1 /***************************************************************************
2  *   Copyright (C) 2009 by BUI Quang Minh   *
3  *   minh.bui@univie.ac.at   *
4  *                                                                         *
5  *   This program is free software; you can redistribute it and/or modify  *
6  *   it under the terms of the GNU General Public License as published by  *
7  *   the Free Software Foundation; either version 2 of the License, or     *
8  *   (at your option) any later version.                                   *
9  *                                                                         *
10  *   This program is distributed in the hope that it will be useful,       *
11  *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
12  *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
13  *   GNU General Public License for more details.                          *
14  *                                                                         *
15  *   You should have received a copy of the GNU General Public License     *
16  *   along with this program; if not, write to the                         *
17  *   Free Software Foundation, Inc.,                                       *
18  *   59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.             *
19  ***************************************************************************/
20 #include "modelprotein.h"
21 #include "nclextra/myreader.h"
22 #include <string>
23 
24 /*
25 	following are definitions for various protein models encoded in a string.
26 	This string contains the lower triangle of the rate matrix and the state frequencies at the end.
27 	It should follow the amino acid order:
28 	A   R   N   D   C   Q   E   G   H   I   L   K   M   F   P   S   T   W   Y   V
29 	Ala Arg Asn Asp Cys Gln Glu Gly His Ile Leu Lys Met Phe Pro Ser Thr Trp Tyr Val
30 */
31 const char* builtin_prot_models = R"(
32 #nexus;
33 
34 begin models;
35 
36 model POISSON=
37 1
38 1 1
39 1 1 1
40 1 1 1 1
41 1 1 1 1 1
42 1 1 1 1 1 1
43 1 1 1 1 1 1 1
44 1 1 1 1 1 1 1 1
45 1 1 1 1 1 1 1 1 1
46 1 1 1 1 1 1 1 1 1 1
47 1 1 1 1 1 1 1 1 1 1 1
48 1 1 1 1 1 1 1 1 1 1 1 1
49 1 1 1 1 1 1 1 1 1 1 1 1 1
50 1 1 1 1 1 1 1 1 1 1 1 1 1 1
51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
52 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
53 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
54 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
55 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
56 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05;
57 
58 model DAYHOFF=
59 27
60 98 32
61 120 0 905
62 36 23 0 0
63 89 246 103 134 0
64 198 1 148 1153 0 716
65 240 9 139 125 11 28 81
66 23 240 535 86 28 606 43 10
67 65 64 77 24 44 18 61 0 7
68 41 15 34 0 0 73 11 7 44 257
69 26 464 318 71 0 153 83 27 26 46 18
70 72 90 1 0 0 114 30 17 0 336 527 243
71 18 14 14 0 0 0 0 15 48 196 157 0 92
72 250 103 42 13 19 153 51 34 94 12 32 33 17 11
73 409 154 495 95 161 56 79 234 35 24 17 96 62 46 245
74 371 26 229 66 16 53 34 30 22 192 33 136 104 13 78 550
75 0 201 23 0 0 0 0 0 27 0 46 0 0 76 0 75 0
76 24 8 95 0 96 0 22 0 127 37 28 13 0 698 0 34 42 61
77 208 24 15 18 49 35 37 54 44 889 175 10 258 12 48 30 157 0 28
78 0.08712691 0.04090396 0.04043196 0.04687195 0.03347397 0.03825496 0.04952995 0.08861191 0.03361897 0.03688596 0.08535691 0.08048092 0.01475299 0.03977196 0.05067995 0.06957693 0.05854194 0.01049399 0.02991597 0.06471794;
79 [ NOTE 2019-06-04: normalised from original Dayhoff freqs, which do not sum to 1.0
80  https://www.ebi.ac.uk/goldman-srv/dayhoff/dayhoff-dcmut.dat ]
81 
82 model DCMUT=
83 26.7828
84 98.4474 32.7059
85 119.9805 0.0000 893.1515
86 36.0016 23.2374 0.0000 0.0000
87 88.7753 243.9939 102.8509 134.8551 0.0000
88 196.1167 0.0000 149.3409 1138.8659 0.0000 708.6022
89 238.6111 8.7791 138.5352 124.0981 10.7278 28.1581 81.1907
90 22.8116 238.3148 529.0024 86.8241 28.2729 601.1613 43.9469 10.6802
91 65.3416 63.2629 76.8024 23.9248 43.8074 18.0393 60.9526 0.0000 7.6981
92 40.6431 15.4924 34.1113 0.0000 0.0000 73.0772 11.2880 7.1514 44.3504 255.6685
93 25.8635 461.0124 314.8371 71.6913 0.0000 151.9078 83.0078 26.7683 27.0475 46.0857 18.0629
94 71.7840 89.6321 0.0000 0.0000 0.0000 112.7499 30.4803 17.0372 0.0000 333.2732 523.0115 241.1739
95 18.3641 13.6906 13.8503 0.0000 0.0000 0.0000 0.0000 15.3478 47.5927 195.1951 156.5160 0.0000 92.1860
96 248.5920 102.8313 41.9244 13.3940 18.7550 152.6188 50.7003 34.7153 93.3709 11.9152 31.6258 33.5419 17.0205 11.0506
97 405.1870 153.1590 488.5892 95.6097 159.8356 56.1828 79.3999 232.2243 35.3643 24.7955 17.1432 95.4557 61.9951 45.9901 242.7202
98 368.0365 26.5745 227.1697 66.0930 16.2366 52.5651 34.0156 30.6662 22.6333 190.0739 33.1090 135.0599 103.1534 13.6655 78.2857 543.6674
99 0.0000 200.1375 22.4968 0.0000 0.0000 0.0000 0.0000 0.0000 27.0564 0.0000 46.1776 0.0000 0.0000 76.2354 0.0000 74.0819 0.0000
100 24.4139 7.8012 94.6940 0.0000 95.3164 0.0000 21.4717 0.0000 126.5400 37.4834 28.6572 13.2142 0.0000 695.2629 0.0000 33.6289 41.7839 60.8070
101 205.9564 24.0368 15.8067 17.8316 48.4678 34.6983 36.7250 53.8165 43.8715 881.0038 174.5156 10.3850 256.5955 12.3606 48.5026 30.3836 156.1997 0.0000 27.9379
102  0.08712691 0.04090396 0.04043196 0.04687195 0.03347397 0.03825496 0.04952995 0.08861191 0.03361897 0.03688596 0.08535691 0.08048092 0.01475299 0.03977196 0.05067995 0.06957693 0.05854194 0.01049399 0.02991597 0.06471794;
103 [ NOTE 2019-06-04: normalised from original Dayhoff-DCMUT freqs, which do not sum to 1.0
104   https://www.ebi.ac.uk/goldman-srv/dayhoff/dayhoff-dcmut.dat ]
105 
106 model JTT=
107 58
108 54 45
109 81 16 528
110 56 113 34 10
111 57 310 86 49 9
112 105 29 58 767 5 323
113 179 137 81 130 59 26 119
114 27 328 391 112 69 597 26 23
115 36 22 47 11 17 9 12 6 16
116 30 38 12 7 23 72 9 6 56 229
117 35 646 263 26 7 292 181 27 45 21 14
118 54 44 30 15 31 43 18 14 33 479 388 65
119 15 5 10 4 78 4 5 5 40 89 248 4 43
120 194 74 15 15 14 164 18 24 115 10 102 21 16 17
121 378 101 503 59 223 53 30 201 73 40 59 47 29 92 285
122 475 64 232 38 42 51 32 33 46 245 25 103 226 12 118 477
123 9 126 8 4 115 18 10 55 8 9 52 10 24 53 6 35 12
124 11 20 70 46 209 24 7 8 573 32 24 8 18 536 10 63 21 71
125 298 17 16 31 62 20 45 47 11 961 180 14 323 62 23 38 112 25 16
126 0.07674792 0.05169095 0.04264496 0.05154395 0.01980298 0.04075196 0.06182994 0.07315193 0.02294398 0.05376095 0.09190391 0.05867594 0.02382598 0.04012596 0.05090095 0.06876493 0.05856494 0.01426099 0.03210197 0.06600493;
127 [ NOTE 2019-06-04: original JTT freqs do not sum to 1.0, taken from PAML package ]
128 
129 model MTREV=
130 23.18
131 26.95 13.24
132 17.67 1.90 794.38
133 59.93 103.33 58.94 1.90
134 1.90 220.99 173.56 55.28 75.24
135 9.77 1.90 63.05 583.55 1.90 313.56
136 120.71 23.03 53.30 56.77 30.71 6.75 28.28
137 13.90 165.23 496.13 113.99 141.49 582.40 49.12 1.90
138 96.49 1.90 27.10 4.34 62.73 8.34 3.31 5.98 12.26
139 25.46 15.58 15.16 1.90 25.65 39.70 1.90 2.41 11.49 329.09
140 8.36 141.40 608.70 2.31 1.90 465.58 313.86 22.73 127.67 19.57 14.88
141 141.88 1.90 65.41 1.90 6.18 47.37 1.90 1.90 11.97 517.98 537.53 91.37
142 6.37 4.69 15.20 4.98 70.80 19.11 2.67 1.90 48.16 84.67 216.06 6.44 90.82
143 54.31 23.64 73.31 13.43 31.26 137.29 12.83 1.90 60.97 20.63 40.10 50.10 18.84 17.31
144 387.86 6.04 494.39 69.02 277.05 54.11 54.71 125.93 77.46 47.70 73.61 105.79 111.16 64.29 169.90
145 480.72 2.08 238.46 28.01 179.97 94.93 14.82 11.17 44.78 368.43 126.40 136.33 528.17 33.85 128.22 597.21
146 1.90 21.95 10.68 19.86 33.60 1.90 1.90 10.92 7.08 1.90 32.44 24.00 21.71 7.84 4.21 38.58 9.99
147 6.48 1.90 191.36 21.21 254.77 38.82 13.12 3.21 670.14 25.01 44.15 51.17 39.96 465.58 16.21 64.92 38.73 26.25
148 195.06 7.64 1.90 1.90 1.90 19.00 21.14 2.53 1.90 1222.94 91.67 1.90 387.54 6.35 8.23 1.90 204.54 5.37 1.90
149 0.072 0.019 0.039 0.019 0.006 0.025 0.024 0.056 0.028 0.088 0.169 0.023 0.054 0.061 0.054 0.072 0.086 0.029 0.033 0.043;
150 [ NOTE 2019-06-04: The PI's used to sum to 0.999 and I (Z. Yang) changed one of the freq from 0.168
151   into 0.169 so that the sum is 1.  Prepared by Z. Yang ]
152 
153 model WAG=
154 55.15710
155 50.98480 63.53460
156 73.89980 14.73040 542.94200
157 102.70400 52.81910 26.52560 3.02949
158 90.85980 303.55000 154.36400 61.67830 9.88179
159 158.28500 43.91570 94.71980 617.41600 2.13520 546.94700
160 141.67200 58.46650 112.55600 86.55840 30.66740 33.00520 56.77170
161 31.69540 213.71500 395.62900 93.06760 24.89720 429.41100 57.00250 24.94100
162 19.33350 18.69790 55.42360 3.94370 17.01350 11.39170 12.73950 3.04501 13.81900
163 39.79150 49.76710 13.15280 8.48047 38.42870 86.94890 15.42630 6.13037 49.94620 317.09700
164 90.62650 535.14200 301.20100 47.98550 7.40339 389.49000 258.44300 37.35580 89.04320 32.38320 25.75550
165 89.34960 68.31620 19.82210 10.37540 39.04820 154.52600 31.51240 17.41000 40.41410 425.74600 485.40200 93.42760
166 21.04940 10.27110 9.61621 4.67304 39.80200 9.99208 8.11339 4.99310 67.93710 105.94700 211.51700 8.88360 119.06300
167 143.85500 67.94890 19.50810 42.39840 10.94040 93.33720 68.23550 24.35700 69.61980 9.99288 41.58440 55.68960 17.13290 16.14440
168 337.07900 122.41900 397.42300 107.17600 140.76600 102.88700 70.49390 134.18200 74.01690 31.94400 34.47390 96.71300 49.39050 54.59310 161.32800
169 212.11100 55.44130 203.00600 37.48660 51.29840 85.79280 82.27650 22.58330 47.33070 145.81600 32.66220 138.69800 151.61200 17.19030 79.53840 437.80200
170 11.31330 116.39200 7.19167 12.97670 71.70700 21.57370 15.65570 33.69830 26.25690 21.24830 66.53090 13.75050 51.57060 152.96400 13.94050 52.37420 11.08640
171 24.07350 38.15330 108.60000 32.57110 54.38330 22.77100 19.63030 10.36040 387.34400 42.01700 39.86180 13.32640 42.84370 645.42800 21.60460 78.69930 29.11480 248.53900
172 200.60100 25.18490 19.62460 15.23350 100.21400 30.12810 58.87310 18.72470 11.83580 782.13000 180.03400 30.54340 205.84500 64.98920 31.48870 23.27390 138.82300 36.53690 31.47300
173 0.08662791 0.043972 0.0390894 0.05704511 0.0193078 0.0367281 0.05805891 0.08325181 0.0244313 0.048466 0.08620901 0.06202861 0.0195027 0.0384319 0.0457631 0.06951791 0.06101271 0.0143859 0.0352742 0.07089561;
