372:
called the CS05 model, is a generalized non-homogeneous version of the HKY (Hasegawa-Kishino-Yano) model constrained to have equal distribution of the pairs of bases A,T and C,G at each node of the tree and no assumption regarding a stable base distribution. All models listed above are submodels of the general Markov model (GMM). The ability to perform tests using non-homogeneous models represents a major benefit of the invariants methods relative to the more commonly used maximum likelihood methods for phylogenetic model testing.
94:), which can be written as a vector. This site pattern frequency vector has 255 degrees of freedom because the frequencies must sum to one. However, any set of site pattern frequencies that resulted from some specific process of sequence evolution on a specific tree must obey many constraints. and therefore have many fewer degrees of freedom. Thus, there should be polynomials involving those frequencies that take on a value of zero if the DNA sequences were generated on a specific tree given a particular
910:(SVD) of matrices generated by "flattening" the nucleotides associated with each of the leaves (i.e., the site pattern frequency spectrum). Different flattening matrices are produced for each topology. However, comparisons of the original Eriksson SVD method (ErikSVD) to neighbor joining and the maximum likelihood approach implemented in the
894:
the correct tree). This inefficiency has caused most empiricists to abandon the use of Lake's invariants. Also, because Lake's invariants are based on the Kimura two-parameter model phylogenetic estimation using Lake's invariants may not yield the true tree when the model that generated the data strongly violates that model.
919:
project. The original ErikSVD method was improved by Fernández-Sánchez and
Casanellas, who proposed a normalization they called Erik+2. The original ErikSVD method is statistically consistent (it converges on. the true tree. as the empirical distribution approaches the theoretical distribution); the
902:
The low efficiency of Lake's invariants reflects the fact that it used a limited set of generators for the phylogenetic invariants. Casanellas et al. introduced methods to derive a much larger set of set of generators for DNA data and this has led to the development of invariants methods that are as
893:
found that Lake's invariants converges on the true tree over all of the branch length space they examined when the underlying model of evolution is the Kimura two-parameter model. However, they also found that Lake's invariants are very inefficient (large amounts of data are necessary to converge on
371:
The asterisk after the JC69, K80, and K81 models is used to emphasize the non-homogeneous nature of the models that can be examined using invariants. These non-homogeneous models include the commonly used continuous-time JC69, K80, and K81 models as submodels. The SSM (strand-specific model), also
309:
Symmetry invariants are non-phylogenetic in nature; they take on the expected value of zero regardless of the tree topology. However, it is possible to determine whether a particular multiple sequence alignment fits the Jukes-Cantor model of evolution (i.e., by testing whether the site patterns of
51:
At this point the number of programs that allow empirical datasets to be analyzed using invariants is limited. However, phylogenetic invariants may provide solutions to other problems in phylogenetics and they represent an area of active research for that reason. Felsenstein stated it best when he
386:
Lake's invariants (which he called "evolutionary parsimony") provide an excellent example of phylogenetic invariants. Lake's invariants involve quartets, two of which (the incorrect topologies) yield values of zero and one of which yields a value greater than zero. This can be used to construct a
101:
Invariants are formulas in the expected pattern frequencies, not the observed pattern frequencies. When they are computed using the observed pattern frequencies, we will usually find that they are not precisely zero even when the model and tree topology are correct. By testing whether such
939:) represents another example of an invariants method hat has been implemented in software package that is practical to be used with empirical datasets. Squangles permit the choice among the three possible quartets assuming that DNA sequences have evolved under the general
310:
the appropriate types are present in equal numbers). More general tests for the best-fitting model using invariants are also possible. For example
Kedzierska et al. 2012 used invariants to establish the best-fitting model out from a specific model set.
882:. Similar χ tests can be performed for Y and Z. If one of the three values is significantly different from zero the corresponding topology is the best estimate of phylogeny. The advantage of using Lake's invariants relative to maximum likelihood or
914:
program dnaml were mixed; ErikSVD underperformed the other two methods when used with simulated data but it appeared to perform better than dnaml when applied to an empirical mammalian dataset based on an early release of data from the
39:
analyses is that invariants can yield information about the tree without requiring the estimation of branch lengths of model parameters. The idea of using phylogenetic invariants was introduced independently by James
Cavender and
378:, which are defined as the subset of invariants that take on a value of zero only when the sequences were (or were not) generated on a specific topology, are likely to be the most useful invariants for phylogenetic studies.
