2710:
words, it compares how different trees predict the observed data. The introduction of a model of evolution in ML analyses presents an advantage over MP as the probability of nucleotide substitutions and rates of these substitutions are taken into account, explaining the phylogenetic relationships of taxa in a more realistic way. An important consideration of this method is the branch length, which parsimony ignores, with changes being more likely to happen along long branches than short ones. This approach might eliminate long branch attraction and explain the greater consistency of ML over MP. Although considered by many to be the best approach to inferring phylogenies from a theoretical point of view, ML is computationally intensive and it is almost impossible to explore all trees as there are too many. Bayesian inference also incorporates a model of evolution and the main advantages over MP and ML are that it is computationally more efficient than traditional methods, it quantifies and addresses the source of uncertainty and is able to incorporate complex models of evolution.
1160:
which all branch lengths are changed in every cycle. The LOCAL algorithms modifies the tree by selecting an internal branch of the tree at random. The nodes at the ends of this branch are each connected to two other branches. One of each pair is chosen at random. Imagine taking these three selected edges and stringing them like a clothesline from left to right, where the direction (left/right) is also selected at random. The two endpoints of the first branch selected will have a sub-tree hanging like a piece of clothing strung to the line. The algorithm proceeds by multiplying the three selected branches by a common random amount, akin to stretching or shrinking the clothesline. Finally the leftmost of the two hanging sub-trees is disconnected and reattached to the clothesline at a location selected uniformly at random. This would be the candidate tree.
3029:
2720:
lead to overconfidence in the results? Are bootstrap values more robust than posterior probabilities? One fact underlying this controversy is that all data are used during
Bayesian analysis and the calculation of posterior probabilities, while the nature of bootstrapping means that most bootstrap replicates will be missing some of the original data. As a result, bipartitions (branches) supported by relatively few characters in the dataset may receive very high posterior probabilities but moderate or even low bootstrap support, as many of the bootstrap replicates don't contain enough of the critical characters to retrieve the bipartition.
2706:, a phylogenetic phenomenon where taxa with long branches (numerous character state changes) tend to appear more closely related in the phylogeny than they really are. For morphological data, recent simulation studies suggest that parsimony may be less accurate than trees built using Bayesian approaches, potentially due to overprecision, although this has been disputed. Studies using novel simulation methods have demonstrated that differences between inference methods result from the search strategy and consensus method employed, rather than the optimization used.
2746:
models, the most standard model of DNA substitution, the 4x4 also called JC69, which assumes that changes across nucleotides occur with equal probability. It also implements a number of 20x20 models of amino acid substitution, and codon models of DNA substitution. It offers different methods for relaxing the assumption of equal substitutions rates across nucleotide sites. MrBayes is also able to infer ancestral states accommodating uncertainty to the phylogenetic tree and model parameters.
2669:
255:
maximum parsimony (MP), maximum likelihood (ML), and minimum evolution (ME) criteria, and the same can be expected for stochastic tree search using MCMC. This problem will result in samples not approximating correctly to the posterior density. The (MCÂł) improves the mixing of Markov chains in presence of multiple local peaks in the posterior density. It runs multiple (m) chains in parallel, each for n iterations and with different stationary distributions
101:
5898:
5575:
109:
5910:
2677:
92:
three independent groups: Bruce
Rannala and Ziheng Yang in Berkeley, Bob Mau in Madison, and Shuying Li in University of Iowa, the last two being PhD students at the time. The approach has become very popular since the release of the MrBayes software in 2001, and is now one of the most popular methods in molecular phylogenetics.
140:
of times. The number of times a single tree is visited during the course of the chain is an approximation of its posterior probability. Some of the most common algorithms used in MCMC methods include the
Metropolis–Hastings algorithms, the Metropolis-Coupling MCMC (MC³) and the LOCAL algorithm of Larget and Simon.
