yeast HKY+geneconv with tau=0¶
In this example we estimate parameters of a molecular model of the evolution of the DNA sequences of some paralogous genes using the following molecular data from yeast.
1 | ((((((cerevisiae,paradoxus),mikatae),kudriavzevii), bayanus),castellii),kluyveri);
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | bayanusYDR502C
ATGAGCAAAACCTTTTTATTTACTTCTGAATCTGTCGGTGAAGGTCACCCAGACAAGATTTGTGATCAAGTCTCTGATGCTGTCTTGGATGCTTGTTTGGAACAAGATCCATACTCTAAGGTCGCTTGTGAAACTGCTGCCAAGACTGGTATGATTATGGTTTTTGGTGAAATTACCACTAAGGCTAAGTTGGACTACCAACAAATTGTTAGAGACACTATCAAGAAGATTGGTTACGACGATTCTGCCAAGGGTTTCGATTACAAAACTTGTAACGTTTTGGTTGCTATTGAACAGCAATCTCCAGATATTGCTCAAGGTTTACATTATGAACAAAACTTGGAAGATTTAGGTGCCGGTGACCAAGGTATCATGTTTGGTTACGCTACTGATGAAACTCCAGAAGGTTTGCCATTGACCATTCTATTGGCTCACAAATTGAATATGGCTATGGCCGACGCTAGAAGAGACGGTTCCATTCCATGGTTGAGACCAGACACAAAGACCCAGGTCACAGTTGAATACGAAGATGACAATGGTAGATGGGTTCCAAAGAGAATAGACACCGTTGTTATCTCTGCTCAACATGCTGAGGAAATTTCCACAGCTGATTTGAGAGCTCAGCTACAAACAGATATCGTCGAAAAGGTCATTCCTAAAGACATGTTAGACGAAAACACCAAGTACTTCATCCAACCCTCCGGTAGATTCGTTATCGGTGGTCCTCAAGGTGATGCTGGTTTGACCGGTAGAAAGATTATTGTCGATGCTTACGGTGGTGCTTCATCCGTTGGTGGTGGTGCCTTTTCCGGTAAGGATTACTCCAAGGTCGATCGTTCTGCTGCTTATGCCGCTAGATGGGTTGCTAAATCTTTAGTTGCCGCTGGCTTGTGTAAGAGAGTGCAAGTTCAATTCTCTTATGCTATCGGTATTGCCGAACCATTGTCCTTGCACGTCGACACCTACGGTACCGCTACCAAGTCCGACGATGAAATCATTGCTATCATTAAGAAGAATTTCGACTTGAGACCTGGTGTCTTAGTGAAGGAATTGGATTTGGCTAGACCAATTTACTTGCCAACTGCTTCTTACGGTCATTTTACCAACCAAGAATACTCCTGGGAAAAACCAAAGAAATTGGAC
bayanusYLR180W
ATGGCCGGTACATTTTTATTCACTTCTGAATCCGTCGGTGAAGGTCACCCAGACAAGATCTGTGACCAAGTCTCCGACGCCATCTTGGACGCTTGTTTGGCCGAGGACCCTCATTCCAGGGTTGCGTGCGAAACGGCCGCTAAGACCGGTATGATCATGGTCTTTGGTGAAATCACGACCAAGGCGCAACTGGACTACCAGAAGATCGTCAGAGACACCATCCAAAAGATCGGCTACGACGACTCCGCCAAGGGGTTCGACTACAAGACCTGTAACGTTCTTGTCGCCATCGAACAGCAGTCTCCGGACATCGCCCAAGGTGTGCACGAAGAGAAGGACCTAGAAGACATCGGTGCCGGTGACCAAGGTATCATGTTTGGCTACGCCACCGATGAGACCCCAGAAGGTCTACCCTTGACCATTCTGCTGGCTCACAAGCTGAACATGGTCATGGCCGACGCTAGAAGAGACGGCTCCTTGCCATGGTTGAGACCAGACACCAAGACCCAAGTCACCGTCGAGTACAAGGACGACCACGGCAGATGGGTCCCACAAAGGATCGACACCGTTGTCGTTTCCGCCCAACATGCGGACGACATCTCCACCGAGGACCTAAGAGCGCAATTGAAGTCCGAGATCATCGAAAAAGTCATCCCAAGCGACATGCTGGACGAAAACACCAAGTACTTCATCCAACCCTCCGGTAGATTCGTTATCGGTGGTCCTCAAGGTGACGCTGGTTTGACCGGTAGAAAGATTATCGTCGATGCCTACGGTGGTGCCTCCTCCGTCGGTGGTGGTGCCTTCTCCGGGAAGGATTACTCCAAGGTCGACCGTTCCGCCGCCTACGCTGCCAGATGGGTCGCCAAGTCCCTGCTTGCCGCCGGTCTGTGTAAGAGAGTCCAAGTCCAATTCTCCTACGCCATCGGTATTGCCGAGCCATTGTCCTTGCACGTCGACACCTACGGTACCGCTACCAAGTCCGACGAGGAAATCATCGCCATCATCAAGAAGAACTTCGACTTGAGACCCGGTGTATTGGTCAAGGAATTGGACTTGGCCAGACCAATCTACTTGCCAACCGCTTCTTACGGCCACTTCACTAACCAAGAATACCCATGGGAAAAGCCAAAGACCTTGAAG
cerevisiaeYDR502C
ATGAGCAAAACTTTCTTATTTACCTCTGAATCCGTCGGTGAAGGTCACCCAGACAAGATTTGTGACCAAGTTTCTGATGCTATTTTGGACGCTTGTTTAGAACAAGATCCATTCTCCAAGGTTGCCTGTGAAACAGCTGCCAAAACTGGTATGATTATGGTTTTCGGTGAAATTACCACCAAAGCTAGACTTGACTACCAACAAATAGTAAGAGATACCATCAAGAAGATTGGTTATGACGATTCTGCCAAGGGTTTCGACTACAAGACATGTAATGTTTTAGTAGCTATCGAACAACAATCTCCAGATATCGCTCAAGGTCTGCACTATGAAAAGAGCTTAGAAGACTTAGGTGCTGGTGACCAAGGTATAATGTTTGGTTACGCTACAGACGAAACTCCAGAAGGGTTACCATTGACCATTCTTTTGGCTCACAAATTGAACATGGCTATGGCAGATGCTAGAAGAGATGGTTCTCTCCCATGGTTGAGACCAGACACAAAGACTCAAGTCACTGTCGAATACGAAGACGACAATGGTAGATGGGTTCCAAAGAGGATAGATACCGTTGTTATTTCTGCTCAACATGCTGATGAAATTTCCACCGCTGACTTGAGAACTCAACTTCAAAAAGATATTGTTGAAAAGGTCATACCAAAGGATATGTTAGACGAAAATACCAAATATTTCATCCAACCATCCGGTAGATTCGTCATCGGTGGTCCTCAAGGTGACGCTGGTTTGACCGGTAGAAAGATTATTGTCGACGCTTACGGTGGTGCCTCATCCGTCGGTGGTGGTGCCTTCTCCGGTAAGGACTATTCCAAGGTCGATCGTTCCGCTGCTTACGCTGCTAGATGGGTTGCCAAGTCTCTAGTTGCCGCTGGTTTGTGTAAGAGAGTCCAAGTCCAATTTTCATATGCTATTGGTATTGCTGAACCATTGTCTTTACATGTGGACACCTATGGTACAGCTACAAAATCAGATGACGAAATCATTGAAATTATTAAGAAGAACTTCGACTTGAGACCAGGTGTGTTAGTAAAGGAATTAGATTTGGCTAGACCAATTTACTTACCAACCGCTTCTTATGGTCACTTCACTAATCAAGAGTACTCATGGGAAAAACCAAAGAAATTGGAA
cerevisiaeYLR180W
