# Visualization#

Yan Wong

It is often helpful to visualize a single tree — or multiple trees along a tree sequence — together with sites and mutations. Tskit provides functions to do this, outputting either plain ascii or unicode text, or the more flexible Scalable Vector Graphics (SVG) format. This tutorial illustrates various examples, based on a few 50kb tree sequences generated by msprime, in which genomes have been sampled from one of 3 contemporary populations (labelled A, B, and C).

import tskit
# See the notebook code if you want to know how these tree sequences were produced


If you just want a quick look at visualization possibilities, you might want to skip to the Examples.

Note

This tutorial is primarily focussed on showing a tree sequence as a set of marginal trees along a genome. The section titled Other visualizations provides examples of other representations of tree sequences, or the processes that can create them.

## Text format#

The TreeSequence.draw_text() and Tree.draw_text() methods provide a quick way to print out a tree sequence, or an individual tree within it. They are primarily useful for looking at topologies in small datasets (e.g. fewer than 20 sampled genomes), and do not display mutations.

# Print a tree sequence
print(ts_tiny.draw_text())

print("The first tree in the tree sequence above, but replacing some node ids with names:")
print(ts_tiny.first().draw_text(
# An example of how to change or omit node labels: unspecified nodes are omitted
# The same convention applies to SVG graphics
node_labels={0: "Alice", 1: "Bob", 2:"Chris", 3: "Dora", 6: "MRCA"}
))

11428.48┊         ┊         ┊         ┊         ┊   13    ┊         ┊         ┊         ┊
┊         ┊         ┊         ┊         ┊  ┏━┻━┓  ┊         ┊         ┊         ┊
11144.74┊         ┊         ┊         ┊         ┊  ┃   ┃  ┊   12    ┊         ┊         ┊
┊         ┊         ┊         ┊         ┊  ┃   ┃  ┊  ┏━┻━┓  ┊         ┊         ┊
9753.69 ┊         ┊         ┊         ┊         ┊  ┃   ┃  ┊  ┃   ┃  ┊   11    ┊         ┊
┊         ┊         ┊         ┊         ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┏━┻━┓  ┊         ┊
6204.42 ┊         ┊         ┊         ┊   10    ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊         ┊
┊         ┊         ┊         ┊  ┏━┻━┓  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊         ┊
3893.05 ┊         ┊         ┊         ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊    9    ┊
┊         ┊         ┊         ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┏━┻━┓  ┊
3378.92 ┊         ┊    8    ┊    8    ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊
┊         ┊  ┏━┻━┓  ┊  ┏━┻━┓  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊  ┃   ┃  ┊
2076.43 ┊         ┊  ┃   ┃  ┊  7   ┃  ┊  7   ┃  ┊  7   ┃  ┊  7   ┃  ┊  7   ┃  ┊  7   ┃  ┊
┊         ┊  ┃   ┃  ┊ ┏┻┓  ┃  ┊ ┏┻┓  ┃  ┊ ┏┻┓  ┃  ┊ ┏┻┓  ┃  ┊ ┏┻┓  ┃  ┊ ┏┻┓  ┃  ┊
1941.72 ┊   6     ┊  6   ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊
┊ ┏━┻━┓   ┊ ┏┻┓  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊
1439.14 ┊ ┃   5   ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊
┊ ┃ ┏━┻┓  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊ ┃ ┃  ┃  ┊
33.99   ┊ ┃ ┃  4  ┊ ┃ ┃  4  ┊ ┃ ┃  4  ┊ ┃ ┃  4  ┊ ┃ ┃  4  ┊ ┃ ┃  4  ┊ ┃ ┃  4  ┊ ┃ ┃  4  ┊
┊ ┃ ┃ ┏┻┓ ┊ ┃ ┃ ┏┻┓ ┊ ┃ ┃ ┏┻┓ ┊ ┃ ┃ ┏┻┓ ┊ ┃ ┃ ┏┻┓ ┊ ┃ ┃ ┏┻┓ ┊ ┃ ┃ ┏┻┓ ┊ ┃ ┃ ┏┻┓ ┊
0.00    ┊ 0 1 2 3 ┊ 0 1 2 3 ┊ 0 1 2 3 ┊ 0 1 2 3 ┊ 0 1 2 3 ┊ 0 1 2 3 ┊ 0 1 2 3 ┊ 0 1 2 3 ┊
0       9855      13901     21285     23424     25213     30463     46237     50000

The first tree in the tree sequence above, but replacing some node ids with names:
MRCA
┏━━━┻━━━━┓
┃        ┃
┃    ┏━━━┻━━━┓
┃    ┃       ┃
┃    ┃    ┏━━┻━━┓
Alice Bob Chris Dora


## SVG format#

Most users will want to use the SVG drawing functions TreeSequence.draw_svg() and Tree.draw_svg() for visualization. Being a vectorised format, SVG files are suitable for presentations, publication, and editing or converting to other graphic formats; some basic forms of animation are also possible. Both functions produce an SVG string which is automatically drawn if the string is the result of the last call in a Jupyter notebook:

from IPython.display import display
svg_size = (800, 250) # Height and width for the SVG: optional but useful for this notebook
svg_string = ts_tiny.draw_svg(
size=svg_size,
y_axis=True, y_label=" ",  # optional: show a time scale on the left
time_scale="rank", x_scale="treewise",  # Force same axis settings as the text view
)
display(svg_string)  # If the last line in a cell, wrapping this in display() is not needed


By default, sample nodes are drawn as black squares, and non-sample nodes are drawn as black circles (but see below for ways to e.g. hide or colour these node symbols - NB. apologies to US readers: the British spelling of “colour” will be used in the rest of this tutorial).

