive foraging

2009-10-14T21:51:00.006+01:00

I've already written a bit about how useful optimal optimal foraging theory is for structuring research into resource acquisition and information search. Well, a further application for the foraging perspective came to my attention last year and it is both novel and thought provoking. In his 2006 paper, the psychologist Thomas Hills gives his account of the evolution of goal-directed cognition from its behavioural precursors. The account moves from area restricted search in invertebrates to more abstract resource acquisition learning such as operant conditioning and finally to the kind of highly abstracted internal search that humans engage in as we search our memories for concepts and ideas. He further suggests that dopamine could be a common driving force behind these behaviours. The following is Hills's 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).

There are loads of reasons to read the paper such as the clever incorporation of neuroscience, ecology, evolutionary theory and cognitive psychology; but, for me, something very simple stood out. Hills reminds us that successful behavioural strategies tend not to undergo abrupt and wholesale changes over evolutionary time just as physical characteristics do not 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, something I will come to in my next post.

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

Area restricted search and preytaxis

2009-10-01T21:55:00.006+01:00

Foraging strategies don't come much more basic or effective than area restricted search. The key to this strategy is that, even with very little in the way of a nervous system, an animal can respond effectively to an abundant food resource simply by slowing down and turning more frequently. This simple behavioural response ensures that the animal is more likely to fully exploit a patch of food because its behaviour reduces the chances of it leaving that patch.

It is rather difficult to attribute the idea of area-restricted search to anyone in particular. This is probably due to how simple and ubiquitous the strategy is; that is to say, anyone who has observed foraging animals would have a good chance of witnessing such behaviour. The earliest use of the term that I know of is Tinbergen, Impekoven and Franck (1967). However, the paper that really stands out for me is by Peter Kareiva and Garrett Odell (1987) who give a fine explication of what it is for an animal to engage in area restricted search, in their detailed coverage of predator dispersal models. An interesting conclusion they draw from their own model and experimental work is that when there are mulitiple animals engaging in area restricted search, we should sometimes expect the emergence of what they term 'preytaxis'. In other words, the interactions of lots of predators, all following simple rules, will sometimes result in the emergence of group behaviour whereby the swarm "flows toward regions of high prey density" (p.265).

References

- Kareiva, P. & Odell, G. (1987). Swarms of predators exhibit "preytaxis" if individual predators use area-restricted search. The American Naturalist, 130, 233-270.

- Tinbergen, N., Impekoven, M. & Franck, D. (1967). An experiment on spacing-out as a defence against predation. Behaviour, 28, 307-321.

Patch enrichment in information foraging

2009-09-27T23:13:00.005+01:00

Ecologists have developed a rich vocabulary and sophisticated mathematical models for describing the foraging behaviour of animals. Like Pamela Sandstrom before them, Peter Pirolli and Stu Card recognised that there are striking similarities between food foraging behaviour and the way humans search for information and that the hard work of ecologists could be put to wider use. Pirolli and Card (1999) were the first to term this approach ‘information foraging theory’. They looked at the way people search for information with the currency of interest being the maximisation of the quality of the information gathered.

An interesting aspect of their work is the concept of patch enrichment. Unlike Sandstrom, they embraced the abstractness, and therefore the flexibility, of information. 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, it 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 of relevant information and therefore lower search times which helps the forager to reduce the chances of investing time in poor quality sources of information.

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

From robotic foraging to robotic feeding

2009-09-22T13:46:00.002+01:00

For a while now people have been interested in producing foraging behaviour in robots; the Bristol Robotics Laboratory is an excellent example of this. Whilst I love that these projects are informed by foraging theory, the unreasonable expectations that come from exposure to science fiction leave me a bit disappointed that the robots aren't actually eating anything. Well, imagine my delight when I found out that Robotic Technology Incorporated are working on EATR (Energetically Autonomous Tactical Robot Project), a robot that will actually eat stuff: twigs, dry grass and other small pieces of organic matter, to be precise. It's very early days for the project but, if they are successful (a big 'if'), we might be able to look toward a future of detritus fueled robots.

The birth of information foraging studies

2009-09-17T20:38:00.003+01:00

I could be wrong but I believe that Pamela Sandstrom's (1994) paper about foraging for information is the first bona fide study into what is now called information foraging. In the article, she describes similarities between humans as hunter-gatherers and scholars collecting information. She then goes on to suggest ways 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. In order to make the analogy stick, it was necessary for her to choose a currency by which information might be measured. She decided that novelty of citation was a suitable currency for an optimality model of scholarly information foraging; the goal being to maximise novelty. Sandstrom assumed that, for a scholar, using novel information is highly desirable because it has the effect of demonstrating the scholar’s experience and expertise with the literature.