ATGGCCGGTACATTTTTATTCACTTCTGAATCCGTTGGTGAAGGTCACCCAGATAAGATCTGTGACCAAGTTTCCGACGCCATCTTGGACGCTTGTTTAGCCGAGGACCCTCACTCCAAAGTTGCGTGTGAAACCGCGGCAAAGACTGGTATGATTATGGTCTTTGGTGAAATTACTACCAAGGCACAGTTGGATTACCAAAAAATCGTCAGAGACACCATCAAGAAGATTGGTTACGATGATTCCGCCAAGGGTTTCGACTATAAGACCTGTAACGTCCTTGTCGCCATTGAGCAACAATCTCCAGATATCGCCCAAGGTGTCCACGAGGAGAAGGATTTGGAAGACATCGGTGCCGGTGACCAAGGTATCATGTTTGGTTACGCCACAGATGAAACTCCAGAGGGTTTGCCTTTGACTATTCTTTTGGCTCATAAACTAAACATGGCCATGGCTGACGCGAGAAGAGATGGCTCTTTAGCGTGGTTGAGACCAGACACCAAGACTCAAGTCACCGTCGAATACAAGGATGACCACGGTAGATGGGTTCCACAAAGAATCGACACCGTCGTCGTCTCCGCTCAACATGCTGACGAAATCACGACCGAGGACTTAAGAGCGCAACTAAAGTCCGAGATCATTGAAAAAGTCATCCCAAGAGACATGTTGGACGAAAACACCAAATACTTTATCCAACCTTCCGGTAGATTCGTCATCGGTGGTCCTCAAGGTGACGCTGGTTTGACCGGTAGAAAGATCATCGTCGACGCTTACGGTGGTGCCTCATCCGTCGGTGGTGGTGCCTTCTCCGGTAAGGACTACTCTAAGGTTGATCGTTCTGCCGCTTATGCCGCTAGATGGGTTGCCAAGTCCCTAGTTGCCGCTGGTTTATGTAAGAGAGTTCAAGTTCAATTTTCTTATGCCATCGGTATTGCGGAACCATTGTCCTTGCACGTTGACACCTATGGTACTGCGACCAAGTCTGACGAAGAAATTATCGACATTATCAGCAAGAACTTTGACTTGAGACCTGGTGTATTGGTCAAGGAGTTGGACTTAGCTAGACCAATCTACTTGCCAACCGCTTCTTATGGCCATTTCACAAACCAAGAATACCCATGGGAAAAGCCTAAGACTTTGAAG
kudriavzeviiYDR502C
ATGAGCAAAACCTTTTTATTCACTTCTGAATCCGTCGGGGAAGGTCACCCAGACAAGATCTGCGATCAGGTCTCTGATGCCATCTTGGATGCTTGTCTGGAACAAGATCCATACTCCAAGGTTGCTTGTGAGACCGCTGCCAAGACTGGTATGATCATGGTTTTCGGTGAAATTACCACCAAGGCTAACCTAGACTACCAAAAAATCGTCAGAGACACCATCAAGAAGATTGGTTATGATGATTCTGCCAAGGGTTTCGACTACAAGACTTGTAATGTTTTAGTTGCCATCGAGCAACAATCGCCAGATATCGCTCAAGGTCTACATTACGAAAAGAATTTGGAAGACCTAGGTGCTGGTGACCAAGGTATCATGTTTGGTTATGCTACGGATGAAACTCCTGAGGGTTTGCCATTGACCATTCTTTTGGCCCACAAATTGAACATGGCCATGGCAGACGCTAGAAGAGACGGTTCCATCCCATGGTTGAGACCAGACACAAAGACCCAAGTCACCGTTGAATATGAAGATGACAACGGTAGATGGGTCCCAAAGAGAATAGACACCGTCGTTATCTCTGCCCAACACGCTGATGAAGTTTCCACCGCTGACTTGAGAACTCAACTACAAAGTGACATTGTTGAAAAGGTTATTCCAAAGGACATGTTAGATGAAAACACCAAATATTTCATTCAACCATCCGGTAGATTTGTTATCGGTGGTCCTCAAGGTGATGCTGGTTTGACAGGTAGAAAGATTATTGTCGATGCTTATGGTGGTGCCTCATCCGTTGGTGGTGGTGCCTTTTCTGGTAAGGACTACTCTAAGGTCGACCGTTCTGCTGCCTACGCTGCTAGATGGGTCGCCAAATCTTTAGTTGCTGCCGGTTTGTGTAAGAGAGTTCAAGTCCAATTCTCTTATGCTATCGGTATTGCTGAACCATTGTCTTTACACGTGGACACTTATGGTACAGCTACTAAATCTGATGACGAAATTATTGCAATCATCAAGAAGAACTTCGACTTAAGACCAGGTGTTTTAGTGAGAGAATTGGACTTGGCTAGGCCAATCTACTTGCCAACCGCATCTTATGGTCATTTCACGAACCAAGAATACTCTTGGGAAAAACCAAAGAAATTGGAG
kudriavzeviiYLR180W
ATGGCCGGTACATTTTTATTTACTTCTGAATCAGTTGGTGAAGGTCACCCAGATAAGATCTGTGACCAAGTCTCTGACGCCATCTTGGACGCTTGTTTGGCCGAGGACCCTCACTCCAAGGTTGCTTGTGAGACCGCGGCAAAGACCGGTATGATTATGGTCTTCGGCGAAATTACTACAAAGGCGCAATTGGACTACCAAAAGATCGTCAGAGACACCATTCAAAAGATCGGCTACGATGATTCCGCCAAGGGTTTCGACTACAAGACCTGTAACGTTCTTGTCGCAATCGAACAACAATCCCCAGATATCGCTCAAGGTGTCCACGAAGAAAAAGACTTGGAAGACATCGGTGCCGGTGATCAAGGTATCATGTTTGGTTACGCTACAGATGAAACCCCAGAAGGTCTGCCTTTGACTATTCTTCTGGCCCATAAGTTGAACATGGCCATGGCCGACGCCAGAAGAGATGGGTCCTTGCCTTGGTTGAGACCAGACACCAAGACCCAAGTCACCGTCGAATACAAGAACGACCACGGTAGATGGATCCCACTGAGGATCGACACCGTAGTCGTATCTGCTCAACACGCCGACGAGATCACCACCGAGGACTTAAGAGCCCAACTGAAATCCGAAATCATCGAGAAAGTCATTCCAAAGGACATGTTAGATGAAAACACCAAATACTTCATTCAACCCTCCGGTAGATTTGTCATCGGTGGTCCTCAAGGTGACGCTGGTTTGACCGGTAGAAAGATCATCGTTGACGCCTACGGTGGTGCTTCCTCTGTCGGTGGTGGTGCCTTCTCCGGTAAGGACTACTCCAAGGTCGACCGTTCAGCCGCCTACGCCGCCAGATGGGTCGCCAAGTCGCTCGTCGCTGCTGGTCTATGTAAGAGAGTCCAAGTCCAATTCTCGTATGCCATCGGTATTGCCGAGCCATTATCCTTGCACGTCGACACCTACGGTACCGCTTCCAAGTCCGACGAGGAAATCATTGCAATCATCAGCAAGAACTTCGACTTAAGACCTGGTGTGTTAGTCAAGGAACTGGACTTGGCTAGACCAATCTACTTGCCAACCGCCTCTTACGGTCACTTCACTAACCAAGAATACCCATGGGAAAAACCAAAGACTTTGAAA
mikataeYDR502C