### Axes and scaling#

For ease of drawing, the text representation and the SVG image above use unconventional non-linear X and Y coordinate systems. By default, the SVG output uses a more conventional linear scale for both time (Y) and genome position (X), and indicates the position of each tree along the genome by an alternating shaded background. Although more intuitive, linear scales can obscure some features of the trees, for example causing labels to overlap:

ts_tiny.draw_svg(size=svg_size, y_axis=True)


One way to avoid overlapping labels on the Y axis is to use the y_ticks parameter, which will be used in most subsequent examples in this tutorial.

### Larger tree sequences#

So far, we have plotted only very small tree sequences. To visualize larger tree sequences it is sometimes advisable to focus on a small region of the genome, possibly even a single tree. The x_lim parameter allows you to plot the part of a tree sequence that spans a particular genomic region: here’s a slighly larger tree sequence with 8 samples, but where we’ve restricted the amount of the tree sequence we plot:

x_limits = [5000, 15000]
# Create evenly-spaced y tick positions to avoid overlap
y_tick_pos = [0, 1000, 2000, 3000, 4000]

print("The tree sequence between positions {} and {} ...".format(*x_limits))
display(ts_small.draw_svg(y_axis=True, y_ticks=y_tick_pos, x_lim=x_limits))

third_tree = ts_small.at_index(2)
print("... or just look at (say) the third tree")
display(third_tree.draw_svg())

The tree sequence between positions 5000 and 15000 ...

... or just look at (say) the third tree


As the number of sample nodes increases, internal nodes often bunch up at recent time points, obscuring relationships. Setting time_scale="rank", as in the first SVG plot, is one way to solve this. Another is to use a log-scale on the time axis, which can be done by specifying time_scale="log_time", as below. To compare node times across the plot, this example also uses the y_gridlines option, which puts a very faint grid line at each y tick (if you are finding the lines difficult to see, note that the line intensity, along with many other plot features, can be modified through styling, which we also use in this example to avoid overlapping text by shrinking the node labels and rotating those associated with leaves; styling is detailed later in this tutorial).

print("A larger tree, on a log timescale")
wide_fmt = (1200, 250)
# Create a stylesheet that shrinks labels and rotates leaf labels, to avoid overlap
node_label_style = (
".node > .lab {font-size: 80%}"
".leaf > .lab {text-anchor: start; transform: rotate(90deg) translate(6px)}"
)
ts_full.first().draw_svg(
size=wide_fmt,
time_scale="log_time",
y_gridlines=True,
y_axis=True,
y_ticks=[1, 10, 100, 1000],
style=node_label_style,
)

A larger tree, on a log timescale


### Plotting mutations#

The SVG visualization also allows mutations to displayed on the tree or tree sequence. Here are the same plots as above but where the tree sequence now contains mutations. Each mutation is plotted as a red cross on the branch where it occurs. This mutation symbol is placed either at the mutation’s known time, or spaced evenly along the branch (if the mutation time is unknown or the time_scale parameter has been set to "rank"). By default, each mutation is also labelled with its mutation ID.

If the X axis is shown (which it is by default when drawing a tree sequence, but not when drawing an individual tree) then the sites are plotted using a black tickmark above the axis line. Each plotted mutation at the site is then overlaid on top of this as a red downwards-pointing chevron.

ts_mutated = msprime.sim_mutations(ts_small, rate=1e-7, random_seed=342)
ts_mutated.draw_svg(y_axis=True, y_ticks=y_tick_pos, x_lim=x_limits)


Note that, unusually, the rightmost site on the axis has more than one stacked chevron, indicating that multiple mutations in the tree occur at the same site. These could be mutations to different allelic states, or recurrent/back mutations. In this case the mutations, 14 and 15 (above nodes 1 and 6) are recurrent mutations from T to G.

ts_mutated = tskit.load("data/viz_ts_small_mutated.trees")
site_descr = str(next(ts_mutated.at_index(2).sites()))
print(site_descr.replace("[", "[\n  ").replace("),", "),\n ").replace("],", "],\n"))

Site(id=14, position=13963.0, ancestral_state='T', mutations=[
Mutation(id=14, site=14, node=1, derived_state='G', parent=-1, metadata=b'', time=619.6499091610359, edge=14),
Mutation(id=15, site=14, node=6, derived_state='G', parent=-1, metadata=b'', time=370.24979591084764, edge=4)],


#### Which mutations are shown?#

When using the x_lim parameter, only the mutations in the plotted region are shown. For the third tree in the tree sequence visualization above, we thus haven’t plotted mutations above position 15000. We can see all the mutations in the tree by changing the plot region, or simply plotting the tree itself:

third_tree = ts_mutated.at_index(2)
print(f"The third tree in the mutated tree sequence, which covers {third_tree.interval}")
third_tree.draw_svg(size=(200, 300))

The third tree in the mutated tree sequence, which covers Interval(left=13901.0, right=21285.0)


