def K80(mu=1., kappa=0.1, **kwargs):
"""
Kimura 1980 model. Assumes equal concentrations across nucleotides, but
allows different rates between transitions and transversions. The ratio
of the transversion/transition rates is given by kappa parameter.
For more info, see
Kimura (1980), J. Mol. Evol. 16 (2): 111–120. doi:10.1007/BF01731581.
Current implementation of the model does not account for the gaps.
Parameters
-----------
mu : float
Overall substitution rate
kappa : float
Ratio of transversion/transition rates
"""
from gtr import GTR
num_chars = len(alphabets['nuc_nogap'])
pi = np.ones(len(alphabets['nuc_nogap']), dtype=float) / len(
alphabets['nuc_nogap'])
W = _create_transversion_transition_W(kappa)
gtr = GTR(alphabet=alphabets['nuc_nogap'])
gtr.assign_rates(mu=mu, pi=pi, W=W)
return gtr
def JC69(mu=1.0, alphabet="nuc", **kwargs):
"""
Jukes-Cantor 1969 model. This model assumes equal concentrations
of the nucleotides and equal transition rates between nucleotide states.
For more info, see: Jukes and Cantor (1969). Evolution of Protein Molecules.
New York: Academic Press. pp. 21–132
Parameters
-----------
mu : float
substitution rate
alphabet : str
specify alphabet to use.
Available alphabets are:
'nuc' - nucleotides only, gaps ignored
'nuc_gap' - nucleotide alphabet with gaps, gaps can be ignored optionally
"""
from gtr import GTR
num_chars = len(alphabets[alphabet])
W, pi = np.ones((num_chars, num_chars)), np.ones(num_chars)
gtr = GTR(alphabet=alphabet)
gtr.assign_rates(mu=mu, pi=pi, W=W)
return gtr
def T92(mu=1.0, pi_GC=0.5, kappa=0.1, **kwargs):
"""
Tamura 1992 model. Extending Kimura (1980) model for the case where a
G+C-content bias exists. Link:
Tamura K (1992), Mol. Biol. Evol. 9 (4): 678–687. DOI: 10.1093/oxfordjournals.molbev.a040752
Current implementation of the model does not account for the gaps
Parameters
-----------
mu : float
substitution rate
pi_GC : float
relative GC content
kappa : float
relative transversion/transition rate
"""
from gtr import GTR
W = _create_transversion_transition_W(kappa)
# A C G T
if pi_CG >= 1.:
raise ValueError(
"The relative CG content specified is larger than 1.0!")
pi = np.array([(1. - pi_CG) * 0.5, pi_CG * 0.5, pi_CG * 0.5,
(1 - pi_CG) * 0.5])
gtr = GTR(alphabet=alphabets['nuc_nogap'])
gtr.assign_rates(mu=mu, pi=pi, W=W)
return gtr
def TN93(mu=1.0, kappa1=1., kappa2=1., pi=None, **kwargs):
"""
Tamura and Nei 1993. The model distinguishes between the two different types of
transition: (A <-> G) is allowed to have a different rate to (C<->T).
Transversions have the same rate. The frequencies of the nucleotides are allowed
to be different. Link:
Tamura, Nei (1993), MolBiol Evol. 10 (3): 512–526. DOI:10.1093/oxfordjournals.molbev.a040023
Parameters
-----------
mu : float
Substitution rate
kappa1 : float
relative A<-->C, A<-->T, T<-->G and G<-->C rates
kappa2 : float
relative C<-->T rate
Note
----
Rate of A<-->G substitution is set to one. All other rates (kappa1, kappa2)
are specified relative to this rate
"""
from gtr import GTR
if pi is None:
pi = 0.25 * np.ones(4, dtype=float)
W = np.ones((4, 4))
W = np.array([[1, kappa1, 1, kappa1], [kappa1, 1, kappa1, kappa2],
[1, kappa1, 1, kappa1], [kappa1, kappa2, kappa1, 1]],
dtype=float)
pi /= pi.sum()
num_chars = len(alphabets['nuc_nogap'])
if num_chars != pi.shape[0]:
pi = np.ones((num_chars, ), dtype=float)
print(
"GTR: Warning!The number of the characters in the alphabet does not match the "
"shape of the vector of equilibrium frequencies Pi -- assuming equal frequencies for all states."
)
gtr = GTR(alphabet=alphabets['nuc'])
gtr.assign_rates(mu=mu, pi=pi, W=W)
return gtr
def F81(mu=1.0, pi=None, alphabet="nuc", **kwargs):
"""
Felsenstein 1981 model. Assumes non-equal concentrations across nucleotides,
but the transition rate between all states is assumed to be equal. See
Felsenstein (1981), J. Mol. Evol. 17 (6): 368–376. doi:10.1007/BF01734359
for details.
