Are pigeons ideal-free foragers?


Ideal free foraging theory predicts that a group of foraging animals should distribute themselves between two patches in a ratio proportional to the availability of food in the two patches (the Ideal Free Distribution), assuming that foragers are competitively equal, have perfect knowledge, and are free to move between patches with negligible travel costs. However, violations of these assumptions are common, and may result in 'undermatching' between foragers and food availability (disproportionately few foragers in the patches of highest food availability) or 'overmatching' (a disproportionately large number of foragers in the richest patches).

Controlled feeding experiments were conducted in which peanuts were thrown continuously to free-living feral pigeons (Columba livia), at two sites 20 metres apart in urban parkland. The overall 'sensitivity' (s) of the pigeons to food availability at the sites was 0.46, indicating significant undermatching (in an Ideal Free Distribution, s=1). This broadly agrees with the findings of Baum & Kraft (1998), who also observed undermatching in the distribution of foraging pigeons, due to the 'despotic' behaviour of dominant birds that congregated in the richer foraging patches (although the degree of undermatching in their experiments was less dramatic, perhaps because their experimental setup created less intense competition between birds).

The sensitivity was found to be higher in experiments in which the frequency of food throwing varied between sites (s=0.57) than in experiments in which the quantity of food in each throw varied (s=0.34). This may have been because competition between birds was more intense when several peanuts were thrown simultaneously.



In a group foraging situation, in which animals are competing for a limited food resource, the Evolutionarily Stable Strategy is one in which each member of the group acts to maximise its own individual energy intake. Given two patches of differing food availability, this will theoretically result in animals distributing themselves between the patches in such a way that...

N1 / N2 = r1 / r2

...where N1 and N2 are the numbers of individuals present in the two patches, and r1 and r2 represent the availability of food in the patches. In other words, foraging animals will distribute themselves between patches in proportion to the amount of food available at each patch. This is known as the Ideal Free Distribution. In this distribution, each animal receives an equal food intake (assuming equal competitive ability) and no individual can benefit by altering its strategy. It can be shown, theoretically and by simulations, that this optimal distribution can arise out of the behaviour of animals acting individually in response to their own hunger, and requires no co-ordination at the level of the group (Beauchamp 2000, Ollason & Yearsley 2001).

The behaviour of foraging animals can only be expected to conform to the Ideal Free Distribution if the following assumptions are fulfilled (Kennedy & Gray 1993, Ollason & Yearsley 2001):

  • All individuals are acting to maximise their food intake.
  • All individuals feed at the maximum possible rate.
  • All individuals have perfect knowledge of the availability of food at different patches.
  • All individuals are free to search wherever they wish, and the cost of travel between patches is negligible.
  • All individuals have equal competitive ability.
  • An individual's food intake decreases as a function of competitor density.

In reality, these assumptions are rarely met (Milinski & Parker 1991). Deviations from the simple Ideal Free Distribution are described by the equation...

log (N1 / N2) = s log (r1 / r2) + log b which the parameters b and s specify bias (any overall tendency for animals to prefer one feeding site over the other regardless of food availability) and sensitivity (the extent to which animals respond to differences in the availability of food between the two patches), respectively. In a perfect Ideal Free Distribution, b and s will both have values of 1. A sensitivity of less than 1 indicates undermatching, with fewer animals than expected in the patch of higher food availability, and a sensitivity greater than 1 indicates overmatching, with more animals than expected in the patch of higher food availability (Kennedy & Gray 1993, Ollason & Yearsley 2001).

Many real-life studies of foraging animals have found a significant degree of undermatching - fewer individuals than predicted were found in the patches of highest food availability (Kennedy & Gray 1993). In some cases - such as in the experiments carried out by Harper (1982) on mallards - this was clearly due to the 'despotic' behaviour of dominant individuals that congregated in richer patches and took a disproportionate share of the food. The presence of these despotic individuals made the richer patches less profitable than they otherwise would have been for competitively-weaker members of the group.