2753:
MrBayes 3.2 was released in 2012 The new version allows the users to run multiple analyses in parallel. It also provides faster likelihood calculations and allow these calculations to be delegated to graphics processing unites (GPUs). Version 3.2 provides wider outputs options compatible with FigTree
2723:
Controversy of using prior probabilities. Using prior probabilities for
Bayesian analysis has been seen by many as an advantage as it provides a way of incorporating information from sources other than the data being analyzed. However, when such external information is lacking, one is forced to use a
91:
combines the information in the prior and in the data likelihood to create the so-called posterior probability of trees, which is the probability that the tree is correct given the data, the prior and the likelihood model. Bayesian inference was introduced into molecular phylogenetics in the 1990s by
2719:
Bootstrap values vs posterior probabilities. It has been observed that bootstrap support values, calculated under parsimony or maximum likelihood, tend to be lower than the posterior probabilities obtained by
Bayesian inference. This leads to a number of questions such as: Do posterior probabilities
139:
is proposed. Secondly, the probability of this new state to be correct is calculated. Thirdly, a new random variable (0,1) is proposed. If this new value is less than the acceptance probability the new state is accepted and the state of the chain is updated. This process is run thousands or millions
2745:
MrBayes uses MCMC to approximate the posterior probabilities of trees. The user can change assumptions of the substitution model, priors and the details of the MCÂł analysis. It also allows the user to remove and add taxa and characters to the analysis. The program includes, among several nucleotide
2737:
MrBayes is a free software tool that performs
Bayesian inference of phylogeny. It was originally written by John P. Huelsenbeck and Frederik Ronquist in 2001. As Bayesian methods increased in popularity, MrBayes became one of the software of choice for many molecular phylogeneticists. It is offered
2749:
MrBayes 3 was a completely reorganized and restructured version of the original MrBayes. The main novelty was the ability of the software to accommodate heterogeneity of data sets. This new framework allows the user to mix models and take advantages of the efficiency of
Bayesian MCMC analysis when
2709:
As in maximum parsimony, maximum likelihood will evaluate alternative trees. However it considers the probability of each tree explaining the given data based on a model of evolution. In this case, the tree with the highest probability of explaining the data is chosen over the other ones. In other
2688:
There are many approaches to reconstructing phylogenetic trees, each with advantages and disadvantages, and there is no straightforward answer to “what is the best method?”. Maximum parsimony (MP) and maximum likelihood (ML) are traditional methods widely used for the estimation of phylogenies and
1159:
The LOCAL algorithms offers a computational advantage over previous methods and demonstrates that a
Bayesian approach is able to assess uncertainty computationally practical in larger trees. The LOCAL algorithm is an improvement of the GLOBAL algorithm presented in Mau, Newton and Larget (1999) in
254:
Metropolis-coupled MCMC algorithm (MCÂł) has been proposed to solve a practical concern of the Markov chain moving across peaks when the target distribution has multiple local peaks, separated by low valleys, are known to exist in the tree space. This is the case during heuristic tree search under
705:
has the effect of flattening out the distribution, similar to heating a metal. In such a distribution, it is easier to traverse between peaks (separated by valleys) than in the original distribution. After each iteration, a swap of states between two randomly chosen chains is proposed through a
1026:
At the end of the run, output from only the cold chain is used, while those from the hot chains are discarded. Heuristically, the hot chains will visit the local peaks rather easily, and swapping states between chains will let the cold chain occasionally jump valleys, leading to better mixing.
131:
The
Bayesian approach to phylogenetic reconstruction combines the prior probability of a tree P(A) with the likelihood of the data (B) to produce a posterior probability distribution on trees P(A|B). The posterior probability of a tree will be the probability that the tree is correct, given the
2701:
percentage. For the same reason that it has been widely used, its simplicity, MP has also received criticism and has been pushed into the background by ML and
Bayesian methods. MP presents several problems and limitations. As shown by Felsenstein (1978), MP might be statistically inconsistent,
2727:
Model choice. The results of the Bayesian analysis of a phylogeny are directly correlated to the model of evolution chosen so it is important to choose a model that fits the observed data, otherwise inferences in the phylogeny will be erroneous. Many scientists have raised questions about the
123:
Bayesian inference or the inverse probability method was the standard approach in statistical thinking until the early 1900s before RA Fisher developed what's now known as the classical/frequentist/Fisherian inference. Computational difficulties and philosophical objections had prevented the
1021:
2696:
and it does not require a model of evolutionary change. MP gives the most simple explanation for a given set of data, reconstructing a phylogenetic tree that includes as few changes across the sequences as possible. The support of the tree branches is represented by
227:. When this is not the case Hastings corrections are applied. The aim of Metropolis-Hastings algorithm is to produce a collection of states with a determined distribution until the Markov process reaches a stationary distribution. The algorithm has two components:
2738:
for Macintosh, Windows, and UNIX operating systems and it has a command-line interface. The program uses the standard MCMC algorithm as well as the Metropolis coupled MCMC variant. MrBayes reads aligned matrices of sequences (DNA or amino acids) in the standard
2100:
2724:
prior even if it is impossible to use a statistical distribution to represent total ignorance. It is also a concern that the Bayesian posterior probabilities may reflect subjective opinions when the prior is arbitrary and subjective.