1748:
Reddy, Sushma; Kimball, Rebecca T.; Pandey, Akanksha; Hosner, Peter A.; Braun, Michael J.; Hackett, Shannon J.; Han, Kin-Lan; Harshman, John; Huddleston, Christopher J.; Kingston, Sarah; Marks, Ben D. (September 2017).
105:
Some invariants are straightforward consequences of symmetries in the model of nucleotide substitution and they will take on a value of zero regardless of the underlying tree topology. For example, if we assume the
1610:
Eriksson N. (2005) "Tree construction using singular value decomposition," in
Algebraic statistics for computational biology, ed. Pachter L, Sturmfels B., Cambridge University Press (Chapter 19, pp.
1412:
Casanellas M, Sullivant S. (2005) "The strand symmetric model," in
Algebraic statistics for computational biology, ed. Pachter L, Sturmfels B., Cambridge University Press (Chapter 16, pp.
698:
625:
552:
1542:
Casanellas M, Sullivant S. Pachter L, Sturmfels B. (2005) Catalog of small trees, Algebraic statistics for computational biology. Chapter 15, Cambridge (UK) Cambridge
University Press
453:
102:
polynomials for various trees are 'nearly zero' when evaluated on the observed frequencies of patterns in real data sequences one should be able infer which tree best explains the data.
1422:
Pachter L, Sturmfels B. (2005) "Biology," in
Algebraic statistics for computational biology, ed. Pachter L, Sturmfels B., Cambridge University Press (Chapter 4, pp. 125-159)
872:
796:
746:
182:. The equation shown above is only one of a large number of symmetry invariants for the Jukes-Cantor model; in fact, there are a total of 241 symmetry invariants for that model.
174:
886:
of Kimura two-parameter distances is that the invariants should hold regardless of the model parameters, branch lengths, or patterns of among-sites rate heterogeneity.
387:
test based on following invariant relationship, which holds for the two incorrect trees when sites evolve under the Kimura two-parameter model of sequence evolution:
943:; the quartets can then be assembled using a supertree method. There are three squangles that are useful for differentiating among quartets, which can be denoted as
457:
The indices of these site pattern frequencies indicate the bases scored relative to the base in the first taxon (which we call taxon A). If base 1 is a
903:
efficient as maximum likelihood methods. Several of these methods have implementations that are practical for analyses of empirical datasets.
178:
This is a simple outgrowth of the fact that base frequencies are constrained to be equal under the Jukes-Cantor model. Thus, they are called
24:
1750:
1329:
1267:
920:
Erik+2 normalization improves the performance of the method given finite datasets. It has been implemented in the software package
52:
said, "invariants are worth attention, not for what they do for us now, but what they might lead to in the future." (p. 390)
36:
1751:"Why Do Phylogenomic Data Sets Yield Conflicting Trees? Data Type Influences the Avian Tree of Life more than Taxon Sampling"
1182:
are all zero on the star topology (a quartet with an internal branch length of zero). For practicality, Holland et al. used
631:
558:
485:
32:
392:
907:
27:, and they can be used to choose among phylogenetic tree topologies in an empirical setting. The primary advantage of
20:
805:
1505:
19:
invariants are polynomial relationships between the frequencies of various site patterns in an idealized DNA
1679:
Sumner J.G.. Entanglement, invariants, and phylogenetics, 2006 University of
Tasmania. Available from: URL
465:. If base 1 is a pyrimidine, then base 2 is the other pyrimidine and. bases 3 and 4 are the purines.
314:
107:
1803:
755:
705:
115:
1623:"Invariant Versus Classical Quartet Inference When Evolution is Heterogeneous Across Sites and Lineages"
1553:
1357:
1190:
values. Empirical tests of the squangles method have been limited but they appear to be promising.