However, when plotting a single tree it may not be evident that identical branches may exist in several adjacent trees, indicating an edge that persists across adjacent trees. For instance the rightmost branch in the tree above, from node 10 down to 7, exists in the previous two trees too. Indeed, this edge has a mutation on it at position 6295, in the first tree. This mutation is not plotted in the tree above, but if you want all the mutations on each edge to be plotted, you can set the all_edge_mutations parameter to True. This adds any extra mutations that are associated with an edge in the tree but which fall outside the interval of that tree; by default these mutations are drawn in a slightly different shade (e.g. mutation 64 below).

third_tree.draw_svg(size=(200, 300), all_edge_mutations=True)


### Labelling#

Although the default node and mutation labels show unique identifiers, they are’t terribly intuituive. The node_labels and mutation_labels parameters can be used to set more meaningful labels (for example from the tree sequence Metadata).

nd_labels = {}  # An array of labels for the nodes
for n in ts_mutated.nodes():
# Set sample node labels from metadata. Here we use the population name, but you might want
# to use the *individual* name instead, if the individuals in your tree sequence have names
if n.is_sample():

mut_labels = {}  # An array of labels for the mutations
for mut in ts_mutated.mutations():  # Make pretty labels showing the change in state
site = ts_mutated.site(mut.site)
older_mut = mut.parent >= 0  # is there an older mutation at the same position?
prev = ts_mutated.mutation(mut.parent).derived_state if older_mut else site.ancestral_state
mut_labels[mut.id] = f"{prev}→{mut.derived_state}"

ts_mutated.draw_svg(
y_axis=True, y_ticks=y_tick_pos, x_lim=x_limits,
node_labels=nd_labels,
mutation_labels=mut_labels,
)


### Styling#

The SVG output produced by tskit contains a large number of classes which can be used to target different elements of the drawing, allowing them to be hidden, styled, or otherwise manipulated. This is done by passing a cascading style sheet (CSS) string to draw_svg. A common use of styles is to colour nodes by their population:

styles = []
# Create a style for each population, programmatically (or just type the string by hand)
for colour, p in zip(['red', 'green', 'blue'], ts_full.populations()):
# target the symbols only (class "sym")
s = f".node.p{p.id} > .sym " + "{" + f"fill: {colour}" + "}"
styles.append(s)
print(f'"{s}" applies to nodes from population {p.metadata["name"]} (id {p.id})')
css_string = " ".join(styles)
print(f'CSS string applied:\n    "{css_string}"')

ts_full.first().draw_svg(
size=wide_fmt,
node_labels={},    # Remove all node labels for a clearer viz
style=css_string,  # Apply the stylesheet
)

".node.p0 > .sym {fill: red}" applies to nodes from population A (id 0)
".node.p1 > .sym {fill: green}" applies to nodes from population B (id 1)
".node.p2 > .sym {fill: blue}" applies to nodes from population C (id 2)
CSS string applied:
".node.p0 > .sym {fill: red} .node.p1 > .sym {fill: green} .node.p2 > .sym {fill: blue}"


Colouring nodes by population makes it immediately clear that, while the tree structure does not exactly reflect the population divisions, there’s still considerable population substructure present in this larger tree.

Todo

The (older) Tree.draw() function also has a node_colour argument that can be used to colour tree nodes, which is used in some of the other tskit tutorials. Under the hood, this function simply sets appropriate SVG styles on nodes. We intend to make it easier to set colours in a similar way: see https://github.com/tskit-dev/tskit/issues/579.

The CSS string used to style the tree above takes advantage of the general classes defined in a tskit SVG file: a node symbol always has a class named sym, which is contained within a grouping element of class node. Moreover, elements such as node have additional classes, such as p1, indicating that the node in this case belongs to the population with ID 1.

#### Available css classes#

Here are the css classes in a tskit SVG which can be used to style specific elements.

##### Within the plotting area#
• tree: a grouping element containing each tree

• node: a grouping element within a tree, containing a node and its descendant elements such as a node symbol, an edge, mutations, and other nodes.

• mut: a grouping element containing a mutation symbol and label

• extra: an extra class for mutations outside the tree

• lab: a label element (for a node, mutation, axis, tick number, etc.)

• sym: a symbol element (e.g. a node, mutation, or site symbol)

• edge: an edge element (i.e. a branch in a tree)

• root, leaf and sample: additional classes applied to a node group if the node is a root node, a leaf node or a sample node

• unknown_time: a class added to mut groups if the time of the mutation is tskit.UNKNOWN_TIME.

• rgt and lft: additional classes applied to labels for left- or right-justification

##### Outside the plotting area#
• axes: a grouping element containing the X and Y axes, if either are present

• x-axis, y-axis: more specific grouping elements contained within axes

• tick: a single tick on an axis, containing a tickmark line and a label

• site: a grouping element representing a site (plotted on the X axis), containing a site symbol (a tick line) and zero or more mut groups, each containing a chevron-shaped mutation symbol

• background: the shaded background of a tree sequence plot

• grid: a gridline

##### ID-based classes#

Elements have additional classes based on the IDs of trees, nodes, parent (ancestor) nodes, individuals, populations, mutations, and sites. These class names start with a single letter (respectively t, n, a, i, p, m, and s) followed by a numerical ID. For example, here’s a typical node in an tskit SVG plot:

<g class="a10 i3 leaf m16 m17 node n7 p2 s15 s16 sample">...</g>


This corresponds to node 7, the rightmost leaf in the third tree in the mutated tree sequence (plotted in the previous section but one). The classes indicate that it has an immediate ancestor (parent) node with ID 10 (a10), and that the node belongs to an individual with ID 3 (i3). The classes n7 and p2 tell us that the node ID is 7 and is is from the population with ID 2 (p2). Other ID classes on the node tell us about the mutations above that node, of which there are two in this case, with IDs 16 and 17 (m16, m17); those mutations are associated with site IDs 15 and 16 (s16, s17).