ATGAGCAAAACCTTTTTATTTACTTCTGAATCCGTCGGTGAAGGTCACCCAGACAAGATTTGTGATCAAGTTTCTGATGCTATTTTGGACGCCTGTTTGGAGCAAGATCCATTTTCAAAGGTTGCTTGTGAAACGGCTGCTAAGACTGGTATGATTATGGTGTTTGGTGAGATTACCACTAAGGCTAGACTTGACTATCAACAGATCGTAAGGGATACCATTAAGAAAATCGGTTATGATGATTCTGCTAAGGGTTTCGACTACAAGACATGTAATGTTTTAGTTGCTATCGAACAGCAATCTCCAGATATCGCTCAAGGTCTACATTATGAAAAGAGCTTGGAAGACTTAGGTGCTGGTGACCAAGGTATAATGTTCGGTTATGCTACTGACGAAACTCCAGAAGGTTTGCCATTGACCATTCTTCTAGCTCATAAGTTGAATATGGCCATGGCAGATGCCAGAAGAGATGGTTCCATCCCATGGTTGAGACCAGACACAAAGACTCAGGTTACGGTCGAATACGAAGATGATAACGGTAGATGGGTTCCAAAGAGAATAGATACCGTTGTTATTTCTGCCCAACACGCCGATGAAATCTCTACTGCCGATTTAAGAACTCAGTTACAAAAAGACATCGTTGAAAAGGTCATACCAAAGGAGATGTTAGACGAAAATACCAAGTATTTCATTCAACCTTCTGGTAGATTCGTCATTGGTGGTCCTCAAGGTGATGCTGGTTTGACCGGTAGAAAGATCATTGTTGATGCCTACGGTGGTGCTTCATCCGTCGGTGGTGGTGCCTTCTCCGGTAAGGACTACTCTAAGGTCGATCGTTCTGCTGCCTACGCTGCTAGATGGGTTGCCAAATCTTTAGTCGCTGCTGGTTTGTGTAAGAGAGTCCAAGTTCAATTTTCTTATGCAATCGGTATTGCTGAACCATTGTCTTTGCACGTGGACACCTATGGCACAGCTAGTAAATCGGATGATGAAATCATTGAAATCATCAAAAAGAACTTCGACTTGAGACCAGGTGTTTTAGTGAGAGAATTAGATCTGGCTAGACCTATCTATTTGCCAACCGCTTCTTATGGTCACTTCACCAACCAGGAATACTCATGGGAAAAACCAAAGAAATTGGAA
mikataeYLR180W
ATGGCCGGTACATTTTTATTTACTTCTGAATCTGTTGGTGAAGGTCACCCAGATAAGATATGTGATCAAGTCTCTGACGCCATTTTAGACGCTTGTTTGGCTGAGGACCCTCACTCTAAGGTTGCTTGTGAGACCGCGGCAAAGACCGGTATGATTATGGTCTTTGGTGAAATTACCACCAAGGCACAATTAGATTACCAAAAAATTGTCAGGGACACGATTCAAAAAATCGGTTACGACGATTCTGCCAAAGGGTTCGACTACAAGACCTGTAATGTTCTTGTTGCCATTGAACAGCAATCTCCAGACATTGCTCAAGGTGTGCACGAAGAAAAGAACTTGGAAGATATTGGTGCCGGTGATCAAGGTATCATGTTTGGTTATGCTACCGATGAAACTCCAGAAGGTTTACCATTGACTATTCTTTTGGCCCACAAATTGAACATGGCTATGGCCGACGCCAGAAGAGATGGTTCTTTGGCATGGTTGAGACCAGACACCAAGACTCAAGTCACTGTCGAATACAAGGACGACCACGGTAGATGGGTTCCACAAAGAATCGACACTATCGTCGTTTCTGCCCAACATGCTGACGAGATTACTACCGAGGACTTGAGAGCCCAACTAAAATCCGAGATCATCGAGAAGGTCATCCCAAGAGACATGTTGGACGAAAACACCAAATACTTCATCCAACCTTCCGGTAGATTCGTCATCGGTGGTCCTCAAGGTGACGCTGGTTTGACTGGTAGAAAGATCATTGTTGACGCTTACGGTGGTGCCTCATCTGTTGGTGGTGGTGCCTTCTCTGGTAAGGACTACTCCAAGGTTGATCGTTCTGCCGCTTATGCCGCCAGATGGGTGGCCAAGTCTCTTGTCGCTGCTGGCCTATGTAAGAGAGTTCAAGTTCAATTTTCTTATGCCATTGGTATTGCTGAACCACTATCTTTGCACGTCGACACTTATGGTACCGCAACCAAGTCCGATGAAGAAATTATCGACATCATTAGCAAGAACTTTGACTTGAGACCTGGTGTATTGGTCAAGGAATTGGACTTGGCTAGACCAATCTACTTACCAACTGCTTCTTATGGTCACTTCACCAATCAAGAATACCCATGGGAAAAGCCAAAGACTTTGAAG
paradoxusYDR502C
ATGAGCAAAACTTTTTTATTTACCTCTGAATCTGTCGGTGAAGGTCACCCAGACAAGATTTGTGACCAAGTTTCTGATGCTATCTTGGATGCTTGTTTAGAACAAGATCCATTCTCCAAGGTCGCCTGTGAAACAGCTGCCAAAACTGGTATGATCATGGTTTTCGGTGAAATTACTACGAAAGCTAAACTTGACTACCAACAAATCGTAAGAGACACCATCAAGAAGATTGGTTATGACGATTCTGCCAAGGGTTTCGACTACAAGACATGTAATGTTTTAGTTGCCATCGAACAACAATCTCCAGACATTGCTCAAGGTCTGCATTATGAAAAGAGCTTGGAAGACTTAGGTGCTGGTGATCAAGGTATAATGTTTGGTTACGCTACAGATGAAACTCCGGAAGGTTTGCCATTGACCATTCTTTTGGCTCATAAATTGAACATGGCTATGGCAGATGCTAGAAGGGATGGTTCCATCCCATGGTTAAGACCAGACACAAAGACTCAAGTCACTGTTGAATACGAAGATGACAACGGTAGATGGGTTCCAAAGAGAATAGATACCGTTGTCATTTCTGCTCAACATGCCGATGAAATTTCCACCGCTGACTTGAGAACCCAACTTCAAAAAGACATCGTTGAAAAGGTCATACCAAAGGACATGTTAGACGAAAATACGAAATATTTCATCCAACCTTCCGGTAGATTCGTCATCGGTGGTCCTCAAGGTGATGCCGGTTTGACTGGTAGAAAGATTATTGTTGACGCTTACGGTGGTGCCTCATCTGTCGGTGGTGGTGCCTTCTCTGGTAAGGACTACTCAAAGGTCGATCGTTCGGCTGCTTACGCTGCTAGATGGGTTGCCAAATCTCTAGTTGCCGCTGGCTTGTGTAAGAGAGTCCAAGTTCAATTTTCTTATGCTATTGGTATTGCTGAACCATTGTCACTACATGTGGACACATATGGTACAGCTACTAAATCAGATGACGAAATCATTGAAATTATTAAGAAGAACTTCGACTTGAGACCAGGTGTTTTAGTGAAAGAATTGGACTTGGCTAGACCAATTTACTTGCCAACTGCTTCTTATGGTCACTTCACCAATCAAGAATACTCGTGGGAAAAGCCAAAGAAATTGGAA
paradoxusYLR180W
ATGGCTGGTACATTTTTATTCACTTCTGAATCCGTCGGTGAAGGTCATCCAGATAAGATCTGTGACCAAGTCTCCGACGCCATCTTAGATGCCTGTTTGGCCGAAGACCCTCACTCCAAGGTTGCCTGTGAAACCGCGGCAAAAACAGGTATGATCATGGTCTTCGGTGAAATTACCACCAAAGCACAGTTGGATTACCAAAAAATTGTCAGAGACACCATTAAACAAATTGGTTACGACGATTCCGCCAAGGGATTCGACTATAAGACCTGTAATGTTCTTGTTGCCATTGAGCAACAATCTCCAGACATCGCTCAAGGTGTCCACGAGGAGAAGGATTTGGAAGATATCGGTGCCGGTGACCAAGGTATTATGTTTGGTTACGCCACAGACGAAACTCCAGAGGGACTACCTTTGACTATTCTTTTGGCTCATAAATTAAACATGGCCATGGCTGACGCCAGAAGAGATGGTTCTTTGGCGTGGTTGAGACCAGACACCAAGACCCAAGTCACCGTCGAATACAAGGATGACCACGGTAGATGGGTTCCGCAAAGAATCGACACCGTTGTCGTCTCCGCCCAACATGCTGACGAAATCACCACCGAGGACTTAAGAGCGCAACTAAAATCCGAGATTATTGAAAAAGTCATCCCTAGAGATATGTTGGATGAAAACACCAAATACTTTATCCAGCCTTCCGGTAGATTCGTCATCGGTGGCCCTCAAGGTGACGCTGGTTTGACCGGTAGAAAAATCATTGTTGATGCTTACGGTGGTGCCTCATCCGTCGGTGGTGGTGCCTTCTCCGGTAAGGACTACTCTAAGGTTGATCGTTCCGCCGCTTATGCCGCCAGATGGGTAGCCAAGTCCCTAGTCGCTGCTGGTCTATGTAAGAGAGTTCAAGTTCAATTTTCTTATGCCATCGGTATTGCCGAACCATTATCCTTGCACGTTGACACCTATGGCACCGCTACCAAGTCCGACGAAGAAATTATCAACATTATTAGCAAGAACTTTGACTTGAGACCTGGTGTATTGGTCAAGGAGTTGGACTTGGCTAGACCAATCTACTTGCCAACCGCTTCTTATGGTCATTTCACAAACCAAGAATACCCATGGGAAAAGCCTAAGACTTTGAAG