Baum & Kraft (1998) conducted experiments in which pigeons were provided with a food at two different sites, and also observed significant undermatching in their distribution. When pigeons were fed from small bowls, creating intense competition, the degree of undermatching was found to be greater (s=0.38) than when food was spread over larger areas (s=0.79). This supports the idea that undermatching results from competition between individuals.

The pigeon is a suitable animal in which to study competitive foraging behaviour because it is a "gregarious, opportunistic generalist" (Inman et al 1987) - a species that is likely to have evolved strategies that enable it to maximise its energy intake in a variety of foraging situations, and that take into account the effect of competitors. Learning, as well as evolution, may play a part in the development of foraging techniques, and the ability of pigeons to learn behavioural strategies was demonstrated by Palamete & Lefebvre (1985). The hypothesis that pigeons have developed feeding strategies that take into account the presence of competitors is supported by the experiments of Plowright & Landry (2000), which showed that, when pigeons are given a choice of food types, their feeding preferences are altered by the presence of a competitor.

Overmatching - a disproportionately high number of individuals congregating in patches of greater food availability - may occur if the costs of travel between patches are significant (Kennedy & Gray 1993, Beauchamp 2000). This is because the theoretical effect of including travel costs in the equation is to decrease the profitability of both food patches by an equal amount (represented in the following equation by k), and subtracting a constant from both sides results in a more extreme ratio:

N1 / N2 = (r1 - k) / (r2 - k)

The work of Baum & Kraft (1998) on pigeons supports this prediction. In their experiments, the distribution of pigeons between feeding sites showed a higher sensitivity (in other words, a greater tendency towards overmatching) when the feeding sites were separated by 1.2 metres than when the feeding sites were closer together.

Another assumption of the Ideal Free Distribution that may perhaps be violated is that animals have perfect knowledge about the availability of food at the different sites. It is clear that birds are able to make relatively good comparisons between feeding sites, but the mechanism by which they do this is not fully understood.

In experiments on mallards, Harper (1982) found that the ducks were capable of using indirect visual cues to gauge the availability of food at different sites. Over short periods, the birds could be misled into overestimating the availability of food at a site by increasing the frequency at which it was thrown without increasing the overall quantity provided, but during the course of an experiment this effect lessened, as the birds sampled both feeding patches and determined the true availability of food at each.

In pigeons, however, Baum & Kraft found that the presence of an opaque barrier between the two feeding sites had no effect upon the distribution of individuals, and came to the conclusion that the pigeons' distribution arose entirely from judgements made by the birds about conditions within each patch, not from simultaneous visual comparison of the sites. However, although Baum & Kraft's work showed that pigeons were not relying on long-range visual comparisons in this particular situation, it does not rule out the possibility that pigeons are capable of responding to long-range visual cues if suitably obvious ones are provided.

In investigating the distribution of foraging pigeons between two alterative feeding sites, this study aims to follow on from the work of Baum & Kraft, and extend it into a more realistic situation. Whereas Baum & Kraft focused upon caged pigeons kept in artificial conditions, this investigation deals with free-living pigeons in a relatively natural environment. Although the scenario of living in gardens and competing for food thrown at regular intervals by humans could hardly be described as 'natural' in the broader sense, for urban pigeons living in parkland crowded with people this may be a common situation. We did not attempt to quantify the extent to which food taken directly from humans features in the typical diet of the pigeons being studied, but the apparent fearlessness with which the birds were willing to take food from the experimenters (some individual birds would land on the experimenters and peck food directly out of their hands when given the opportunity) suggested that they were relatively accustomed to this mode of feeding. It is therefore reasonable to speculate that the birds may have become adapted to this form of 'foraging', either by learning or by long-term natural selection.



During this investigation, whole peanuts were thrown to free-living feral pigeons (Columba livia), in Princes Street Gardens, Edinburgh (Figure 1).