174 [ NOTE 2019-06-04: normalised from original WAG freqs, which do not sum to 1.0 ]
175 
176 model RTREV=
177 34
178 51 35
179 10 30 384
180 439 92 128 1
181 32 221 236 78 70
182 81 10 79 542 1 372
183 135 41 94 61 48 18 70
184 30 90 320 91 124 387 34 68
185 1 24 35 1 104 33 1 1 34
186 45 18 15 5 110 54 21 3 51 385
187 38 593 123 20 16 309 141 30 76 34 23
188 235 57 1 1 156 158 1 37 116 375 581 134
189 1 7 49 1 70 1 1 7 141 64 179 14 247
190 97 24 33 55 1 68 52 17 44 10 22 43 1 11
191 460 102 294 136 75 225 95 152 183 4 24 77 1 20 134
192 258 64 148 55 117 146 82 7 49 72 25 110 131 69 62 671
193 5 13 16 1 55 10 17 23 48 39 47 6 111 182 9 14 1
194 55 47 28 1 131 45 1 21 307 26 64 1 74 1017 14 31 34 176
195 197 29 21 6 295 36 35 3 1 1048 112 19 236 92 25 39 196 26 59
196 0.0646 0.0453 0.0376 0.0422 0.0114 0.0606 0.0607 0.0639 0.0273 0.0679 0.1018 0.0751 0.0150 0.0287 0.0681 0.0488 0.0622 0.0251 0.0318 0.0619;
197 
198 model CPREV=
199 105
200 227 357
201 175 43 4435
202 669 823 538 10
203 157 1745 768 400 10
204 499 152 1055 3691 10 3122
205 665 243 653 431 303 133 379
206 66 715 1405 331 441 1269 162 19
207 145 136 168 10 280 92 148 40 29
208 197 203 113 10 396 286 82 20 66 1745
209 236 4482 2430 412 48 3313 2629 263 305 345 218
210 185 125 61 47 159 202 113 21 10 1772 1351 193
211 68 53 97 22 726 10 145 25 127 454 1268 72 327
212 490 87 173 170 285 323 185 28 152 117 219 302 100 43
213 2440 385 2085 590 2331 396 568 691 303 216 516 868 93 487 1202
214 1340 314 1393 266 576 241 369 92 32 1040 156 918 645 148 260 2151
215 14 230 40 18 435 53 63 82 69 42 159 10 86 468 49 73 29
216 56 323 754 281 1466 391 142 10 1971 89 189 247 215 2370 97 522 71 346
217 968 92 83 75 592 54 200 91 25 4797 865 249 475 317 122 167 760 10 119
218 0.0755 0.0621 0.0410 0.0371 0.0091 0.0382 0.0495 0.0838 0.0246 0.0806 0.1011 0.0504 0.0220 0.0506 0.0431 0.0622 0.0543 0.0181 0.0307 0.0660;
219 [ NOTE 2019-06-04: CPREV freqs taken from PAML package with higher precision ]
220 
221 model VT=
222 1.2412691067876198
223 1.2184237953498958 1.5720770753326880
224 1.3759368509441177 0.7550654439001206 7.8584219153689405
225 2.4731223087544874 1.4414262567428417 0.9784679122774127 0.2272488448121475
226 2.2155167805137470 5.5120819705248678 3.0143201670924822 1.6562495638176040 0.4587469126746136
227 2.3379911207495061 1.3542404860613146 2.0093434778398112 9.6883451875685065 0.4519167943192672 6.8124601839937675
228 3.3386555146457697 1.3121700301622004 2.4117632898861809 1.9142079025990228 1.1034605684472507 0.8776110594765502 1.3860121390169038
229 0.9615841926910841 4.9238668283945266 6.1974384977884114 2.1459640610133781 1.5196756759380692 7.9943228564946525 1.6360079688522375 0.8561248973045037
230 0.8908203061925510 0.4323005487925516 0.9179291175331520 0.2161660372725585 0.9126668032539315 0.4882733432879921 0.4035497929633328 0.2888075033037488 0.5787937115407940
231 1.0778497408764076 0.8386701149158265 0.4098311270816011 0.3574207468998517 1.4081315998413697 1.3318097154194044 0.5610717242294755 0.3578662395745526 1.0765007949562073 6.0019110258426362
232 1.4932055816372476 10.0173308173660018 4.4034547578962568 1.4521790561663968 0.3371091785647479 6.0519085243118811 4.3290086529582830 0.8945563662345198 1.8085136096039203 0.6244297525127139 0.5642322882556321
233 1.9006455961717605 1.2488638689609959 0.9378803706165143 0.4075239926000898 1.2213054800811556 1.9106190827629084 0.7471936218068498 0.5954812791740037 1.3808291710019667 6.7597899772045418 8.0327792947421148 1.7129670976916258
234 0.6883439026872615 0.4224945197276290 0.5044944273324311 0.1675129724559251 1.6953951980808002 0.3573432522499545 0.2317194387691585 0.3693722640980460 1.3629765501081097 2.2864286949316077 4.3611548063555778 0.3910559903834828 2.3201373546296349
235 2.7355620089953550 1.3091837782420783 0.7103720531974738 1.0714605979577547 0.4326227078645523 2.3019177728300728 1.5132807416252063 0.7744933618134962 1.8370555852070649 0.4811402387911145 1.0084320519837335 1.3918935593582853 0.4953193808676289 0.3746821107962129
236 6.4208961859142883 1.9202994262316166 6.1234512396801764 2.2161944596741829 3.6366815408744255 2.3193703643237220 1.8273535587773553 3.0637776193717610 1.9699895187387506 0.6047491507504744 0.8953754669269811 1.9776630140912268 1.0657482318076852 1.1079144700606407 3.5465914843628927
237 5.2892514169776437 1.3363401740560601 3.8852506105922231 1.5066839872944762 1.7557065205837685 2.1576510103471440 1.5839981708584689 0.7147489676267383 1.6136654573285647 2.6344778384442731 1.0192004372506540 2.5513781312660280 3.3628488360462363 0.6882725908872254 1.9485376673137556 8.8479984061248178
238 0.5488578478106930 1.5170142153962840 0.1808525752605976 0.2496584188151770 1.6275179891253113 0.8959082681546182 0.4198391148111098 0.9349753595598769 0.6301954684360302 0.5604648274060783 1.5183114434679339 0.5851920879490173 1.4680478689711018 3.3448437239772266 0.4326058001438786 0.6791126595939816 0.4514203099376473
239 0.5411769916657778 0.8912614404565405 1.0894926581511342 0.7447620891784513 2.1579775140421025 0.9183596801412757 0.5818111331782764 0.3374467649724478 7.7587442309146040 0.8626796044156272 1.2452243224541324 0.7835447533710449 1.0899165770956820 10.3848523331334590 0.4819109019647465 0.9547229305958682 0.8564314184691215 4.5377235790405388
240 4.6501894691803214 0.7807017855806767 0.4586061981719967 0.4594535241660911 2.2627456996290891 0.6366932501396869 0.8940572875547330 0.6193321034173915 0.5333220944030346 14.8729334615190609 3.5458093276667237 0.7801080335991272 4.0584577156753401 1.7039730522675411 0.5985498912985666 0.9305232113028208 3.4242218450865543 0.5658969249032649 1.0000000000000000
241 0.0770764620135024 0.0500819370772208 0.0462377395993731 0.0537929860758246 0.0144533387583345 0.0408923608974345 0.0633579339160905 0.0655672355884439 0.0218802687005936 0.0591969699027449 0.0976461276528445 0.0592079410822730 0.0220695876653368 0.0413508521834260 0.0476871596856874 0.0707295165111524 0.0567759161524817 0.0127019797647213 0.0323746050281867 0.0669190817443274;
242 
243 model BLOSUM62=
244 0.735790389698
245 0.485391055466 1.297446705134
246 0.543161820899 0.500964408555 3.180100048216
247 1.459995310470 0.227826574209 0.397358949897 0.240836614802
248 1.199705704602 3.020833610064 1.839216146992 1.190945703396 0.329801504630
249 1.170949042800 1.360574190420 1.240488508640 3.761625208368 0.140748891814 5.528919177928
250 1.955883574960 0.418763308518 1.355872344485 0.798473248968 0.418203192284 0.609846305383 0.423579992176
251 0.716241444998 1.456141166336 2.414501434208 0.778142664022 0.354058109831 2.435341131140 1.626891056982 0.539859124954
252 0.605899003687 0.232036445142 0.283017326278 0.418555732462 0.774894022794 0.236202451204 0.186848046932 0.189296292376 0.252718447885
253 0.800016530518 0.622711669692 0.211888159615 0.218131577594 0.831842640142 0.580737093181 0.372625175087 0.217721159236 0.348072209797 3.890963773304
254 1.295201266783 5.411115141489 1.593137043457 1.032447924952 0.285078800906 3.945277674515 2.802427151679 0.752042440303 1.022507035889 0.406193586642 0.445570274261
255 1.253758266664 0.983692987457 0.648441278787 0.222621897958 0.767688823480 2.494896077113 0.555415397470 0.459436173579 0.984311525359 3.364797763104 6.030559379572 1.073061184332
256 0.492964679748 0.371644693209 0.354861249223 0.281730694207 0.441337471187 0.144356959750 0.291409084165 0.368166464453 0.714533703928 1.517359325954 2.064839703237 0.266924750511 1.773855168830
257 1.173275900924 0.448133661718 0.494887043702 0.730628272998 0.356008498769 0.858570575674 0.926563934846 0.504086599527 0.527007339151 0.388355409206 0.374555687471 1.047383450722 0.454123625103 0.233597909629
258 4.325092687057 1.122783104210 2.904101656456 1.582754142065 1.197188415094 1.934870924596 1.769893238937 1.509326253224 1.117029762910 0.357544412460 0.352969184527 1.752165917819 0.918723415746 0.540027644824 1.169129577716
259 1.729178019485 0.914665954563 1.898173634533 0.934187509431 1.119831358516 1.277480294596 1.071097236007 0.641436011405 0.585407090225 1.179091197260 0.915259857694 1.303875200799 1.488548053722 0.488206118793 1.005451683149 5.151556292270
260 0.465839367725 0.426382310122 0.191482046247 0.145345046279 0.527664418872 0.758653808642 0.407635648938 0.508358924638 0.301248600780 0.341985787540 0.691474634600 0.332243040634 0.888101098152 2.074324893497 0.252214830027 0.387925622098 0.513128126891
261 0.718206697586 0.720517441216 0.538222519037 0.261422208965 0.470237733696 0.958989742850 0.596719300346 0.308055737035 4.218953969389 0.674617093228 0.811245856323 0.717993486900 0.951682162246 6.747260430801 0.369405319355 0.796751520761 0.801010243199 4.054419006558
262 2.187774522005 0.438388343772 0.312858797993 0.258129289418 1.116352478606 0.530785790125 0.524253846338 0.253340790190 0.201555971750 8.311839405458 2.231405688913 0.498138475304 2.575850755315 0.838119610178 0.496908410676 0.561925457442 2.253074051176 0.266508731426 1.000000000000
263 0.074 0.052 0.045 0.054 0.025 0.034 0.054 0.074 0.026 0.068 0.099 0.058 0.025 0.047 0.039 0.057 0.051 0.013 0.032 0.073;
264 
265 model MTMAM=
266 32
267 2 4
268 11 0.000001 864
269 0.000001 186 0.000001 0.000001
270 0.000001 246 8 49 0.000001
271 0.000001 0.000001 0.000001 569 0.000001 274
272 78 18 47 79 0.000001 0.000001 22
273 8 232 458 11 305 550 22 0.000001
274 75 0.000001 19 0.000001 41 0.000001 0.000001 0.000001 0.000001
275 21 6 0.000001 0.000001 27 20 0.000001 0.000001 26 232
276 0.000001 50 408 0.000001 0.000001 242 215 0.000001 0.000001 6 4
277 76 0.000001 21 0.000001 0.000001 22 0.000001 0.000001 0.000001 378 609 59
278 0.000001 0.000001 6 5 7 0.000001 0.000001 0.000001 0.000001 57 246 0.000001 11
279 53 9 33 2 0.000001 51 0.000001 0.000001 53 5 43 18 0.000001 17
280 342 3 446 16 347 30 21 112 20 0.000001 74 65 47 90 202
281 681 0.000001 110 0.000001 114 0.000001 4 0.000001 1 360 34 50 691 8 78 614
282 5 16 6 0.000001 65 0.000001 0.000001 0.000001 0.000001 0.000001 12 0.000001 13 0.000001 7 17 0.000001