Current implementation of the model does not account for the gaps (treatment of
gaps as characters is possible if specify alphabet='nuc_gap').
Parameters
-----------
mu : float
Substitution rate
pi : numpy.array
Nucleotide concentrations
alphabet : str
Alphabet to use. POsiible values are: ['nuc', 'nuc_gap'] Default 'nuc', which discounts al gaps.
'nuc_gap' alphabet enables treatmen of gaps as characters.
"""
from gtr import GTR
if pi is None:
pi = 0.25 * np.ones(4, dtype=float)
num_chars = len(alphabets[alphabet])
pi = np.array(pi, dtype=float)
if num_chars != len(pi):
pi = np.ones((num_chars, ), dtype=float)
print(
"GTR: Warning!The number of the characters in the alphabet does not match the "
"shape of the vector of equilibrium frequencies Pi -- assuming equal frequencies for all states."
)
W = np.ones((num_chars, num_chars))
pi /= (1.0 * np.sum(pi))
gtr = GTR(alphabet=alphabets[alphabet])
gtr.assign_rates(mu=mu, pi=pi, W=W)
return gtr
def HKY85(mu=1.0, pi=None, kappa=0.1, **kwargs):
"""
Hasegawa, Kishino and Yano 1985 model. Allows different concentrations of the
nucleotides (as in F81) + distinguishes between transition/transversionsubstitutions
(similar to K80). Link:
Hasegawa, Kishino, Yano (1985), J. Mol. Evol. 22 (2): 160–174. doi:10.1007/BF02101694
Current implementation of the model does not account for the gaps
Parameters
-----------
mu : float
Substitution rate
pi : numpy.array
Nucleotide concentrations
kappa : float
Ratio of transversion/transition substitution rates
"""
from gtr import GTR
if pi is None:
pi = 0.25 * np.ones(4, dtype=float)
num_chars = len(alphabets['nuc_nogap'])
if num_chars != pi.shape[0]:
pi = np.ones((num_chars, ), dtype=float)
print(
"GTR: Warning!The number of the characters in the alphabet does not match the "
"shape of the vector of equilibrium frequencies Pi -- assuming equal frequencies for all states."
)
W = _create_transversion_transition_W(kappa)
pi /= pi.sum()
gtr = GTR(alphabet=alphabets['nuc_nogap'])
gtr.assign_rates(mu=mu, pi=pi, W=W)
return gtr
def JTT92(mu=1.0):
from gtr import GTR
# stationary concentrations:
pis = np.array([
0.07674789, 0.05169087, 0.04264509, 0.05154407, 0.01980301, 0.04075195,
0.06182989, 0.07315199, 0.02294399, 0.05376110, 0.09190390, 0.05867583,
0.02382594, 0.04012589, 0.05090097, 0.06876503, 0.05856501, 0.01426057,
0.03210196, 0.06600504
])
# attempt matrix (FIXME)
Q = np.array([[
-1.247831, 0.044229, 0.041179, 0.061769, 0.042704, 0.043467, 0.08007,
0.136501, 0.02059, 0.027453, 0.022877, 0.02669, 0.041179, 0.011439,
0.14794, 0.288253, 0.362223, 0.006863, 0.008388, 0.227247
],
[
0.029789, -1.025965, 0.023112, 0.008218, 0.058038,
0.159218, 0.014895, 0.070364, 0.168463, 0.011299,
0.019517, 0.33179, 0.022599, 0.002568, 0.038007,
0.051874, 0.032871, 0.064714, 0.010272, 0.008731
],
[
0.022881, 0.019068, -1.280568, 0.223727, 0.014407,
0.03644, 0.024576, 0.034322, 0.165676, 0.019915,
0.005085, 0.11144, 0.012712, 0.004237, 0.006356,
0.213134, 0.098304, 0.00339, 0.029661, 0.00678
],
[
0.041484, 0.008194, 0.270413, -1.044903, 0.005121,
0.025095, 0.392816, 0.066579, 0.05736, 0.005634,
0.003585, 0.013316, 0.007682, 0.002049, 0.007682,
0.030217, 0.019462, 0.002049, 0.023559, 0.015877
],
[
0.011019, 0.022234, 0.00669, 0.001968, -0.56571,
0.001771, 0.000984, 0.011609, 0.013577, 0.003345,
