[Science] Ideal free ducks.

It’s been a while since I’ve had the chance to sit down and write another of these posts, but it’s been bugging me and so I’ve set aside some time today to try and to it justice.  This time, I’m going to look at a great experimental paper from the early ’80s that shows how you can do good science by just keeping your wits about you:

D. G. C. Harper. Competitive foraging in mallards: ’ideal free’ ducks. Animal Behaviour, 30:575–584, 1982. doi:10.1016/S0003-3472(82)80071-7

An important aspect of social foraging – foraging in which the decisions of one animal hinge upon the decisions of all of the other animals in the group – is the exploitation of patchy resources.  When animals are faced with multiple patches of food to choose from, how should they distribute themselves to maximize individual gain?  One of the more influential models in this area has been the ideal free distribution (Fretwell and Lucas, 1969), which when stated in words goes something like this:  in a situation with multiple patches of a resource (we’ll discuss food, though the idea is generalizable to other types of resources), individuals can do best by distributing themselves among the available patches according to patch profitability so that each individual’s payoff is the same.  Here’s an example to clarify what I mean.  Take the example of three hypothetical patches, where patch A gives out 1 food item per minute, patch B gives out 2 food items per minute, and patch C gives out 3 food items per minute. Now say that we have six ducks sitting in the middle, trying to determine how to distribute themselves so that they can maximize their individual food intake.  Here’s what this would look like, hypothetically:

How do they do it?  Well, if they are ideal (able to perfectly assess patch quality) and free (able to choose whatever patch they like without interference) ducks, then they would probably spread out like this:

Now, assuming that the ducks consume food at equal rates, each duck will have the maximum possible individual food intake of 1 food item per minute.  A little imagination should show that any other distribution of ducks only means that some ducks are better off to switch to the above arrangement – for example, if one of the ducks from patch B found itself at patch C, then each duck there would be getting less than 1 food item per minute, and the lone remaining duck at patch B would be getting more than 1 food item per minute.  In this situation, it would be a better decision for one of the four ducks at patch C to move to patch B, thus increasing their own intake rate (which has the effect of improving the intake rates of the ducks at patch C, but don’t mistake that for a group selection effect – the duck making the switch is acting solely in its own best interest).

What if individuals aren’t ideal and free?  Well, let’s violate one of the assumptions and see what happens.  For example, suppose that one of the ducks is a super-duck, which can fend off its fellow ducks and monopolize a patch by itself.  Then the other ducks aren’t free to sort themselves in the way that would maximize their intake and would have to settle for something like this (our super-duck is (did you guess it?)  red, and a little bigger too):

This is an example of the despotic model.  Now the duck at patch C is able to do better by monopolizing that patch and the other five ducks have to do the best they can with the lesser resources of patches A and B.

[ Note:  the above examples are assuming renewable patches, mainly because Harper’s experimental set up uses them.  But the IDF would work just as well for non-renewable patches, though adjustments to the model might have to be made for handling and travel times. ]

Now, the question that Harper found himself asking was this:  how do we know if animals are conforming to an ideal free distribution (IDF from here on).  To know that, we have to be able to measure the payoff that each individual is receiving to see if they are all receiving an equal share.  When Harper wrote the paper, nobody had managed to do this yet.  Some lab experiments had been done, such as using sticklebacks in the lab as Manfred Milinski had, but Milinski hadn’t recorded the individual payoffs so there was no way to prove that the sticklebacks were using the IDF, though they did distribute themselves according to patch profitability.

To take the next step, Harper took what he had to hand and did some cool science with it.  In his own words:

In my study I have been throwing pieces of bread to ducks on a garden pond and recording both the distribution of the birds between food patches and the individual food intake of some of the ducks at one of these patches (p. 575).

The paper itself contains four experiments, and though each of them is equally intriguing I don’t wish this recap of the paper to get out of hand.  Therefore, I am going to describe the methodology and the first experiment, and briefly describe the rest of the results but leave the reader to view the rest of the paper.  I strongly suggest that if you’re interested in this subject you read the rest of the paper.