283 0.000001 0.000001 156 0.000001 530 54 0.000001 1 1525 16 25 67 0.000001 682 8 107 0.000001 14
284 398 0.000001 0.000001 10 0.000001 33 20 5 0.000001 2220 100 0.000001 832 6 0.000001 0.000001 237 0.000001 0.000001
285 0.0692 0.0184 0.0400 0.0186 0.0065 0.0238 0.0236 0.0557 0.0277 0.0905 0.1675 0.0221 0.0561 0.0611 0.0536 0.0725 0.0870 0.0293 0.0340 0.0428;
286 
287 model LG=
288 0.425093
289 0.276818 0.751878
290 0.395144 0.123954 5.076149
291 2.489084 0.534551 0.528768 0.062556
292 0.969894 2.807908 1.695752 0.523386 0.084808
293 1.038545 0.363970 0.541712 5.243870 0.003499 4.128591
294 2.066040 0.390192 1.437645 0.844926 0.569265 0.267959 0.348847
295 0.358858 2.426601 4.509238 0.927114 0.640543 4.813505 0.423881 0.311484
296 0.149830 0.126991 0.191503 0.010690 0.320627 0.072854 0.044265 0.008705 0.108882
297 0.395337 0.301848 0.068427 0.015076 0.594007 0.582457 0.069673 0.044261 0.366317 4.145067
298 0.536518 6.326067 2.145078 0.282959 0.013266 3.234294 1.807177 0.296636 0.697264 0.159069 0.137500
299 1.124035 0.484133 0.371004 0.025548 0.893680 1.672569 0.173735 0.139538 0.442472 4.273607 6.312358 0.656604
300 0.253701 0.052722 0.089525 0.017416 1.105251 0.035855 0.018811 0.089586 0.682139 1.112727 2.592692 0.023918 1.798853
301 1.177651 0.332533 0.161787 0.394456 0.075382 0.624294 0.419409 0.196961 0.508851 0.078281 0.249060 0.390322 0.099849 0.094464
302 4.727182 0.858151 4.008358 1.240275 2.784478 1.223828 0.611973 1.739990 0.990012 0.064105 0.182287 0.748683 0.346960 0.361819 1.338132
303 2.139501 0.578987 2.000679 0.425860 1.143480 1.080136 0.604545 0.129836 0.584262 1.033739 0.302936 1.136863 2.020366 0.165001 0.571468 6.472279
304 0.180717 0.593607 0.045376 0.029890 0.670128 0.236199 0.077852 0.268491 0.597054 0.111660 0.619632 0.049906 0.696175 2.457121 0.095131 0.248862 0.140825
305 0.218959 0.314440 0.612025 0.135107 1.165532 0.257336 0.120037 0.054679 5.306834 0.232523 0.299648 0.131932 0.481306 7.803902 0.089613 0.400547 0.245841 3.151815
306 2.547870 0.170887 0.083688 0.037967 1.959291 0.210332 0.245034 0.076701 0.119013 10.649107 1.702745 0.185202 1.898718 0.654683 0.296501 0.098369 2.188158 0.189510 0.249313
307 0.07906592 0.05594094 0.04197696 0.05305195 0.01293699 0.04076696 0.07158593 0.05733694 0.02235498 0.06215694 0.0990809 0.06459994 0.02295098 0.04230196 0.04403996 0.06119694 0.05328695 0.01206599 0.03415497 0.06914693;
308 [ NOTE 2019-06-04: normalised from original LG freqs, which do not sum to 1.0
309   http://www.atgc-montpellier.fr/download/datasets/models/lg_LG.PAML.txt ]
310 
311 model MTART=
312 0.2
313 0.2 0.2
314 1.0 4.0 500.0
315 254.0 36.0 98.0 11.0
316 0.2 154.0 262.0 0.2 0.2
317 0.2 0.2 183.0 862.0 0.2 262.0
318 200.0 0.2 121.0 12.0 81.0 3.0 44.0
319 0.2 41.0 180.0 0.2 12.0 314.0 15.0 0.2
320 26.0 2.0 21.0 7.0 63.0 11.0 7.0 3.0 0.2
321 4.0 2.0 13.0 1.0 79.0 16.0 2.0 1.0 6.0 515.0
322 0.2 209.0 467.0 2.0 0.2 349.0 106.0 0.2 0.2 3.0 4.0
323 121.0 5.0 79.0 0.2 312.0 67.0 0.2 56.0 0.2 515.0 885.0 106.0
324 13.0 5.0 20.0 0.2 184.0 0.2 0.2 1.0 14.0 118.0 263.0 11.0 322.0
325 49.0 0.2 17.0 0.2 0.2 39.0 8.0 0.2 1.0 0.2 12.0 17.0 5.0 15.0
326 673.0 3.0 398.0 44.0 664.0 52.0 31.0 226.0 11.0 7.0 8.0 144.0 112.0 36.0 87.0
327 244.0 0.2 166.0 0.2 183.0 44.0 43.0 0.2 19.0 204.0 48.0 70.0 289.0 14.0 47.0 660.0
328 0.2 0.2 8.0 0.2 22.0 7.0 11.0 2.0 0.2 0.2 21.0 16.0 71.0 54.0 0.2 2.0 0.2
329 1.0 4.0 251.0 0.2 72.0 87.0 8.0 9.0 191.0 12.0 20.0 117.0 71.0 792.0 18.0 30.0 46.0 38.0
330 340.0 0.2 23.0 0.2 350.0 0.2 14.0 3.0 0.2 1855.0 85.0 26.0 281.0 52.0 32.0 61.0 544.0 0.2 2.0
331 0.054116 0.018227 0.039903 0.020160 0.009709 0.018781 0.024289 0.068183 0.024518 0.092638 0.148658 0.021718 0.061453 0.088668 0.041826 0.091030 0.049194 0.029786 0.039443 0.057700;
332 
333 model MTZOA=
334 3.3
335 1.7 33.6
336 16.1 3.2 617.0
337 272.5 61.1 94.6 9.5
338 7.3 231.0 190.3 19.3 49.1
339 17.1 6.4 174.0 883.6 3.4 349.4
340 289.3 7.2 99.3 26.0 82.4 8.9 43.1
341 2.3 61.7 228.9 55.6 37.5 421.8 14.9 7.4
342 33.2 0.2 24.3 1.5 48.8 0.2 7.3 3.4 1.6
343 15.6 4.1 7.9 0.5 59.7 23.0 1.0 3.5 6.6 425.2
344 0.2 292.3 413.4 0.2 0.2 334.0 163.2 10.1 23.9 8.4 6.7
345 136.5 3.8 73.7 0.2 264.8 83.9 0.2 52.2 7.1 449.7 636.3 83.0
346 26.5 0.2 12.9 2.0 167.8 9.5 0.2 5.8 13.1 90.3 234.2 16.3 215.6
347 61.8 7.5 22.6 0.2 8.1 52.2 20.6 1.3 15.6 2.6 11.4 24.3 5.4 10.5
348 644.9 11.8 420.2 51.4 656.3 96.4 38.4 257.1 23.1 7.2 15.2 144.9 95.3 32.2 79.7
349 378.1 3.2 184.6 2.3 199.0 39.4 34.5 5.2 19.4 222.3 50.0 75.5 305.1 19.3 56.9 666.3
350 3.1 16.9 6.4 0.2 36.1 6.1 3.5 12.3 4.5 9.7 27.2 6.6 48.7 58.2 1.3 10.3 3.6
351 2.1 13.8 141.6 13.9 76.7 52.3 10.0 4.3 266.5 13.1 5.7 45.0 41.4 590.5 4.2 29.7 29.0 79.8
352 321.9 5.1 7.1 3.7 243.8 9.0 16.3 23.7 0.3 1710.6 126.1 11.1 279.6 59.6 17.9 49.5 396.4 13.7 15.6
353 0.06887993 0.02103698 0.03038997 0.02069598 0.00996599 0.01862298 0.02498898 0.07196793 0.02681397 0.08507191 0.15671684 0.01927598 0.05065195 0.08171192 0.04480296 0.08053492 0.05638594 0.02799797 0.03740396 0.06608293;
354 [ NOTE 2019-06-04: original mtzoa freqs do not sum to 1.0, modified from PAML package ]
355 
356 model PMB=
357 0.674995699
358 0.589645178 1.189067034
359 0.462499504 0.605460903 3.573373315
360 1.065445546 0.314448330 0.589852457 0.246951424
361 1.111766964 2.967840934 2.299755865 1.686058219 0.245163782
362 1.046334652 1.201770702 1.277836748 4.399995525 0.091071867 4.159678990
363 1.587964372 0.523770553 1.374854049 0.734992057 0.317066320 0.596789898 0.463812837
364 0.580830874 1.457127446 2.283037894 0.839348444 0.411543728 1.812173605 0.877842609 0.476331437
365 0.464590585 0.359645860 0.426069419 0.266775558 0.417547309 0.315256838 0.304215290 0.180198883 0.285186418
366 0.804404505 0.520701585 0.410094470 0.269124919 0.450795211 0.625792937 0.320784710 0.259854426 0.363981358 4.162454693
367 0.831998835 4.956476453 2.037575629 1.114178954 0.274163536 3.521346591 2.415974716 0.581001076 0.985885486 0.374784947 0.498011337
368 1.546725076 0.813462540 0.737846301 0.341932741 0.618614612 2.067388546 0.531773639 0.465349326 0.380925433 3.658070120 5.002338375 0.661095832
369 0.546169219 0.303437244 0.425193716 0.219005213 0.669206193 0.406042546 0.224154698 0.354028910 0.576231691 1.495264661 2.392638293 0.269496317 2.306919847
370 1.241586045 0.655773380 0.711495595 0.775624818 0.198679914 0.850116543 0.794584081 0.588254139 0.456058589 0.366232942 0.430073179 1.036079005 0.337502282 0.481144863
371 3.452308792 0.910144334 2.572577221 1.440896785 0.998700980 1.348272505 1.205509425 1.402122097 0.799966711 0.530641901 0.402471997 1.234648153 0.945453716 0.613230817 1.217683028
372 1.751412803 0.895171490 1.823161023 0.994227284 0.847312432 1.320626678 0.949599791 0.542185658 0.830392810 1.114132523 0.779827336 1.290709079 1.551488041 0.718895136 0.780913179 4.448982584
373 0.350110510 0.618778365 0.422407388 0.362495245 0.445669347 0.720384740 0.261258229 0.378748270 0.724367510 0.516260502 0.794797115 0.433409620 0.768395107 3.295193440 0.499869138 0.496334956 0.383723610
374 0.573154753 0.628599063 0.720013799 0.436220437 0.556261630 0.728970584 0.507200030 0.284727562 2.210952064 0.570562395 0.811019594 0.664884513 0.932536060 5.894735673 0.433748126 0.593795813 0.523549536 2.996248013
375 2.063050067 0.388680158 0.474418852 0.275658381 0.998911631 0.634408285 0.527640634 0.314700907 0.305792277 8.002789424 2.113077156 0.526184203 1.737356217 0.983844803 0.551333603 0.507506011 1.899650790 0.429570747 0.716795463
376 
377  0.07559244 0.05379462 0.03769623 0.04469553 0.02849715 0.03389661 0.05349465 0.0779922 0.029997 0.05989401 0.09579042 0.0519948 0.02189781 0.0449955 0.0419958 0.06819318 0.05639436 0.01569843 0.0359964 0.07149285;
378  [ NOTE 2019-06-04: normalised from original PMB freqs, which do not sum to 1.0:
379   0.0756 0.0538 0.0377 0.0447 0.0285 0.0339 0.0535 0.0780 0.0300 0.0599 0.0958 0.0520 0.0219 0.0450 0.0420 0.0682 0.0564 0.0157 0.0360 0.0715 ]
380 
381 model HIVB=
382 0.30750700
383 0.00500000 0.29554300
384 1.45504000 0.00500000 17.66120000
385 0.12375800 0.35172100 0.08606420 0.00500000
386 0.05511280 3.42150000 0.67205200 0.00500000 0.00500000
387 1.48135000 0.07492180 0.07926330 10.58720000 0.00500000 2.56020000
388 2.13536000 3.65345000 0.32340100 2.83806000 0.89787100 0.06191370 3.92775000
389 0.08476130 9.04044000 7.64585000 1.91690000 0.24007300 7.05545000 0.11974000 0.00500000
390 0.00500000 0.67728900 0.68056500 0.01767920 0.00500000 0.00500000 0.00609079 0.00500000 0.10311100
391 0.21525600 0.70142700 0.00500000 0.00876048 0.12977700 1.49456000 0.00500000 0.00500000 1.74171000 5.95879000
392 0.00500000 20.45000000 7.90443000 0.00500000 0.00500000 6.54737000 4.61482000 0.52170500 0.00500000 0.32231900 0.08149950
393 0.01866430 2.51394000 0.00500000 0.00500000 0.00500000 0.30367600 0.17578900 0.00500000 0.00500000 11.20650000 5.31961000 1.28246000
394 0.01412690 0.00500000 0.00500000 0.00500000 9.29815000 0.00500000 0.00500000 0.29156100 0.14555800 3.39836000 8.52484000 0.03426580 0.18802500
395 2.12217000 1.28355000 0.00739578 0.03426580 0.00500000 4.47211000 0.01202260 0.00500000 2.45318000 0.04105930 2.07757000 0.03138620 0.00500000 0.00500000
396 2.46633000 3.47910000 13.14470000 0.52823000 4.69314000 0.11631100 0.00500000 4.38041000 0.38274700 1.21803000 0.92765600 0.50411100 0.00500000 0.95647200 5.37762000
397 15.91830000 2.86868000 6.88667000 0.27472400 0.73996900 0.24358900 0.28977400 0.36961500 0.71159400 8.61217000 0.04376730 4.67142000 4.94026000 0.01412690 2.01417000 8.93107000
398 0.00500000 0.99133800 0.00500000 0.00500000 2.63277000 0.02665600 0.00500000 1.21674000 0.06951790 0.00500000 0.74884300 0.00500000 0.08907800 0.82934300 0.04445060 0.02487280 0.00500000
399 0.00500000 0.00991826 1.76417000 0.67465300 7.57932000 0.11303300 0.07926330 0.00500000 18.69430000 0.14816800 0.11198600 0.00500000 0.00500000 15.34000000 0.03043810 0.64802400 0.10565200 1.28022000
400 7.61428000 0.08124540 0.02665600 1.04793000 0.42002700 0.02091530 1.02847000 0.95315500 0.00500000 17.73890000 1.41036000 0.26582900 6.85320000 0.72327400 0.00500000 0.07492180 0.70922600 0.00500000 0.04105930