152:, a modified version of the original Metropolis algorithm. It is a widely used method to sample randomly from complicated and multi-dimensional distribution probabilities. The Metropolis algorithm is described in the following steps:
2241:
1588:
120:. Published posthumously in 1763 it was the first expression of inverse probability and the basis of Bayesian inference. Independently, unaware of Bayes' work, Pierre-Simon Laplace developed Bayes' theorem in 1774.
569:
864:
4912:"Mass extinction, gradual cooling, or rapid radiation? Reconstructing the spatiotemporal evolution of the ancient angiosperm genus Hedyosmum (Chloranthaceae) using empirical and simulated approaches"
1432:
1088:
5057:"Ancestral state reconstruction reveals multiple independent evolution of diagnostic morphological characters in the "Higher Oribatida" (Acari), conflicting with current classification schemes"
1936:
1840:
1747:
72:
3032:
Chronogram obtained from molecular clock analysis using BEAST. Pie chart in each node indicates the possible ancestral distributions inferred from Bayesian Binary MCMC analysis (BBM)
1359:
2768:
This table includes some of the most common phylogenetic software used for inferring phylogenies under a Bayesian framework. Some of them do not use exclusively Bayesian methods.
2456:
4867:
Alonso R, Crawford AJ, Bermingham E (March 2012). "Molecular phylogeny of an endemic radiation of Cuban toads (Bufonidae: Peltophryne) based on mitochondrial and nuclear genes".
1149:
2322:
810:
452:
339:
740:
375:
614:
292:
2531:
2495:
1693:
405:
3973:"Bayes or bootstrap? A simulation study comparing the performance of Bayesian Markov chain Monte Carlo sampling and bootstrapping in assessing phylogenetic confidence"
703:
2612:
2583:
1497:
1462:
1297:
1267:
1191:
643:
2658:
1670:
1643:
674:
2374:
2635:
2554:
2397:
2348:
2267:
1947:
1237:
1214:
1114:
856:
833:
763:
5114:
Filipowicz N, Renner SS (July 2012). "Brunfelsia (Solanaceae): a genus evenly divided between South America and radiations on Cuba and other Antillean islands".
1616:
3028:
2728:
interpretation of Bayesian inference when the model is unknown or incorrect. For example, an oversimplified model might give higher posterior probabilities.
2111:
5941:
1505:
3075:
Rannala, Bruce; Yang, Ziheng (September 1996). "Probability distribution of molecular evolutionary trees: A new method of phylogenetic inference".
5513:
1151:
is ideally suited for implementation on parallel machines, since each chain will in general require the same amount of computation per iteration.
4716:
Pagel M, Meade A (June 2006). "Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo".
460:
5936:
5708:
3463:
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (June 1953). "Equation of state calculations by fast computing machines".
211:
The algorithm keeps running until it reaches an equilibrium distribution. It also assumes that the probability of proposing a new tree T
3727:"Bayesian methods outperform parsimony but at the expense of precision in the estimation of phylogeny from discrete morphological data"
3025:
Bayesian Inference has extensively been used by molecular phylogeneticists for a wide number of applications. Some of these include:
149:
5668:
3893:
2750:
dealing with different type of data (e.g. protein, nucleotide, and morphological). It uses the Metropolis-Coupling MCMC by default.
1090:
is unstable, proposed swaps will seldom be accepted. This is the reason for using several chains which differ only incrementally.
65:
4123:"Bayesian selection of misspecified models is overconfident and may cause spurious posterior probabilities for phylogenetic trees"
1016:{\displaystyle \alpha ={\frac {\pi _{i}(\theta ^{(j)})\pi _{j}(\theta ^{(i)})}{\pi _{i}(\theta ^{(i)})\pi _{j}(\theta ^{(j)})}}\ }
5748:
4820:"TOPALi v2: a rich graphical interface for evolutionary analyses of multiple alignments on HPC clusters and multi-core desktops"
2702:
meaning that as more and more data (e.g. sequence length) is accumulated, results can converge on an incorrect tree and lead to
5753:
4400:
Ronquist F, Teslenko M, van der Mark P, Ayres DL, Darling A, Höhna S, Larget B, Liu L, Suchard MA, Huelsenbeck JP (May 2012).
