14. Dot plots — two values in a single dot · Dr. Seonggu Sohn's Data Visualization, First Steps

In single-cell papers this appears more often than the heatmap. Seven panels of this paper are dot plots.

One dot is one gene × one cell type. And it carries two values.

Channel	Value carried	Question answered
dot size	percent of cells expressing	how many cells switched this on
dot colour	mean expression (usually z-scored)	how hard the ones that did switched it on

Why separate them? Because a mean alone cannot tell two situations apart — 100% of cells switching on a little, and 10% of cells switching on hard, can have the same mean. Only the second makes a useful marker gene.

Turn size and colour on and off. What disappears when you keep only one?

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The same grammar as Fig. 5C of the paper. The data is real TCGA lung expression, and the groups are immune-desert, intermediate and immune-inflamed.

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import matplotlib.pyplot as plt
import viz, numpy as np, json

F = json.load(open("viz_facts.json"))
D = F["dot"]
genes = D["genes"]
groups = ["desert", "intermediate", "inflamed"]
pct = np.array(D["pct"]); avg = np.array(D["avg"])
z = (avg - avg.mean(axis=1, keepdims=True)) / (avg.std(axis=1, keepdims=True) + 1e-9)

fig, ax = plt.subplots(figsize=(5.2, 5.6))
for i in range(len(genes)):
    for j in range(len(groups)):
        ax.scatter(j, i, s=pct[i, j]*4.5, c=[z[i, j]], cmap="RdBu_r",
                   vmin=-1.6, vmax=1.6, edgecolors="#00000022", linewidths=.5)
ax.set_xticks(range(len(groups))); ax.set_xticklabels(groups, fontsize=8)
ax.set_yticks(range(len(genes))); ax.set_yticklabels(genes, fontsize=8)
ax.set_xlim(-.6, len(groups)-.4); ax.set_ylim(-.7, len(genes)-.3)
ax.set_title("size = % above median,  colour = row z", fontsize=9)
viz.bare(ax, ())
fig.tight_layout()
print("CD8A and GZMB are large and red in the inflamed group - which is what a marker gene looks like.")

A dot plot must always carry two legends — one for size and one for colour. Miss either and half of every dot is unreadable.

You also have to decide whether the colour is a row z-score or raw expression. The legend of Fig. 5C says “scaled average expression” — meaning z-scores. So that colour means “high for this gene”, not “highly expressed”.

A heatmap would have coloured those two cells the same. A dot plot exposes the difference through size.

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import matplotlib.pyplot as plt
import viz, numpy as np

# Two things can share a mean and still be completely different inside
rng = np.random.default_rng(4)
a = rng.normal(1.0, .2, 200)                       # everyone, a little
b = np.concatenate([np.zeros(180), rng.normal(10, 1, 20)])   # 10%, a lot

fig, ax = plt.subplots(1, 2, figsize=(8.5, 3))
for j, (v, tag) in enumerate([(a, "everyone, a little"), (b, "10%, a lot")]):
    ax[j].hist(v, bins=30, color=viz.PAL[j])
    ax[j].set_title("%s  (mean %.2f, on in %.0f%%)" % (tag, v.mean(), 100*(v > .5).mean()),
                    fontsize=8.5)
    ax[j].set_xlabel("expression", fontsize=8); viz.bare(ax[j])
fig.tight_layout()
print("Means %.2f versus %.2f - but the fraction switched on is %.0f%% versus %.0f%%."
      % (a.mean(), b.mean(), 100*(a > .5).mean(), 100*(b > .5).mean()))

🤔 Check yourself

What does dot size usually represent in a dot plot?

🤔 Check yourself

What happens if you make the dot radius proportional to the value?

🤔 Check yourself

What does 'scaled average expression' in the legend mean?