401 0.060490222 0.066039665 0.044127815 0.042109048 0.020075899 0.053606488 0.071567447 0.072308239 0.022293943 0.069730629 0.098851122 0.056968211 0.019768318 0.028809447 0.046025282 0.050604330 0.053636813 0.033011601 0.028350243 0.061625237;
402 
403 model HIVW=
404 0.0744808
405 0.6175090 0.1602400
406 4.4352100 0.0674539 29.4087000
407 0.1676530 2.8636400 0.0604932 0.0050000
408 0.0050000 10.6746000 0.3420680 0.0050000 0.0050000
409 5.5632500 0.0251632 0.2015260 12.1233000 0.0050000 3.2065600
410 1.8685000 13.4379000 0.0604932 10.3969000 0.0489798 0.0604932 14.7801000
411 0.0050000 6.8440500 8.5987600 2.3177900 0.0050000 18.5465000 0.0050000 0.0050000
412 0.0050000 1.3406900 0.9870280 0.1451240 0.0050000 0.0342252 0.0390512 0.0050000 0.0050000
413 0.1602400 0.5867570 0.0050000 0.0050000 0.0050000 2.8904800 0.1298390 0.0489798 1.7638200 9.1024600
414 0.5927840 39.8897000 10.6655000 0.8943130 0.0050000 13.0705000 23.9626000 0.2794250 0.2240600 0.8174810 0.0050000
415 0.0050000 3.2865200 0.2015260 0.0050000 0.0050000 0.0050000 0.0050000 0.0489798 0.0050000 17.3064000 11.3839000 4.0956400
416 0.5979230 0.0050000 0.0050000 0.0050000 0.3629590 0.0050000 0.0050000 0.0050000 0.0050000 1.4828800 7.4878100 0.0050000 0.0050000
417 1.0098100 0.4047230 0.3448480 0.0050000 0.0050000 3.0450200 0.0050000 0.0050000 13.9444000 0.0050000 9.8309500 0.1119280 0.0050000 0.0342252
418 8.5942000 8.3502400 14.5699000 0.4278810 1.1219500 0.1602400 0.0050000 6.2796600 0.7251570 0.7400910 6.1439600 0.0050000 0.3925750 4.2793900 14.2490000
419 24.1422000 0.9282030 4.5420600 0.6303950 0.0050000 0.2030910 0.4587430 0.0489798 0.9595600 9.3634500 0.0050000 4.0480200 7.4131300 0.1145120 4.3370100 6.3407900
420 0.0050000 5.9656400 0.0050000 0.0050000 5.4989400 0.0443298 0.0050000 2.8258000 0.0050000 0.0050000 1.3703100 0.0050000 0.0050000 0.0050000 0.0050000 1.1015600 0.0050000
421 0.0050000 0.0050000 5.0647500 2.2815400 8.3483500 0.0050000 0.0050000 0.0050000 47.4889000 0.1145120 0.0050000 0.0050000 0.5791980 4.1272800 0.0050000 0.9331420 0.4906080 0.0050000
422 24.8094000 0.2794250 0.0744808 2.9178600 0.0050000 0.0050000 2.1995200 2.7962200 0.8274790 24.8231000 2.9534400 0.1280650 14.7683000 2.2800000 0.0050000 0.8626370 0.0050000 0.0050000 1.3548200
423 0.0377494 0.0573210 0.0891129 0.0342034 0.0240105 0.0437824 0.0618606 0.0838496 0.0156076 0.0983641 0.0577867 0.0641682 0.0158419 0.0422741 0.0458601 0.0550846 0.0813774 0.0195970 0.0205847 0.0515638;
424 
425 model JTTDCMUT=
426 0.531678
427 0.557967 0.451095
428 0.827445 0.154899 5.549530
429 0.574478 1.019843 0.313311 0.105625
430 0.556725 3.021995 0.768834 0.521646 0.091304
431 1.066681 0.318483 0.578115 7.766557 0.053907 3.417706
432 1.740159 1.359652 0.773313 1.272434 0.546389 0.231294 1.115632
433 0.219970 3.210671 4.025778 1.032342 0.724998 5.684080 0.243768 0.201696
434 0.361684 0.239195 0.491003 0.115968 0.150559 0.078270 0.111773 0.053769 0.181788
435 0.310007 0.372261 0.137289 0.061486 0.164593 0.709004 0.097485 0.069492 0.540571 2.335139
436 0.369437 6.529255 2.529517 0.282466 0.049009 2.966732 1.731684 0.269840 0.525096 0.202562 0.146481
437 0.469395 0.431045 0.330720 0.190001 0.409202 0.456901 0.175084 0.130379 0.329660 4.831666 3.856906 0.624581
438 0.138293 0.065314 0.073481 0.032522 0.678335 0.045683 0.043829 0.050212 0.453428 0.777090 2.500294 0.024521 0.436181
439 1.959599 0.710489 0.121804 0.127164 0.123653 1.608126 0.191994 0.208081 1.141961 0.098580 1.060504 0.216345 0.164215 0.148483
440 3.887095 1.001551 5.057964 0.589268 2.155331 0.548807 0.312449 1.874296 0.743458 0.405119 0.592511 0.474478 0.285564 0.943971 2.788406
441 4.582565 0.650282 2.351311 0.425159 0.469823 0.523825 0.331584 0.316862 0.477355 2.553806 0.272514 0.965641 2.114728 0.138904 1.176961 4.777647
442 0.084329 1.257961 0.027700 0.057466 1.104181 0.172206 0.114381 0.544180 0.128193 0.134510 0.530324 0.089134 0.201334 0.537922 0.069965 0.310927 0.080556
443 0.139492 0.235601 0.700693 0.453952 2.114852 0.254745 0.063452 0.052500 5.848400 0.303445 0.241094 0.087904 0.189870 5.484236 0.113850 0.628608 0.201094 0.747889
444 2.924161 0.171995 0.164525 0.315261 0.621323 0.179771 0.465271 0.470140 0.121827 9.533943 1.761439 0.124066 3.038533 0.593478 0.211561 0.408532 1.143980 0.239697 0.165473
445 0.07686192 0.05105695 0.04254596 0.05126895 0.02027898 0.04106096 0.06181994 0.07471393 0.02298298 0.05256895 0.09111091 0.05949794 0.02341398 0.04052996 0.05053195 0.06822493 0.05851794 0.01433599 0.03230297 0.06637393;
446 [ NOTE 2019-06-04: normalised from original JTTDCMUTT freqs, which do not sum to 1.0
447   https://www.ebi.ac.uk/goldman-srv/dayhoff/jtt-dcmut.dat ]
448 
449 model FLU=
450 0.138658765
451 0.053366579 0.161000889
452 0.584852306 0.006771843 7.737392871
453 0.026447095 0.167207008 0.000013000 0.014100000
454 0.353753982 3.292716942 0.530642655 0.145469388 0.002547334
455 1.484234503 0.124897617 0.061652192 5.370511279 0.000000000 1.195629122
456 1.132313122 1.190624465 0.322524648 1.934832784 0.116941459 0.108051341 1.593098825
457 0.214757862 1.879569938 1.387096032 0.887570549 0.021800000 5.330313412 0.256491863 0.058774527
458 0.149926734 0.246117172 0.218571975 0.014085917 0.001112158 0.028839950 0.014200000 0.000016300 0.243190142
459 0.023116952 0.296045557 0.000836000 0.005730682 0.005613627 1.020366955 0.016499536 0.006516229 0.321611694 3.512072282
460 0.474333610 15.300096620 2.646847965 0.290042980 0.000003830 2.559587177 3.881488809 0.264148929 0.347302791 0.227707997 0.129223639
461 0.058745423 0.890162346 0.005251688 0.041762964 0.111457310 0.190259181 0.313974351 0.001500467 0.001273509 9.017954203 6.746936485 1.331291619
462 0.080490909 0.016100000 0.000836000 0.000001060 0.104053666 0.032680657 0.001003501 0.001236645 0.119028506 1.463357278 2.986800036 0.320000000 0.279910509
463 0.659311478 0.154027180 0.036400000 0.188539456 0.000000000 0.712769599 0.319558828 0.038631761 0.924466914 0.080543327 0.634308521 0.195750632 0.056900000 0.007132430
464 3.011344519 0.950138410 3.881310531 0.338372183 0.336263345 0.487822499 0.307140298 1.585646577 0.580704250 0.290381075 0.570766693 0.283807672 0.007026588 0.996685670 2.087385344
465 5.418298175 0.183076905 2.140332316 0.135481233 0.011975266 0.602340963 0.280124895 0.018808030 0.368713573 2.904052286 0.044926357 1.526964200 2.031511321 0.000134906 0.542251094 2.206859934
466 0.196000000 1.369429408 0.000536000 0.000014900 0.094106680 0.044000000 0.155245492 0.196486447 0.022400000 0.032132150 0.431277663 0.000049800 0.070460039 0.814753094 0.000431021 0.099835753 0.207066206
467 0.018289288 0.099855497 0.373101927 0.525398543 0.601692431 0.072205935 0.104092870 0.074814997 6.448954446 0.273934263 0.340058468 0.012416222 0.874272175 5.393924245 0.000182000 0.392552240 0.124898020 0.427755430
468 3.532005270 0.103964386 0.010257517 0.297123975 0.054904564 0.406697814 0.285047948 0.337229619 0.098631355 14.394052190 0.890598579 0.073127930 4.904842235 0.592587985 0.058971975 0.088256423 0.654109108 0.256900461 0.167581647
469 0.04707195 0.05090995 0.07421393 0.04785995 0.02502197 0.03330397 0.05458695 0.07637292 0.01996398 0.06713393 0.07149793 0.05678494 0.01815098 0.03049597 0.05065595 0.08840891 0.07433893 0.01852398 0.03147397 0.06322894;
470 [ NOTE 2019-06-04: normalised from FLU freqs in PhyML, which do not sum 1.0 ]
471 
472 model MTMET=
473 0.058078177576542
474 0.032893910131824 0.141364232590718
475 0.119156819252943 0.049700397089876 4.658418673473980
476 0.633255658023246 0.739813635055843 0.292999912100000 0.077399976780000
477 0.052454931263516 2.673107287067570 0.832791283162540 0.131355662593289 0.152595162221438
478 0.179163834250834 0.080835456749356 0.812240880327663 6.033787171863310 0.050599984820000 2.236616952014710
479 1.465861840241320 0.219967058009863 0.543750593874773 0.630753109774010 0.914125315762323 0.072395514281339 0.768853064344011
480 0.030192120942361 1.522256408322940 1.738679122396110 0.479790968062666 0.603999818800000 4.518449535464730 0.105414703375579 0.025252648424203
481 0.367600338719865 0.012428572271427 0.244934691519570 0.010668852799343 0.235804174258726 0.008875683337294 0.013999995800000 0.013799995860000 0.017140133857958
482 0.109872733038170 0.058179997545996 0.046299986110000 0.005529142341257 0.299518907144301 0.254452390664260 0.019157613252714 0.027264545820634 0.111638903508319 1.897973798607690
483 0.020509501847148 1.057185315844310 2.530397670880470 0.049007441297763 0.015799995260000 1.827217637834540 1.379217369234670 0.134187134743847 0.135153622453901 0.064936591519017 0.061324501602644
484 0.653363796990802 0.013494029951790 0.399827603051683 0.026109939167016 0.492339996297957 0.237094294871690 0.128410015476984 0.145331422400560 0.032834304149706 2.918352332494040 3.425552681333890 0.659310562206772
485 0.062762236171324 0.008039997588000 0.138999958300000 0.012599996220000 0.925810586256741 0.026306317108103 0.017716302685108 0.068139260558216 0.090353039894080 0.750900315729838 1.811100689669630 0.097099970870000 0.748424772472501
486 0.408076930576884 0.155008519497430 0.080299975910000 0.044609549617131 0.029399991180000 0.849512180146269 0.048786284364110 0.005914204225738 0.519954219013687 0.024850013544994 0.270260699921766 0.121234884629524 0.032699990190000 0.054271872718433
487 2.771685183494200 0.197379125786245 2.634377723686450 0.360804672758566 3.283013886095540 0.384800168559915 0.363104357068660 1.746569621028960 0.297585994724175 0.096272835118141 0.311525037542461 0.695087919473562 0.458733958379771 0.499349751195030 1.231180449645750
488 6.730883140734450 0.056079796176056 0.961284804614472 0.102136190359134 0.338668094399541 0.274195864741216 0.134802630559199 0.024558282632513 0.221010542696817 2.453457406962560 0.253366627989989 0.393851585844489 3.035214815435280 0.053947726815677 0.734604689618527 3.114741972577130
489 0.013599995920000 0.370819780754032 0.048999985300000 0.040899987730000 1.018410179476850 0.122999963100000 0.086028769191362 0.233963300810989 0.037499988750000 0.028656788402961 0.253242937027096 0.073499977950000 0.167575267727405 0.330781828765422 0.029433857169840 0.169211978236391 0.014378611686415