Figure 1
Figure 1: pigeons in Princes Street Gardens.

The experiments took place at two feeding sites, 20 metres apart, on a wide concrete pathway (see Figure 2). At each site, an experimenter threw whole peanuts at regular intervals to a waiting group of pigeons. (The peanuts were aimed at a spot approximately a metre in front of the experimenter.) On the smooth concrete surface, the peanuts were highly visible to nearby pigeons once thrown, resulting in negligible search and handling times. During each experiment, each feeding site was photographed at 30 second intervals using a digital camera; later examination of the photographs allowed the number of pigeons present at each feeding site to be counted. (Pigeons were considered to be 'present' at a particular feeding site if they were within 3 metres of the spot at which food was being thrown; it was observed that those birds that appeared to be 'interested' in the food being thrown generally congregated within this radius.)

Figure 2
Figure 2: layout of the area in which the experiments took place.

Three main sets of experiments were carried out:

  • Experiments in which identical quantities of food were provided, at equal rates, at the two feeding sites.
  • 'Differing-frequency' experiments, in which the frequency with which food was thrown differed between the two feeding sites.
  • Differing-quantity experiments, in which the quantity of food provided with each throw differed between the two feeding sites.

Prior to the start of each experiment, a small amount of food was scattered halfway in between the two feeding sites, to attract the attention of the pigeons and to disperse the birds randomly in relation to the two feeding sites.

Each experiment was continued, where possible, for five minutes. During some experiments, a 'startle event' was observed, in which the entire group of pigeons would suddenly fly away for no obvious reason. (Similar behaviour was also noted by Baum & Kraft (1998) during their experiments.) On most occasions, the pigeons merely flew around in a short circle and would return to the feeding site within thirty seconds, allowing the experiment to be continued. Unfortunately, in a few such cases the pigeons departed for long periods of time and caused experiments to be prematurely abandoned.

The number of pigeons that congregated at the feeding sites varied during and between experiments; on most occasions there were between 20 and 40 individuals present in total. Few other birds were present at the site during the experiments; on some occasions isolated members of smaller bird species (such as blue tits) were observed close by, but these birds were too small to take whole peanuts (especially when in competition with the pigeons) and did not appear to interfere with the experiments in any way. Other humans were sometimes present in the vicinity, but these were largely ignored by the feeding pigeons, and did not have an observable effect on the birds' behaviour.


Results and analysis

Distribution of pigeons between feeding sites over time

Figure 3 compares the observed distribution of pigeons with the Ideal Free Distribution, during the 5-minute course of the experiments. Theoretically, we would expect to see a steady downwards curve in this graph, as the pigeons slowly detect and respond to the differing availability of food at the two sites, with the graph eventually flattening out as an equilibrium distribution of pigeons is established between the sites. Although the graph in Figure 3 does not fit this prediction perfectly, it comes relatively close.

Figure 3
Figure 3: mean difference between the observed distribution of pigeons and that predicted by the Ideal Free Distribution, during the course of the experiments.

During the first minute of the experiments, the distribution of pigeons typically differed dramatically from the Ideal Free Distribution, as would be expected, since at this stage the birds have had little time in which to detect and respond to the difference in food availability. During the rest of an experiment (from 90 seconds onwards), the curve in Figure 3 flattens out somewhat, with the observed ratio of pigeons differing from the 'ideal' ratio by between 40% and 70%. This part of Figure 3 does show a slight downwards trend, with the observed ratio of pigeons becoming gradually closer to the Ideal Free Distribution. This suggests that the experiments were not continued for a sufficient length of time for an equilibrium to be completely established between the numbers of pigeons at the two foraging sites.