4053:
GarcĂa-Sandoval R (January 2014). "Why some clades have low bootstrap frequencies and high Bayesian posterior probabilities".
58:
5763:
5693:
2763:
1364:
1030:
2951:
3884:
Swofford DL, Olsen GJ, Waddell PJ, Hillis DM (1996). "Phylogenetic inference". In Hillis DM, Moritz C, Mable BK (eds.).
1851:
1755:
5673:
5580:
5536:
5506:
87:
2692:
Maximum Parsimony recovers one or more optimal trees based on a matrix of discrete characters for a certain group of
1698:
3649:
Felsenstein J (December 1978). "Cases in which parsimony or compatibility methods will be positively misleading".
5863:
5789:
4761:"Armadillo 1.1: an original workflow platform for designing and conducting phylogenetic analysis and simulations"
3776:"Weighted parsimony outperforms other methods of phylogenetic inference under models appropriate for morphology"
5914:
125:
3678:"Fluctuations in population fecundity drive variation in demographic connectivity and metapopulation dynamics"
2797:
A program for Bayesian inference and model choice across a wide range of phylogenetic and evolutionary models.
5743:
5541:
38:
4498:
Bouckaert R, Heled J, KĂĽhnert D, Vaughan T, Wu CH, Xie D, Suchard MA, Rambaut A, Drummond AJ (April 2014).
1302:
5902:
5626:
5499:
2703:
2681:
2405:
4685:"Inferences from DNA data: population histories, evolutionary processes and forensic match probabilities"
4320:"Maximum-likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites"
1119:
5878:
5556:
5200:"A phylogenetic framework for evolutionary study of the nightshades (Solanaceae): a dated 1000-tip tree"
2275:
3725:
O'Reilly JE, Puttick MN, Parry L, Tanner AR, Tarver JE, Fleming J, Pisani D, Donoghue PC (April 2016).
768:
410:
297:
5715:
5621:
5319:
5211:
5123:
5068:
4974:
4876:
4772:
4511:
4134:
3925:
3544:
Geyer CJ (1991). "Markov chain Monte Carlo maximum likelihood.". In Keramidas EM, Kaufman SM (eds.).
3472:
3434:
3425:
Hastings WK (April 1970). "Monte Carlo sampling methods using Markov chains and their applications".
3381:
3084:
709:
344:
135:
MCMC methods can be described in three steps: first using a stochastic mechanism a new state for the
28:
4402:"MrBayes 3.2: efficient Bayesian phylogenetic inference and model choice across a large model space"
2668:
5758:
5640:
581:
258:
3676:
Castorani MC, Reed DC, Raimondi PT, Alberto F, Bell TW, Cavanaugh KC, et al. (January 2017).
2860:
Non-parametric methods for modeling among-site variation in nucleotide or amino-acid propensities.
231:
A potential transition from one state to another (i → j) using a transition probability function q
5681:
5635:
5551:
4892:
4741:
3631:
3496:
3256:
3248:
3228:
3209:
3193:
3108:
48:
4559:"A Bayesian mixture model for across-site heterogeneities in the amino-acid replacement process"
2500:
2464:
1675:
380:
116:
Bayesian inference refers to a probabilistic method developed by Reverend Thomas Bayes based on
5367:"Assessing phenotypic correlation through the multivariate phylogenetic latent liability model"
5609:
5461:
5443:
5404:
5386:
5347:
5288:
5239:
5180:
5139:
5096:
5037:
5002:
4943:
4849:
4800:
4733:
4665:
4621:
4580:
4539:
4480:
4431:
4382:
4341:
4285:
4244:
4203:
4162:
4103:
4035:
4014:"Comparison of Bayesian and maximum likelihood bootstrap measures of phylogenetic reliability"
3994:
3953:
3889:
3866:
3815:
3807:
3756:
3707:
3623:
3549:
3488:
3407:
3324:
3297:
3201:
3152:
3100:
679:
117:
2844:
R Bouckaert, J Heled, D KĂĽhnert, T Vaughan, CH Wu, D Xie, MA Suchard, A Rambaut, AJ Drummond.