Other grouping elements apart from nodes can also contain ID-based classes. For example the tree group contains the ID of the tree (e.g. t0), the site group on the X axis contains the site ID (e.g. s15) the mut class contains the mutation ID (e.g. m16), and so on.

#### Styling graphical elements#

The classes above make it easy to target specific nodes or edges in one or multiple trees. For example, we can colour branches that are shared between trees (identified here as ones that have the same parent and child):

css_string = ".a15.n9 > .edge {stroke: cyan; stroke-width: 2px}"  # branches from 15->9
ts_small.draw_svg(time_scale="rank", size=wide_fmt, style=css_string)


By generating the css string programatically, you can target all the edges present in a particular tree, and see how they gradually disappear from adjacent trees. Here, for example the branches in the central tree have been coloured red, as have the identical branches in adjacent trees. The central tree represents a location in the genome that has seen a selective sweep, and therefore has short branch lengths: adjacent trees are not under direct selection and thus the black branches tend to be longer. These (red) shared branches extending far on either side represent shared haplotypes, and this shows how long, shared haplotypes can extend much further away from a sweep than the region of reduced diversity (which is the region spanned by the short tree in the middle). For visual clarity, node symbols and labels have been turned off.

# See the notebook code if you want to know how these tree sequences were produced

css_edge_targets = []  # collect the css targets of all the edges in the selected tree
sweep_location = ts_selection.sequence_length / 2  # NB: sweep is in the middle of the ts
focal_tree = ts_selection.at(sweep_location)
for node_id in focal_tree.nodes():
parent_id = focal_tree.parent(node_id)
if parent_id != tskit.NULL:
css_edge_targets.append(f".a{parent_id}.n{node_id}>.edge")
css_string = ",".join(css_edge_targets) + "{stroke: red} .sym {display: none}"

wide_tall_fmt = (1200, 400)
ts_selection.draw_svg(
style=css_string,
size=wide_tall_fmt,
x_lim=[1.74e4, 3.25e4],
node_labels={},
)


Note

Branches in multiple trees that have the same parent and child do not always correspond to a single edge in a tree sequence: for example, edges have the additional constraint that they must belong to adjacent trees.

#### Moving graphical elements#

We can also use styles to transform elements of the drawing, shifting them into different locations or changing their orientation. For example, earlier in this tutorial we used the following CSS string to rotate leaf labels:

.leaf > .lab {text-anchor: start; transform: rotate(90deg) translate(6px)}


Transformations not only allow us to shift e.g. labels about, but also change the size of symbols, which can create rather different formatting styles:

css_string = (
# Draw large yellow circles for nodes ...
".node > .sym {transform: scale(2.2); fill: yellow; stroke: black; stroke-width: 0.5px}"

# ...but for leaf nodes, override the yellow circle using a more specific CSS target
".node.leaf > .sym {transform: scale(1); fill:black}"

# Override default node text position to be based at (0, 0) relative to the node pos
# Note that the .tree specifier is needed to make this more specific than the default
# positioning which is targetted at ".lab.lft" and ".lab.rgt"
".tree .node > .lab {transform: translate(0, 0); text-anchor: middle; font-size: 7pt}"

# For leaf nodes, override the above positioning using a subsequent CSS style
".node.leaf > .lab {transform: translate(0, 12px); font-size: 10pt}"
)
ts_small.first().draw_svg(style=css_string)


Note

Using transform in styles is an SVG2 feature, and has not yet been implemented in the software programs Inkscape or librsvg. Therefore if you are converting or editing the examples above, symbol sizes and label positions may be incorrect. The symbol_size option can be used if you want to simply change the size of all symbols in the plot, but otherwise you may need to use the chromium workaround documented here.

#### Styling and SVG structure#

To take full advantage of the SVG styling capabilities in tskit, it is worth knowing how the SVG file is structured. In particular tskit SVGs use a hierarchical grouping structure that reflects the tree topology. This allows easy styling and manipulation of both individual elements and entire subtrees. Currently, the hierarchical structure of a simple 2-tip SVG tree produced by tskit looks something like this:

<g class="tree t0">
<g class="plotbox">
<g class="node n2 root">
<g class="node n1 a2 i1 p1 m0 s0 sample leaf">
<path class="edge" ... />
<g class="mut m0 s0" ...>
<line .../>
<path class="sym" .../>
<text class="lab">Mutation 0</text>
</g>
<rect class="sym" ... />
<text class="lab" ...>Node 1</text>
</g>
<g class="node n0 a2 i2 p1 sample leaf">
<path class="edge" ... />
<rect class="sym" .../>
<text class="lab" ...>Node 0</text>
</g>
<path class="edge" ... />
<circle class="sym" ... />
<text class="lab">Root (Node 2)</text>
</g>
</g>
</g>


And in a tree sequence plot, the SVG simply consists of a set of such trees, together with groups containing the background and axes, if required.

