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Collective behaviour

A starling tracks about seven neighbours — a number, not a distance. That is what holds a flock together when a predator stretches it.

Thousands of animals moving as one without a leader or a plan. The measurement that explains it is unexpectedly specific: a starling attends to about seven neighbours — a number, not a distance — which is what keeps the flock together when it stretches.

A murmuration invites two bad explanations: that something is directing it, or that the birds are doing something we cannot understand. What the measurements show is stranger and better: local rules producing global coherence, with one detail that had to be measured rather than guessed. That detail is what a bird pays attention to. The obvious assumption is that each responds to whatever is within some distance of it. Reconstruct thousands of birds in three dimensions, across flocks of different densities, and it turns out the interaction extends to a roughly fixed number of nearest neighbours, about six or seven, whatever the distances involved. The difference sounds academic and is not. A flock stretches and compresses constantly, and it stretches most when a predator is on it. A bird tracking a fixed distance would lose contact exactly then. A bird tracking a fixed count does not. The second measurement explains why size does not slow the flock down. In most systems influence fades with distance, so a bigger group should respond more sluggishly as a whole. In starling flocks the correlations are scale-free — they stretch to fit the flock — so a turn started at one edge is felt at the other, whatever the flock’s extent. And the most conspicuous feature, the dark bands rippling across the flock, turns out to be a wave: local changes in density and in how the birds are oriented, propagating faster than any bird flies, associated with raptor attack. Nothing about a bird changes colour; what moves is the pattern. The last point is a warning rather than a finding. This is the subject where a 1987 graphics model did most of the public explaining. Three local rules — avoid crowding, align with neighbours, move towards them — produce something that looks convincingly like a flock, and it does not follow that birds do that. Establishing what the animals actually do required going out with cameras.

Early coverage · 53% complete · reviewed 2026-09-03

What this page covers

The measurements here are from starlings, because starlings are what got reconstructed in three dimensions. Fish schools, insect swarms and ungulate herds raise the same questions and have separate, less complete evidence.

Often confused with: A leader directing the group, which nothing here requires; Birds reading each other’s minds or responding faster than reaction time allows; A simulation that looks right being evidence about what the animals do

Quick facts

Seven neighbours, not a radius
Interaction extends to a fixed count, whatever the distances
Size does not slow it
Correlations stretch to fit the flock, whatever its extent
The dark bands are waves
Density and orientation, travelling faster than the birds
No leader required
In models, an unidentifiable minority is enough to steer a group

Seven neighbours, not a radius

A distinction that sounds academic and decides whether the flock survives.

A starling attends to a roughly fixed number of nearest neighbours — about six or seven — not to everything within some distance. That is what keeps a flock together when it stretches.

Well supported

Good evidence backs this, though some details remain open.

Three-dimensional reconstruction of wild starling flocks shows anisotropic neighbour structure extending to a roughly fixed number of nearest neighbours rather than to a fixed metric distance, and this holds as flock density varies.

Who this applies to
Measured in wild starling flocks; whether other flocking or schooling species interact the same way is not established here.Do not extend this beyond the taxa listed — the popular version over-reaches.
Studied in
Sturnus vulgaris
Why we rate it this way, and what the caveats are
Well supportedHigh confidence

Direct three-dimensional measurement of thousands of birds in real flocks, with the density variation that distinguishes the two hypotheses occurring naturally.

How far it can be extended

One species, reconstructed over one city. The principle is suggestive elsewhere and unmeasured elsewhere.

Caveats

  • The measurement establishes the interaction range, not the sensory mechanism that implements it.
  • The number is approximate and is a property of the analysis as much as of any individual bird.

Still unanswered

  • How a bird tracks a fixed count of neighbours — what visual or attentional mechanism produces that.

Last reviewed 2026-09-03

The evidence (1 study)

How we know

Photographing a flock from two places at once

Does a bird in a flock respond to everything within a certain distance, or to a certain number of nearest neighbours?

Synchronised cameras at known separations photographed wild starling flocks, and every bird’s three-dimensional position was reconstructed by matching individuals between images. The angular arrangement of each bird’s neighbours was then analysed to find how far the structure extends — measured both as a distance and as a count of neighbours — across flocks of naturally varying density.

What happened

Neighbour structure was anisotropic out to a roughly fixed count of nearest neighbours — around six or seven — rather than out to a fixed distance, and the count held as density changed.

What it shows

Why a flock holds together when it stretches. A bird tracking everything within a set distance would lose contact exactly when the flock spread out — which is precisely when a predator is forcing it to. Counting neighbours removes that failure mode, and the count stays constant while the distances do not.

