---
title: "Range Expansion Sectors: Why a Mixed Colony Grows in Stripes Interactive Lab | Sandbox Physics"
description: "Why does a colony started from well-mixed colours grow into a few single-colour sectors? Only cells at the edge divide, so the edge drifts."
canonical_url: "https://sandboxphysics.com/labs/range-expansion-sectors/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/range-expansion-sectors/"
last_modified: "2026-10-30"
---

FR24 · Evolution and ecology

# Range Expansion Sectors: Why a Mixed Colony Grows in Stripes

**Why does a colony started from well-mixed colours grow into a few single-colour sectors?** Only cells at the edge divide, so the edge drifts. It behaves like a small population: neighbouring lineages crowd each other out, colour boundaries wander until they meet, and the surviving colours form sectors. A faster founder opens a wedge whose angle is set by its speed ratio, but a big sector alone does not prove an advantage.

Grow an Eden-model colony from a mixed homeland. Neutral founders split into sectors at the edge, a faster founder opens a wedge and a rock leaves a shadow.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Cells on a square lattice divide into an empty neighbour; descendants of the gold founder divide faster by the chosen advantage, and daughters keep their colour. Only cells at the edge can still divide, so a few founders end up owning the whole front. Sector boundaries wander; on this rough front they wander faster than a random walk. The dashed wedge is the Huygens construction of Hallatschek and Nelson (2008). Over the distances shown here, the simulated wedge opens more slowly than that construction predicts; the benchmark records quantify the gap. The colony is a lattice model, not a measured bacterial colony.

Sectors left as the front advances

Share of the front held by each founder

More numbers and how they are computed

- **Wedge opening angle from front speeds**: $0$
- **Gold share expected from the wedge**: $0$
- **Colours still at the front**: $0$
- **Cells in the colony**: $0$
- **Colony shown**: $0$

Sectors are counted from the colour of the outermost cell along each ray or column. The wedge prediction uses the speed ratio of pure colonies and ignores the rough edge, so in a colony this size the measured wedge is narrower. The exported file lists the seed, the settings and every recorded front.

Physics tutorial

## Only the edge reproduces, so the edge forgets

**Background** In a colony growing on agar, cells deep inside run out of room and food; only a thin rim keeps dividing. That rim is a small population moving into empty space, so drift acts on it strongly.

**Why it matters** Experiments with fluorescently labelled bacteria and yeast show colonies started from a fine mixture growing into a few large single-colour sectors. The pattern is a record of drift at the front, and it changes how we should read spatial genetic data.

Start with the essentials

- **Focus question**: Why does a colony started from well-mixed colours grow into a few single-colour sectors?
- **One-sentence intuition**: Neighbouring founders compete only along the front, so each boundary between colours wanders as the front advances. When two boundaries meet, a colour is lost. On a straight front the number of sectors falls as $\Delta r^{-\zeta}$; on a round colony the growing circumference stops the loss and freezes a finite number of sectors.

### Core mathematical model

#### Boundary wandering

$$
\langle\Delta x^2\rangle\propto\Delta r^{2\zeta},\qquad \zeta=\tfrac12\ \text{(smooth)},\quad \zeta=\tfrac23\ \text{(rough, Eden)}
$$

A random walk has $\zeta=1/2$. Rough fronts carry boundaries along their bumps, which gives the larger exponent $\zeta=2/3$ predicted for Eden growth and measured as $0.65\pm0.05$ in E. coli colonies.

#### Huygens wedge of a faster founder

$$
\cos\frac{\Phi}{2}=\frac{v}{v_{\mathrm{gold}}}=\frac{1}{1+s}
$$

If the gold lineage alone would spread faster by the factor $1+s$, geometric optics gives a wedge of opening angle $\Phi$. In this lattice model the simulated wedge approaches that angle only slowly.

### Common difficulties

#### A large sector is not proof of an advantage

**Typical misconception** The biggest sector must belong to the fittest founder.

**Better mental model** With twelve equally fit colours on the straight front of this Lab, the luckiest colour typically ends up holding about two fifths of the edge. Only comparing many colonies, or the shape of the sector boundaries, can separate luck from selection.

### Run the experiment

1. 01

   #### Watch two colours split

   Let the round colony grow from the start.

   **What to observe:** The fine mixture at the homeland gives way to a handful of sectors whose number stops changing once the colony is large.

2. 02

   #### Straighten the front

   Choose A straight front loses colours and watch the sector chart.

   **What to observe:** Sectors keep merging, and the curve follows the rough-front guide more closely than the random-walk guide.

3. 03

   #### Add an advantage

   Choose A faster founder opens a wedge, then drag the ring onto the gold sector.

   **What to observe:** The gold sector widens linearly with distance, and every gold cell traces back to the single gold founder.

Physical conclusion

At an expanding edge, a few founders inherit the whole front by chance. Sector boundaries record that drift; a faster lineage turns its boundary into a wedge.

## Related experiments and articles

Evolution as statistical physics · Reading path

### From random sampling to pulled and pushed waves

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Sectors at an expanding edge split a growing colony into colours**](https://sandboxphysics.com/stories/evolution-statistical-physics/sectors-at-an-expanding-edge/)
2. [Article **Does a big sector mean selection? Opening angles and luck in colonies**](https://sandboxphysics.com/stories/evolution-statistical-physics/does-a-big-sector-mean-selection/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)