<g class="tree-sequence">
<g class="background"></g>
<g class="axes"></g>
<g class="trees">
<g class="tree t0">...</g>
<g class="tree t1">...</g>
<g class="tree t2">...</g>
...
</g>
</g>
</g>



#### Styling subtrees#

The nested grouping structure makes it easy to target a node and all its descendants. For instance, here’s how to draw all the edges of node 13 and its descendants using a thicker blue line:

edge_style = ".n13 .edge {stroke: blue; stroke-width: 2px}"
nd_labs = {n: n for n in [0, 1, 2, 3, 4, 5, 6, 7, 13, 17]}
ts_mutated.draw_svg(x_lim=x_limits, node_labels=nd_labs, style=edge_style)


This might not be quite what you expected: the branch leading from node 13 to its parent (node 17) has also been coloured. That’s because the SVG node group deliberately contains the branch that leads to the parent (this can be helpful, for example, for hiding the entire subtree leading to node 13, using e.g. .n13 {display: none}). To colour the branches descending from node 13, you therefore need to target the nodes nested at least one level deep within the n13 group. One way to do that is to add an extra .node class to the style, e.g.

edge_style = ".n13 .node .edge {stroke: blue; stroke-width: 2px}"
# NB to target the edges in only (say) the 1st tree you could use ".t0 .n13 .node .edge ..."
ts_mutated.draw_svg(x_lim=x_limits, node_labels=nd_labs, style=edge_style)


If you want to colour the branches descending from a particular mutation (say mutation 7) then you need to colour not only the edges, but also part of an edge (i.e. the line that connects a mutation downwards to its associated node). The tskit SVG format provides a special <line> element to enable this, which is normally made invisible using fill: none stroke: none in the default stylesheet. Here’s an example of activating this normally-hidden line:

default_muts = ".mut .lab {fill: gray} .mut .sym {stroke: gray}"  # all other muts in gray
m8_mut = (
".m8 .node .edge, "  # the descendant edges
".mut.m8 line, "  # activate the hidden line between the mutation and the node
".mut.m8 .sym "  # the mutation symbols on the tree and the axis
"{stroke: red; stroke-width: 2px}"
".mut.m8 .lab {fill: red}"  # colour the label "8" in red too
)
css_string = default_muts + m8_mut
ts_mutated.draw_svg(x_lim=x_limits, node_labels=nd_labs, style=css_string)


#### Restricting styling#

Sometimes the hierarchical nesting leads to styles being applied too widely. For example, since style selectors include all the descendants of a target, to target just the node itself (and not its descendants) a slightly different specification is required, involving, the “>” symbol, or child combinator (we have, in fact, used it in several previous examples). The following plot shows the difference when all decendant symbols are targetted, versus just the immediate child symbol:

node_style1 = ".n13 .sym {fill: yellow}"  # All symbols under node 13
node_style2 = ".n15 > .sym {fill: cyan}"  # Only symbols that are an immediate child of node 15
css_string = node_style1 + node_style2
ts_small.draw_svg(y_axis=True, y_ticks=y_tick_pos, x_lim=x_limits, style=css_string)


Another example of modifying the style target is negation. This is needed, for example, to target nodes that are not leaves (i.e. internal nodes). One way to do this is to target all the node symbols first, then replace the style with a more specific targetting of the leaf symbols only:

hide_internal_symlabs = ".node > .sym, .node > .lab {display: none}"
show_leaf_symlabs = ".node.leaf > .sym, .node.leaf > .lab {display: initial}"
css_string = hide_internal_symlabs + show_leaf_symlabs
ts_small.draw_svg(y_axis=True, y_ticks=y_tick_pos, x_lim=x_limits, style=css_string)


Alternatively, the :not selector can be used to target nodes that are not leaves, so the following style specification should produce the same effect in SVG viewers that support it (note, however, as of v1.2 Inkscape does not appear to support this selector).

style_string = ".node:not(.leaf) > .sym, .node:not(.leaf) > .lab {display: none}"


NOTE: if your SVG is embedded directly into an HTML page (a common way for jupyter notebooks to render SVGs), then according to the HTML specifications, any styles applied to one SVG will apply to all SVGs in the document. To avoid this confusing state of affairs, we recommend that you tag the SVG with a unique ID using the root_svg_attributes parameter, then prepend this ID to the style string:

ts_small.draw_svg(
x_lim=x_limits,
root_svg_attributes={'id': "myUID"},
style="#myUID .background * {fill: #00FF00}",  # apply any old style to this specific SVG
)


SVG styles allow a huge amount of flexibility in formatting your plot, even extending to animations. Feel free to browse the examples for inspiration.

### Converting and editing SVG#

#### Converting#

Inkscape is an open source SVG editor that can also be scripted to output bitmap files.

Imagemagick is a common piece of software used to convert between image formats. It can be configured to delegate to one of several different SVG libraries when converting SVGs to bitmap formats. Currently, both the librsvg library or the Inkscape library produce reasonable output, although librsvg currently misaligns some labels due to ignoring certain SVG properties.

Note

A few stylesheet specifications, such as the transform property, are SVG2 features, and have not yet been implemented in Inkscape or librsvg. Therefore if you use these in your own custom SVG stylesheet (such as the example above where we rotated leaf labels), they will not be applied properly when converted with those tools. For custom stylesheets like this, a workaround is to convert the SVG to PDF first, using e.g. the programmable chromium engine:

chromium --headless --print-to-pdf=out.pdf in.svg


The resulting PDF file can then be converted by Inkscape, retaining the correct transformations.