Although, on average, the distribution of pigeons between the foraging sites moved closer to that predicted by the Ideal Free Distribution as each experiment progressed, the pigeons' actual behaviour in the individual experiments was highly chaotic. When the distribution of pigeons at each time in each experiment was compared with that recorded 30 seconds previously, on 98% of occasions a change in the distribution of pigeons was observed. On 59% of occasions, the change resulted in a distribution of pigeons that was closer to the Ideal Free Distribution; on the remaining 39% of occasions the change resulted in a less 'ideal' distribution. There was thus an average trend towards a more 'ideal' distribution, but if the pigeon distribution in a single experiment were plotted, it would typically show dramatic fluctuations rather than a steady curve.

The fact that the balance (or near-balance) established between pigeon numbers at the two feeding sites was a highly dynamic one is nicely illustrated by Figure 4, which shows the average rate at which pigeons arrived or departed from each of the two feeding sites during the course of an experiment. Rather than settling down in their chosen feeding sites, the pigeons continued to come and go at the two sites at a relatively steady rate throughout the experiments. (During the final minute of the experiments, the rate at which pigeons came and went from each of the two sites actually increased - this may have been an experimental anomaly, or it may reflect increasing 'boredom' or restlessness amongst the pigeons.)

Figure 4
Figure 4: average difference between the number of pigeons observed at each feeding site, and the number observed 30 seconds previously, during the course of an experiment. (Increases and decreases in number are both treated as positive differences on this graph.)

Relationship between distribution of pigeons and availability of food

Table 1 summarises the results of the experiments, comparing the distribution of food between the two sites with the distribution of pigeons. (The 'ratio of average pigeon numbers' is based upon the mean numbers of pigeons recorded at the two sites during the course of an experiment. Data gathered during the first minute of an experiment was excluded from this average, since it takes time for the birds to analyse the situation and distribute themselves appropriately between sites. The distribution of pigeons in the very early stages of an experiment may be unrepresentative of the distribution that is eventually established, as Figure 3 illustrated.)

  Differing quantity of peanuts per throw Identical feeding regimes Differing frequency of peanut throwing
(in last two experiments, quantity also differed)
Site #1 Peanuts per throw 2 1 3 1 4 1 5 1 2 1 1 1 1 1 1 1 1 1 1 1 1 5
Time between throws (s) 5 5 5 5 5 5 5 5 5 5 2 10 5 2.5 5 2 10 2 9 3 5 10
Site #2 Peanuts per throw 1 2 1 3 1 4 1 5 2 1 1 1 1 1 1 1 1 1 1 1 5 1
Time between throws (s) 5 5 5 5 5 5 5 5 5 5 2 10 2.5 5 2 5 2 10 3 9 10 5
Ratio of food availability between sites (r1/r2) 2.0 2.0 0.3 3.0 0.3 4.0 0.2 5.0 1.0 1.0 1.0 1.0 2.0 0.5 2.5 0.4 5.0 0.2 3.0 0.3 2.5 0.4
Ratio of average pigeon numbers (N1/N2) 1.3 1.6 0.4 1.2 0.5 0.8 0.6 1.5 1.0 0.8 0.6 0.8 1.6 0.3 1.1 0.7 2.0 0.3 1.3 0.6 1.4 0.3

Table 1: summary of experimental results, comparing the ratio of food availability and the ratio of average pigeon numbers at the two sites (excluding data from the first minute).

Across different experiments, there was a strong positive correlation (r=0.79) between the ratio of food availability between the two sites and the ratio of pigeon numbers. The ratio of pigeons was also correlated, more weakly, with the ratio of frequencies at which food was thrown (r=0.57), and more weakly still with the ratio of peanuts in each throw (r=0.41).

There was very little correlation between the combined availability of food at the two sites and the combined number of pigeons present (r=0.09). This suggests that the variation in numbers of pigeons observed at each feeding site was influenced largely by the movement of pigeons between the two sites, rather than by the arrival and departure of pigeons from other parts of the gardens.