2588:
2559:
1467:
1437:
1272:
1242:
1166:
619:
5698:
5652:
5451:
5435:
5394:
5378:
5337:
5327:
5278:
5270:
5229:
5219:
5170:
5131:
5086:
5076:
5029:
4992:
4982:
4933:
4923:
4884:
4839:
4831:
4790:
4780:
4725:
4696:
4655:
4611:
4570:
4529:
4519:
4470:
4462:
4421:
4413:
4372:
4331:
4275:
4234:
4193:
4182:"Reliability of Bayesian posterior probabilities and bootstrap frequencies in phylogenetics"
4152:
4142:
4093:
4062:
4025:
3984:
3943:
3933:
3856:
3846:
3797:
3787:
3746:
3738:
3697:
3689:
3658:
3613:
3580:
3480:
3442:
3397:
3389:
3348:
3287:
3240:
3183:
3142:
3092:
2640:
2095:{\displaystyle h(t)=\left(1/4\right)^{n_{1}+n_{2}}\left(1/4+3/4{e^{-4/3t}}^{n_{1}}\right)\ }
454:
are chosen to improve mixing. For example, one can choose incremental heating of the form:
5423:
4639:
2905:
2901:
2246:
Update branch length by choosing new value uniformly at random from a window of half-width
1648:
1621:
648:
5799:
4818:
Milne I, Lindner D, Bayer M, Husmeier D, McGuire G, Marshall DF, Wright F (January 2009).
4336:
4319:
3585:
3568:
3147:
3130:
2955:
2353:
5259:"Bayesian estimation of speciation and extinction from incomplete fossil occurrence data"
2617:
2536:
2379:
2330:
2249:
1219:
1196:
1096:
838:
815:
745:
5323:
5215:
5159:"Miocene dispersal drives island radiations in the palm tribe Trachycarpeae (Arecaceae)"
5127:
5072:
4978:
4880:
4776:
4515:
4138:
3929:
3476:
3438:
3385:
3131:"Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method"
3088:
100:
5773:
5456:
5399:
5366:
5342:
5307:
5283:
5258:
5234:
5199:
5091:
5056:
4997:
4962:
4844:
4819:
4795:
4760:
4534:
4499:
4475:
4450:
4426:
4401:
4157:
4122:
3861:
3834:
3751:
3726:
3702:
3677:
3402:
3369:
1601:
4239:
4222:
3948:
3913:
3292:
3275:
2236:{\displaystyle h(t)=\left(1/4-1/4{e^{-4/3t}}^{n_{2}}\right)(\lambda e^{-\lambda t})\ }
5930:
5768:
5738:
5645:
5522:
4888:
4745:
3618:
3601:
3569:"Markov chain Monte Carlo algorithms for the Bayesian analysis of phylogenetic trees"
3260:
3188:
3171:
2698:
4835:
4616:
4599:
4377:
4360:
3546:
Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface
2904:, B. Larget, D.A. Baum, S.D. Smith, A. Rokas and B. Larget, S.K. Kotha, C.N. Dewey,
5873:
5819:
5814:
5809:
5794:
5602:
5597:
4896:
3500:
3244:
3112:
1239:
from the rest. Suppose also that we have (randomly) selected branches with lengths
136:
3635:
3213:
1499:. Then for the LOCAL algorithm, the acceptance probability can be computed to be:
5332:
4785:
4524:
4066:
2857:
Bayesian Monte Carlo Markov Chain (MCMC) sampler for phylogenetic reconstruction.
5868:
5561:
5135:
5033:
4963:"Bayesian models for comparative analysis integrating phylogenetic uncertainty"
3918:
Proceedings of the National Academy of Sciences of the United States of America
2974:
2948:
5570:
5546:
4280:
4263:
4198:
4181:
3662:
3393:
3315:
Laplace P (1774). "Memoire sur la Probabilite des Causes par les Evenements".
2965:
Workflow platform dedicated to phylogenetic and general bioinformatic analysis
2739:
1583:{\displaystyle {\frac {h(y)}{h(x)}}\times {\frac {{m^{\star }}^{3}}{m^{3}}}\ }
575:
5447:
5390:
5224:
5081:
5055:
Schäffer S, Koblmüller S, Pfingstl T, Sturmbauer C, Krisper G (August 2010).
