fit discrete traits

Fitting Discrete Markov Models¶

This notebook demonstrates fitting discrete-state continuous-time Markov models and inferring ancestral states with infer_ancestral_states_discrete_mk().

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import toytree

tree = toytree.rtree.unittree(12, treeheight=1.0, seed=2)

import toytree tree = toytree.rtree.unittree(12, treeheight=1.0, seed=2)

Simulate tip data and fit a model¶

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traits = toytree.pcm.simulate_discrete_data(
    tree=tree,
    nstates=3,
    model='ER',
    nreplicates=1,
    trait_name='state',
    tips_only=True,
)
fit = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ER',
    inplace=False,
)
fit['model_fit']

traits = toytree.pcm.simulate_discrete_data( tree=tree, nstates=3, model='ER', nreplicates=1, trait_name='state', tips_only=True, ) fit = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ER', inplace=False, ) fit['model_fit']

Inspect inferred states and probabilities¶

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df = fit['data']
df.head()

df = fit['data'] df.head()

Plot inferred states on the tree¶

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cm = toytree.color.CMAPS['Set2'] if hasattr(toytree, 'color') else None
states = df['state_anc']
# use a simple palette for three states
palette = ['#4c78a8', '#f58518', '#54a24b']
node_colors = [palette[int(states[i])] if str(states[i]) != 'nan' else '#c7c7c7' for i in range(tree.nnodes)]
c, a, m = tree.draw(layout='r', node_colors=node_colors, node_sizes=14, tip_labels=True, scale_bar=True)
c

cm = toytree.color.CMAPS['Set2'] if hasattr(toytree, 'color') else None states = df['state_anc'] # use a simple palette for three states palette = ['#4c78a8', '#f58518', '#54a24b'] node_colors = [palette[int(states[i])] if str(states[i]) != 'nan' else '#c7c7c7' for i in range(tree.nnodes)] c, a, m = tree.draw(layout='r', node_colors=node_colors, node_sizes=14, tip_labels=True, scale_bar=True) c

Plot posterior probabilities as pie markers¶

Use add_node_pie_markers with the posterior probabilities to visualize ancestral state uncertainty at each node.

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# infer and store posterior probabilities on the tree
out = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ER',
    inplace=True,
)
c, a, m = tree.draw(layout='d', tip_labels=True, scale_bar=True)
tree.annotate.add_node_pie_markers(
    a, 'state_anc_posterior', size=10, istroke_width=1, mask=False
)
c

# infer and store posterior probabilities on the tree out = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ER', inplace=True, ) c, a, m = tree.draw(layout='d', tip_labels=True, scale_bar=True) tree.annotate.add_node_pie_markers( a, 'state_anc_posterior', size=10, istroke_width=1, mask=False ) c

Parameter effects¶

Below are short examples showing how key fitting parameters influence inference.

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import numpy as np

# Example: constrain relative rates (ARD)
rates = np.array([[0, 2.0, 0.5], [1.0, 0, 0.2], [0.8, 1.5, 0]])
fit_rates = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ARD',
    fixed_rates=rates,
    inplace=False,
)
fit_rates['model_fit']

import numpy as np # Example: constrain relative rates (ARD) rates = np.array([[0, 2.0, 0.5], [1.0, 0, 0.2], [0.8, 1.5, 0]]) fit_rates = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ARD', fixed_rates=rates, inplace=False, ) fit_rates['model_fit']

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# Example: constrain state frequencies
freqs = np.array([0.7, 0.2, 0.1])
fit_freqs = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ER',
    fixed_state_frequencies=freqs,
    inplace=False,
)
fit_freqs['model_fit']

# Example: constrain state frequencies freqs = np.array([0.7, 0.2, 0.1]) fit_freqs = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ER', fixed_state_frequencies=freqs, inplace=False, ) fit_freqs['model_fit']

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# Example: set a root prior
root_prior = np.array([0.05, 0.05, 0.90])
fit_root = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ER',
    root_prior=root_prior,
    inplace=False,
)
fit_root['model_fit']

# Example: set a root prior root_prior = np.array([0.05, 0.05, 0.90]) fit_root = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ER', root_prior=root_prior, inplace=False, ) fit_root['model_fit']

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# Example: scale overall rate
fit_slow = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ER',
    rate_scalar=0.2,
    inplace=False,
)
fit_fast = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ER',
    rate_scalar=2.0,
    inplace=False,
)
fit_slow['model_fit']
fit_fast['model_fit']

# Example: scale overall rate fit_slow = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ER', rate_scalar=0.2, inplace=False, ) fit_fast = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ER', rate_scalar=2.0, inplace=False, ) fit_slow['model_fit'] fit_fast['model_fit']

Fossil constraints: with vs without¶

Compare inference with and without internal-node observations.

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# Without fossil constraint
base = tree.pcm.infer_ancestral_states_discrete_mk(
    data=traits,
    nstates=3,
    model='ER',
    inplace=False,
)

# With a fossil constraint on an internal node
fossil_series = traits.copy().reindex(range(tree.nnodes))
fossil_series.loc[tree[-2]._idx] = 1
fossil = tree.pcm.infer_ancestral_states_discrete_mk(
    data=fossil_series,
    nstates=3,
    model='ER',
    inplace=False,
)

# Plot a comparison of inferred states
palette = ['#4c78a8', '#f58518', '#54a24b']
def plot_states(df, title):
    states = df['state_anc']
    node_colors = [palette[int(states[i])] if str(states[i]) != 'nan' else '#c7c7c7' for i in range(tree.nnodes)]
    c, a, m = tree.draw(layout='r', node_colors=node_colors, node_sizes=12, tip_labels=True, scale_bar=True)
    a.label.text = title
    return c

c_base = plot_states(base['data'], 'no fossil constraint')
c_fossil = plot_states(fossil['data'], 'with fossil constraint')
c_base

# Without fossil constraint base = tree.pcm.infer_ancestral_states_discrete_mk( data=traits, nstates=3, model='ER', inplace=False, ) # With a fossil constraint on an internal node fossil_series = traits.copy().reindex(range(tree.nnodes)) fossil_series.loc[tree[-2]._idx] = 1 fossil = tree.pcm.infer_ancestral_states_discrete_mk( data=fossil_series, nstates=3, model='ER', inplace=False, ) # Plot a comparison of inferred states palette = ['#4c78a8', '#f58518', '#54a24b'] def plot_states(df, title): states = df['state_anc'] node_colors = [palette[int(states[i])] if str(states[i]) != 'nan' else '#c7c7c7' for i in range(tree.nnodes)] c, a, m = tree.draw(layout='r', node_colors=node_colors, node_sizes=12, tip_labels=True, scale_bar=True) a.label.text = title return c c_base = plot_states(base['data'], 'no fossil constraint') c_fossil = plot_states(fossil['data'], 'with fossil constraint') c_base

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c_fossil

c_fossil