castelliiYDR502C
ATGAACAAAAGATTTTTATTCACCTCAGAATCCGTAGGTGAGGGCCATCCAGATAAAATTTGTGATCAAGTCTCCGATGCTATTCTCGATGCCTGTCTAGCGGAAGACCCACTATCCAAAGTAGCTTGTGAAACTGCCGCCAAAACTGGGATGATTATGGTCTTTGGTGAAATTACCACTAAGGCTGAGTTGGACTATCAACAGATTGTCAGAGACACTATCAAGAAGATTGGTTATGACTCCTCCGCTAAAGGGTTCGATTATAAGACTTGTAACGTGTTGGTTGCTATTGAAAAGCAATCTCCTGATATTGCTCAAGGTTTGCATTATGAGAAGGCTATTGAAGACTTGGGTGCAGGGGACCAGGGGATTATGTTTGGTTATGCTACTGATGAAACACCAGAGGGATTACCATTAACTATCCTTTTAGCTCACAAATTGAATATGGCCATGGCTGATGCCAGAAGAGATGGGTCATTGGAATGGATGAGACCAGACACTAAGACTCAAGTGACTGTCGAATATGAAGATGATCACGGAAGATGGGTGCCATTGAGAATAGATACAGTCGTGGTCTCCGCTCAACATGCTGAGGAAATTAGTACTGAAGACTTAAGGTCCCAAATCAAGACTGAAATTATTGATAAAGTCATCCCAGCTGATATGATGGATGAAAACACTAAATTCTATATTCAACCTTCAGGAAGATTCGTCATTGGGGGACCTCAAGGTGATGCCGGTTTAACTGGGAGAAAGATTATTGTGGATGCCTATGGTGGTGCTTCCTCCGTTGGGGGTGGTGCTTTCTCTGGTAAGGATTATTCCAAAGTGGATCGTTCAGCTGCTTATGCTGCAAGATGGGTGGCCAAGTCATTGGTAGCTGCTGGTTTATGTAAAAGAGTTCAAGTGCAATTCTCATATGCTATTGGTATTGCTGAACCATTATCCTTGCATGTAGATACTTACGGAACTTCAGCCAAGTCGGATGAAGAAATTATTGCCATTATTAAGAAGAATTTTGATTTAAGACCAGGTGTCTTAGTCAGGGAATTAGATTTGGCAAGACCAATTTATTTCCCAACTGCTTCATATGGTCATTTTACCAACCAAGACTATCCATGGGAGAAACCAAAAACTTTGATT
castelliiYLR180W
ATGGCTGGTACTTTCTTATTTACTTCTGAATCCGTCGGTGAAGGTCATCCAGACAAGATCTGTGACCAAGTCTCCGATGCCATCCTAGACGCCTGTTTGGCTGAAGACCCTCACTCCAAGGTCGCCTGTGAAACCGCCGCTAAGACTGGTATGATCATGGTCTTCGGTGAAATTACCACTAAGGCTACCCTAGATTACCAAAAGATTGTCAGAGACACCATCAAGCAAATCGGGTACGATGACTCTGCTAAAGGGTTCGACTACAAGACTTGTAACGTTTTGGTTGCCATCGAACAACAATCTCCAGATATTGCTCAAGGTGTCCATGAAGAGAAGGATTTGGAAAACATTGGTGCCGGTGATCAAGGTATCATGTTCGGTTATGCTACTGATGAAACCCCAGAAGGGTTACCATTAACTATCTTATTGGCTCATAAATTGAACATGGCCATGGCTGACGCTAGAAGAGATGGTTCATTAGCTTGGTTGAGACCTGATACTAAGACTCAAGTCACTGTTGAATATAAGGACGATAACGGTAGATGGGTTCCTCAAAGAATCGACACAGTCGTTGTCTCTGCTCAACATGCTGACGAAATTTCCACTGAAGATTTGAGATCTTTGATCCAATCTGAAATTGTCGAAAAGGTTATTCCAAAGGACATGTTAGATGAAAACACTAAATACTTCATTCAACCTTCCGGTAGATTCGTCATTGGTGGTCCTCAAGGTGATGCTGGTTTGACCGGTAGAAAAATTATTGTCGATGCTTACGGTGGTGCTTCTTCCGTTGGTGGTGGTGCTTTCTCTGGTAAGGATTACTCCAAGGTGGATCGTTCTGCTGCTTACGCCGCTAGATGGGTCGCAAAATCTTTAGTCGCTGCTGGTCTATGTAAGAGAGTGCAAGTTCAATTCTCTTACGCCATTGGTATCGCTGAACCATTATCTTTACACGTCGACACTTACGGTACTGCTACCAAGTCTGATGAAGAAATTATTGCTATTATTAAGAAGAACTTTGACTTGAGACCAGGTATCTTAGTTAAGGAATTAGACTTGGCTAGACCAATCTATTTACCAACAGCTTCTTACGGTCATTTCACCAACCAAGAATACCCATGGGAAAAGCCAAAGACTCTACAA
kluyveriYDR502C
ATGGAAAAAACTTTTTTGTTCACCTCTGAATCCGTCGGTGAAGGTCACCCAGACAAGATCTGTGACCAAGTCTCCGATGCCATCCTAGACGCTTGTTTGACCGAGGACCCATTGTCCAAGGTTGCCTGTGAAACTGCCGCCAAGACCGGTATGATCATGGTGTTTGGTGAAATCACCACCAGCGCCAAGTTGGACTACCAAAAAATTGTCAGAGACACCATCAAGAAGATTGGCTACGACTCCTCCGATAAGGGTTTCGACTACAAGACCTGTAACGTGTTGGTTGCTGTCGAACAACAGTCTCCAGACATTGCTCAGGGTTTGCACTACGAACAAGCGCTAGAAGACCTAGGTGCCGGTGACCAAGGTATCATGTTTGGTTACGCCACCGACGAAACCCCAGAAGGTTTGCCGTTGACCATTTTGTTGGCCCACAAGCTGAACATCGCCATGGCCGACGCCAGAAGAGACGGCTCTTTGGCATGGTTGAGACCTGACACCAAGACCCAGGTCACCGTCGAGTACAAGGAAGACCACGGTAGATGGATTCCATTGAGAATTGACACCGTTGTTGTGTCTGCCCAACACGCCGACGAGATCTCCACCGAAGACTTGAGATCTTTGATCAAGTCCGAGATCATCCAAAAGGTCATCCCAGCCGACATGTTGGACGAAAAGACCAAGTACTACATCCAGCCTTCCGGCAGATTCGTGATTGGTGGTCCTCAAGGTGACGCCGGTTTGACCGGTAGAAAGATCATCGTCGACGCCTACGGTGGTGCCTCTGCCGTCGGTGGTGGTGCCTTCTCCGGTAAGGACTACTCCAAGGTCGACCGTTCCGCTGCCTACGCCGCCAGATGGGTGGCCAAGTCCTTGGTGCACGCCGGTTTGTGCAAGAGAGTCCAAGTGCAATTCTCCTACGCCATCGGTATTGCCGAGCCTCTGTCCTTGCACGTCGATACCTACGGTACCGCCACCAAGTCCGACGAGGAAATCATCGAGATCATCAAGAAGAACTTTGACTTGAGACCAGGTGTCTTGGTCAAGGAGTTGGACTTGGCTAGACCAATCTACTTGCCAACTGCTTCCTACGGTCACTTTACCAACCAGGAATACCCATGGGAACAGCCAAAGGAGTTGAAG
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The molecular model is an HKY85 nucleotide substitution process with the additional constraint that paralogous branches of the gene tree have identical lengths. There is no molecular clock constraint.