4987:
3914:"Overcredibility of molecular phylogenies obtained by Bayesian phylogenetics"
3851:
3811:
3446:
2866:
5883:
5847:
5842:
5837:
5732:
5614:
5439:
5274:
5175:
5158:
4928:
4911:
4701:
4684:
4660:
4643:
4575:
4558:
4466:
4417:
4147:
4098:
4081:
4030:
4013:
3989:
3972:
3835:"Morphological phylogenetics evaluated using novel evolutionary simulations"
3553:
3353:
3336:
3328:
108:
5465:
5408:
5351:
5292:
5243:
5184:
5143:
5100:
5041:
5006:
4947:
4853:
4804:
4737:
4669:
4625:
4584:
4543:
4484:
4435:
4386:
4289:
4248:
4207:
4166:
4107:
4039:
3998:
3957:
3938:
3870:
3819:
3760:
3742:
3711:
3693:
3627:
3411:
3301:
3205:
1361:, be the current length of the clothesline. We select the new length to be
1116:
chains are run and only one chain is used for inference. For this reason,
5574:
5020:
Ronquist F (September 2004). "Bayesian inference of character evolution".
4689:
Journal of the Royal Statistical Society, Series A (Statistics in Society)
4345:
4012:
Douady CJ, Delsuc F, Boucher Y, Doolittle WF, Douzery EJ (February 2003).
3156:
3104:
170:
The ratio, R, of the probabilities (or probability density functions) of T
3833:
Keating JN, Sansom RS, Sutton MD, Knight CG, Garwood RJ (February 2020).
2898:
Bayesian concordance using modified greedy consensus of unrooted quartets
5365:
Cybis G, Sinsheimer J, Bedford T, Mather A, Lemey P, Suchard MA (2015).
5382:
5257:
Silvestro D, Schnitzler J, Liow LH, Antonelli A, Salamin N (May 2014).
4938:
3802:
3368:
Nascimento, FabrĂcia F.; Reis, Mario dos; Yang, Ziheng (October 2017).
3252:
3197:
3096:
2910:
2829:
2803:
2676:
564:{\displaystyle \pi _{j}(\theta )=\pi (\theta )^{1/},\ \ \lambda >0,}
4600:"BAli-Phy: simultaneous Bayesian inference of alignment and phylogeny"
3792:
3775:
3602:"Bayesian phylogenetic inference via Markov chain Monte Carlo methods"
3492:
3484:
3172:"Bayesian Phylogenetic Inference via Markov Chain Monte Carlo Methods"
2942:
Bayesian inference, multiple models, mixture model (auto-partitioning)
2684:. Longer branches (A & C) appear to be more closely related.
4082:"Fair-Balance Paradox, Star-tree Paradox, and Bayesian Phylogenetics"
2672:
Tiger phylogenetic relationships, bootstrap values shown in branches.
4729:
2929:
124:
widespread adoption of the Bayesian approach until the 1990s, when
5703:
5631:
5481:
4961:
de Villemereuil P, Wells JA, Edwards RD, Blomberg SP (June 2012).
3027:
2939:
Bayesian inference of trees using Markov Chain Monte Carlo methods
2675:
107:
4500:"BEAST 2: a software platform for Bayesian evolutionary analysis"
2838:
2689:
both use character information directly, as Bayesian methods do.
5491:
2816:
Bayesian inference, relaxed molecular clock, demographic history
2693:
5495:
4361:"MrBayes 3: Bayesian phylogenetic inference under mixed models"
3229:"Phylogenetic Tree Construction Using Markov Chain Monte Carlo"
200:
is accepted as the current tree with probability R, otherwise T
5306:
Lemey P, Rambaut A, Drummond AJ, Suchard MA (September 2009).
1672:
are variable, assume exponential prior distribution with rate
1163:
Suppose we began by selecting the internal branch with length
132:
prior, the data, and the correctness of the likelihood model.
5486:
4264:"NEXUS: an extensible file format for systematic information"
4180:
Erixon P, Svennblad B, Britton T, Oxelman B (October 2003).
5198:
Särkinen T, Bohs L, Olmstead RG, Knapp S (September 2013).
4759:
Lord E, Leclercq M, Boc A, Diallo AB, Makarenkov V (2012).
3548:. Fairfax Station: Interface Foundation. pp. 156–163.
2971:
E. Lord, M. Leclercq, A. Boc, A.B. Diallo and V. Makarenkov
5422:
Tolkoff M, Alfaro M, Baele G, Lemey P, Suchard MA (2018).