What it does not show

It establishes what the interaction range is, not how a bird achieves it: what visual or attentional mechanism lets an animal track a fixed number of neighbours is unknown. It is also one species over one city, and other flocking and schooling animals have not been measured this way.

The controls — what makes this evidence rather than a story
  • Flocks at different densities, which is the only condition under which the two hypotheses differ.
  • The full three-dimensional reconstruction, so neighbour relationships are real rather than projections onto a photograph.
  • Thousands of birds across many flocks, so the structure is a population property rather than a few individuals.

From Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study

Diagram

What happens when the flock spreads out

The one condition under which the two rival rules differ.

What happens when the flock spreads outFlock packed tightFlock stretchedFixed distanceMany neighboursFew or noneFixed countSeven neighboursSeven neighboursA flock stretches most under attack — the worst moment to lose contact.Measured in wild flocks: the count holds while the distances do not.
The same explanation in words

Two rules are compared across two conditions. Under a fixed-distance rule, a bird in a tightly packed flock has many neighbours within range, and in a stretched flock has few or none — the failing case, marked as such. Under a fixed-count rule, the bird has seven neighbours in both conditions. A note records that a flock stretches most when a predator is on it, which is the worst moment to lose contact, and that measurement in wild flocks found the count holding while the distances did not.

Correlations between birds stretch to fit the flock: whatever its size, a disturbance at one edge is felt at the other. A big flock does not react more sluggishly than a small one.

Well supported

Good evidence backs this, though some details remain open.

Velocity-fluctuation correlations in starling flocks are scale-free — the correlation length scales with flock size rather than saturating at a fixed value — so perturbations propagate across the entire group irrespective of its extent.

Who this applies to
Measured across starling flocks spanning a wide range of sizes.Do not extend this beyond the taxa listed — the popular version over-reaches.
Studied in
Sturnus vulgaris
Why we rate it this way, and what the caveats are
Well supportedModerate confidence

A clear statistical result from real flocks. It characterises the state the flock is in without identifying what maintains it.

How far it can be extended

One species; the property has not been established for others here.

Caveats

  • This describes a statistical state, not a mechanism.
  • Scale-free correlation is inferred from reconstructed flocks and depends on the analysis choices made.

Still unanswered

  • What keeps a flock in this state, and whether it is actively maintained or falls out of the interaction rules.

Last reviewed 2026-09-03

The evidence (1 study)

Put the two results together and the flock’s most impressive property stops being mysterious. Each bird is doing something local and cheap — watch a handful of neighbours, match what they do. Because the handful is a count rather than a radius, the rule keeps working as the flock’s density changes. And because the correlations are scale-free, what any one bird does propagates across the whole group rather than dying out. No bird knows what the flock is doing, and the flock does it anyway.

What the ripples actually are

A wave, moving faster than any bird in it.

The dark ripples that sweep across a murmuration are waves of local density and orientation travelling through the flock, associated with predator attack. They move faster than any bird does.

Well supported

Good evidence backs this, though some details remain open.

Dark bands propagating across starling flocks are waves of local density and orientation change associated with raptor attack, travelling at speeds exceeding individual bird velocity.

Who this applies to
Observed in starling flocks during natural raptor attacks.Do not extend this beyond the taxa listed — the popular version over-reaches.
Studied in
Sturnus vulgaris
Why we rate it this way, and what the caveats are
Well supportedModerate confidence

Filmed and analysed during natural attacks. Observational rather than manipulated, since raptor attacks cannot be arranged.

How far it can be extended

Documented for one species under attack by one main predator.

Caveats

  • That the waves accompany attacks is established; what an individual bird gains by taking part is not measured.
  • Natural attacks cannot be controlled, so attack and non-attack flocks differ in other ways too.

Still unanswered

  • Whether the waves impair a raptor’s ability to single out a target, which is the obvious hypothesis and is untested.

Last reviewed 2026-09-03

The evidence (1 study)

The bands look like the flock thickening and thinning, and in a sense they are: what sweeps across is a local change in density and in how the birds are oriented, so that more or less wing surface faces the observer. Because what travels is a pattern rather than a set of birds, the band can move faster than any individual flies — the same reason a wave crosses water faster than the water moves.

Why a group at all

  • Group defence

    Dilution, confusion, and what a group actually buys

  • Mobbing

    Collective action aimed directly at a predator

  • Predation

    The sequence these flocks are interrupting

The model that explained it before anybody measured it

Looking right is not evidence.

Three local rules in a 1987 graphics model produce convincing flocking. That shows the appearance is achievable that way — not that any bird does it. The field measurement had to come separately.

Established

Specialists would state this without hedging. Multiple independent lines of evidence agree.