#### Editing the SVG#

• Editing can be done in Inkscape (subject to the note above)

Todo

Tips on how to cope with the hierarchical grouping when editing (e.g. in Inkscape using Extensions menu > Arrange > Deep Ungroup, but note that this will mess with the styles!)

## Examples#

### Text examples#

#### Tree orientation#

In the text format, trees (but not tree sequences) can be displayed in different orientations

from IPython.display import HTML
orient = "top", "left", "bottom", "right"
html = []
for o in orient:
tree_string = ts_small.first().draw_text(orientation=o)
html.append(f"<pre style='display: inline-block'>{tree_string}</pre>")
HTML(("&nbsp;"*10).join(html))

      17
┏━━━━┻━━━━┓
┃        16
┃       ┏━┻┓
13       ┃  ┃
┏━┻━┓     ┃  ┃
┃  12     ┃  ┃
┃ ┏━┻━┓   ┃  ┃
┃ ┃   ┃   ┃ 10
┃ ┃   ┃   ┃ ┏┻┓
┃ ┃   9   ┃ ┃ ┃
┃ ┃  ┏┻━┓ ┃ ┃ ┃
┃ ┃  8  ┃ ┃ ┃ ┃
┃ ┃ ┏┻┓ ┃ ┃ ┃ ┃
0 1 2 3 4 5 6 7


       ┏━━━━━━━━━0
┃
┏━━13┫  ┏━━━━━━1
┃    ┃  ┃
┃    ┗12┫     ┏2
┃       ┃   ┏8┫
┃       ┗━━9┫ ┗3
17┫           ┃
┃           ┗━━4
┃
┃  ┏━━━━━━━━━━━5
┃  ┃
┗16┫      ┏━━━━6
┗━━━━10┫
┗━━━━7


0 1 2 3 4 5 6 7
┃ ┃ ┗┳┛ ┃ ┃ ┃ ┃
┃ ┃  8  ┃ ┃ ┃ ┃
┃ ┃  ┗┳━┛ ┃ ┃ ┃
┃ ┃   9   ┃ ┃ ┃
┃ ┃   ┃   ┃ ┗┳┛
┃ ┃   ┃   ┃ 10
┃ ┗━┳━┛   ┃  ┃
┃  12     ┃  ┃
┗━┳━┛     ┃  ┃
13       ┃  ┃
┃       ┗━┳┛
┃        16
┗━━━━┳━━━━┛
17


0━━━━━━━━━┓
┃
1━━━━━━┓  ┣13━━┓
┃  ┃    ┃
2┓     ┣12┛    ┃
┣8┓   ┃       ┃
3┛ ┣9━━┛       ┃
┃           ┣17
4━━┛           ┃
┃
5━━━━━━━━━━━┓  ┃
┃  ┃
6━━━━┓      ┣16┛
┣10━━━━┛
7━━━━┛


### SVG examples#

#### A standard ts plot#

Note that this tree sequence also illustrates a few features which are not normally produced e.g. by msprime simulations, in particular a “empty” site (with no associated mutations) at position 50, and some mutations that occur above root nodes in the trees. Graphically, root mutations necessitate a line above the root node on which to place them, so each tree in this SVG has a nominal “root branch” at the top. Normally, root branches are not drawn, unless the force_root_branch parameter is specified.

ts = tskit.load("data/viz_root_mut.trees")
ts.draw_svg()


#### A fancy formatted plot#

Here we have activated the Y axis, and changed the node style. In particular, we have coloured nodes by time, and increased the internal node symbol size while moving the internal node labels into the symbol; node labels have also been plotted in a sans-serif font. Axis tick labels have been changed to avoid potential overlapping (some Y tick labels have been removed, and the X tick labels rotated).

import numpy as np
seed=370009
ts = msprime.sim_ancestry(7, ploidy=1, sequence_length=1000, random_seed=seed, recombination_rate=0.001)
y_ticks = ts.tables.nodes.time
# Thin the tick values so we don't get labels within 0.01 of each other
y_ticks = np.delete(y_ticks, np.argwhere(np.ediff1d(y_ticks) <= 0.01))

css_string = (
".tree .lab {font-family: sans-serif}"
# Normal X axis tick labels have dominant baseline: hanging, but it needs centring when rotated
+ ".x-axis .tick .lab {text-anchor: start; dominant-baseline: central; transform: rotate(90deg)}"
+ ".y-axis .grid {stroke: #DDDDDD}"
+ ".tree :not(.leaf).node > .lab  {transform: translate(0,0); text-anchor:middle; fill: white}"
+ ".tree :not(.leaf).node > .sym {transform: scale(3.5)}"
+ "".join(f".tree .n{n.id} > .sym {{fill: hsl({int((1-n.time/ts.max_root_time)*260)}, 50%, 50%)}}" for n in ts.nodes())
)
ts.draw_svg(size=(1000, 350), y_axis=True, y_gridlines=True, y_ticks=y_ticks, style=css_string)


#### Highlighted mutations#

Specific mutations can be given a different colour. Moreover, the descendant lineages of specific mutations can be coloured and the branch colours overlay each other as expected. Note that in this example, internal node labels and symbols have been hidden for clarity.