1634:
1565:
1469:
1248:
940:
879:
95:
41:
186:
Symmetry invariants for the Jukes-Cantor model of DNA evolution (adapted from
Felsenstein 2004)
1486:
Barry, D., & Hartigan, J. A. (1987). Statistical analysis of hominoid molecular evolution.
1780:
1772:
1730:
1722:
1662:
1654:
1593:
1585:
1525:
1461:
1453:
1395:
1387:
1335:
1325:
1297:
1289:
1240:
1268:"A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony"
1762:
1712:
1644:
1575:
1517:
1445:
1377:
1369:
1279:
1232:
883:
875:
480:. We can calculate three values from the data to identify the best topology given the data:
1700:
1284:
66:
possible site patterns. For example, there are 256 possible site patterns for four taxa (
1554:"Performance of a New Invariants Method on Homogeneous and Nonhomogeneous Quartet Trees"
1797:
1252:
1183:
45:
16:
1473:
890:
1521:
1433:
1220:
462:
1776:
1726:
1658:
1589:
1529:
1457:
1434:"Dating of the human-ape splitting by a molecular clock of mitochondrial DNA"
1391:
1293:
1244:
964:(f) (f is a 256 element vector containing the site frequency spectrum). Each
906:
Eriksson proposed an invariants method for the general Markov model based on
1767:
1717:
1649:
1622:
1580:
1373:
1339:
1784:
1734:
1666:
1597:
1399:
1465:
1301:
1319:
1209:, ed. by O. Gascuel and M. Steel. Oxford University Press, 2007, 108--147
317:
that can be tested using the
Kedzierska et al. (2012) invariants method
1699:
Holland, Barbara R.; Jarvis, Peter D.; Sumner, Jeremy G. (2013-01-01).
1449:
1358:"SPIn: Model Selection for Phylogenetic Mixtures via Linear Invariants"
1236:
1570:
1382:
1356:
Kedzierska, A. M.; Drton, M.; Guigo, R.; Casanellas, M. (2012-03-01).
1701:"Low-Parameter Phylogenetic Inference Under the General Markov Model"
1207:
Reconstructing Evolution: New Mathematical and Computational Advances
916:
911:
458:
1432:
Hasegawa, Masami; Kishino, Hirohisa; Yano, Taka-aki (October 1985).
1680:
1639:
921:
1221:"Invariants of phylogenies in a simple case with discrete states"
1205:
Allman, E. S. and. Rhodes, J. A., "Phylogenetic invariants,'' in
993:
values). Each possible quartet has different expected values for
968:
has 66,744 terms and together they satisfy the linear relation
802:) and suggests testing for deviation from zero by calculating
461:, then base 2 is the other purine and bases 3 and 4 are the
1621:
Fernández-Sánchez, Jesús; Casanellas, Marta (March 2016).
31:
relative to other methods of phylogenetic estimation like
702:
Lake broke these values up into a "parsimony-like term" (
1506:"Success of Phylogenetic Methods in the Four-Taxon Case"
23:. They have received substantial study in the field of
1219:
Cavender, James A.; Felsenstein, Joseph (March 1987).
989:= 0 (i.e., up to linear dependence there are only two
808:
758:
708:
693:{\displaystyle Z=N_{1331}-N_{1332}-N_{1341}+N_{1342}}
634:
620:{\displaystyle Y=N_{1313}-N_{1323}-N_{1314}+N_{1324}}
561:
547:{\displaystyle X=N_{1133}-N_{1233}-N_{1134}+N_{1234}}
488:
395:
118:
1552:
Casanellas, M; Fernández-Sánchez, J (January 2007).
448:{\displaystyle f_{1133}+f_{1234}=f_{1233}+f_{1134}}
866:
790:
740:
692:
619:
546:
447:
168:
55:If we consider a multiple sequence alignment with
1504:Huelsenbeck, J. P.; Hillis, D. M. (1993-09-01).
898:Modern approaches using phylogenetic invariants
8:
468:We will call three possible quartet trees T
59:taxa and no gaps or missing data (i.e., an
1766:
1716:
1648:
1638:
1579:
1569:
1381:
1324:. Sunderland, Mass.: Sinauer Associates.
