Ideal Free Distribution

Origins and basic prediction

Fretwell and Lucas (1969) proposed the model to explain how birds choose breeding habitats. Better habitats offer higher basic payoffs, but as more individuals settle in the same place they must share food and space, so the payoff per individual declines. If every individual knows habitat quality exactly (ideal) and can move without constraint (free), the distribution stabilizes when no individual can gain by moving elsewhere, at which point payoffs per individual are equal in all habitats. This equilibrium follows the same logic as the evolutionarily stable strategy, a game-theoretic concept developed by Maynard Smith (1982). When habitat quality is set by the rate of food input, the model yields the input matching rule: the proportion of individuals in each patch equals the proportion of food supplied there.

Experimental tests

Manfred Milinski (1979) dropped food at different rates at the two ends of a tank and observed sticklebacks quickly dividing themselves in line with the input ratio. Harper (1982) had two people throw bread to a flock of mallards on a pond at different rates and found that within a minute the ducks had split in proportion to the supply. Whitham (1980) showed that aphids choosing leaves aggregate more on large leaves so that reproductive success per individual becomes similar. Kennedy and Gray (1993), however, reanalyzed many experiments and noted that undermatching, with fewer animals than expected in rich patches and more in poor ones, is common in practice.

Relaxed assumptions and applications

Parker and Sutherland (1986) presented phenotype-limited models in which, when individuals differ in competitive ability, it is competitive units rather than individuals that match food input, and Sutherland (1983) analyzed the effect of interference among individuals on distributions. Tregenza (1995) reviewed extensions incorporating perceptual limits, travel costs and territoriality. Fretwell (1972) also proposed the ideal despotic distribution, in which territorial behavior restricts access to good habitats. Pulliam's (1988) source–sink model addresses movement between habitats where births exceed deaths and those where the reverse holds, linking the idea to metapopulation research. Cressman and Křivan (2006) analyzed mathematically which movement rules converge on the ideal free distribution. The model is also used in fisheries research to analyze how fishing fleets distribute among grounds (Gillis, 2003), and, together with optimal foraging theory, it explains how individual choices produce population distributions.

FAQ

What is the ideal free distribution in simple terms?

If everyone knows where the good spots are and can move freely, animals end up spread out so that each individual gets the same share wherever it is.

What is the input matching rule?

When food is supplied continuously, the proportion of individuals gathering in each patch equals that patch's share of the food supply.

Sources reviewed: 2026-10-26

References

1. Fretwell, S. D., & Lucas, H. L. (1969). On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica, 19(1), 16–36.
2. Fretwell, S. D. (1972). Populations in a Seasonal Environment. Princeton: Princeton University Press.
3. Milinski, M. (1979). An evolutionarily stable feeding strategy in sticklebacks. Zeitschrift für Tierpsychologie, 51(1), 36–40.
4. Harper, D. G. C. (1982). Competitive foraging in mallards: 'Ideal free' ducks. Animal Behaviour, 30(2), 575–584.
5. Whitham, T. G. (1980). The theory of habitat selection: Examined and extended using Pemphigus aphids. American Naturalist, 115(4), 449–466.
6. Parker, G. A., & Sutherland, W. J. (1986). Ideal free distributions when individuals differ in competitive ability: Phenotype-limited ideal free models. Animal Behaviour, 34(4), 1222–1242.
7. Kennedy, M., & 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(1), 158–166.
8. Tregenza, T. (1995). Building on the ideal free distribution. Advances in Ecological Research, 26, 253–307.
9. Sutherland, W. J. (1983). Aggregation and the 'ideal free' distribution. Journal of Animal Ecology, 52(3), 821–828.
10. Pulliam, H. R. (1988). Sources, sinks, and population regulation. American Naturalist, 132(5), 652–661.
11. Gillis, D. M. (2003). Ideal free distributions in fleet dynamics: A behavioral perspective on vessel movement in fisheries analysis. Canadian Journal of Zoology, 81(2), 177–187.
12. Maynard Smith, J. (1982). Evolution and the Theory of Games. Cambridge: Cambridge University Press.
13. Cressman, R., & Křivan, V. (2006). Migration dynamics for the ideal free distribution. American Naturalist, 168(3), 384–397.