490 0.014501402649578 0.127519293744200 1.020785184764350 0.160289909913013 1.967370664788620 0.319105692268264 0.093214693035584 0.046746326976098 3.907917378624430 0.135319420404162 0.123555294933400 0.281699089490248 0.316598936020291 3.209082340275010 0.053999983800000 0.374184173744714 0.091031759690464 0.481044171686705
491 2.815162240451070 0.041063671680895 0.051741611477512 0.084589003623291 1.394527625641590 0.027669224699230 0.227826982651885 0.417148828855314 0.003511006946698 10.953422553972199 0.958273455517877 0.055461418361570 2.562484126254530 0.466243302126967 0.054078516776440 0.267109384867160 1.514059219782100 0.093136228059123 0.069964519010638
492 0.043793213137964 0.012957803887341 0.057001317100395 0.016899005069702 0.011330503399151 0.018018105405432 0.022538506761552 0.047050114115034 0.017183705155112 0.089779426933828 0.155226046567814 0.039913511974054 0.067444320233296 0.088448026534408 0.037528211258463 0.093752228125668 0.063579019073706 0.022671306801392 0.041568212470464 0.053317415995225;
493 
494 model MTVER=
495 0.064684593342281
496 0.032311373155679 0.153152767576346
497 0.159447300723611 0.060872136436053 8.760497104246360
498 0.246553724276801 1.223667683833540 0.336000168000000 0.121000060500000
499 0.030870542435264 3.170387139192780 0.392967223483514 0.083338219669089 0.116173343086643
500 0.191894227947066 0.094355879177916 0.335734154866994 6.603638632817670 0.036400018200000 2.018143897071440
501 1.094200939100200 0.292471267235560 0.566907089453403 0.999256939628220 0.916865240432391 0.042512995256487 1.162715978357700
502 0.023294179647084 2.204735655367280 2.462271663135220 0.818112173055882 1.400000700000000 4.282733559365710 0.081141411570686 0.013333256666625
503 0.412485044242419 0.001173176586588 0.126395609197773 0.002450024225012 0.067512580756274 0.004179092089545 0.001250000625000 0.003120001560000 0.022239993119991
504 0.078175506087734 0.078821952410957 0.004520002260000 0.002303982151991 0.170993012496464 0.251583784791830 0.007547828773913 0.007030631515314 0.148659642329784 1.378981921490620
505 0.020785858392924 0.418858706429249 2.458223875111320 0.019527849763920 0.024800012400000 2.001705573852290 2.154179684089300 0.106373697186822 0.176407170203541 0.005826060913029 0.022236503118246
506 0.751880839940232 0.003339427669713 0.036342279171131 0.005454655727327 0.084565948282953 0.118300117150029 0.064939181469575 0.034441699220841 0.024341806170897 2.709085270541960 3.102549285273870 0.440831886415833
507 0.064446525223247 0.002480001240000 0.010300005150000 0.005850002925000 1.071950287974880 0.012628428314211 0.000332940166470 0.015567819783906 0.173363959681937 0.516016662008202 2.403419459709130 0.010400005200000 0.123894605947272
508 0.285569393784626 0.223106325553107 0.034500017250000 0.027518484759236 0.018900009450000 0.918408714204128 0.027495640747814 0.001858863929432 0.679485296742479 0.018484697242344 0.366808261404039 0.141827309913619 0.030900015450000 0.070221307110636
509 2.481817894908330 0.135104231552082 3.854777098387590 0.371726663863239 3.359148754573540 0.243906745953312 0.097749778874865 1.247283625641500 0.445289314644546 0.044145011072495 0.440667041333411 0.187506484753196 0.137172898586415 0.886724514362035 1.961395669697340
510 5.562701612349420 0.028643207321597 0.865443620721594 0.090462201231078 0.152312893156409 0.113601717800831 0.095055222527588 0.008518901259449 0.150502737251331 2.439178561588670 0.173310979655447 0.399752584876193 3.736806509402320 0.061993007996489 0.573808396904055 2.845373550686060
511 0.008420004210000 0.558540909270315 0.006680003340000 0.026900013450000 1.778859743429430 0.124000062000000 0.062341391170680 0.258646151323011 0.030600015300000 0.001901139950570 0.186367686183797 0.029400014700000 0.056840260420116 0.091906956953456 0.020008909004450 0.144081317040623 0.003186142593071
512 0.012484943242469 0.146342752171340 0.856969809484690 0.186328057163982 5.248219583108480 0.228833221416554 0.037356125678054 0.021047207523599 9.175812436903930 0.045429850714914 0.103344604672277 0.062036757018363 0.079617080808521 3.987260862629440 0.071900035950000 0.543167000583365 0.084368299184129 0.288348349174103
513 3.196938070468240 0.037629752814867 0.013796210898102 0.128208017103977 0.381860130929970 0.010633051316523 0.216260948130420 0.442992988496384 0.002759961379980 13.505144232568700 0.856259496129534 0.025253726626857 4.499326020661890 0.336159506079669 0.025768082884035 0.058280992140482 1.317930995965170 0.047174784587381 0.028686388343187
514 0.070820264589868 0.014049892975054 0.045209877395061 0.014793692603154 0.006814196592902 0.026340886829557 0.021495189252405 0.044239977880011 0.024230987884506 0.090735054632473 0.172309913845043 0.027381186309407 0.056193971903014 0.049775775112112 0.054386272806864 0.074421862789069 0.108809945595027 0.025652687173656 0.026484686757657 0.045853677073162;
515 
516 model MTINV=
517 0.074334218266301
518 0.023989052404375 0.147604222958287
519 0.100963342614647 0.070670662731724 3.471722830310310
520 1.303663674534320 0.680711975715101 0.279969423012186 0.058303793678473
521 0.090980768607678 2.507737031904790 1.287188991124200 0.204531412187402 0.163006102797533
522 0.145240519903769 0.121635259345877 1.159082473366830 6.962509289995170 0.047068462172608 2.559965106013550
523 1.931554281377980 0.217695106921922 0.551419739432016 0.591216665513239 0.883545088581823 0.114080027367971 0.599017294392986
524 0.045194564922167 1.283366609653150 1.728634951545740 0.358935283425829 0.341191895523187 4.708030703786970 0.217387593044928 0.064352344259052
525 0.209390225243876 0.028420823631666 0.310892189643074 0.017124804150076 0.287547507980951 0.025100268959888 0.020795063681971 0.024809855076054 0.025529460788212
526 0.153999806400053 0.052763470894603 0.075114618954140 0.010524108790355 0.381393499442539 0.211473478410575 0.033099595760156 0.050781943687214 0.080842277663076 2.159573277170340
527 0.014824597070159 1.631885373245590 2.642319727071690 0.096074070570356 0.004392611242955 1.933672173530820 1.172486892005060 0.156144354542233 0.250218937912385 0.100258540896568 0.081982070207159
528 0.592864803853984 0.022385985045602 0.566989926203939 0.049089594364154 0.461585949365546 0.397060773175627 0.189458582216537 0.207637097945128 0.070807578676957 2.830888275644240 3.494915172033370 0.694473233210596
529 0.111082013567177 0.015357906856835 0.194205108317926 0.017157066137171 0.887097013161053 0.052545508981788 0.027169124132346 0.103612477554992 0.151813232274683 0.879509584196026 1.735138890944170 0.098766126493534 0.916539999383854
530 0.629531950187119 0.130198008920776 0.224156768337257 0.104690593123746 0.069312726274898 0.581011232595414 0.120987616604934 0.028323516670589 0.312042686182876 0.070886389645433 0.154372892250818 0.183146598741331 0.092516642993328 0.105108133956730
531 3.368752649498400 0.309426794229233 2.084469247211970 0.505643420742551 3.042784023885900 0.538789467484127 0.580233013906702 2.020140264943570 0.368422261631036 0.126690032323967 0.225488005804762 0.879840867063512 0.633585250565799 0.398961585415302 1.042509719995950
532 3.327041763182760 0.108593900562422 1.186265342493670 0.141991497203378 0.736861629255230 0.554297413280946 0.241928620228513 0.043791194483515 0.270595503761755 1.958518039592470 0.298279746688054 0.511283878486367 2.192058660176190 0.121269516492174 0.746916803233159 3.833298761679880
533 0.026501471399407 0.321740677303678 0.075398643840530 0.071630764347683 0.758571851571138 0.118046810781257 0.107622585950948 0.244698162120696 0.081171865531241 0.062889026844379 0.298463138614697 0.106016335593449 0.254195659321696 0.478876889449168 0.059737825104860 0.204318441272591 0.049859203056311
534 0.021939769224089 0.182762501894970 1.139165041333800 0.192759935895995 1.342951983818990 0.476209340516188 0.137649645940120 0.072268115092742 2.321701900318870 0.177138315144646 0.161052630578922 0.348477651608884 0.393193176722666 3.234681510126880 0.081395316441860 0.345719568712117 0.174898633040519 0.636664640334042
535 2.751362222454670 0.072153227138698 0.065420927831618 0.088077392769029 1.555396905840990 0.065221940911213 0.231186486525368 0.396428077428706 0.008043434782625 8.542589373962890 1.075872855650690 0.056252073499162 1.509852171058890 0.534676724129225 0.162975872809625 0.377288666084473 1.885338569864270 0.128598566560553 0.080346083861554
536 0.031742312696925 0.010900704360282 0.061579224631690 0.016149206459683 0.013570105428042 0.014644105857642 0.022311208924484 0.047847519139008 0.011641804656722 0.094322337728935 0.149407059762824 0.044438717775487 0.077262530905012 0.102287040914816 0.026290210516084 0.105939042375617 0.042869117147647 0.020701008280403 0.046556718622687 0.059540023816010;
537 
538 model Q.PFAM=
539 0.531344742
540 0.266631781 0.610524242
541 0.479415354 0.145193836 4.395589145
542 2.490407258 0.797726764 0.617331366 0.086320436
543 1.058818226 2.850794598 1.685541958 0.623180282 0.163023963
544 1.178483844 0.358512949 0.572153867 4.775857514 0.004224284 4.045465925
545 1.897932882 0.427923043 1.417171473 0.993358642 0.723368327 0.349584077 0.412573692
546 0.453464468 2.765967911 4.395995003 0.944775779 1.220289602 4.992256584 0.444851397 0.432227777
547 0.176454495 0.103023046 0.192557924 0.012280201 0.599859067 0.090487083 0.045755066 0.025135568 0.108027826
548 0.419433650 0.307712278 0.070917051 0.019106538 0.827369996 0.609556427 0.066812844 0.070095729 0.420152907 4.316039810
549 0.501174376 5.070603955 2.126974783 0.311739636 0.042113153 3.211891588 1.628511729 0.323774881 0.779002069 0.188076678 0.128912693
550 1.175077280 0.565654138 0.405987508 0.044371788 1.330027314 1.704580053 0.217689890 0.196370346 0.488138895 5.052397990 6.674964742 0.790881216
551 0.266730243 0.050284344 0.098902029 0.023281590 1.570975979 0.044860498 0.016021778 0.116848629 0.754840320 1.333037626 2.539936322 0.022355802 1.944915128
552 1.371519672 0.396818483 0.230865860 0.538351193 0.117103191 0.764761023 0.532587532 0.323334201 0.635697033 0.101194285 0.285369684 0.446883087 0.146079999 0.106999973