Experimental setup

Similar to the pictures above, Harper found a group of ducks – 33 in total, though only 24 were immediately recognizable and so they were the ones tracked – living on a lake in the Cambridge Botanic garden during the winter of 1979-80.  Two observers threw pre-cut and pre-weighed bread into the water at points on the lake 20 metres apart, which were labelled site A and B.  Profitability of the patch could be manipulated by changing the rate at which the bread was thrown into the water, or by changing the weight of the bread (2 or 4 grams each).  The distribution of the ducks was recorded over time as the bread was thrown into the water.  This allowed Harper to track the individual payoffs to each duck.

Results from Experiment 1

In experiment 1, Harper set up the site profitabilities at 50-50 so that the flock should split themselves accordingly;  remembering that there were 33 ducks living on the pond, he expected that 16.5 ducks should go to each patch.  Obviously, this would mean that there would be 17 ducks at one patch and 15 at another, so he recorded the mean number of ducks at each patch over multiple trials (29 in total).  The results are in Figure 1 of the paper, which I’ve reproduced here:

The graph shows that the ducks did indeed sort themselves out along the lines predicted by the IDF:  since the patch profitability was equal, half the ducks should have gone to patch A and half should have gone to patch B, and this is what we see from the graph.  A similar picture was obtained when he manipulated the patch food ratios to be 2:1 – again, the ducks set themselves up in a 2:1 ratio.  Further, as evidenced by the graph, the ducks assessed the patch profitabilities quite quickly, since equilibrium was achieved by the time that about 90 seconds had elapsed.

But is that all there is to the story?  No:  if you recall from above, to be an IDF, individual payoffs must be equal.  That is, all the ducks must have received the same amount of bread.  Did they?  Harper found that the answer to this was no, they didn’t.  In fact, by recording the individual payoffs he was able to determine that several of the ducks ate a disproportionate amount of food, meaning that payoffs were higher to some ducks than others.  This violates one of the key IDF assumptions, and validates Harper’s criticism of previous studies;  studies like the one done by Milinski on the sticklebacks seemed to show an IDF-like distribution of foragers just like the one observed here, but by recording individual payoffs Harper was able to show that the IDF behaviour was only skin-deep (as it were).  In fact, the ducks’ behaviour followed that of a despotic model like the one discussed above, though unlike above it wasn’t patch access that was monopolized but food intake.

The remaining results: experiments 2, 3, and 4.

Why did some ducks eat more food than others?  Harper hypothesized that dominance might be a key relation here, and in experiment 2 he was able to determine the dominance rank of the recognizeable birds and correlated it to the (heavy) skew in food intake that observed.  In fact, six dominant individuals were able to monopolize up to 60% of the available food items!  In experiments 3 and 4, Harper refined and tested further hypotheses on how the ducks assessed patch profitabilities and showing that the distribution of ducks was indeed sensitive to the presence of dominant ducks at a particular patch.

Why do we care?

Unlike the paper that I tackled in my first in-depth post on peer-reviewed research, this paper is less well known to the wider biological audience, though it is reasonably well-cited in foraging research.  But the reason I chose to write about this paper is not that it was a famous paper, but that it is an example of good science.  It identified a weakness in previous work that needed to be dealt with, and used a simple and robust methodology to thoroughly explore the issue while highlighting complex behaviour in a seemingly simple system.  In doing so, it advanced our knowledge on the validity of the ideal free distribution model in real populations, in an experimental setting with good ecological validity.  As the conclusion to the paper states:

The experiments described above mimic the problem that ducks face every day when being fed by the public. Except when being controlled by experimenters the rate of food item input is likely to be erratic and to be an imperfect indication of patch profitability.  However it has the advantage of being detectable from a distance, and the results of experiment 4 show that other cues can be used by the ducks to correct their assessment of the patch profitability ratio.  It is clear that the behaviour of ducks being fed bread on a park pond is more complicated than might be thought.

Amen.

Acknowledgements

Photo credit for the duck silhouette:  Silhouettes Clip-Art.

References

S. D. Fretwell and H. L. Lucas. On territorial behavior and other factors influencing habitat distribution in birds: I. theoretical development. Acta Biotheoretica, 19(1):1–36, 1969.

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