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Winter 2013

Urban Jungle

The changing natural world at our doorsteps | Illustration and text by Patterson Clark      

Starlings on a power line, Sturnus vulgaris

January 22, 2013

Spacing out: Plotting the distance between individuals


Stark winter landscapes bring into sharp contrast the flocks of pigeons and starlings gathered on power lines. On a crowded wire, the distance between individuals seems fairly regular, yet with some variation. Surprisingly, a statistical plot of the distances between birds shows the same pattern as do the spaces separating parked cars, bunched-up pedestrians, freeway traffic and moving flocks of sheep.

Unlike the symmetrical bell curve, below, which works well for plotting random datapoints, such
as IQ scores
and shoe sizes,
the graph
depicting spaces
between units
that are aware
of each other

makes a curve resembling a cracking whip. The pattern was described in 2009 by Czech mathematical physicist Petr Seba.

On Seba's curve, snuggling birds or kissing bumpers would register at the left-hand extreme of the curve, where space between birds or cars is absent. The curve's peak, or mode, signals the distance most likely to occur between parties, which turns out to be a little more than half of the average distance.

On this curve, the average, or mean, has a larger value than the mode because of a broad range of increasingly wide gaps between individuals, created perhaps by birds needing a little extra room, pedestrians who appear threatening to others — or parallel parkers feeling timid.

Spacing between individuals is a result of numerous variables, including speed, body size, available space and social interaction. But a common denominator is what Seba describes as a "universal distance-controlling mechanism" hard-wired into each animal's eye and brain.

NASCAR drivers and house flies share a very similar response to a psychophysical time-to-collision estimate triggered by

the rate that an image expands on the retina of the animal's or person's eye.

That internal calculation of impending impact kicks in and helps carve a comfortable space every time a starling swoops in to negotiate a spot on a wire and every time you pull up behind another car at a stop light.

Sources: Petr Seba, University of Hradec Kralove; Perception; Journal of Statistical Mechanics:
Theory and Experiment

bell curve, normal distribution curve Petr Seba's curve for spaces separating individuals

On Seba's curve, the mean
  (average) distance between
    individuals is given the unit
      value of 1. Spaces between
        perched starlings and between
            parallel-parked* cars tightly
                conform to this curve.

*

In unmarked spaces

PROBABILITY DENSITY

RELATIVE DISTANCE BETWEEN INDIVIDUALS

Mean

Mode

Mean,
mode

SHOE SIZES