A particularly interesting aspect of Sandstrom’s use of novelty as a currency is that she chose it because it solves another problem when adapting optimal foraging theory to the study of information search. As mentioned in my previous post, food and information differ in that food is used up during the act of foraging, an important constraint assumption in models. Sandstrom suggests that the use of novelty as a currency provides a similar constraint assumption because the citation of another’s work loses its novelty the more it is cited. The upshot of this is that Sandstrom’s rendering of information foraging can be mapped more closely onto readymade models from behavioural ecology as the assumptions are, in her view, very similar. The overall effect of Sandstrom’s approach was to create a plausible theoretical framework for investigating the topic of information gathering by scholars from a completely new perspective.

References

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

Information foraging: the fun is in stretching an analogy

2009-09-15T00:08:00.006+01:00

There are two key differences between food, a physical commodity, and information, an abstact commodity, and these are a real headache for anyone wanting to use optimal foraging theory to investigate information search and gathering:

The first difference is 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. By contrast, information does not build up in the same way and certainly doesn't leave any leftovers. Measurement is, consequently, an extremely challenging problem for experimental design.
The second difference manifests itself when it comes to choosing a suitable currency. In the case of food the currency is primarily energy but will also include some other dietary elements like vitamins, with animals seeking to maximise these commodities. The point is that food has intrinsic value and there is generally no dispute over currency assumptions other than how inclusive they are within a particular model; in economics the currency assumption is almost tautological. Information is fundamentally different to both food and money in this respect because its value is based on the ever changing qualities we ascribe to it and the utility of these qualities is itself dynamic. Choosing an information currency is therefore another difficulty when applying optimality models of acquisition to information gathering.

Happily, lots of people have found clever ways around these problems but I felt it necessary to show just how challenging it is to use the foraging framework when studying information before I wade in with a load of posts on information foraging experiments.

The three golden assumptions of foraging theory

2009-09-14T22:53:00.006+01:00

Stephens and Krebs's, 1986, monograph, Foraging Theory, has been the definitive text on the subject for the past twenty years. This is true for all sorts of reasons, but for me the book’s finest feature is the way they clearly set out how optimality modelling can be applied to any situation in which we want to understand decisions. In particular, they explain three types of assumption which should be identified:

The decision assumption refers to a specific aspect of an agent’s behaviour that requires a decision to be made. For example, in the marginal value theorem, this would be patch abandonment: specifically when to leave a patch. It is an assumption because it relies on the supposition that the choice of when to leave the patch is related to the endeavour of energy acquisition.
The currency assumption is a postulation as to what constitutes good performance. In the marginal value theorem, this corresponds to energy gain.
The constraint assumption includes “(…) those factors that limit and define the relationship between the currency and the decision variables” (p. 9). In other words, potentially anything that is related to achieving that which is defined by the other two assumptions but, in practice, only those factors deemed to be most important. In the marginal value theorem this would include, for example, the assumption that the animal doesn’t return to a previously foraged patch and that the resources within a patch decrease with time spent foraging.

This procedure of defining terms isn't hard-boiled for the sake of it; it's extremely valuable when approaching a new topic. Chalmers (1996) refers to this part of the discovery process as explication and differentiates it from the process of explanation which occurs once we are clear about what our questions are.

References

- Chalmers, D.J. (1996). The conscious mind: In search of a fundamental theory. Oxford: Oxford University Press.

- Stephens, David. W. & Krebs, J. R. (1986). Foraging theory. Guildford: Princeton University Press.

Diet-width and the distinction between search and handling time

2009-09-13T22:28:00.006+01:00

Different phenotypes have different abilities at harvesting resources, and the resources are distributed in a patchwork in three dimensions of the environment (MacArthur & Pianka, 1966, p.603).

MacArthur and Pianka demonstrated that the spatial distribution of food (its ‘patchiness’) in the environment should have an effect on an animal’s diet. This idea was based on their important insight that the time an animal spends foraging can be split into two distinct periods: search time, which is the time it takes the animal to find its next prey item; and what is today known as handling-time, which they defined as the time it takes to pursue, capture and eat a prey item once it has been chosen. The difference between the two isn’t immediately apparent. Why, for example, does searching for prey not count as handling-time since the search ultimately results in eating a particular prey item? The reason, according to MacArthur and Pianka, is that the search element of the foraging process could result in the consumption of any number of individual prey items; each item is not investigated one at a time, instead a specific item is picked from a choice of many. By contrast, the handling time refers to a period necessarily devoted to a single prey item.