A chi-squared test showed that the mean ratios of pigeons between the foraging sites in the experiments did not match the ratios predicted by the Ideal Free Distribution (chi²=12.35, p=0.93, d.f.=21). To quantify the way in which the pigeons' distribution differed from the Ideal Free Distribution, the bias (b) and sensitivity (s) values were determined; this was done by plotting log (N1/N2) against log (r1/r2) and obtaining a line of best fit (Figure 5). The gradient of this line gives the value of s, and the antilogarithm of the intercept gives b.

Figure 5
Figure 5: double logarithmic plot of the ratio of availability of food at the two feeding sites (r1/r2) against the mean number of pigeons observed at those sites (N1/N2), with a regression line shown.

This analysis showed that there was significant undermatching between the distribution of birds and the availability of food (disproportionately few birds were present in the areas with greater food supply); the overall sensitivity value was 0.46.

The pigeons displayed a consistent bias for one feeding site over the other (the bias value was 0.79; it would have been 1 if the pigeons had treated the two sites equally). The reason for this bias is unknown; it may have been due to physical features of the landscape (such as proximity to cover), or it may reflect the birds' past experiences (pigeons may be more accustomed to receiving food in particular areas of the gardens).

Comparison of differing-frequency and differing-quantity experiments

The sensitivity of the distribution was significantly higher in the differing-frequency experiments (s=0.57) than in the differing-quantity experiments (s=0.34).

It is possible the pigeons, like the ducks studied by Harper (1982), were able to use the frequency of throwing as a visual cue that enabled them to judge the availability of food more accurately in the case of the differing-frequency experiments. The presence of such a visual cue should not alter the equilibrium distribution of birds between the two feeding sites, just the speed with which this equilibrium is attained. We would thus expect that the distribution of birds during the early stages of each experiment would be closer to the Ideal Free Distribution in the differing-frequency experiments than in the differing-quantity experiments, but the distribution established later in the experiment would be similar in both cases. However, as Figure 6 illustrates, this was not the pattern observed: the distribution of birds in the differing-frequency experiments was consistently lower than in the differing-quantity experiments, throughout the experiment.

Figure 6
Figure 6: mean difference between the observed distribution of pigeons, and that predicted by the Ideal Free Distribution, during the course of an experiment. This graph is similar to Figure 3, but it separates differing-frequency experiments, differing-quantity experiments, and experiments in which the frequency and quantity at which food was provided at the two sites were identical.

A more plausible explanation for the difference in sensitivities between differing-frequency and differing-quantity experiments is that competition between the birds was more intense (or was perceived by them to be more intense) in experiments in which several peanuts were thrown simultaneously. This enhanced competition could account for the higher degree of undermatching in the differing-quantity experiments.



The main conclusion of this investigation largely confirms the results obtained in previous studies on pigeons (Baum & Kraft 1998) and other foraging animals (Harper 1982, Kennedy & Gray 1993): foragers respond to differences in food availability between two foraging patches, but their distribution does not exactly match that predicted by Ideal Free Foraging theory. There was significant undermatching between food availability and pigeon numbers, with fewer birds than expected in the patches of highest food availability; the best explanation for this is that certain 'despotic' individuals are able to dominate the richest patches and obtain a disproportionate share of the food. This investigation did not seek to identify individual birds within the flock and determine their food intake or social rank (this would have been difficult to do, since the study involved a continuously-changing group of free-living feral birds). However, other studies into foraging behaviour in pigeons and other birds (Baum & Kraft 1998, Harper 1982) have tracked individual birds, and found that certain dominant individuals do indeed monopolise a vastly disproportionate share of the available food - the presence of such a 'despot' in a patch would significantly alter the patch's profitability for the other foraging birds. During the course of this investigation, the experimenters did observe apparent 'bullying' of some pigeons by other individuals in pursuit of food, but no attempt was made to quantify this behaviour.

