# Now a function must be defined, that converts the similarity depicted
# by a substitution matrix into a distance required by the UPGMA method.
# In this case, the distance is defined as the difference between the
# similarity of the two symbols and the average maximum similarity of
# the symbols to themselves.
#
# Finally the obtained (phylogenetic) tree is plotted as dendrogram.
def get_distance(similarities, i, j):
s_max = (similarities[i, i] + similarities[j, j]) / 2
return s_max - similarities[i, j]
distances = np.zeros(similarities.shape)
for i in range(distances.shape[0]):
for j in range(distances.shape[1]):
distances[i, j] = get_distance(similarities, i, j)
tree = phylo.upgma(distances)
fig = plt.figure(figsize=(8.0, 5.0))
ax = fig.add_subplot(111)
# Use the 3-letter amino acid code aa label
labels = [
seq.ProteinSequence.convert_letter_1to3(letter).capitalize()
for letter in matrix.get_alphabet1()
]
graphics.plot_dendrogram(ax, tree, orientation="top", labels=labels)
ax.set_ylabel("Distance")
# Add grid for clearer distance perception
ax.yaxis.grid(color="lightgray")
plt.show()
# Create tree from root node
tree = phylo.Tree(root=root)
# Trees can be converted into Newick notation
print("Tree:", tree.to_newick(labels=fruits))
# Distances can be omitted
print("Tree w/o distances:",
tree.to_newick(labels=fruits, include_distance=False))
# Distances can be measured
distance = tree.get_distance(fruits.index("Apple"), fruits.index("Banana"))
print("Distance Apple-Banana:", distance)
########################################################################
# You can also plot a tree as dendrogram.
fig, ax = plt.subplots(figsize=(6.0, 6.0))
graphics.plot_dendrogram(ax, tree, labels=fruits)
fig.tight_layout()
########################################################################
# From distances to trees
# ^^^^^^^^^^^^^^^^^^^^^^^
#
# When you want to create a :class:`Tree` from distances obtained for
# example from sequence alignments, you can use the UPGMA algorithm
# implemented in the function of the same name :func:`upgma()`.
distances = np.array([[0, 17, 21, 31, 23], [17, 0, 30, 34, 21],
[21, 30, 0, 28, 39], [31, 34, 28, 0, 43],
[23, 21, 39, 43, 0]])
tree = phylo.upgma(distances)
fig, ax = plt.subplots(figsize=(6.0, 3.0))
def _show_tree(tree):
import biotite.sequence.graphics as graphics
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
graphics.plot_dendrogram(ax, tree)
plt.show()
app.join()
alignment = app.get_alignment()
print(alignment)
########################################################################
# In most MSA software even more information than the mere alignment can
# be extracted.
# For instance the guide tree that was used for the alignment can be
# obtained from the MUSCLE output.
import matplotlib.pyplot as plt
import biotite.sequence.graphics as graphics
tree = app.get_guide_tree()
fig, ax = plt.subplots()
graphics.plot_dendrogram(
ax, tree, labels=[str(sequence) for sequence in [seq1, seq2, seq3, seq4]])
ax.set_xlabel("Distance")
fig.tight_layout()
########################################################################
# For the lazy people there is also a convenience method,
# that handles the :class:`Application` execution internally.
# However, this shortcut returns only the :class:`Alignment`.
alignment = muscle.MuscleApp.align([seq1, seq2, seq3, seq4])
########################################################################
# The alternatives to MUSCLE are Clustal-Omega and MAFFT.
# To use them, simply replace :class:`MuscleApp` with
# :class:`ClustalOmegaApp` or :class:`MafftApp` and you are done.
for name, seq_str in zip(UNIPROT_IDS.keys(), fasta_file.values())
}
### create a simple phylogenetic tree
# create MSA
alignment = clustalo.ClustalOmegaApp.align(list(sequences.values()))
# build simple tree based on deviation from sequence identity
distances = 1 - align.get_pairwise_sequence_identity(alignment,
mode="shortest")
tree = phylo.upgma(distances)
### plot the tree
fig, ax = plt.subplots(1, 1, figsize=(8, 5))
graphics.plot_dendrogram(ax,
tree,
orientation="left",
labels=list(UNIPROT_IDS.keys()),
show_distance=False,
linewidth=2)
ax.grid(False)
ax.set_xticks([])
# distance indicator
indicator_len = 0.1
indicator_start = (ax.get_xlim()[0] + ax.get_xlim()[1] * 0.02,
ax.get_ylim()[1] - ax.get_ylim()[1] * 0.15)
indicator_stop = (indicator_start[0] + indicator_len, indicator_start[1])
indicator_center = ((indicator_start[0] + indicator_stop[0]) / 2,
(indicator_start[1] + 0.25))
ax.annotate("",
xy=indicator_start,
xytext=indicator_stop,