The result of the distinction between the two components of foraging time was that it allowed them to make broad predictions as to an animal’s diet-width; that is to say, the number of different kinds of food items the animal should be prepared to include in its diet. They suggested that the costs to an animal can be thought of as the energetic costs associated with search and handling; the gains are represented by the energy stored within each prey item. On the assumption that an animal’s diet is determined optimally, they reasoned that an animal should only increase its diet-width to include lower quality items if, in doing so, the energy gain is higher than the current average energy intake. By this reasoning, changes in handling time and search time should affect behaviour with respect to diet choice. This conclusion becomes obvious when we consider extreme hypothetical examples, for instance, if the search time is low but handling-times are extremely high, the animal can afford to ignore many prey items because alternatives are abundant and it will have to invest a lot of effort in the items it does choose. By contrast, if search times for the animal are very high and handling-times of potential food items are comparatively low, the animal should have a large diet-width, i.e. it'll eat whatever it can find.

References
- MacArthur, R. H. and Pianka, E. R. (1966). Optimal use of a patchy environment. The American Naturalist, 100, 603-609.

Support for the marginal value theorem

2009-09-13T21:27:00.007+01:00

Cowie (1977) used wild great tits and artificial trees to investigate the effect of travelling time between patches on, amongst other things, time spent foraging within a patch. Experimental patches were created by putting mealworm in containers full of sawdust and placing the containers in the trees. The travel time between patches was manipulated by covering the containers with lids that were either relatively easy or relatively difficult to remove. Cowie found that the birds in the condition with the high inter-patch travel time foraged for significantly longer periods within each patch, in line with the prediction from the marginal value theorem.

References
- Cowie, R. J. (1977). Optimal foraging in great tits (Parus major). Nature, 268, 137-139.

The marginal value theorem

2009-09-13T21:08:00.010+01:00

The evolutionary ecologist Eric Charnov made an influential contribution to the foraging literature when he considered how a predator should behave when foraging for prey items that occur in patches. With respect to how a predator allocates its time, Charnov suggested that there are two main concerns: how long it spends foraging within a patch and how long it spends looking for the next patch. On the face of it there is no choice at all: the predator should spend all of its time within patches as, after all, no food can be had when travelling from one patch of prey to another. However, Charnov assumed that the rate of return of prey items would decrease with time spent in a patch due to the prey items being consumed. As a consequence of this, the predatory animal spends progressively more time searching for the next prey item. Clearly, there must come a point when search time within the current patch is so long that it should be abandoned in favour of a fresh one, notwithstanding the expenditure of energy and guaranteed lack of foraging that travelling between patches entails. In fact, Charnov modelled the patch choice problem and derived a rule to determine the optimum point at which the current patch should be abandoned: the rule has come to be known as 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 the patch it is currently foraging in when the rate of return of prey items falls to the average rate of return for all of the 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.

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

Welcome to my new website

2009-09-13T09:44:00.002+01:00

Optimal Foraging is less than a day old and, as you can see, pretty bereft of foraging content; please bear with me! I will be adding links and posts regularly over the next few weeks and hopefully start to build up a useful resource for those who are interested in optimal foraging and information foraging. If you have any ideas about new content I'd love to hear them.

Privacy policy

2009-09-12T22:41:00.003+01:00

This website uses Google Analytics, a web analytics service provided by Google, Inc. (“Google”). Google Analytics uses “cookies”, which are text files placed on your computer, to help the website analyze how users use the site. The information generated by the cookie about your use of the website (including your IP address) will be transmitted to and stored by Google on servers in the United States . Google will use this information for the purpose of evaluating your use of the website, compiling reports on website activity for website operators and providing other services relating to website activity and internet usage. Google may also transfer this information to third parties where required to do so by law, or where such third parties process the information on Google's behalf. Google will not associate your IP address with any other data held by Google. You may refuse the use of cookies by selecting the appropriate settings on your browser, however please note that if you do this you may not be able to use the full functionality of this website. By using this website, you consent to the processing of data about you by Google in the manner and for the purposes set out above.