553 3.745215188 0.711941869 3.559567653 1.188991720 3.084090802 1.178336151 0.587105765 1.645856748 1.047872072 0.078854093 0.182164122 0.756113129 0.449949835 0.319772739 1.499944856
554 2.134156546 0.664457704 1.923647217 0.498902533 1.382576296 1.172710577 0.733559201 0.232722239 0.648977470 1.067438502 0.303042511 1.169845557 2.176841262 0.185666747 0.667935113 5.538833003
555 0.198118657 0.503943335 0.048383536 0.030638664 0.964172901 0.185024339 0.044029570 0.199917400 0.592439554 0.143667666 0.614180565 0.040725071 0.765641182 2.174974075 0.133590865 0.217347672 0.125958817
556 0.208747809 0.263834003 0.570488409 0.134714779 1.863419357 0.264729772 0.100447410 0.074554161 5.545635324 0.271724216 0.338670344 0.138599247 0.651180870 7.474120415 0.108442089 0.374198514 0.267599595 2.604411280
557 2.688525915 0.201107356 0.119873351 0.052396485 2.371412865 0.282178057 0.297627071 0.134209258 0.229732340 11.786948184 2.030164484 0.222793132 2.397008325 0.758096789 0.362295352 0.127446562 2.284500453 0.201953893 0.337688120
558 0.085788000 0.057731000 0.042028000 0.056462000 0.010447000 0.039548000 0.067799000 0.064861000 0.021040000 0.055398000 0.100413000 0.059401000 0.019898000 0.042789000 0.039579000 0.069262000 0.055498000 0.014430000 0.033233000 0.064396000;
559 
560 model Q.PFAM_GB=
561 0.365164838
562 0.267954861 0.668182618
563 0.412395647 0.109946883 5.109280517
564 2.729878231 0.826085083 0.726938192 0.087850737
565 0.877084208 2.867777221 1.690914729 0.549211875 0.175083471
566 1.030653110 0.296644302 0.531939174 5.408576458 0.009322812 4.263791122
567 2.118558237 0.406823565 1.377653412 0.873060903 0.782691675 0.293835651 0.404384209
568 0.350857800 2.639511515 4.957438759 0.957717365 1.116928692 5.496513866 0.357768891 0.337006729
569 0.117950785 0.097118281 0.189788694 0.007265312 0.427089565 0.083014733 0.034316792 0.014707735 0.086519266
570 0.265550676 0.256367291 0.059881044 0.010401807 0.642230229 0.589163556 0.053257602 0.037254822 0.365721292 3.923176859
571 0.457693311 5.846934542 2.118089709 0.248389767 0.027767460 3.282211527 1.530154625 0.267310479 0.632651172 0.148725361 0.106747583
572 0.983716229 0.449899179 0.360441883 0.019663070 1.089667442 1.579564776 0.178533992 0.144384262 0.390780590 5.076767492 6.772375029 0.740162467
573 0.184682627 0.034838076 0.079279076 0.013765656 1.373741900 0.033977644 0.013172775 0.066574829 0.649373699 0.993172189 2.231416771 0.015878425 1.671492831
574 1.208554025 0.298720644 0.164723116 0.340542665 0.126175761 0.713343366 0.393866840 0.185899793 0.585878841 0.068750403 0.259147052 0.350619140 0.101213184 0.074341327
575 4.632633836 0.692974365 4.084102769 1.010171060 3.782357424 1.053657420 0.483380661 1.759872389 0.936824568 0.067637494 0.172313759 0.617037785 0.391313179 0.312203677 1.419107393
576 2.317571767 0.564138173 2.051675662 0.400824407 1.655895774 1.036694976 0.582434600 0.163002252 0.527116986 1.125002936 0.262729464 1.039042636 2.278959095 0.137832417 0.601398020 6.382983692
577 0.107582893 0.435536872 0.047263468 0.026999980 0.817007211 0.206727272 0.030420354 0.141119644 0.501645686 0.086205240 0.414640307 0.024983931 0.528052784 1.764940773 0.070162265 0.201322252 0.086102239
578 0.157118656 0.205907035 0.544230162 0.119435501 1.653471491 0.208926712 0.080278936 0.047930460 5.372406910 0.169889476 0.258512719 0.100866499 0.460416547 7.845710592 0.075597432 0.317057267 0.177135947 2.300580433
579 2.411548529 0.146939179 0.105041792 0.041670032 2.240651656 0.235573727 0.256746635 0.094430216 0.142765142 12.429218156 1.730591322 0.181062532 2.353311726 0.601728375 0.266981380 0.093044732 2.271589526 0.130636191 0.212433758
580 0.087660000 0.058154000 0.037239000 0.048117000 0.013233000 0.038080000 0.063213000 0.059035000 0.021871000 0.061155000 0.111580000 0.056999000 0.022763000 0.046732000 0.035355000 0.065285000 0.052818000 0.015550000 0.035618000 0.069541000;
581 
582 model Q.LG=
583 0.424057540
584 0.271250376 0.764825201
585 0.401980425 0.140794893 5.062142812
586 2.327453440 0.519625401 0.507639701 0.071616388
587 1.072849735 3.123615724 1.879768813 0.664578644 0.104402693
588 1.069798507 0.402468665 0.595330390 5.601033240 0.000110712 4.776313857
589 1.793212924 0.339928462 1.257892965 0.741295542 0.488516386 0.272681884 0.332128789
590 0.392890955 2.558126695 4.639398318 0.987385467 0.677157762 5.468173089 0.498257950 0.296507145
591 0.138014910 0.132223556 0.192515195 0.013803595 0.328676783 0.094404276 0.045491635 0.009271038 0.121398119
592 0.367358512 0.278306063 0.065286972 0.014185552 0.536563257 0.592378803 0.071724886 0.041522603 0.366698667 3.930811583
593 0.563978915 6.845986165 2.226004549 0.353825055 0.002829803 3.797608224 2.027714606 0.282308308 0.801983530 0.169487062 0.141910872
594 1.128143826 0.489462975 0.408708404 0.023806440 0.904437688 1.839460723 0.196671330 0.125388186 0.497496251 4.359960777 6.201341249 0.706300529
595 0.236258684 0.055016203 0.092864269 0.016998748 0.957089079 0.037738461 0.018574182 0.075225605 0.703446369 1.021152682 2.226104190 0.019952549 1.726515479
596 1.158823278 0.344518589 0.176377788 0.403179438 0.080797749 0.708201457 0.456455246 0.180072253 0.538060086 0.083244488 0.235273346 0.427986716 0.111914514 0.092858734
597 4.667976453 0.835065436 3.955582326 1.241154390 2.628965883 1.346684133 0.670392140 1.526697708 1.067966220 0.054379608 0.183116838 0.828615345 0.354736216 0.335899646 1.341323449
598 2.159899413 0.617964388 2.022264246 0.477448489 1.129405944 1.248400502 0.659780378 0.124572237 0.649139830 1.017998492 0.303426657 1.225974643 2.088967227 0.169151604 0.605969830 6.645417766
599 0.151862790 0.477052140 0.039141184 0.025562335 0.529678067 0.221132079 0.066497056 0.187213189 0.555296865 0.099536892 0.479069315 0.048841785 0.606743708 1.854514258 0.076842003 0.202206939 0.123868108
600 0.192903795 0.274767702 0.526873728 0.124040819 1.020373268 0.276139426 0.112342970 0.044355728 5.074607897 0.213437583 0.276570096 0.143396629 0.480201901 6.641252774 0.081147599 0.358925565 0.235545698 2.373266140
601 2.511548974 0.180665670 0.088670492 0.042435978 1.853035143 0.252220059 0.270634816 0.078641075 0.148865811 11.081231885 1.642242475 0.209350089 2.027034834 0.628362476 0.310510022 0.091930966 2.286257438 0.164177306 0.267739693
602 0.080009000 0.052947000 0.041171000 0.050146000 0.015018000 0.035929000 0.061392000 0.064793000 0.021709000 0.063895000 0.106292000 0.057047000 0.023440000 0.047712000 0.039604000 0.062980000 0.052863000 0.014987000 0.037434000 0.070634000;
603 
604 model Q.BIRD=
605 0.086772353
606 0.041489234 0.145522693
607 0.684872641 0.038182359 4.588509426
608 0.214514127 2.310001798 0.094392928 0.085866464
609 0.104071310 4.326376802 0.119230449 0.051178971 0.037945162
610 0.768984102 0.089892499 0.080461407 5.114292481 0.028175939 1.988992665
611 2.215762795 1.937855330 0.295994975 2.041821920 1.073717504 0.105321639 1.420133178
612 0.080617856 6.927918567 3.653639043 1.071049041 2.585629399 6.123585849 0.058085432 0.108840477
613 0.046084289 0.203642191 0.465074580 0.025094905 0.142117407 0.031239309 0.016280777 0.029795942 0.047732049
614 0.116389136 0.336043365 0.021519291 0.026444908 0.269064319 0.527627637 0.038528060 0.047328310 0.607702969 1.935765980
615 0.093630870 5.781174762 2.258646191 0.026415889 0.011551984 1.637753572 1.761938656 0.087005765 0.004280896 0.148647886 0.044628305
616 0.235654912 0.732190858 0.048983640 0.016856105 0.129334019 0.168730118 0.077835842 0.072799197 0.035426840 7.398376755 3.334268838 0.708348805
617 0.092004559 0.061734224 0.047373731 0.043468817 1.575630749 0.045946765 0.043087788 0.049575370 0.141447452 0.962852023 2.950112395 0.040069839 0.134340383
618 2.022526978 0.407828168 0.021912937 0.057096272 0.124231767 1.446258879 0.060414502 0.063511937 1.485608296 0.042135216 1.450911972 0.054326874 0.048270788 0.072731066
619 2.352357809 0.961653423 5.657997764 0.161901882 2.848589688 0.086837961 0.056173980 2.558621780 0.248112786 0.287491221 0.653587912 0.105167714 0.055804307 0.936346554 2.818055661
620 9.189210510 0.711833578 1.856292472 0.041327738 0.117750493 0.075637987 0.075603922 0.085458940 0.064922501 3.670916550 0.086159175 0.827391264 6.908142924 0.086710531 1.546051817 3.320463486
621 0.067881151 2.240359335 0.029075520 0.024018688 2.572562133 0.667514386 0.057387721 0.561105174 0.032498470 0.045679288 0.687156290 0.024744157 0.188378332 0.454841057 0.054773510 0.269153898 0.048484013
622 0.062428150 0.069988164 0.632160724 0.452258389 5.266555093 0.049244809 0.032418984 0.035199737 6.764718412 0.083433936 0.094733583 0.036104364 0.043823350 3.894213263 0.056354401 0.461507798 0.048169854 0.308629484
623 5.126996382 0.063299974 0.037743293 0.240637305 0.199254052 0.052218599 0.307081397 0.848692284 0.058399592 13.397205976 2.035426441 0.054281453 7.643787012 0.780383422 0.081010240 0.082620150 0.391832532 0.082144494 0.059610809
624 0.066363000 0.054021000 0.037784000 0.047511000 0.022651000 0.048841000 0.071571000 0.058368000 0.025403000 0.045108000 0.100181000 0.061361000 0.021069000 0.038230000 0.053861000 0.089298000 0.053536000 0.012313000 0.027173000 0.065359000;
625 
626 model Q.INSECT=
627 0.245103884
628 0.396680459 0.602596590
629 0.388851211 0.169418318 4.002207051
630 1.687379028 0.888477494 0.707887462 0.137794758
631 0.813368876 2.004043618 1.229351544 0.369955633 0.230607800
632 0.797312266 0.224720163 0.413998478 7.046040747 0.061906941 2.610915158
633 2.835188240 0.639959824 1.963743484 1.231717882 1.043646688 0.393592403 0.553182381
634 0.362258381 2.615490291 4.573260980 0.797011018 0.896230099 5.675152800 0.330930746 0.378124450
635 0.228513969 0.141228769 0.208490043 0.053173950 0.460428950 0.116150694 0.064283924 0.068021312 0.140874297
636 0.286953900 0.240779967 0.098667680 0.058795467 0.493466139 0.643789822 0.079309054 0.089730309 0.500992010 3.381560080
637 0.325994754 5.655671758 1.541274942 0.211396072 0.082097991 2.054032646 0.761883191 0.341199781 0.396451596 0.144888450 0.103298167
638 0.854941063 0.469236454 0.344916944 0.082042638 0.564344515 1.049351234 0.169182004 0.214023208 0.337275045 4.607657510 5.779760276 0.501772274