2993:
2923:
Bayesian inference, demographic history, population splits
2885:
2876:
Simultaneous Bayesian inference of alignment and phylogeny
2822:
207:
At this point the process is repeated from Step 2 N times.
4449:
Drummond AJ, Suchard MA, Xie D, Rambaut A (August 2012).
3170:
Mau, Bob; Newton, Michael A.; Larget, Bret (March 1999).
2614:. In each case, we will begin with an initial length of
1299:
from each side, and that we oriented these branches. Let
4642:, Larget B, Baum DA, Smith SD, Rokas A (February 2007).
3052:
Model dynamics of species diversification and extinction
3012:
2920:
Bayesian Analysis of Trees With Internal Node Generation
2847:
4262:
Maddison DR, Swofford DL, Maddison WP (December 1997).
3370:"A biologist's guide to Bayesian phylogenetic analysis"
3227:
Li, Shuying; Pearl, Dennis K.; Doss, Hani (June 2000).
3040:
Inference and evaluation of uncertainty of phylogenies.
1749:. The probabilities of the possible site patterns are:
1427:{\displaystyle m^{\star }=m\exp(\lambda (U_{1}-0.5))\ }
4451:"Bayesian phylogenetics with BEAUti and the BEAST 1.7"
2834:
A software platform for Bayesian evolutionary analysis
4644:"Bayesian estimation of concordance among gene trees"
2800:
Zangh, Huelsenbeck, Der Mark, Ronquist & Teslenko
2643:
2620:
2591:
2562:
2539:
2503:
2467:
2408:
2382:
2356:
2333:
2278:
2252:
2114:
1950:
1854:
1758:
1701:
1678:
1651:
1624:
1604:
1508:
1470:
1440:
1367:
1305:
1275:
1245:
1222:
1199:
1169:
1122:
1099:
1083:{\displaystyle \pi _{i}(\theta )/\pi _{j}(\theta )\ }
1033:
867:
841:
818:
771:
748:
712:
682:
651:
622:
584:
463:
413:
383:
347:
300:
261:
2984:
Geneious provides genome and proteome research tools
2879:
Bayesian inference, alignment as well as tree search
96:
Bayesian inference of phylogeny background and bases
5856:
5830:
5782:
5724:
5661:
5590:
5529:
4223:"MRBAYES: Bayesian inference of phylogenetic trees"
3337:"Memoir on the Probability of the Causes of Events"
3276:"MRBAYES: Bayesian inference of phylogenetic trees"
237:
Movement of the chain to state j with probability α
44:
34:
24:
3274:Huelsenbeck, J. P.; Ronquist, F. (1 August 2001).
2652:
2629:
2606:
2577:
2548:
2525:
2489:
2450:
2391:
2368:
2342:
2316:
2261:
2235:
2094:
1931:{\displaystyle 1/4\left(1/4-1/4e^{-4/3t}\right)\ }
1930:
1835:{\displaystyle 1/4\left(1/4+3/4e^{-4/3t}\right)\ }
1834:
1741:
1687:
1664:
1637:
1610:
1582:
1491:
1456:
1426:
1353:
1291:
1261:
1231:
1208:
1185:
1143:
1108:
1082:
1015:
850:
827:
804:
757:
734:
697:
668:
637:
616:are heated chains. Note that raising the density
608:
563:
446:
399:
369:
333:
286:
3458:
3456:
3043:Inference of ancestral character state evolution.
1941:Thus the unnormalized posterior distribution is:
1093:An obvious disadvantage of the algorithm is that
3971:Alfaro ME, Zoller S, Lutzoni F (February 2003).
3518:. Sunderland, Massachusetts: Sinauer Associates.
2863:N. Lartillot, N. Rodrigue, D. Stubbs, J. Richer
148:One of the most common MCMC methods used is the
128:algorithms revolutionized Bayesian computation.
4127:Proceedings of the National Academy of Sciences
3907:
3905:
3233:Journal of the American Statistical Association
2819:A. J. Drummond, A. Rambaut & M. A. Suchard
4121:Yang, Ziheng; Zhu, Tianqi (20 February 2018).
578:with the correct target density, while chains
16:Statistical method for molecular phylogenetics
5507:
4683:Wilson IJ, Weale ME, Balding DJ (June 2003).
3888:. Sunderland, MA: Sinauer. pp. 407–514.