EM-like initialization plus quasi-Newton¶
The maximum likelihood search has two phases. The first phase is an ad-hoc iterative procedure that tries to find reasonable guesses of the parameter values, and the second phase is a quasi-Newton search that uses L-BFGS-B. In this second phase, the derivatives of the log likelihood with respect to edge-specific rate scaling factors are supplied using a closed-form calculation, while the derivatives with respect to the mutational nucleotide frequency parameters and the kappa parameter are supplied using finite-difference approximations.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 | """
Maximum likelihood estimates of HKY model parameters.
Use an iterative EM-like but not statistically consistent initial guess,
then refine it using a quasi-Newton search with some gradient information
to get maximum likelihood estimates.
This example combines aspects of a couple of existing examples.
From the first example we use the idea of applying a few iterations of
an iterative algorithm to get an initial guess of the parameter values.
From the second example we use the model itself, which constrains
paralogous branches to have identical lengths as each other.
"""
from __future__ import print_function, division, absolute_import
import time
import argparse
import itertools
from functools import partial
from collections import defaultdict
import copy
import json
import pyparsing
import numpy as np
from numpy.testing import assert_equal, assert_
import scipy.optimize
from jsonctmctree.interface import process_json_in
from jsonctmctree.extras import optimize_quasi_newton
def gen_paragraphs(fin):
lines = []
for line in fin:
line = line.rstrip()
if line:
lines.append(line)
else:
if lines:
yield lines
lines = []
if lines:
yield lines
def _help_build_tree(parent, root, node, name_to_node, edges):
if parent is not None:
edges.append((parent, node))
neo = node + 1
if isinstance(root, basestring):
name_to_node[root] = node
else:
for element in root:
neo = _help_build_tree(node, element, neo, name_to_node, edges)
return neo
def get_tree_info(tree_string):
# Return a dictionary mapping name to node index,
# and return a list of edges as ordered pairs of node indices.
assert_(tree_string.endswith(';'))
tree = tree_string[:-1].replace(',', ' ')
nestedItems = pyparsing.nestedExpr(opener='(', closer=')')
tree = (nestedItems + pyparsing.stringEnd).parseString(tree).asList()[0]
name_to_node = {}
edges = []
_help_build_tree(None, tree, 0, name_to_node, edges)
return name_to_node, edges
def parse_full_name(full_name, paralog_names):
# Return (species_name, paralog_name_index).
for i, paralog_name in enumerate(paralog_names):
if full_name.endswith(paralog_name):
species_name = full_name[:-len(paralog_name)]
return species_name, i
raise Exception(full_name)
def get_alignment_info(fasta_fd, name_to_node, paralog_names):
"""
Read the alignment data.
Parameters
----------
fasta_fd : open file-like object
The nucleotide alignment.
name_to_node : dict
Map the species name to the tree node.
paralog_names : sequence of strings
Sequence of paralog names.
Returns
-------
nodes : sequence of integers
Sequence of observable nodes.
Nodes may be repeated if multiple variables are observable per node.
variables : sequence of integers
Sequence of observable variables.
columns : sequence of integer lists
Sequence of observation lists.
"""
nodes = []
variables = []
rows = []
for lines in gen_paragraphs(fasta_fd):
if len(lines) != 2:
raise Exception('expected two lines per paragraph')
# Process the name line, containing the species and paralog.
name_line = lines[0].strip()
name, variable = parse_full_name(name_line, paralog_names)
nodes.append(name_to_node[name])
variables.append(variable)
# Process the sequence line, containing the DNA sequence.
sequence_line = lines[1].strip()
row = ['ACGT'.index(x) for x in sequence_line]
rows.append(row)
columns = [list(x) for x in zip(*rows)]
return nodes, variables, columns
def gen_hky():
# Yield a tuple for each state transition.
# Currently, this tuple consists of the univariate initial state,
# the univariate final state, a ts indicator, and a tv indicator.
# ts: A<->G, C<->T
ts_pairs = ((0, 2), (2, 0), (1, 3), (3, 1))
for i in range(4):
for j in range(4):
if i != j:
ts = 1 if (i, j) in ts_pairs else 0
tv = 1 - ts
yield i, j, ts, tv
def gen_joint_hky():
# Yield a tuple for each state transition.
# The tuple consists of the multivariate initial state,
# the multivariate final state,
# a ts indicator, a tv indicator,
# and a final mutational nucleotide index.
# Precompute the transitions out of each nucleotide state.
row_idx_to_info = [[] for i in range(4)]
for info in gen_hky():
i, j, ts, tv = info
row_idx_to_info[i].append(info)
# Compute the joint state transitions.
for ia, ib in itertools.product(range(4), repeat=2):
# Iterate over all transitions for the first nucleotide.
for i, j, ts, tv in row_idx_to_info[ia]:
ja, jb = j, ib
yield [ia, ib], [ja, jb], ts, tv, j
# Iterate over all transitions for the second nucleotide.
for i, j, ts, tv in row_idx_to_info[ib]:
ja, jb = ia, j
yield [ia, ib], [ja, jb], ts, tv, j
def get_joint_hky_process_definition(pi, kappa):
