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tmap example: dot density map

Source: vignettes/examples_dot_density.Rmd
examples_dot_density.Rmd
library(tmap)
tmap_options(scale = 0.75)

In a dot density map, each dot represents a number of units, for instance inhabitants. Dense areas get many dots, sparse areas few. This example shows the population of the Netherlands for each of its 3340 districts (NLD_dist), first with one color, and then colored by income class.

Dot density maps are made with a dot pattern (see the vignette about fill patterns): the map variable pattern_density determines the number of dots per area. With the scale tm_scale_continuous_area(), the number of dots is proportional to the data, so each dot represents the same number of inhabitants.

Population density

The population density (inhabitants per km2) has the units 1/km2, since the area of the districts is in km2:

NLD = NLD_dist
NLD$pop_dens = NLD$population / NLD$area
summary(NLD$pop_dens)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>     0.0    96.9   375.6  1969.1  3083.2 28672.4

At the scale of the whole country, the dots should be small and close together: otherwise, most districts are smaller than the area of one dot, and each dot would represent many inhabitants. Therefore, the density ranges from 0 to 5 (values = c(0, 5)) instead of from 0 to 1, and the dots are small (pattern_size = 0.5). The size of the dots does not change the number of inhabitants per dot, which only depends on the density; in the densest areas, the dots merge. The few districts with more than 10,000 inhabitants per km2 get the densest pattern (outliers.trunc). Instead of the district borders, the province borders are drawn:

dens_scale = tm_scale_continuous_area(
  limits = c(0, 10000),
  values = c(0, 5),
  outliers.trunc = c(FALSE, TRUE),
  ticks = c(1000, 5000, 10000))

tm_shape(NLD) +
  tm_polygons(fill = "white", col = NULL,
              pattern = "stipple", pattern_size = 0.5, pattern_col = "grey10",
              pattern_density = "pop_dens",
              pattern_density.scale = dens_scale,
              pattern_density.legend = tm_legend(
                "Inhabitants per km2",
                dot.value = "1 dot ≈ {n} inhabitants")) +
tm_shape(NLD_prov) +
  tm_borders(col = "grey50", lwd = 0.8)

The number of inhabitants per dot depends on the map scale, and is computed when the map is drawn (legend argument dot.value). The dots are spread over each district; they do not show where people live within a district. A district that is smaller than the area of one dot gets either one dot or none, so the number of dots is only correct on average.

Interactive version

In view mode, the number of inhabitants per dot is updated after zooming. To keep the map light, the district polygons are simplified (which is hardly visible at this scale), popups are disabled, and the district names are shown when hovering:

NLD_simple = sf::st_simplify(NLD, preserveTopology = TRUE, dTolerance = 100)

tmap_mode("view")
tm_shape(NLD_simple) +
  tm_polygons(fill = "white", col = NULL,
              popup = FALSE, id = "name",
              pattern = "stipple", pattern_size = 0.5, pattern_col = "grey10",
              pattern_density = "pop_dens",
              pattern_density.scale = dens_scale,
              pattern_density.legend = tm_legend(
                "Inhabitants per km2",
                dot.value = "1 dot \u2248 {n} inhabitants")) +
tm_shape(NLD_prov) +
  tm_borders(col = "grey50", lwd = 1.5)
tmap_mode("plot")

In view mode, the dots keep their size and spacing on the screen when zooming in, so zooming in shows more dots, each representing fewer inhabitants. With opt_tm_polygons(pattern.zoom = TRUE), the dots stick to the map instead, and each dot keeps representing the same number of inhabitants.

Income classes

The data contain the percentage of individuals with a low income (the lowest 40% nationwide) and a high income (the highest 20% nationwide). The remaining percentage has a middle income. The population density of each class is the population density times this percentage:

NLD$income_middle = 100 - NLD$income_low - NLD$income_high
NLD$dens_low = NLD$pop_dens * NLD$income_low / 100
NLD$dens_middle = NLD$pop_dens * NLD$income_middle / 100
NLD$dens_high = NLD$pop_dens * NLD$income_high / 100

A polygon can have only one pattern, so each class is drawn as a separate layer, with its own dot color. To make each dot represent the same number of inhabitants in all three layers, the same scale is used for each layer. The dots of the three layers would be placed at the same positions in a district where two classes have the same density. Therefore, each layer uses a different seed for the random placement of the dots (see tm_patterns()).

The dots are slightly larger than in the map above (pattern_size = 0.7), so that their colors can be distinguished. The legends of the three layers would only differ in color. Instead, the first one is shown in gray (the legend argument pattern_col), and the colors are explained in a manual legend (tm_add_legend()):

cols = c(low = "#D95F02", middle = "#1B9E77", high = "#7570B3")

dot_layer = function(var, col, seed, legend = tm_legend_hide(), fill = NULL) {
  tm_polygons(fill = fill, col = NULL,
              pattern = tm_patterns("stipple", seed = seed),
              pattern_size = 0.7, pattern_col = col,
              pattern_density = var,
              pattern_density.scale = dens_scale,
              pattern_density.legend = legend)
}

tm_shape(NLD) +
  dot_layer("dens_low", cols["low"], seed = 1, fill = "white",
            legend = tm_legend("Inhabitants per km2",
                               dot.value = "1 dot ≈ {n} inhabitants",
                               pattern_col = "grey20")) +
  dot_layer("dens_middle", cols["middle"], seed = 2) +
  dot_layer("dens_high", cols["high"], seed = 3) +
  tm_add_legend(type = "symbols", title = "Income",
                labels = c("Low (lowest 40%)", "Middle", "High (highest 20%)"),
                fill = cols, col = NA, size = 0.5) +
tm_shape(NLD_prov) +
  tm_borders(col = "grey50", lwd = 0.8)

The share of high incomes is largest in the provinces Utrecht, Noord-Holland, and Zuid-Holland, especially around Amsterdam, Utrecht, and The Hague, whereas the share of low incomes is largest in the north (Groningen and Friesland). For 196 districts with few inhabitants, the income data are missing, so no dots are drawn there.

Note that the order of the layers matters: dots of later layers are drawn on top of dots of earlier layers. Since the dots are small and spread randomly, few dots overlap.