639 0.202912169 0.083503104 0.104497835 0.062211382 1.265119124 0.061813267 0.037371750 0.130615907 0.693502085 0.880367224 2.142804923 0.038837539 1.068089269
640 2.098306482 0.448091631 0.295630473 0.393309252 0.214758763 1.226945820 0.411528885 0.517165713 0.865174971 0.164903860 0.371130819 0.335358981 0.264037782 0.131445137
641 4.447741802 0.609758408 3.798086697 0.731000508 3.467889377 0.737657764 0.379154866 2.320367575 0.697254375 0.107585891 0.228053049 0.417871055 0.387566384 0.273240209 1.842353422
642 3.173624632 0.474607818 2.267368199 0.310254294 1.125638230 0.924249331 0.410818877 0.401697351 0.490764490 1.310627756 0.287148699 0.827466845 2.368908910 0.164073566 1.031968282 5.706447436
643 0.113618297 0.421211392 0.052343656 0.053998922 1.063048958 0.118187043 0.058461221 0.275756639 0.303820579 0.088741408 0.404916338 0.067974475 0.484518123 1.412153565 0.131745320 0.257205952 0.121214423
644 0.159463305 0.209585392 0.485673084 0.153134973 1.990179836 0.174718362 0.083149696 0.137582926 6.378949466 0.188267059 0.280539346 0.067140987 0.264484864 10.165067155 0.155778076 0.294006077 0.191009158 1.616501717
645 2.466363084 0.145305726 0.149535968 0.109375281 1.295115095 0.258250207 0.287452076 0.247675666 0.177412560 10.861831869 1.518647299 0.149072919 2.157390423 0.496751123 0.367029379 0.180581516 1.639361417 0.103038434 0.189789265
646 0.063003000 0.049585000 0.047550000 0.048622000 0.015291000 0.044058000 0.072012000 0.037810000 0.022358000 0.066563000 0.107325000 0.080621000 0.023976000 0.041578000 0.028532000 0.081767000 0.055167000 0.009698000 0.032219000 0.072265000;
647 
648 model Q.MAMMAL=
649 0.164520503
650 0.133786660 0.301753825
651 0.667759687 0.102671327 4.669240542
652 0.375561674 1.878554130 0.218506732 0.132842206
653 0.172392722 3.619009961 0.250359878 0.124852096 0.095864103
654 0.781197529 0.208357490 0.202345038 5.379197337 0.056958677 1.746841825
655 2.076338500 1.797395963 0.679494500 1.991708503 1.179185026 0.168866582 1.453533780
656 0.161623558 4.710380602 3.940278094 0.956160014 1.796411770 5.600293701 0.164776154 0.227985715
657 0.203510704 0.217922574 0.520603634 0.071028795 0.233803448 0.064010956 0.054619397 0.086763961 0.094641478
658 0.178925750 0.403058144 0.048270492 0.042419644 0.297464704 0.583097899 0.070620812 0.086464596 0.627289885 2.383373587
659 0.150019883 5.862144662 2.011938106 0.109850770 0.049580542 1.705745478 1.499396112 0.184898463 0.108290367 0.192452773 0.074328424
660 0.426954296 0.737495653 0.124928924 0.058185276 0.192839562 0.273324822 0.142904022 0.172462927 0.119658259 7.422424301 4.121859707 0.760101625
661 0.156046906 0.098468307 0.074017139 0.075986849 1.649041128 0.061484905 0.059915230 0.098183513 0.275397853 1.183422487 2.957377967 0.060573566 0.338235196
662 1.899027463 0.525891518 0.068009985 0.123677157 0.200110404 1.590125986 0.137838674 0.136748511 1.445166153 0.107833373 1.381061149 0.129943936 0.137065096 0.146012906
663 2.359299936 0.843914331 5.427387027 0.263292147 2.507254736 0.189228647 0.139146074 2.427076788 0.376188219 0.330866332 0.498124825 0.193144225 0.150312624 0.827642694 2.786459548
664 7.524532664 0.539886133 1.955763604 0.132705770 0.233037817 0.165733855 0.155868082 0.198123473 0.145627442 3.528654954 0.153102275 0.889109054 4.911310946 0.119728464 1.529988220 3.075670543
665 0.101039395 2.131494369 0.058369398 0.043905868 2.144674342 0.521419600 0.088844939 0.579178348 0.134177423 0.088684660 0.683790243 0.064089109 0.276245610 0.603795093 0.100007515 0.264443242 0.079630880
666 0.091694198 0.139818982 0.655149301 0.420781565 5.685285320 0.126113134 0.070592995 0.083304052 7.287086510 0.172110578 0.176288430 0.080506454 0.165573576 5.877878503 0.112513257 0.458878972 0.102291161 0.645002709
667 4.300445029 0.107177686 0.082093349 0.228482448 0.278600785 0.094238794 0.325642029 0.868890049 0.081513165 12.950251994 1.879650916 0.097391390 7.158497660 0.733119107 0.145626117 0.152049202 0.573328824 0.113423271 0.125003102
668 0.067997000 0.055503000 0.036288000 0.046867000 0.021435000 0.050281000 0.068935000 0.055323000 0.026410000 0.041953000 0.101191000 0.060037000 0.019662000 0.036237000 0.055146000 0.096864000 0.057136000 0.011785000 0.024730000 0.066223000;
669 
670 model Q.PLANT=
671 0.061995451
672 0.071787018 0.324146307
673 0.482723250 0.017012888 5.640569094
674 0.523802485 2.773840824 0.412259505 0.072474815
675 0.266699470 3.319795598 0.641219533 0.101391710 0.105145707
676 0.848857861 0.027378890 0.203417806 6.983296655 0.004325163 3.676487445
677 2.099517664 0.923332845 0.989386407 1.214523767 1.225782488 0.189953993 0.893983216
678 0.086540313 4.386107333 5.633764157 1.133417157 3.025390235 8.135368256 0.117555479 0.127760160
679 0.047711951 0.148339563 0.470979475 0.007582115 0.267133294 0.022845535 0.010786746 0.011450563 0.074259162
680 0.132461376 0.242868565 0.008688476 0.007966889 0.387974066 0.713657288 0.029290769 0.013401682 0.666044528 3.178490964
681 0.135231094 6.796751125 3.253593795 0.018324171 0.000109001 2.561068546 1.166641775 0.150166421 0.040648681 0.143807298 0.022265650
682 0.487603228 0.622545469 0.164436842 0.009922368 0.133016192 0.383963916 0.121953673 0.072782198 0.060192574 6.137883228 5.109951861 0.997263914
683 0.101998846 0.018497482 0.033489490 0.011945428 2.787245776 0.000109001 0.003428084 0.016479873 0.304517393 1.260751123 3.067538770 0.004231422 0.367280212
684 1.679096158 0.423800539 0.020342871 0.080963818 0.083580934 1.394642593 0.104298769 0.064165663 1.150907470 0.036382379 0.559761940 0.059246444 0.049078824 0.049489758
685 3.724953683 0.724887668 4.517199656 0.281847349 5.612663729 0.304709235 0.112097795 1.591990129 0.447466853 0.164991657 0.549645550 0.209386705 0.171531722 0.574024731 2.359864552
686 4.753201153 0.655493224 2.669910479 0.105335369 0.389742063 0.300884387 0.195263436 0.123875362 0.116237656 2.552275429 0.089626134 1.172764365 4.055778486 0.062695238 1.066677979 5.735630021
687 0.016624844 0.808384672 0.005560145 0.000347713 2.878143952 0.176461840 0.013106289 0.196264065 0.066883060 0.000109001 0.582218341 0.002231252 0.229612944 0.597613653 0.009791567 0.216845648 0.000109001
688 0.033775073 0.054821001 0.753418700 0.255631501 4.340476213 0.036965535 0.020444242 0.012699715 7.284279143 0.053844351 0.084699285 0.016433002 0.066804579 8.185198097 0.032534641 0.405822992 0.051593479 0.524555683
689 3.226243245 0.041421498 0.061468976 0.147004300 0.560195764 0.088095759 0.303691165 0.297902118 0.066305354 10.911840366 1.918251057 0.050145945 2.585318015 0.627525728 0.114608090 0.058704709 0.972725592 0.026833885 0.133140453
690 0.074923000 0.050500000 0.038734000 0.053195000 0.011300000 0.037499000 0.068513000 0.059627000 0.021204000 0.058991000 0.102504000 0.067306000 0.022371000 0.043798000 0.037039000 0.084451000 0.047850000 0.012322000 0.030777000 0.077097000;
691 
692 model Q.YEAST=
693 0.289760345
694 0.342709634 0.718300668
695 0.367886518 0.072562600 4.199522650
696 3.691718604 0.710404342 0.490823952 0.052871678
697 1.043523521 2.008049414 1.553982959 0.449223552 0.070963821
698 1.093168815 0.139582694 0.508273036 5.624270628 0.003118838 3.707570018
699 2.882498207 0.540565704 1.987856240 1.230079486 1.182218128 0.398459557 0.542851891
700 0.417376590 2.637569081 4.921959964 0.793976563 0.971187101 5.448912766 0.394563504 0.492571299
701 0.182603367 0.132608825 0.173586122 0.017141968 0.595831116 0.083860488 0.036837325 0.027627162 0.116377119
702 0.334353188 0.205566131 0.068829530 0.021633405 0.796201770 0.465713591 0.062744857 0.043967523 0.378253079 3.366451402
703 0.483774690 6.326126715 1.772882594 0.193037560 0.025984034 2.595024049 0.980236499 0.351568331 0.667015573 0.108153720 0.090350953
704 0.980143366 0.618539982 0.354791389 0.052464777 0.984440777 1.122348190 0.146156313 0.190256883 0.392801743 4.449605122 5.986085778 0.578286681
705 0.224857913 0.047417869 0.073768891 0.020291850 1.625802715 0.031817027 0.015954525 0.094986525 0.713520963 0.952803363 2.116139937 0.012660509 1.303449237
706 1.902789461 0.327908181 0.288401051 0.418241394 0.119283083 0.994116603 0.453784839 0.361756388 0.717288404 0.097506652 0.200252021 0.383751236 0.146206205 0.091990755
707 4.877234074 0.595474107 3.112134717 0.924744908 3.584581583 1.239592330 0.512666905 1.863057260 0.955917766 0.058056067 0.241269232 0.551359124 0.486660696 0.253426381 1.572179322
708 2.789256813 0.577913042 2.172349980 0.379983795 1.746675706 1.004182700 0.576198956 0.295694231 0.636427012 1.138771705 0.291850288 0.980917255 1.905694316 0.158541858 0.735801862 5.167267165
709 0.082544434 0.297203203 0.023885222 0.009802221 1.098149199 0.061054054 0.021273070 0.132048920 0.320030703 0.103698871 0.411524750 0.030961092 0.442192031 1.474552928 0.057108109 0.136000409 0.072755518
710 0.176505390 0.179523334 0.380460546 0.103068007 1.987376163 0.160373469 0.057915259 0.060539607 6.419218432 0.171959625 0.282755433 0.046896769 0.361827346 7.660749919 0.085482550 0.275364684 0.182111094 1.812622556
711 2.936397672 0.163865947 0.135944973 0.080351380 2.828941339 0.271020707 0.294499028 0.133659895 0.255089465 11.291813609 1.513322757 0.167243117 2.085093473 0.620211936 0.348307577 0.145275987 2.188995240 0.093529663 0.240182683
712 0.059954000 0.042032000 0.052518000 0.054641000 0.008189000 0.040467000 0.070691000 0.039935000 0.018393000 0.069555000 0.109563000 0.081967000 0.018694000 0.046979000 0.031382000 0.091102000 0.055887000 0.010241000 0.033496000 0.064313000;
713 
714 model FLAVI=
715 0.077462
716 0.078037 0.000020
717 0.550515 0.089476 8.801355
718 0.114675 0.572845 0.000020 0.000020
719 0.090490 3.856678 0.093133 0.183601 0.000020
720 0.560685 0.020614 0.000020 7.603314 0.000020 1.058066
721 0.478097 1.281339 0.147801 1.359685 0.221287 0.000020 2.331269
722 0.168719 2.704348 3.326034 0.543235 0.240631 8.958548 0.025386 0.032838
723 0.000020 0.151250 0.538307 0.000020 0.000020 0.000020 0.000020 0.000020 0.037032
724 0.002576 0.114188 0.000020 0.000020 0.085459 0.789751 0.023842 0.037784 0.375616 1.571343
725 0.000020 19.413475 2.764154 0.000020 0.000020 1.545589 2.992960 0.027884 0.000020 0.253247 0.038560