# Note that the expected rate normalization is for
# only a single site, not for both sites.
# This is intentional.
# So the expected number of changes along an edge
# is about twice the edge rate scaling factor of that edge.
expected_rate = get_expected_univariate_rate(pi, kappa)
info = get_unnormalized_transitions(pi, kappa)
row_states, column_states, transition_rates = info
normalized_rates = [r / expected_rate for r in transition_rates]
process_definition = dict(
row_states = row_states,
column_states = column_states,
transition_rates = normalized_rates)
return process_definition
def get_root_prior(pi):
root_prior = dict(
states = [[i, i] for i in range(4)],
probabilities = list(pi))
return root_prior
def get_expected_univariate_rate(pi, kappa):
raw_exit_rates = get_unnormalized_univariate_exit_rates(pi, kappa)
return np.dot(pi, raw_exit_rates)
def get_univariate_exit_rates(pi, kappa):
raw_exit_rates = get_unnormalized_univariate_exit_rates(pi, kappa)
expectation = np.dot(pi, raw_exit_rates)
return [r / expectation for r in raw_exit_rates]
def get_unnormalized_univariate_exit_rates(pi, kappa):
exit_rates = [0, 0, 0, 0]
for i, j, ts, tv in gen_hky():
rate = (kappa * ts + tv) * pi[j]
exit_rates[i] += rate
return exit_rates
def get_unnormalized_ts_exits(pi, kappa):
row_state_to_exit_rate = defaultdict(float)
for row_state, column_state, ts, tv, j in gen_joint_hky():
if ts:
exit_rate = (kappa * ts + tv) * pi[j]
row_state_to_exit_rate[tuple(row_state)] += exit_rate
row_states = []
exit_rates = []
for row_state, exit_rate in row_state_to_exit_rate.items():
row_states.append(list(row_state))
exit_rates.append(exit_rate)
return row_states, exit_rates
def get_unnormalized_tv_exits(pi, kappa):
row_state_to_exit_rate = defaultdict(float)
for row_state, column_state, ts, tv, j in gen_joint_hky():
if tv:
exit_rate = (kappa * ts + tv) * pi[j]
row_state_to_exit_rate[tuple(row_state)] += exit_rate
row_states = []
exit_rates = []
for row_state, exit_rate in row_state_to_exit_rate.items():
row_states.append(list(row_state))
exit_rates.append(exit_rate)
return row_states, exit_rates
def get_unnormalized_exits(pi, kappa):
row_state_to_exit_rate = defaultdict(float)
for row_state, column_state, ts, tv, j in gen_joint_hky():
exit_rate = (kappa * ts + tv) * pi[j]
row_state_to_exit_rate[tuple(row_state)] += exit_rate
row_states = []
exit_rates = []
for row_state, exit_rate in row_state_to_exit_rate.items():
row_states.append(list(row_state))
exit_rates.append(exit_rate)
return row_states, exit_rates
def get_unnormalized_ts_transitions(pi, kappa):
row_states = []
column_states = []
transition_rates = []
for row_state, column_state, ts, tv, j in gen_joint_hky():
if ts:
exit_rate = (kappa * ts + tv) * pi[j]
row_states.append(row_state)
column_states.append(column_state)
transition_rates.append(exit_rate)
return row_states, column_states, transition_rates
def get_unnormalized_tv_transitions(pi, kappa):
row_states = []
column_states = []
transition_rates = []
for row_state, column_state, ts, tv, j in gen_joint_hky():
if tv:
exit_rate = (kappa * ts + tv) * pi[j]
row_states.append(row_state)
column_states.append(column_state)
transition_rates.append(exit_rate)
return row_states, column_states, transition_rates
def get_unnormalized_transitions(pi, kappa):
ts_row, ts_col, ts_rate = get_unnormalized_ts_transitions(pi, kappa)
tv_row, tv_col, tv_rate = get_unnormalized_tv_transitions(pi, kappa)
row_states = ts_row + tv_row
column_states = ts_col + tv_col
transition_rates = ts_rate + tv_rate
return row_states, column_states, transition_rates
def get_requests(edge_rates, pi, kappa):
# Precompute the structure of the sparse matrix.
edge_count = len(edge_rates)
expected_rate = get_expected_univariate_rate(pi, kappa)
# Define the log likelihood request.
log_likelihood_request = {"property" : "SNNLOGL"}
# Define the requests for expectations that are used
# to update the branch length parameter estimates.
row_states, exit_rates = get_unnormalized_exits(pi, kappa)
normalized_exit_rates = [r / expected_rate for r in exit_rates]
per_edge_opportunity_request = dict(
property = "SDWDWEL",
state_reduction = dict(
states = row_states,
weights = [r / expected_rate for r in exit_rates]))
info = get_unnormalized_transitions(pi, kappa)
row_states, column_states, transition_rates = info
per_edge_change_request = dict(
property = "SDNTRAN",
transition_reduction = dict(
row_states = row_states,
column_states = column_states,
weights = [1] * len(row_states)))
# Define the requests for expectations that are used
# to update the kappa estimates.
info = get_unnormalized_ts_transitions(pi, kappa)
ts_row_states, ts_column_states, ts_rates = info
info = get_unnormalized_tv_transitions(pi, kappa)
tv_row_states, tv_column_states, tv_rates = info
# Get unnormalized ts and tv exit rates.
ts_exit_states, ts_exit_rates = get_unnormalized_ts_exits(pi, kappa)
tv_exit_states, tv_exit_rates = get_unnormalized_tv_exits(pi, kappa)
edge_reduction = dict(
edges = range(edge_count),
weights = edge_rates)
ts_opportunity_request = dict(
property = "SWWDWEL",
edge_reduction = edge_reduction,
state_reduction = dict(
states = ts_exit_states,
weights = ts_exit_rates))
tv_opportunity_request = dict(
property = "SWWDWEL",
edge_reduction = edge_reduction,
state_reduction = dict(
states = tv_exit_states,
weights = tv_exit_rates))
ts_change_request = dict(
property = "SWNTRAN",
edge_reduction = edge_reduction,
transition_reduction = dict(
row_states = ts_row_states,
column_states = ts_column_states,
weights = ts_rates))
tv_change_request = dict(
property = "SWNTRAN",
edge_reduction = edge_reduction,
transition_reduction = dict(
row_states = tv_row_states,
column_states = tv_column_states,
weights = tv_rates))
return [
log_likelihood_request,
per_edge_opportunity_request,
per_edge_change_request,
ts_opportunity_request,
tv_opportunity_request,
ts_change_request,
tv_change_request]
def pack_global_params(pi, kappa):
a, c, g, t = pi
acgt = pi.sum()
at = a+t
cg = c+g
a_div_at = a / at
c_div_cg = c / cg
arr = np.concatenate([
scipy.special.logit([at, a_div_at, c_div_cg]),
np.log([kappa])])
return arr
def unpack_global_params(P):
nt_info = scipy.special.expit(P[0:3])
at, a_div_at, c_div_cg = nt_info
a = a_div_at * at
t = (1 - a_div_at) * at
cg = 1 - at
c = c_div_cg * cg
g = (1 - c_div_cg) * cg
pi = np.array([a, c, g, t])
kappa = np.exp(P[-1])
return pi, kappa
def _get_process_definitions(P):
# This is called within the optimization.
pi, kappa = unpack_global_params(P)
return [get_joint_hky_process_definition(pi, kappa)]
def _get_root_prior(P):
# This is called within the optimization.
pi, kappa = unpack_global_params(P)
return get_root_prior(pi)
def main(args):
# Get the paralog names.
paralog_names = args.paralogs
# Read the tree.
with open(args.tree) as fin:
tree_string = fin.read().strip()
name_to_node, edges = get_tree_info(tree_string)
edge_count = len(edges)
node_count = edge_count + 1
# Read the alignment.
with open(args.alignment) as alignment_fd:
info = get_alignment_info(alignment_fd, name_to_node, paralog_names)
nodes, variables, iid_observations = info
nsites = len(iid_observations)
print('number of sites in the alignment:', nsites)
print('number of sequences:', len(nodes))
# Compute the empirical distribution of the nucleotides.
counts = np.zeros(4)
for k in np.ravel(iid_observations):
counts[k] += 1
empirical_pi = counts / counts.sum()
# Initialize some guesses.
edge_rates = [0.01] * edge_count
pi = empirical_pi
kappa = 2.0
# Define the tree component of the scene
row_nodes, column_nodes = zip(*edges)
tree = dict(
row_nodes = list(row_nodes),
column_nodes = list(column_nodes),
edge_rate_scaling_factors = edge_rates,
edge_processes = [0] * edge_count)
# Define the root distribution.
root_prior = get_root_prior(pi)
# Define the observed data.
observed_data = dict(
nodes = nodes,
variables = variables,
iid_observations = iid_observations)