0.004526, 0.001377, 0.0061, 0.015348, 0.002755, 0.043878,
0.008264, 0.022628, 0.041124, 0.012199
],
[
0.02308, 0.125524, 0.034823, 0.019841, 0.003644,
-1.04415, 0.130788, 0.010528, 0.241735, 0.003644,
0.029154, 0.118235, 0.017411, 0.00162, 0.066406,
0.021461, 0.020651, 0.007288, 0.009718, 0.008098
],
[
0.064507, 0.017816, 0.035632, 0.471205, 0.003072,
0.198435, -0.944343, 0.073107, 0.015973, 0.007372,
0.005529, 0.111197, 0.011058, 0.003072, 0.011058,
0.01843, 0.019659, 0.006143, 0.0043, 0.027646
],
[
0.130105, 0.099578, 0.058874, 0.09449, 0.042884,
0.018898, 0.086495, -0.647831, 0.016717, 0.004361,
0.004361, 0.019625, 0.010176, 0.003634, 0.017444,
0.146096, 0.023986, 0.039976, 0.005815, 0.034162
],
[
0.006155, 0.074775, 0.089138, 0.025533, 0.01573, 0.1361,
0.005927, 0.005243, -1.135695, 0.003648, 0.012767,
0.010259, 0.007523, 0.009119, 0.026217, 0.016642,
0.010487, 0.001824, 0.130629, 0.002508
],
[
0.01923, 0.011752, 0.025106, 0.005876, 0.009081,
0.004808, 0.00641, 0.003205, 0.008547, -1.273602,
0.122326, 0.011218, 0.25587, 0.047542, 0.005342,
0.021367, 0.130873, 0.004808, 0.017094, 0.513342
],
[
0.027395, 0.0347, 0.010958, 0.006392, 0.021003, 0.065748,
0.008219, 0.005479, 0.051137, 0.209115, -0.668139,
0.012784, 0.354309, 0.226465, 0.093143, 0.053877,
0.022829, 0.047485, 0.021916, 0.16437
],
[
0.020405, 0.376625, 0.153332, 0.015158, 0.004081,
0.170239, 0.105525, 0.015741, 0.026235, 0.012243,
0.008162, -0.900734, 0.037896, 0.002332, 0.012243,
0.027401, 0.06005, 0.00583, 0.004664, 0.008162
],
[
0.012784, 0.010416, 0.007102, 0.003551, 0.007339,
0.01018, 0.004261, 0.003314, 0.007812, 0.113397,
0.091854, 0.015388, -1.182051, 0.01018, 0.003788,
0.006865, 0.053503, 0.005682, 0.004261, 0.076466
],
[
0.00598, 0.001993, 0.003987, 0.001595, 0.031098,
0.001595, 0.001993, 0.001993, 0.015948, 0.035484,
0.098877, 0.001595, 0.017144, -0.637182, 0.006778,
0.03668, 0.004784, 0.021131, 0.213701, 0.024719
],
[
0.098117, 0.037426, 0.007586, 0.007586, 0.007081,
0.082944, 0.009104, 0.012138, 0.058162, 0.005058,
0.051587, 0.010621, 0.008092, 0.008598, -0.727675,
0.144141, 0.059679, 0.003035, 0.005058, 0.011632
],
[
0.258271, 0.069009, 0.343678, 0.040312, 0.152366,
0.036213, 0.020498, 0.137334, 0.049878, 0.02733,
0.040312, 0.032113, 0.019814, 0.06286, 0.194728,
-1.447863, 0.325913, 0.023914, 0.043045, 0.025964
],
[
0.276406, 0.037242, 0.135003, 0.022112, 0.02444,
0.029677, 0.018621, 0.019203, 0.026768, 0.142567,
0.014548, 0.059936, 0.131511, 0.006983, 0.068665,
0.27757, -1.335389, 0.006983, 0.01222, 0.065174
],
[
0.001275, 0.017854, 0.001134, 0.000567, 0.016295,
0.002551, 0.001417, 0.007793, 0.001134, 0.001275,
0.007368, 0.001417, 0.003401, 0.00751, 0.00085, 0.004959,
0.0017, -0.312785, 0.010061, 0.003542
],
[
0.003509, 0.006379, 0.022328, 0.014673, 0.066664,
0.007655, 0.002233, 0.002552, 0.182769, 0.010207,
0.007655, 0.002552, 0.005741, 0.170967, 0.00319,
0.020095, 0.006698, 0.022647, -0.605978, 0.005103
],
[
0.195438, 0.011149, 0.010493, 0.020331, 0.040662,
0.013117, 0.029512, 0.030824, 0.007214, 0.630254,
0.11805, 0.009182, 0.211834, 0.040662, 0.015084,
0.024922, 0.073453, 0.016396, 0.010493, -1.241722
]])
Spis = np.sqrt(pis[None, :] / pis[:, None])
W = Q * Spis
gtr = GTR(alphabet=alphabets['aa_nogap'])
gtr.assign_rates(mu=mu, pi=pis, W=W)
return gtr