It might have been expected that the sensitivity values obtained from this investigation would be higher than those found by Baum & Kraft (1998), since the experiments here involved more widely-separated foraging areas (20m apart, compared with 1.2m apart in Baum & Kraft's experiments), and increased travel costs theoretically increase the sensitivity value. However, in fact the sensitivity values recorded here are surprisingly low: 0.46, compared with the 0.79 value that was obtained by Baum & Kraft (when they provided pigeons with food scattered over an area - as in our own experiments - rather than in a trough or bowl). The lower sensitivity values obtained here may be because the experimental setup used created more intense competition between the birds. This increased competition could result from a larger flock size, although the numbers of pigeons recorded here (the mean number of pigeons present at any particular time was 32) were only slightly larger than those in Baum and Kraft's flock (which numbered between 20 and 32 individuals).

The idea that increased competition can lead to decreased sensitivity (increased undermatching) is supported by the observation that sensitivity was lower in differing-quantity experiments (in which competition was perhaps more intense) than in differing-frequency experiments (although it is possible that the difference between differing-frequency and differing-quantity experiments had other explanations).

The balance of pigeons between the two feeding sites was highly dynamic - rather than settling down as each experiment progressed, birds continued to move between the patches at a relatively steady rate. This supports the hypothesis that the birds judge the relative profitabilities of the two patches by moving between them and sampling the conditions at each patch in turn. This investigation did not provide any evidence that pigeons are able to make judgements about the profitability of foraging sites based on long-range visual cues, although nor can it rule out the possibility. One possible approach for future research into pigeon foraging behaviour would be to conduct experiments similar to those carried out by Harper (1982) on ducks, in which attempts were made to deliberately mislead the birds by providing false visual cues to the profitability of the patches. For example, the experiment could be rigged so that one experimenter threw food more frequently, but threw a smaller overall quantity than the other. (In fact, two experiments of this kind were conducted as part of this investigation, but these provided too little data for meaningful conclusions to be drawn.) By determining if and how the birds can be deceived into congregating in less profitable patches, light could be shed on the mechanisms by which pigeons decide which patch to forage in.



This project was carried out jointly with Chris Mellor and Mickie Imrie.



Baum, W.M., and Kraft, J.R., 1998. Group choice: competition, travel and the ideal free distribution. Journal of the Experimental Analysis of Behaviour 69, pp. 227-245.

Beauchamp, G., 2000. Learning rules for social foragers: implications for the producer-scrounger game and ideal free distribution theory. Journal of Theoretical Biology 207, pp. 21-35.

Harper, D.G.C., 1982. Competitive foraging in mallards: 'ideal free' ducks. Animal Behaviour 30, pp. 575-584.

Inman, A.J., Lefebvre, L. and Giraldeau, L., 1987. Individual diet differences in feral pigeons: evidence for resource partitioning. Animal Behaviour 35, pp. 1902-1903.

Kennedy, M., and Gray, R.D., 1993. Can ecological theory predict the distribution of foraging animals? A critical analysis of experiments on the ideal free distribution. Oikos 68, pp. 158-166.

Milinski, M. and Parker, G.A., 1991. Competition for resources. In: Krebs, J.R. and Davies, N.B., Editors, 1991. Behavioural Ecology, An Evolutionary Approach (3rd Edition), Blackwell Scientific, Oxford, pp. 137-168.

Ollason, J.G., and Yearsley, J.M., 2001. The approximately ideal, more or less free distribution. Theoretical Population Biology 59, pp. 87-105.

Palameta, B. and Lefebvre, L., 1985. The social transmission of a food-finding technique in pigeons: what is learned? Animal Behaviour 33, pp. 892-896.

Plowright, C.M.S., and Landry, F., 2000. A direct effect of competition on food choice by pigeons. Behavioural Processes 50, pp. 59-64.

Sol, D., Santos, D.M., and Cuadrado, M., 2000. Age-related feeding site selection in urban pigeons (Columba livia): experimental evidence of the competition hypothesis. Canadian Journal of Zoology 78, pp. 144-149.



This was originally written as a university biology project

More projects and essays


© Andrew Gray, 2004