# Assemble the scene.
scene = dict(
node_count = node_count,
process_count = 1,
state_space_shape = [4, 4],
tree = tree,
root_prior = root_prior,
observed_data = observed_data)
arr = []
j_out = None
iterative_improvement_count = 5
tm_start = time.time()
for i in range(iterative_improvement_count):
# if j_out is available, recompute kappa and edge rates
if j_out is not None:
responses = j_out['responses']
(
ll,
per_edge_opportunity,
per_edge_change,
ts_opportunity,
tv_opportunity,
ts_change,
tv_change) = responses
edge_rates = []
for change, dwell in zip(per_edge_change, per_edge_opportunity):
# In this model, edge rates are with respect to
# the univariate process.
bivariate_rate = change / dwell
univariate_rate = bivariate_rate / 2
edge_rates.append(univariate_rate)
kappa = (ts_change / ts_opportunity) / (tv_change / tv_opportunity)
defn = get_joint_hky_process_definition(pi, kappa)
j_in = dict(scene = scene)
j_in['scene']['tree']['edge_rate_scaling_factors'] = edge_rates
j_in['scene']['process_definitions'] = [defn]
j_in['requests'] = get_requests(edge_rates, pi, kappa)
j_out = process_json_in(j_in)
arr.append(copy.deepcopy(j_out))
tm_stop = time.time()
print(
'seconds for', iterative_improvement_count,
'initial iterations:', tm_stop - tm_start)
# Improve the estimates using a numerical search.
P0 = pack_global_params(pi, kappa)
B0 = np.log(edge_rates)
tm_start = time.time()
verbose = False
observation_reduction = None
result, P_opt, B_opt = optimize_quasi_newton(
verbose,
scene,
observation_reduction,
_get_process_definitions,
_get_root_prior,
P0, B0)
tm_stop = time.time()
print('seconds for quasi-newton search:', tm_stop - tm_start)
# Unpack and report the results.
pi, kappa = unpack_global_params(P_opt)
edge_rates = np.exp(B_opt)
print('negative log likelihood:', result.fun)
print('nucleotide distribution:')
for nt, p in zip('ACGT', pi):
print(nt, ':', p)
print('kappa:', kappa)
print('edge rates:')
print(edge_rates)
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('--alignment', required=True,
help='alignment file')
parser.add_argument('--tree', required=True,
help='tree file')
parser.add_argument('--paralogs', nargs='+', required=True,
help='paralog names')
args = parser.parse_args()
main(args)
|
1 | python main.py --alignment YDR502C_YLR180W.dat --tree newick.tree --paralogs YDR502C YLR180W
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | number of sites in the alignment: 1143
number of sequences: 13
seconds for 5 initial iterations: 4.70695400238
seconds for quasi-newton search: 18.6770720482
negative log likelihood: 6866.30275903
nucleotide distribution:
A : 0.238989118769
C : 0.242714757594
G : 0.191045785324
T : 0.327250338314
kappa: 6.98054758535
edge rates:
[ 0.02405295 0.0461649 0.0253282 0.02555816 0.02481741 0.03314547
0.03198597 0.0603496 0.05721818 0.05031921 0.14825361 0.10323723]
|
EM for edge lengths only¶
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 | """
Use the 'extras' module to help with the inference.
This script has no clock-like constraint on branch length,
but it has a zero inter-locus gene-conversion constraint.
It uses EM only for an improvement of the initial guesses of the
edge-specific rate scaling factors.
The 'extras' module in the jsonctmctree Python package
is used for some EM and quasi-newton optimization.
"""
from __future__ import print_function, division
import argparse
import itertools
import pyparsing
import numpy as np
from numpy.testing import assert_
import scipy.special
from jsonctmctree.interface import process_json_in
from jsonctmctree.extras import optimize_em, optimize_quasi_newton
###############################################################################
# Stuff in this section is related to the data.
def gen_paragraphs(fin):
lines = []
for line in fin:
line = line.rstrip()
if line:
lines.append(line)
else:
if lines:
yield lines
lines = []
if lines:
yield lines
def _help_build_tree(parent, root, node, name_to_node, edges):
if parent is not None:
edges.append((parent, node))
neo = node + 1
if isinstance(root, basestring):
name_to_node[root] = node
else:
for element in root:
neo = _help_build_tree(node, element, neo, name_to_node, edges)
return neo
def get_tree_info(tree_string):
# Return a dictionary mapping name to node index,
# and return a list of edges as ordered pairs of node indices.
assert_(tree_string.endswith(';'))
tree = tree_string[:-1].replace(',', ' ')
nestedItems = pyparsing.nestedExpr(opener='(', closer=')')
tree = (nestedItems + pyparsing.stringEnd).parseString(tree).asList()[0]
name_to_node = {}
edges = []
_help_build_tree(None, tree, 0, name_to_node, edges)
return name_to_node, edges
def parse_full_name(full_name, paralog_names):
# Return (species_name, paralog_name_index).
for i, paralog_name in enumerate(paralog_names):
if full_name.endswith(paralog_name):
species_name = full_name[:-len(paralog_name)]
return species_name, i
raise Exception(full_name)
def get_alignment_info(fasta_fd, name_to_node, paralog_names):
"""
Read the alignment data.
Parameters
----------
fasta_fd : open file-like object
The nucleotide alignment.
name_to_node : dict
Map the species name to the tree node.
paralog_names : sequence of strings
Sequence of paralog names.
Returns
-------
nodes : sequence of integers
Sequence of observable nodes.
Nodes may be repeated if multiple variables are observable per node.
variables : sequence of integers
Sequence of observable variables.
columns : sequence of integer lists
Sequence of observation lists.
"""
nodes = []
variables = []
rows = []
for lines in gen_paragraphs(fasta_fd):
if len(lines) != 2:
raise Exception('expected two lines per paragraph')
# Process the name line, containing the species and paralog.
name_line = lines[0].strip()
name, variable = parse_full_name(name_line, paralog_names)
nodes.append(name_to_node[name])
variables.append(variable)
# Process the sequence line, containing the DNA sequence.
sequence_line = lines[1].strip()
row = ['ACGT'.index(x) for x in sequence_line]
rows.append(row)
columns = [list(x) for x in zip(*rows)]
return nodes, variables, columns
###############################################################################
# Stuff in this section is specific to the parameterization details
# of the model.
def pack_global_params(pi, kappa):
a, c, g, t = pi
acgt = pi.sum()
at = a+t
cg = c+g
a_div_at = a / at
c_div_cg = c / cg
arr = np.concatenate([
scipy.special.logit([at, a_div_at, c_div_cg]),
np.log([kappa])])
return arr
def unpack_global_params(P):
nt_info = scipy.special.expit(P[0:3])
at, a_div_at, c_div_cg = nt_info
a = a_div_at * at
t = (1 - a_div_at) * at
cg = 1 - at
c = c_div_cg * cg
g = (1 - c_div_cg) * cg
pi = np.array([a, c, g, t])
kappa = np.exp(P[-1])
return pi, kappa
def _get_process_definitions(P):
# This is called within the optimization.
pi, kappa = unpack_global_params(P)
return [get_joint_hky_process_definition(pi, kappa)]
def _get_root_prior(P):
# This is called within the optimization.
pi, kappa = unpack_global_params(P)
return get_root_prior(pi)
###############################################################################
# Stuff in this section is specific to the joint paralog HKY model
# and does not care about the input formats of the data.
def gen_hky():
# Yield a tuple for each state transition.
# Currently, this tuple consists of the univariate initial state,
# the univariate final state, a ts indicator, and a tv indicator.
# ts: A<->G, C<->T
ts_pairs = ((0, 2), (2, 0), (1, 3), (3, 1))
for i in range(4):
for j in range(4):
if i != j:
ts = 1 if (i, j) in ts_pairs else 0
tv = 1 - ts
yield i, j, ts, tv
def gen_joint_hky():