ts = tskit.load("data/viz_root_mut.trees")
css_string = (
".edge {stroke: grey}"
".mut .sym{stroke:pink} .mut text{fill:pink}"
".mut.m2 .sym, .m2>line, .m2>.node .edge{stroke:blue} .mut.m2 .lab{fill:blue}"
".mut.m3 .sym, .m3>line, .m3>.node .edge{stroke:cyan} .mut.m3 .lab{fill:cyan}"
".mut.m4 .sym, .m4>line, .m4>.node .edge{stroke:red} .mut.m4 .lab{fill:red}"
# Hide internal node labels & symbols
".node:not(.leaf) > .sym, .node:not(.leaf) > .lab {display: none}"
)
ts.draw_svg(style=css_string, time_scale="rank", x_lim=[0, 30])


#### Leaf, sample & isolated nodes#

By default, sample nodes are square and non-sample nodes circular (at the moment this can’t easily be changed). However, neither need to be at specific times: sample nodes can be at times other than 0, and nonsample nodes can be at time 0. Moreover, leaves need not be samples, and samples need not be leaves. Here we change the previous tree sequence to make some leaves non-samples and some samples internal nodes. To highlight the change, we have plotted sample nodes in green, and leaf nodes (if not samples) in blue.

tables = tskit.load("data/viz_root_mut.trees").dump_tables()
tables.mutations.clear()
tables.sites.clear()
tables.nodes.flags = np.array([0, 0, 1, 1, 0, 0, 0, 1, 1, 0], dtype=tables.nodes.flags.dtype)
ts = tables.tree_sequence()
css_string=".leaf .sym {fill: blue} .sample > .sym {fill: green}"
ts.draw_svg(style=css_string, x_scale="treewise", time_scale="rank", y_axis=True, y_gridlines=True, x_lim=[0, 10])


Note

By definition, if a node is a sample, it must be present in every tree. This means that there can be sample nodes which are “isolated” in a tree. These are drawn unconnected to the main topology in one or more trees (e.g. nodes 7 and 8 above).

#### Tick labels and gridlines#

Y tick labels can be specified explicitly, which allows time scales to be plotted e.g. in years even if the tree sequence ticks in generations. The grid lines associated with each y tick can also be changed or even hidden individually using the CSS nth-child pseudo-selector, where tickmarks are indexed from the bottom. This is used in the Introgression tutorial to show lines behind the trees at specific, important times. Below we show a slightly simpler example than in that tutorial, keeping node and mutation symbols in black, but colouring gridlines instead:

# Function from the introgression tutorial - see there for justification
import msprime
time_units = 1000 / 25  # Conversion factor for kya to generations

def run_simulation(sequence_length, random_seed=None):
demography = msprime.Demography()
# The same size for all populations; highly unrealistic!
Ne = 10**4

# 2% introgression 50 kya
time=50 * time_units, source='Eurasia', dest='Neanderthal', proportion=0.02)
# Eurasian 'merges' backwards in time into Africa population, 70 kya
time=70 * time_units, source='Eurasia', dest='Africa', proportion=1)
# Neanderthal 'merges' backwards in time into African population, 300 kya
time=300 * time_units, source='Neanderthal', dest='Africa', proportion=1)

ts = msprime.sim_ancestry(
recombination_rate=1e-8,
sequence_length=sequence_length,
samples=[
msprime.SampleSet(1, ploidy=1, population='Africa'),
msprime.SampleSet(1, ploidy=1, population='Eurasia'),
# Neanderthal sample taken 30 kya
msprime.SampleSet(1, ploidy=1, time=30 * time_units, population='Neanderthal'),
],
demography = demography,
record_migrations=True,  # Needed for tracking segments.
random_seed=random_seed,
)
return ts

ts = run_simulation(20 * 10**6, 1)

css = ".y-axis .tick .lab {font-size: 85%}"  # Multi-line labels unimplemented: use smaller font
css += ".y-axis .tick .grid {stroke: lightgrey}"  # Default gridline type
css += ".y-axis .ticks .tick:nth-child(3) .grid {stroke-dasharray: 4}"  # 3rd line from bottom
css += ".y-axis .ticks .tick:nth-child(3) .grid {stroke: magenta}"  # also 3rd line from bottom
css += ".y-axis .ticks .tick:nth-child(4) .grid {stroke: blue}"  # 4th line from bottom
css += ".y-axis .ticks .tick:nth-child(5) .grid {stroke: darkgrey}"  # 5th line from bottom
y_ticks = {0: "0", 30: "30", 50: "Introgress", 70: "Eur origin", 300: "Nea origin", 1000: "1000"}
y_ticks = {y * time_units: lab for y, lab in y_ticks.items()}
ts.draw_svg(
size=(1200, 500),
x_lim=(0, 25_000),
time_scale="log_time",
node_labels = {0: "Afr", 1: "Eur", 2: "Neand"},
y_axis=True,
y_label="Time (kya)",
x_label="Genomic position (bp)",
y_ticks=y_ticks,
y_gridlines=True,
style=css,
)


#### Animation#

The classes attached to the SVG also allow elements to be animated. Here’s a d3.js-based animation of sucessive subtree-prune-and-regraft (SPR) operations, using the ARG representation of a tree sequence to allow identification of pruned edges.