1283:
924:as an option for the SVDquartets method.
867:{\displaystyle \chi ^{2}=(P-B)^{2}/(P+B)}
844:
838:
813:
807:
782:
769:
757:
732:
719:
707:
684:
671:
658:
645:
633:
611:
598:
585:
572:
560:
538:
525:
512:
499:
487:
439:
426:
413:
400:
394:
145:
123:
117:
1016:
889:A classic study by John Huelsenbeck and
312:
184:
108:Jukes-Cantor model of sequence evolution
1198:
1694:
1692:
1690:
1688:
1285:10.1093/oxfordjournals.molbev.a040433
61:idealized multiple sequence alignment
7:
1351:
1349:
1313:
1311:
1039:(adapted from Holland et al. 2013)
791:{\displaystyle B=N_{1233}+N_{1134}}
741:{\displaystyle P=N_{1133}+N_{1234}}
169:{\displaystyle f_{ACAT}-f_{CGCA}=0}
14:
381:
110:and a four-taxon tree we expect:
1681:http://eprints.utas.edu.au/709/
1558:Molecular Biology and Evolution
1362:Molecular Biology and Evolution
1272:Molecular Biology and Evolution
1438:Journal of Molecular Evolution
861:
849:
835:
822:
1:
1318:Felsenstein, Joseph. (2004).
279:xyzw (e.g., ACGT, CGTA, ...)
262:xxyz (e.g., AACG, ACGA, ...)
245:xxyy (e.g., AACC, ACCA, ...)
228:xxxy (e.g., AAAC, AACA, ...)
211:xxxx (e.g., AAAA, CCCC, ...)
203:Total invariants that result
908:singular value decomposition
21:multiple sequence alignment
1820:
1266:Lake, J. A. (March 1987).
1225:Journal of Classification
752:) the "background term" (
382:Lake's linear invariants
197:Number of pattern types
194:Example of site pattern
1522:10.1093/sysbio/42.3.247
376:Phylogenetic invariants
349:Kimura three-parameter
315:Models of DNA evolution
29:phylogenetic invariants
868:
792:
742:
694:
621:
548:
449:
357:Strand-specific model
191:Site pattern category
170:
1768:10.1093/sysbio/syx041
1718:10.1093/sysbio/sys072
1650:10.1093/sysbio/syv086
1581:10.1093/molbev/msl153
1374:10.1093/molbev/msr259
1321:Inferring phylogenies
869:
793:
743:
695:
622:
549:
450:
365:General Markov model
341:Kimura two-parameter
171:
1161:The expected values
1018:Expected values for
806:
756:
706:
632:
559:
486:
393:
116:
1488:Statistical Science
1040:
322:Model abbreviation
318:
200:Number of patterns
187:
180:symmetry invariants
1755:Systematic Biology
1705:Systematic Biology
1627:Systematic Biology
1510:Systematic Biology
1450:10.1007/BF02101694
1237:10.1007/BF01890075
1017:
864:
788:
738:
690:
617:
544:
445:
313:
185:
166:
96:substitution model
42:Joseph Felsenstein
33:maximum likelihood
1186:to solve for the
1159:
1158:
1141:AD|BC (or 14|23)
1119:AC|BD (or 13|24)
1097:AB|CD (or 12|34)
880:degree of freedom
874:and performing a
369:
368:
307:
306:
1811:
1789:
1788:
1770:
1745:
1739:
1738:
1720:
1696:
1683:
1677:
1671:
1670:
1652:
1642:
1618:
1612:
1608:
1602:
1601:
1583:
1573:
1549:
1543:
1540:
1534:
1533:
1501:
1495:
1484:
1478:
1477:
1429:
1423:
1420:
1414:
1410:
1404:
1403:
1385:
1353:
1344:
1343:
1315:
1306:
1305:
1287:
1263:
1257:
1256:
1216:
1210:
1203:
1046:(newick format)
