16.3 Dot Density and Proportional Symbol Maps
Two alternatives to choropleths that avoid size distortion — ideal for counts.
Key takeaways
- Dot density and proportional symbol maps represent absolute counts without the MAUP problems of choropleths.
- They complement — rather than replace — choropleths.
- Placement, sizing, and density choices matter as much as colour does for choropleths.
Introduction
A common criticism of choropleths: "this map makes big empty polygons look dominant". Dot-density and proportional-symbol maps sidestep that by representing raw counts rather than normalised rates. Each has its own design challenges.
Dot-density maps
Each dot represents a fixed count (say, 1 dot = 1 000 people). Dots are scattered within each polygon proportional to the polygon's value.
Placement
Uniform random placement is the naive approach. Better:
- Masked — exclude non-populated areas (forests, water) using a land-cover raster.
- Stratified — weight placement by a finer-scale population surface.
- Dasymetric placement produces realistic-looking clusters.
Dot size and value
- Dot value — how many units per dot (10 people? 1000?).
- Dot size — visible but not merging too densely. 1–2 pt typical.
- Colour — contrasts with base map; can indicate category (multi-category dot-density maps).
Strengths
- Intuitive for counts.
- Visually compelling (density of dots = density of phenomenon).
- No MAUP distortion.
Weaknesses
- Dot placement is stochastic — you can't "read" a specific location.
- Dense areas saturate and become blobs.
- Requires careful placement to avoid misleading.
Proportional symbol maps
One symbol per polygon (or point); the symbol's size is proportional to the value.
Sizing
Two schools:
- Scaled by area (sqrt of value) — visually accurate for perception.
- Scaled by diameter (linear) — larger visual impact but inflates small differences.
Standard is square-root scaling — the perceived size matches the data ratio.
Symbol choice
- Circles — most common; easy to scale, clearly read.
- Squares — sometimes preferred for large ranges.
- Icons — only when the icon is directly meaningful (houses for homes, trees for forests).
Overlap
Dense areas produce overlapping symbols. Options:
- Transparency — 50–70 % so overlaps show.
- Dodge — offset overlapping symbols (rarely worth the complexity).
- Aggregate — cluster at zoom-out, disaggregate at zoom-in.
Strengths
- Direct representation of counts.
- No ambiguity about polygon boundaries.
- Easy to compare two symbols.
Weaknesses
- Dense areas occlude.
- Hard to estimate exact values from size.
- Legend design matters — 3 example sizes usually.
Combining with choropleths
A "bivariate thematic map" combines:
- Choropleth for a rate (e.g., cases per capita).
- Proportional symbols for the count (cases).
This gives both intensity and magnitude information. Example: COVID dashboards often used this pattern.
Building in tools
QGIS:
- Vector → Analysis Tools → Random Points in Polygons (for dot density).
- Layer styling → Categorized or Graduated with size proportional to value for symbol maps.
GeoPandas:
1# Proportional symbols
2ax = gdf.plot(markersize=gdf['count'] ** 0.5, color='red', alpha=0.5)Plotly, Mapbox GL, deck.gl all support bubble / proportional symbol layers natively.
Self-check exercises
1. When is a dot-density map preferable to a choropleth?
When you want to convey absolute counts and avoid polygon-size bias. For "number of cases" rather than "cases per capita", dots aggregate visually into patterns that reflect the real-world distribution — people, businesses, events — without misleading the reader about where big polygons dominate. Choropleths are better for rates and densities.
2. Why scale proportional symbols by the square root of the value?
Because the human eye perceives circle size by area, not diameter. If one value is 4× another, the circle should be 4× in area (and thus 2× in diameter). Scaling diameter linearly would make the circle 4× wider and 16× in area — a dramatic visual overstatement. Sqrt scaling matches perception to data.
3. You're mapping "number of restaurants" per city. Would you choose dot density or proportional symbols?
Proportional symbols — restaurants are countable and places are discrete. Dot density over administrative polygons would imply a distribution inside the polygon that dots visualise via scatter, which could be misleading in a sparse urban / rural mixture. Proportional symbols per city give an immediate, accurate count per location. If city boundaries are important, you could add a choropleth base (rate per capita) underneath the symbols.
Summary
- Dot-density: one dot per fixed unit, scattered within polygons.
- Proportional symbols: one symbol per feature, sized by value.
- Both avoid choropleth distortions for absolute counts.
- Combine with choropleths for richer story-telling.
Further reading
- Slocum et al. — Thematic Cartography.
- Monmonier — How to Lie with Maps.
- Tufte — The Visual Display of Quantitative Information.
- D3.js examples of proportional symbol maps.