726 0.000020 0.151495 0.000020 0.000020 0.000020 0.000020 0.031428 0.009423 0.000020 8.538171 2.895172 0.340189
727 0.000020 0.000020 0.000020 0.000020 0.773082 0.000020 0.000020 0.000020 0.092713 1.368786 6.296781 0.000020 0.000020
728 1.256282 0.292376 0.000020 0.000020 0.000020 1.571014 0.000020 0.029602 0.723179 0.000020 1.182805 0.097941 0.000020 0.035125
729 2.104417 0.947496 9.494063 0.127754 1.516267 0.140959 0.000020 1.735582 0.079928 0.211717 1.008880 0.131204 0.073511 1.821906 4.417267
730 6.315368 0.199572 1.329820 0.000020 0.000020 0.057328 0.000020 0.044927 0.144097 6.767791 0.033401 0.567475 2.228245 0.000020 1.543179 3.290965
731 0.000020 0.791312 0.000020 0.000020 2.305902 0.000020 0.000020 0.323982 0.206837 0.000020 0.176249 0.000020 0.173206 0.148283 0.074193 0.154086 0.000020
732 0.043583 0.000020 1.247952 0.771837 4.085694 0.000020 0.029684 0.000020 16.468674 0.000020 0.000020 0.071741 0.228965 5.907642 0.000020 0.431256 0.000020 0.000020
733 8.030561 0.000020 0.000020 0.439809 0.149716 0.000020 0.346045 0.583259 0.067473 16.913225 1.074192 0.006629 3.855848 1.176807 0.036750 0.052613 0.134211 0.000020 0.234116
734 0.077500 0.053813 0.033950 0.034973 0.014056 0.030139 0.054825 0.086284 0.018210 0.063272 0.103857 0.059646 0.040389 0.033630 0.036649 0.060915 0.076327 0.030152 0.020069 0.071343;
735 
736 end;
737 )";
738 
739 
ModelProtein(const char * model_name,string model_params,StateFreqType freq,string freq_params,PhyloTree * tree,ModelsBlock * models_block)740 ModelProtein::ModelProtein(const char *model_name, string model_params, StateFreqType freq, string freq_params, PhyloTree *tree, ModelsBlock* models_block)
741  : ModelMarkov(tree, true, false)
742 {
743     this->models_block = models_block;
744 	init(model_name, model_params, freq, freq_params);
745 }
746 
rescaleRates(double * rates,int nrates)747 void rescaleRates(double *rates, int nrates) {
748     int i;
749 
750     double max_rate = 0.0;
751 
752     for (i = 0; i < nrates; i++)
753         max_rate = max(max_rate, rates[i]);
754 
755     const double AA_SCALE = 10.0;
756     double scaler = AA_SCALE / max_rate;
757 
758     /* SCALING HAS BEEN RE-INTRODUCED TO RESOLVE NUMERICAL  PROBLEMS */
759 
760     for (i = 0; i < nrates; i++)
761         rates[i] *= scaler;
762 }
763 
init(const char * model_name,string model_params,StateFreqType freq,string freq_params)764 void ModelProtein::init(const char *model_name, string model_params, StateFreqType freq, string freq_params) {
765 	ASSERT(num_states == 20);
766     ASSERT(models_block && "models_block uninitialized");
767 	name = model_name;
768 
769 	string name_upper = model_name;
770 	for (string::iterator it = name_upper.begin(); it != name_upper.end(); it++)
771 		(*it) = toupper(*it);
772 
773     NxsModel *nxs_model = models_block->findModel(name_upper);
774     if (nxs_model) {
775         if (nxs_model->flag != NM_ATOMIC)
776             outError("Invalid protein model name ", model_name);
777 
778         readParametersString(nxs_model->description);
779         rescaleRates(rates, getNumRateEntries());
780 
781         int i;
782 		double sum = 0.0;
783 		for (i = 0; i < num_states; i++)
784 			sum += (double) state_freq[i];
785 		if (fabs(sum-1.0) > 1e-7) {
786 			cout.precision(7);
787 			cout << "WARNING: " <<  name_upper << " state frequencies do not sum up to 1: " << sum << endl;
788 		}
789         num_params = 0;
790 
791 	} else if (!model_params.empty()) {
792         readParametersString(model_params);
793         rescaleRates(rates, getNumRateEntries());
794         num_params = 0;
795     } else if (name_upper == "GTR20") {
796         if (!Params::getInstance().link_model) {
797             outWarning("GTR20 model will estimate 189 substitution rates that might be overfitting!");
798             outWarning("Please only use GTR20 with very large data and always test for model fit!");
799         }
800         if (freq == FREQ_UNKNOWN)
801             freq = FREQ_EMPIRICAL;
802         if (Params::getInstance().model_name_init) {
803             nxs_model = models_block->findModel(Params::getInstance().model_name_init);
804             if (nxs_model) {
805                 readParametersString(nxs_model->description, false);
806             } else {
807                 // initialize with custom model file
808                 readParameters(Params::getInstance().model_name_init, false);
809             }
810             rescaleRates(rates, getNumRateEntries());
811             if (!isReversible())
812                 outError("Cannot initialize from non-reversible model");
813         } else {
814             // initialize rate matrix with LG
815             nxs_model = models_block->findModel("LG");
816             ASSERT(nxs_model);
817             readParametersString(nxs_model->description, false);
818             rescaleRates(rates, getNumRateEntries());
819         }
820         // 2018-05-08 bug fix: GTR20 rates are not optimized
821         num_params = getNumRateEntries()-1;
822     } else if (name_upper == "NONREV") {
823         if (!Params::getInstance().link_model) {
824             outWarning("NONREV model will estimate 379 substitution rates that might be overfitting!");
825             outWarning("Please only use NONREV with very large data and always test for model fit!");
826         }
827         if (freq == FREQ_UNKNOWN)
828             freq = FREQ_ESTIMATE;
829         if (Params::getInstance().model_name_init) {
830             nxs_model = models_block->findModel(Params::getInstance().model_name_init);
831             if (nxs_model) {
832                 readParametersString(nxs_model->description, false);
833             } else {
834                 // initialize with custom model file
835                 readParameters(Params::getInstance().model_name_init, false);
836             }
837             rescaleRates(rates, getNumRateEntries());
838             if (isReversible())
839                 setReversible(false);
840         } else {
841             // initialize rate matrix with LG
842             nxs_model = models_block->findModel("LG");
843             ASSERT(nxs_model);
844             readParametersString(nxs_model->description, false);
845             rescaleRates(rates, getNumRateEntries());
846             setReversible(false);
847         }
848         num_params = getNumRateEntries()-1;
849 	} else {
850 		// if name does not match, read the user-defined model
851 		readParameters(model_name);
852         rescaleRates(rates, getNumRateEntries());
853         num_params = 0;
854 	}
855 	if (freq_params != "") {
856 //		stringstream ss(freq_params);
857 		readStateFreq(freq_params);
858 	}
859 
860 	//assert(freq != FREQ_ESTIMATE);
861 	if (freq == FREQ_UNKNOWN) freq = FREQ_USER_DEFINED;
862 	ModelMarkov::init(freq);
863 }
864 
startCheckpoint()865 void ModelProtein::startCheckpoint() {
866     checkpoint->startStruct("ModelProtein");
867 }
868 
869 
saveCheckpoint()870 void ModelProtein::saveCheckpoint() {
871     if (num_params > 0 && !fixed_parameters) {
872         startCheckpoint();
873         CKP_ARRAY_SAVE(getNumRateEntries(), rates);
874         endCheckpoint();
875     }
876     ModelMarkov::saveCheckpoint();
877 }
878 
restoreCheckpoint()879 void ModelProtein::restoreCheckpoint() {
880     ModelMarkov::restoreCheckpoint();
881 
882     if (num_params > 0 && !fixed_parameters) {
883         startCheckpoint();
884         CKP_ARRAY_RESTORE(getNumRateEntries(), rates);
885         endCheckpoint();
886         decomposeRateMatrix();
887         if (phylo_tree)
888             phylo_tree->clearAllPartialLH();
889     }
890 }
891 
readRates(istream & in)892 void ModelProtein::readRates(istream &in) throw(const char*, string) {
893 	int nrates = getNumRateEntries();
894 	int row = 1, col = 0;
895     if (is_reversible) {
896         // since states for protein is stored in lower-triangle, special treatment is needed
897         for (int i = 0; i < nrates; i++, col++) {
898             if (col == row) {
899                 row++; col = 0;
900             }
901             // switch col and row
902             int id = col*(2*num_states-col-1)/2 + (row-col-1);
903             if (id >= nrates) {
904                 cout << row << " " << col << endl;
905             }
906             ASSERT(id < nrates && id >= 0); // make sure that the conversion is correct
907             if (!(in >> rates[id]))
908                 throw name+string(": Rate entries could not be read");
909             if (rates[id] < 0.0)
910                 throw "Negative rates found";
911         }
912     } else {
913         // non-reversible model, read the whole rate matrix
914         int i = 0;
915         for (row = 0; row < num_states; row++) {
916             double row_sum = 0.0;
917             for (col = 0; col < num_states; col++) {
918                 if (row != col) {
919                     if (!(in >> rates[i]))
920                         throw name+string(": Rate entries could not be read");
921                     if (rates[i] < 0.0)
922                         throw "Negative rates found";
923                     row_sum += rates[i];
924                     i++;
925                 } else {
926                     double d;
927                     in >> d;
928                     row_sum += d;
929                 }
930             }
931             if (fabs(row_sum) > 1e-3)
932                 throw "Row " + convertIntToString(row) + " does not sum to 0";
933         }
934     }
935 }
936 
937 
getNameParams()938 string ModelProtein::getNameParams() {
939     ostringstream retname;
940     retname << name;
941     retname << freqTypeString(freq_type, phylo_tree->aln->seq_type, true);
942 
943     if (fixed_parameters)
944         return retname.str();
945 
946     if (freq_type == FREQ_ESTIMATE) {
947         retname << "{" << state_freq[0];
948         for (int i = 1; i < num_states; i++)
949             retname << "," << state_freq[i];
950         retname << "}";
951     }
952     return retname.str();
953 }
954