1041:
884:neighbor joining
873:
871:
870:
865:
848:
843:
842:
818:
817:
797:
795:
794:
789:
787:
786:
774:
773:
747:
745:
744:
739:
737:
736:
724:
723:
699:
697:
696:
691:
689:
688:
676:
675:
663:
662:
650:
649:
626:
624:
623:
618:
616:
615:
603:
602:
590:
589:
577:
576:
553:
551:
550:
545:
543:
542:
530:
529:
517:
516:
504:
503:
454:
452:
451:
446:
444:
443:
431:
430:
418:
417:
405:
404:
325:Full model name
319:
188:
175:
173:
172:
167:
159:
158:
137:
136:
1819:
1818:
1814:
1813:
1812:
1810:
1809:
1808:
1794:
1793:
1792:
1747:
1746:
1742:
1698:
1697:
1686:
1678:
1674:
1620:
1619:
1615:
1609:
1605:
1551:
1550:
1546:
1541:
1537:
1503:
1502:
1498:
1485:
1481:
1431:
1430:
1426:
1421:
1417:
1411:
1407:
1355:
1354:
1347:
1332:
1317:
1316:
1309:
1265:
1264:
1260:
1218:
1217:
1213:
1204:
1200:
1196:
1181:
1174:
1167:
1138:((A,D),(B,C));
1116:((A,C),(B,D));
1094:((A,B),(C,D));
1087:
1074:
1061:
1038:
1031:
1024:
1013:
1006:
999:
988:
981:
974:
963:
956:
949:
900:
834:
809:
804:
803:
801:
778:
765:
754:
753:
751:
728:
715:
704:
703:
680:
667:
654:
641:
630:
629:
607:
594:
581:
568:
557:
556:
534:
521:
508:
495:
484:
483:
479:
475:
471:
435:
422:
409:
396:
391:
390:
384:
276:1x, 1y, 1z, 1w
141:
119:
114:
113:
93:
86:
79:
72:
12:
11:
5:
1817:
1815:
1807:
1806:
1796:
1795:
1791:
1790:
1761:(5): 857–879.
1740:
1684:
1672:
1633:(2): 280–291.
1613:
1603:
1564:(1): 288–293.
1544:
1535:
1516:(3): 247–264.
1496:
1479:
1444:(2): 160–174.
1424:
1415:
1405:
1368:(3): 929–937.
1345:
1330:
1307:
1278:(2): 167–191.
1258:
1211:
1197:
1195:
1192:
1179:
1172:
1165:
1157:
1156:
1153:
1148:
1142:
1139:
1135:
1134:
1128:
1125:
1120:
1117:
1113:
1112:
1107:
1101:
1098:
1095:
1091:
1090:
1085:
1077:
1072:
1064:
1059:
1051:
1048:
1044:Tree topology
1036:
1029:
1022:
1011:
1004:
997:
986:
979:
972:
961:
954:
947:
899:
896:
863:
860:
857:
854:
851:
847:
841:
837:
833:
830:
827:
824:
821:
816:
812:
799:
785:
781:
777:
772:
768:
764:
761:
749:
735:
731:
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687:
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614:
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584:
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541:
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135:
132:
129:
126:
122:
91:
84:
77:
70:
63:), there are 4
25:biomathematics
13:
10:
9:
6:
4:
3:
2:
1816:
1805:
1804:Phylogenetics
1802:
1801:
1799:
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1778:
1774:
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1702:
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1676:
1673:
1668:
1664:
1660:
1656:
1651:
1646:
1641:
1636:
1632:
1628:
1624:
1617:
1614:
1607:
1604:
1599:
1595:
1591:
1587:
1582:
1577:
1572:
1571:q-bio/0610030
1567:
1563:
1559:
1555:
1548:
1545:
1539:
1536:
1531:
1527:
1523:
1519:
1515:
1511:
1507:
1500:
1497:
1494:(2), 191-207.