# Yield a tuple for each state transition.
# The tuple consists of the multivariate initial state,
# the multivariate final state,
# a ts indicator, a tv indicator,
# and a final mutational nucleotide index.
# Precompute the transitions out of each nucleotide state.
row_idx_to_info = [[] for i in range(4)]
for info in gen_hky():
i, j, ts, tv = info
row_idx_to_info[i].append(info)
# Compute the joint state transitions.
for ia, ib in itertools.product(range(4), repeat=2):
# Iterate over all transitions for the first nucleotide.
for i, j, ts, tv in row_idx_to_info[ia]:
ja, jb = j, ib
yield [ia, ib], [ja, jb], ts, tv, j
# Iterate over all transitions for the second nucleotide.
for i, j, ts, tv in row_idx_to_info[ib]:
ja, jb = ia, j
yield [ia, ib], [ja, jb], ts, tv, j
def get_joint_hky_process_definition(pi, kappa):
# Note that the expected rate normalization is for
# only a single site, not for both sites.
# This is intentional.
# So the expected number of changes along an edge
# is about twice the edge rate scaling factor of that edge.
expected_rate = get_expected_univariate_rate(pi, kappa)
info = get_unnormalized_transitions(pi, kappa)
row_states, column_states, transition_rates = info
normalized_rates = [r / expected_rate for r in transition_rates]
process_definition = dict(
row_states = row_states,
column_states = column_states,
transition_rates = normalized_rates)
return process_definition
def get_root_prior(pi):
root_prior = dict(
states = [[i, i] for i in range(4)],
probabilities = list(pi))
return root_prior
def get_unnormalized_ts_transitions(pi, kappa):
row_states = []
column_states = []
transition_rates = []
for row_state, column_state, ts, tv, j in gen_joint_hky():
if ts:
exit_rate = (kappa * ts + tv) * pi[j]
row_states.append(row_state)
column_states.append(column_state)
transition_rates.append(exit_rate)
return row_states, column_states, transition_rates
def get_unnormalized_tv_transitions(pi, kappa):
row_states = []
column_states = []
transition_rates = []
for row_state, column_state, ts, tv, j in gen_joint_hky():
if tv:
exit_rate = (kappa * ts + tv) * pi[j]
row_states.append(row_state)
column_states.append(column_state)
transition_rates.append(exit_rate)
return row_states, column_states, transition_rates
def get_unnormalized_transitions(pi, kappa):
ts_row, ts_col, ts_rate = get_unnormalized_ts_transitions(pi, kappa)
tv_row, tv_col, tv_rate = get_unnormalized_tv_transitions(pi, kappa)
row_states = ts_row + tv_row
column_states = ts_col + tv_col
transition_rates = ts_rate + tv_rate
return row_states, column_states, transition_rates
def get_expected_univariate_rate(pi, kappa):
raw_exit_rates = get_unnormalized_univariate_exit_rates(pi, kappa)
return np.dot(pi, raw_exit_rates)
def get_unnormalized_univariate_exit_rates(pi, kappa):
exit_rates = [0, 0, 0, 0]
for i, j, ts, tv in gen_hky():
rate = (kappa * ts + tv) * pi[j]
exit_rates[i] += rate
return exit_rates
###############################################################################
# The main script function.
def main(args):
# Get the paralog names.
paralog_names = args.paralogs
# Read the tree.
with open(args.tree) as fin:
tree_string = fin.read().strip()
name_to_node, edges = get_tree_info(tree_string)
edge_count = len(edges)
node_count = edge_count + 1
# Read the alignment.
with open(args.alignment) as alignment_fd:
info = get_alignment_info(alignment_fd, name_to_node, paralog_names)
nodes, variables, iid_observations = info
nsites = len(iid_observations)
print('number of sites in the alignment:', nsites)
print('number of sequences:', len(nodes))
# Compute the empirical distribution of the nucleotides.
counts = np.zeros(4)
for k in np.ravel(iid_observations):
counts[k] += 1
empirical_pi = counts / counts.sum()
# Initialize some guesses.
edge_rates = [0.01] * edge_count
pi = empirical_pi
kappa = 2.0
# Define the tree component of the scene
row_nodes, column_nodes = zip(*edges)
tree = dict(
row_nodes = list(row_nodes),
column_nodes = list(column_nodes),
edge_rate_scaling_factors = edge_rates,
edge_processes = [0] * edge_count)
# Define the root distribution.
root_prior = get_root_prior(pi)
# Define the observed data.
observed_data = dict(
nodes = nodes,
variables = variables,
iid_observations = iid_observations)
# Assemble the scene.
process_defn = get_joint_hky_process_definition(pi, kappa)
scene = dict(
node_count = node_count,
process_count = 1,
state_space_shape = [4, 4],
tree = tree,
root_prior = root_prior,
process_definitions = [process_defn],
observed_data = observed_data)
print('computing the log likelihood...')
# Ask for the log likelihood, summed over sites.
log_likelihood_request = dict(property = 'SNNLOGL')
j_in = dict(
scene = scene,
requests = [log_likelihood_request])
j_out = process_json_in(j_in)
print(j_out)
print('updating edge specific rate scaling factors using EM...')
# Use the generic EM edge rate scaling factor updating function.
observation_reduction = None
em_iterations = 1
edge_rates = optimize_em(scene, observation_reduction, em_iterations)
# Update the scene to reflect the edge rates.
print('updated edge rate scaling factors:')
print(edge_rates)
scene['tree']['edge_rate_scaling_factors'] = edge_rates
print('checking log likelihood after having updated edge rates...')
# Check the log likelihood again.
j_in = dict(
scene = scene,
requests = [log_likelihood_request])
j_out = process_json_in(j_in)
print(j_out)
print('computing the maximum likelihood estimates...')
# Improve the estimates using a numerical search.
P0 = pack_global_params(pi, kappa)
B0 = np.log(edge_rates)
verbose = False
observation_reduction = None
result, P_opt, B_opt = optimize_quasi_newton(
verbose,
scene,
observation_reduction,
_get_process_definitions,
_get_root_prior,
P0, B0)
# Unpack and report the results.
pi, kappa = unpack_global_params(P_opt)
edge_rates = np.exp(B_opt)
print('negative log likelihood:', result.fun)
print('nucleotide distribution:')
for nt, p in zip('ACGT', pi):
print(nt, ':', p)
print('kappa:', kappa)
print('edge rates:')
print(edge_rates)
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('--alignment', required=True,
help='alignment file')
parser.add_argument('--tree', required=True,
help='tree file')
parser.add_argument('--paralogs', nargs='+', required=True,
help='paralog names')
args = parser.parse_args()
main(args)
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | number of sites in the alignment: 1143
number of sequences: 13
computing the log likelihood...
{'status': 'feasible', 'responses': [-8154.033674536182]}
updating edge specific rate scaling factors using EM...
updated edge rate scaling factors:
[0.03635438010958045, 0.04894068331595304, 0.029808194683655084, 0.028044031275529947, 0.027882780063411994, 0.03160492124687275, 0.030250252267262096, 0.04946980953408789, 0.048322163730959725, 0.04446585909315688, 0.1075919554038906, 0.04592937767875418]
checking log likelihood after having updated edge rates...
{'status': 'feasible', 'responses': [-7112.766992934574]}
computing the maximum likelihood estimates...
negative log likelihood: 6866.30275825
nucleotide distribution:
A : 0.238990941044
C : 0.242712829008
G : 0.19104441563
T : 0.327251814319
kappa: 6.98030292627
edge rates:
[ 0.02404864 0.04617129 0.02531875 0.02555738 0.02482383 0.03314422
0.03198737 0.06035096 0.05722141 0.05032541 0.1482554 0.10323988]
|