Agent-based models using local avoidance, alignment and cohesion rules reproduce the visual characteristics of flocking, schooling and herding. Reproduction of a phenotype by a model demonstrates sufficiency of the modelled mechanism, not its use by the organism.

Who this applies to
An epistemic point about models of collective behaviour, not a claim about any species.
Studied in
Animalia
Why we rate it this way, and what the caveats are
EstablishedHigh confidence

A statement about what a sufficiency demonstration can and cannot support, which is not in dispute.

How far it can be extended

The reasoning applies to any model that reproduces an observed pattern.

Caveats

  • This is not an argument against models, which are how sufficiency gets established at all.
  • Some model assumptions have since been supported by measurement; the point is that they had to be.

Still unanswered

  • Which further assumptions in current collective-behaviour models remain untested against real animals.

Last reviewed 2026-09-03

The evidence (2 studies)

In models, a small minority who simply keep heading somewhere can steer a large group accurately — with no signal marking them out and no recognition by the rest. The bigger the group, the smaller the minority needed.

Emerging evidence

Real findings exist, but too few or too recent to be settled.

Agent-based models show that a small proportion of informed individuals with a directional preference can guide group movement accurately without signalling or recognition, with the required proportion decreasing as group size increases.

Who this applies to
A modelling result about moving groups; not a measurement of any species.Do not extend this beyond the taxa listed — the popular version over-reaches.
Studied in
Animalia
Why we rate it this way, and what the caveats are
Emerging evidenceLow confidence

A clean modelling result with no direct measurement of animals behind it, which is why the confidence is low rather than the result weak.

How far it can be extended

Demonstrated in simulation. Whether real groups are led this way is a separate empirical question.

Caveats

  • A model showing a mechanism is sufficient does not show any animal uses it.
  • It says nothing about how individuals come to be informed in the first place.

Still unanswered

  • Whether informed minorities can be identified in real flocks, and how one would test it without marking birds.

Last reviewed 2026-09-03

The evidence (1 study)

The 1987 flocking model is one of the most successful pieces of scientific communication never intended as science. It was written for computer graphics, it works beautifully, and its three rules are now the standard explanation of murmurations in popular accounts. What it demonstrates is sufficiency: local rules of that kind can produce that appearance. It cannot show that starlings use them, and in one respect the early models guessed wrong — they assumed a fixed interaction distance, and the birds turned out to use a count.

This is worth stating because the same pattern recurs across biology. A simulation that reproduces a phenomenon is a hypothesis with a demonstration attached, and it is easy to mistake the demonstration for a result. The honest reading is that the model raised a question precisely enough to be answered, and somebody then went and answered it with cameras.

Claims about this, checked

Things people have heard, and what the evidence actually supports.

The research behind this page

5 studies, newest first. Each one has a page explaining what it found and what it could not show.

2011Animal Behaviour

Propagating waves in starling, Sturnus vulgaris, flocks under predation

The dark bands are waves of local density and orientation change propagating across the flock, associated with predator attack, and travelling faster than individual birds move.

2010Proceedings of the National Academy of Sciences

Scale-free correlations in starling flocks

Correlations in velocity fluctuations extended across the whole flock whatever its size: the correlation length scaled with flock size rather than settling at some fixed value.

2008Proceedings of the National Academy of Sciences

Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study

The angular structure of neighbour positions was anisotropic out to a roughly fixed number of nearest neighbours — approximately six or seven — rather than out to a fixed distance, and this held as flock density varied.

2005Nature

Effective leadership and decision-making in animal groups on the move

A small proportion of informed individuals was sufficient to guide a large group accurately, with the required proportion falling as group size increased.

1987ACM SIGGRAPH Computer Graphics

Flocks, herds and schools: a distributed behavioral model

The three local rules produce coherent group motion closely resembling flocking, schooling and herding, including splitting around obstacles and rejoining afterwards.

This page is a stop on a longer route

A guided journey reads several subjects in a deliberate order, with an argument for why one follows another. You can join in the middle.

Where to go from here

Each of these follows from something on this page — a relationship in the evidence, a claim people ask about, or the next mechanism along.

How complete this page is, and what it is still missing

NatureHQ publishes its own gaps. This page is at 53% completeness against what we would call a finished subject, and was last reviewed on 2026-09-03. It carries 5 claims and answers 0 mapped search questions.

  • no research from the last few years is attached — check for newer work
  • more experiments could be explained in plain English
  • Fish schools and insect swarms raise the same questions and are not covered here.
  • What an individual bird gains from a murmuration, as against roosting alone, is not settled and is treated only briefly.
  • The sensory mechanism behind tracking a fixed count of neighbours is unknown and unaddressed.