1493:
1489:
1483:
1480:
1475:
1471:
1467:
1463:
1459:
1455:
1451:
1447:
1443:
1439:
1435:
1428:
1425:
1419:
1416:
1409:
1406:
1401:
1397:
1393:
1389:
1384:
1379:
1375:
1371:
1367:
1363:
1359:
1352:
1350:
1346:
1341:
1337:
1333:
1331:0-87893-177-5
1327:
1323:
1322:
1314:
1312:
1308:
1303:
1299:
1295:
1291:
1286:
1281:
1277:
1273:
1269:
1262:
1259:
1254:
1250:
1246:
1242:
1238:
1234:
1230:
1226:
1222:
1215:
1212:
1208:
1202:
1199:
1193:
1191:
1189:
1185:
1184:least squares
1178:
1171:
1164:
1154:
1152:
1149:
1147:
1143:
1140:
1137:
1136:
1133:
1129:
1126:
1124:
1121:
1118:
1115:
1114:
1111:
1108:
1106:
1102:
1099:
1096:
1093:
1092:
1088:
1081:
1078:
1075:
1068:
1065:
1062:
1055:
1052:
1049:
1047:
1043:
1042:
1035:
1028:
1021:
1015:
1010:
1003:
996:
992:
985:
978:
971:
967:
960:
953:
946:
942:
938:
934:
930:
927:"Squangles" (
925:
923:
918:
913:
909:
904:
897:
895:
892:
887:
885:
881:
877:
858:
855:
852:
845:
839:
831:
828:
825:
819:
814:
810:
783:
779:
775:
770:
766:
762:
759:
733:
729:
725:
720:
716:
712:
709:
700:
685:
681:
677:
672:
668:
664:
659:
655:
651:
646:
642:
638:
635:
627:
612:
608:
604:
599:
595:
591:
586:
582:
578:
573:
569:
565:
562:
554:
539:
535:
531:
526:
522:
518:
513:
509:
505:
500:
496:
492:
489:
481:
476:, and T
466:
464:
460:
455:
440:
436:
432:
427:
423:
419:
414:
410:
406:
401:
397:
388:
379:
377:
373:
364:
361:
360:
356:
353:
352:
348:
345:
344:
340:
337:
336:
333:Jukes-Cantor
332:
329:
328:
324:
321:
320:
316:
311:
302:
300:
297:
295:
292:
291:
287:
284:
281:
278:
275:
274:
270:
267:
264:
261:
258:
257:
253:
250:
247:
244:
241:
240:
236:
233:
230:
227:
224:
223:
219:
216:
213:
210:
207:
206:
202:
199:
196:
193:
190:
189:
183:
181:
176:
163:
160:
155:
152:
149:
146:
142:
138:
133:
130:
127:
124:
120:
111:
109:
103:
99:
97:
90:
83:
76:
69:
65:
62:
58:
53:
49:
47:
46:James A. Lake
43:
38:
37:Bayesian MCMC
34:
30:
26:
22:
18:
1758:
1754:
1743:
1711:(1): 78–92.
1708:
1704:
1675:
1630:
1626:
1616:
1606:
1561:
1557:
1547:
1538:
1513:
1509:
1499:
1491:
1487:
1482:
1441:
1437:
1427:
1418:
1408:
1365:
1361:
1320:
1275:
1271:
1261:
1231:(1): 57–71.
1228:
1224:
1214:
1206:
1201:
1187:
1176:
1169:
1162:
1160:
1150:
1145:
1131:
1122:
1109:
1104:
1083:
1079:
1070:
1066:
1057:
1053:
1045:
1033:
1026:
1019:
1008:
1001:
994:
990:
983:
976:
969:
965:
958:
951:
944:
941:Markov model
936:
932:
928:
926:
905:
901:
891:David Hillis
888:
701:
628:
555:
482:
467:
456:
389:
385:
375:
374:
370:
308:
259:2x, 1y, 1z
179:
177:
112:
104:
100:
88:
81:
74:
67:
64:
60:
56:
54:
50:
28:
17:Phylogenetic
15:
463:pyrimidines
354:SSM (CS05)
1383:2117/14907
1194:References
931:tochastic
1777:1063-5157
1727:1076-836X
1659:1063-5157
1640:1405.6546
1590:1537-1719
1530:1063-5157
1458:0022-2844
1392:0737-4038
1294:1537-1719
1253:121832940
1245:0176-4268
957:(f), and
878:with one
829:−
811:χ
665:−
652:−
592:−
579:−
519:−
506:−
293:Totals =
139:−
48:in 1987.
