def test_node_distance(tree):
"""
Test whether the `distance_to()` and `lowest_common_ancestor()` work
correctly.
"""
# Tree is created via UPGMA
# -> The distances to root should be equal for all leaf nodes
dist = tree.root.distance_to(tree.leaves[0])
for leaf in tree.leaves:
assert leaf.distance_to(tree.root) == dist
# Example topological distances
assert tree.get_distance(0, 19, True) == 9
assert tree.get_distance(4, 2, True) == 10
# All pairwise leaf node distances should be sufficient
# to reconstruct the same tree via UPGMA
ref_dist_mat = np.zeros((len(tree), len(tree)))
for i in range(len(tree)):
for j in range(len(tree)):
ref_dist_mat[i, j] = tree.get_distance(i, j)
assert np.allclose(ref_dist_mat, ref_dist_mat.T)
new_tree = phylo.upgma(ref_dist_mat)
test_dist_mat = np.zeros((len(tree), len(tree)))
for i in range(len(tree)):
for j in range(len(tree)):
test_dist_mat[i, j] = new_tree.get_distance(i, j)
assert np.allclose(test_dist_mat, ref_dist_mat)
# 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()
def tree(distances):
return phylo.upgma(distances)
