diff --git a/getting_started.md b/getting_started.md
index 35ef3baf..3243b4d9 100644
--- a/getting_started.md
+++ b/getting_started.md
@@ -46,7 +46,7 @@ of the chromosome, then throw some neutral mutations onto the resulting tree seq
 ```{code-cell} ipython3
 import msprime
 
-pop_size=10_000
+pop_size=5000
 seq_length=10_000_000
 
 sweep_model = msprime.SweepGenicSelection(
@@ -167,9 +167,11 @@ using the {meth}`Tree.draw_svg` method.
 ```{code-cell} ipython3
 swept_tree = ts.at(5_000_000)  # or you can get e.g. the nth tree using ts.at_index(n)
 intvl = swept_tree.interval
-print(f"Tree number {swept_tree.index}, which runs from position {intvl.left} to {intvl.right}:")
-# Draw it at a wide size, to make room for all 40 tips
-swept_tree.draw_svg(size=(1000, 200))
+
+swept_tree.draw_svg(
+    size=(1000, 200),  # Draw the tree at a wide size, to make room for all 40 tips
+    title=f"Tree number {swept_tree.index}, which runs from position {intvl.left} to {intvl.right}:"
+)
 ```
 :::{margin}
 The {ref}`visualization tutorial<sec_tskit_viz>` gives more drawing possibilities
@@ -193,8 +195,13 @@ more than one tree: either the entire tree sequence, or
 
 ```{code-cell} ipython3
 reduced_ts = ts.simplify([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])  # simplify to the first 10 samples
-print("Genealogy of the first 10 samples for the first 5kb of the genome")
-reduced_ts.draw_svg(x_lim=(0, 5000))
+
+reduced_ts.draw_svg(
+    x_lim=(0, 10000),
+    title="Genealogy of the first 10 samples for the first 10kb of the genome",
+    y_axis=True,
+    y_ticks=[0, 2000, 4000, 6000, 8000],
+)
 ```
 
 These are much more standard-looking coalescent trees, with far longer branches higher
diff --git a/terminology_and_concepts.md b/terminology_and_concepts.md
index f1742114..f148eb3a 100644
--- a/terminology_and_concepts.md
+++ b/terminology_and_concepts.md
@@ -436,8 +436,8 @@ There is a subtle distinction between common ancestry and coalescence. In partic
 
 The term Ancestral Recombination Graph (ARG), is commonly used to describe a genetic
 genealogy. In particular, many (but not all) authors use it to mean a genetic
-genealogy in which details of the position and potentially the timing of all
-recombination and common ancestor events are explicitly stored. For clarity
+genealogy which explictly records details of the position - and potentially the timing -
+of all recombination and common ancestor events. For clarity
 we refer to this sort of genetic genealogy as a "full ARG". Succinct tree sequences can
 represent many different sorts of ARGs, including "full ARGs", by incorporating extra
 non-coalescent nodes (see the {ref}`sec_args` tutorial). However, tree sequences are
diff --git a/what_is.md b/what_is.md
index 31747f34..2fd3edec 100644
--- a/what_is.md
+++ b/what_is.md
@@ -231,7 +231,7 @@ The second tree shows the relationships between positions 367 and 600.
 Note that in the first tree, genome $\mathrm{e}$ (highlighted in red) is closest to
 $\mathrm{a}-\mathrm{d}$, whereas in the second tree $\mathrm{e}$ is closest to
 $\mathrm{f}-\mathrm{h}$. The third tree shows the relationships between positions
-600 and 900 (the end of the genome). In this case, an entire subtree (or "clade"),
+600 and the end of the genome. In this case, an entire subtree (or "clade"),
 composed of nodes $\mathrm{e}-\mathrm{h}$ has changed its relationship with the other six 
 genomes. More specifically, the most recent common ancestor (MRCA) with any of these
 others has switched: in the third tree it is now above $\mathrm{i}$ and $\mathrm{j}$.
@@ -246,9 +246,10 @@ based on a network of *genetic ancestry*, in which
 (represented by red symbols below) has led
 to different regions of the chromosome having different histories. Another way of
 thinking about the tree sequence above is that it describes the full genetic genealogy
-of our 10 genomes. If we combine all the relationships encoded in the trees (you can
-loosely think of this as lying the trees on top of each other), the result is a network or
-_graph_ (hence the term "[ARG](https://doi.org/10.1371/journal.pgen.1011110)")
+of our 10 genomes. If we combine all the relationships encoded in the trees - you can
+loosely think of this as lying the trees on top of each other - the result is a network or
+[_graph_](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)), hence the term
+"[ARG](https://doi.org/10.1371/journal.pgen.1011110)"
 
 ```{code-cell} ipython3
 :"tags": ["hide-input"]