css_string = ".node:not(.sample) > .lab, .node:not(.sample) > .sym {display: none}"
html_string = r"""
<div id="animated_svg_canvas">%s</div>
<script type="text/javascript" src="https://d3js.org/d3.v4.min.js"></script>
<script type="text/javascript">
function diff(A) {return A.slice(1).map((n, i) => { return n - A[i]; });};
function mean(A) {return A.reduce((sum, a) => { return 0 + sum + a },0)/(A.length||1);};
function getRelativeXY(canvas, element, x, y) {
var p = canvas._groups[0][0].createSVGPoint();
var ctm = element.getCTM();
p.x = x || 0;
p.y = y || 0;
return p.matrixTransform(ctm);
};

function animate_SPR(canvas, num_trees) {
d3.selectAll(".tree").attr("opacity", 0);
for(var i=0; i<num_trees - 1; i++)
{
var source_tree = ".tree.t" + i;
var target_tree = ".tree.t" + (i+1);
var dur = 2000;
var delay = i * dur;
d3.select(source_tree)
.datum(function() { return d3.select(this).attr("transform")}) // store the original value
.transition()
.on("start", function() {d3.select(this).attr("opacity", "1");})
.delay(delay)
.duration(dur)
.attr(
"transform", d3.select(target_tree).attr("transform"))
.on("end", function() {
d3.select(this).attr("opacity", "0");
d3.select(this).attr("transform", d3.select(this).datum()); // reset
});
transform_tree(canvas, source_tree, target_tree, dur, delay);
}
};

// NB - this is buggy and doesn't correctly reset the transformations on the elements
// because it is hard to put the subtree back into the correct place in the hierarchy

function transform_tree(canvas, src_tree, target_tree, dur, delay) {
canvas.selectAll(src_tree + " .node").each(function() {
var n_ids = d3.select(this).attr("class").split(/\s+/g).filter(x=>x.match(/^n\d/));
var node_id = n_ids[0].replace(/^n/, "")
var src = src_tree + " .node.n" + node_id;
var target = target_tree + " .node.n" + node_id;

if (d3.select(src).nodes()[0] && d3.select(target).nodes()[0]) {
// The same source and target edges exist, so we can simply move them
d3.select(src).transition()
.delay(delay)
.duration(dur)
.attr("transform", d3.select(target).attr("transform"))
var selection = d3.select(src + " > .edge");
if (!selection.empty()) { // the root may not have an edge
selection.transition()
.delay(delay)
.duration(dur)
.attr("d", d3.select(target +" > .edge").attr("d"))
}
} else {
// No matching node: this could be a recombination
// Hack: the equivalent recombination node is the next one labelled
var target = target_tree + " .node.n" + (1+parseInt(node_id));
// Extract the edge
src_tree_pos = getRelativeXY(canvas, d3.select(src_tree).node());
target_tree_pos = getRelativeXY(canvas, d3.select(target_tree).node());
src_xy = getRelativeXY(canvas, d3.select(src).node());
target_xy = getRelativeXY(canvas, d3.select(target).node());
// Move the subtree out of the hierarchy and into the local tree space,
// so that movements of the containing hierarchy do not affect position
d3.select(src_tree).append(
() => d3.select(src)
.attr(
"transform",
"translate(" + (src_xy.x - src_tree_pos.x) + " " + (src_xy.y - src_tree_pos.y) + ")"
)
.remove()
.node()
);
d3.select(src).transition()
.delay(delay)
.duration(dur)
.attr(
"transform",
"translate(" + (target_xy.x-target_tree_pos.x) + " " + (target_xy.y-target_tree_pos.y) + ")")
selection = d3.select(src + " > .edge");
if (!selection.empty()) {
selection.transition()
.delay(delay)
.duration(dur)
.attr("d", d3.select(target +" > .edge").attr("d"))
}
}
})
};

var svg_text = document.getElementById("animated_svg_canvas").innerHTML;

</script>

<button onclick='animate_SPR(d3.select("#animated_svg_canvas svg"), %s);'>Animate</button>
<button onclick='document.getElementById("animated_svg_canvas").innerHTML = svg_text;'>Reset</button>
"""

# created with record_full_arg needed to track recombination nodes (branch positions)

HTML(html_string % (ts.draw_svg(style=css_string), ts.num_trees))


## Other visualizations#

As well as visualizing a tree sequence as, well, a sequence of local trees, or by plotting statistical summaries, other visualizations are possible, some of which are outlined below.

### Graph representations#

A tree sequence can be treated as a specific form of (directed) graph consisting of nodes connected by edges. Standard graph visualization software, such as graphviz can therefore be used to represent tree sequence topologies. This is a relatively common approach to visualizing the full “Ancestral Recombination Graph” or ARG (a structure in which some nodes are “recombination nodes”, and which is possible to represent as a tree sequence).

Todo

Link to the ARG tutorial, once it is created, and show a picture like this:

(from here)

### Demographic processes#

If you are generating a tree sequence via a Demes model, then you can visualize a schematic of the demography itself (rather than the resulting tree sequence) using the DemesDraw software. For example, here’s the plotting code to generate the demography plot from the “What is a tree sequence?” tutorial:

import matplotlib_inline
import matplotlib.pyplot as plt
%matplotlib inline
matplotlib_inline.backend_inline.set_matplotlib_formats('svg')

import demes
import demesdraw

def size_max(graph):
return max(
max(epoch.start_size, epoch.end_size)
for deme in graph.demes
for epoch in deme.epochs
)

# See https://popsim-consortium.github.io/demes-docs/ for the yml spec for the file below