1798:Category
1785:28369655
1735:22914976
1667:26559009
1611:347-358)
1598:17053050
1474:25554168
1413:305-321)
1400:22009060
1340:52127769
1050:Quartet
1466:3934395
1302:3447007
935:artet t
242:2x, 2y
225:3x, 1y
44:and by
1783:
1775:
1733:
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1665:
1657:
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1588:
1528:
1472:
1464:
1456:
1398:
1390:
1338:
1328:
1300:
1292:
1251:
1243:
1175:, and
1032:, and
1007:, and
937:angles
917:ENCODE
912:PHYLIP
876:χ test
459:purine
330:JC69*
1635:arXiv
1566:arXiv
1470:S2CID
1249:S2CID
950:(f),
922:PAUP*
798:for T
748:for T
346:K81*
338:K80*
1781:PMID
1773:ISSN
1731:PMID
1723:ISSN
1663:PMID
1655:ISSN
1594:PMID
1586:ISSN
1526:ISSN
1462:PMID
1454:ISSN
1396:PMID
1388:ISSN
1336:OCLC
1326:ISBN
1298:PMID
1290:ISSN
1241:ISSN
784:1134
771:1233
734:1234
721:1133
686:1342
673:1341
660:1332
647:1331
613:1324
600:1314
587:1323
574:1313
540:1234
527:1134
514:1233
501:1133
441:1134
428:1233
415:1234
402:1133
362:GMM
303:241
271:138
92:TTTT
87:, …
85:AAAG
78:AAAC
71:AAAA
1763:doi
1713:doi
1645:doi
1576:doi
1518:doi
1446:doi
1378:hdl
1370:doi
1280:doi
1233:doi
472:, T
298:15
288:23
285:24
268:24
254:33
251:12
237:44
234:12
208:4x
35:or
1800::
1779:.
1771:.
1759:66
1757:.
1753:.
1729:.
1721:.
1709:62
1707:.
1703:.
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1661:.
1653:.
1643:.
1631:65
1629:.
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1592:.
1584:.
1574:.
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1556:.
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1440:.
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1386:.
1376:.
1366:29
1364:.
1360:.
1348:^
1334:.
1310:^
1296:.
1288:.
1274:.
1270:.
1247:.
1239:.
1227:.
1223:.
1168:,
1155:0
1127:0
1100:0
1089:)
1076:)
1063:)
1025:,
1014::
1000:,
982:+
975:+
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248:3
231:4
220:3
217:4
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80:,
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1765::
1737:.
1715::
1669:.
1647::
1637::
1600:.
1578::
1568::
1532:.
1520::
1492:2
1476:.
1448::
1402:.
1380::
1372::
1342:.
1304:.
1282::
1276:4
1255:.
1235::
1229:4
1188:q
1180:3
1177:q
1173:2
1170:q
1166:1
1163:q
1151:w
1146:w
1144:-
1132:v
1130:-
1123:v
1110:u
1105:u
1103:-
1086:3
1084:q
1082:(
1080:E
1073:2
1071:q
1069:(
1067:E
1060:1
1058:q
1056:(
1054:E
1037:3
1034:q
1030:2
1027:q
1023:1
1020:q
1012:3
1009:q
1005:2
1002:q
998:1
995:q
991:q
987:3
984:q
980:2
977:q
973:1
970:q
966:q
962:3
959:q
955:2
952:q
948:1
945:q
929:s
862:)
859:B
856:+
853:P
850:(
846:/
840:2
836:)
832:B
826:P
823:(
820:=
815:2
800:X
780:N
776:+
767:N
763:=
760:B
750:X
730:N
726:+
717:N
713:=
710:P
682:N
678:+
669:N
656:N
643:N
639:=
636:Z
609:N
605:+
596:N
583:N
570:N
566:=
563:Y
536:N
532:+
523:N
510:N
497:N
493:=
490:X
478:Z
474:Y
470:X
437:f
433:+
424:f
420:=
411:f
407:+
398:f
164:0
161:=
156:A
153:C
150:G
147:C
143:f
134:T
131:A
128:C
125:A
121:f
89:f
82:f
75:f
68:f
57:t
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