3124:
3122:
2813:Bayesian Evolutionary Analysis Sampling Trees
2533:. We will compare results for two values of
1742:{\displaystyle p(t)=\lambda e^{-\lambda t}\ }
66:
8:
4307:. New York: Academic Press. pp. 21–132.
3912:Suzuki Y, Glazko GV, Nei M (December 2002).
2975:https://github.com/armadilloUQAM/armadillo2/
2949:http://www.evolution.rdg.ac.uk/BayesPhy.html
19:
5157:Bacon CD, Baker WJ, Simmons MP (May 2012).
3533:. Oxford, England: Oxford University Press.
3531:Molecular Evolution: A Statistical Approach
167:, is selected from the collection of trees.
5514:
5500:
5492:
4359:Ronquist F, Huelsenbeck JP (August 2003).
4221:Huelsenbeck JP, Ronquist F (August 2001).
3055:Elucidate patterns in pathogens dispersal.
2867:http://www.atgc-montpellier.fr/phylobayes/
73:
59:
5455:
5398:
5341:
5331:
5308:"Bayesian phylogeography finds its roots"
5282:
5233:
5223:
5174:
5090:
5080:
4996:
4986:
4937:
4927:
4910:Antonelli A, SanmartĂn I (October 2011).
4843:
4794:
4784:
4700:
4659:
4615:
4574:
4533:
4523:
4474:
4425:
4376:
4335:
4279:
4238:
4197:
4156:
4146:
4097:
4055:Israel Journal of Ecology & Evolution
4029:
3988:
3947:
3937:
3860:
3850:
3801:
3791:
3750:
3701:
3617:
3600:Mau B, Newton MA, Larget B (March 1999).
3584:
3401:
3352:
3291:
3187:
3146:
2642:
2619:
2590:
2561:
2538:
2508:
2502:
2472:
2466:
2428:
2419:
2407:
2381:
2355:
2332:
2306:
2292:
2283:
2277:
2251:
2215:
2192:
2187:
2173:
2166:
2161:
2152:
2138:
2113:
2076:
2071:
2057:
2050:
2045:
2036:
2022:
2006:
1993:
1988:
1975:
1949:
1907:
1900:
1888:
1874:
1858:
1853:
1811:
1804:
1792:
1778:
1762:
1757:
1724:
1700:
1677:
1656:
1650:
1629:
1623:
1603:
1569:
1559:
1552:
1547:
1544:
1509:
1507:
1469:
1445:
1439:
1403:
1372:
1366:
1342:
1329:
1316:
1304:
1280:
1274:
1250:
1244:
1221:
1198:
1174:
1168:
1132:
1124:
1121:
1098:
1062:
1053:
1038:
1032:
992:
979:
960:
947:
926:
913:
894:
881:
874:
866:
840:
817:
770:
747:
717:
711:
681:
655:
650:
621:
583:
503:
499:
468:
462:
412:
388:
382:
352:
346:
299:
266:
260:
4598:Suchard MA, Redelings BD (August 2006).
3774:Goloboff PA, Torres A, Arias JS (2018).
3058:Inference of phenotypic trait evolution.
2990:A. J. Drummond,M.Suchard,V.Lefort et al.
2770:
2667:
2664:Maximum parsimony and maximum likelihood
219:, is the same probability of proposing T
99:
3067:
812:. A swap between the states of chains
241:and remains in i with probability 1 – α
112:Metaphor illustrating MCMC method steps
18:
5116:Molecular Phylogenetics and Evolution
4557:Lartillot N, Philippe H (June 2004).
4337:10.1093/oxfordjournals.molbev.a040082
3586:10.1093/oxfordjournals.molbev.a026160
3148:10.1093/oxfordjournals.molbev.a025811
3129:Yang, Z.; Rannala, B. (1 July 1997).
1618:of a 2-taxon tree under JC, in which
1354:{\displaystyle m=t_{1}+t_{8}+t_{9}\ }
7:
5909:
2911:http://www.stat.wisc.edu/~ane/bucky/
2804:https://nbisweden.github.io/MrBayes/
2451:{\displaystyle h(t^{\star })/h(t)\ }
1155:LOCAL algorithm of Larget and Simon
1144:{\displaystyle \mathrm {MC} ^{3}\ }
215:when we are at the old tree state T
5942:Applications of Bayesian inference
3886:Molecular Systematics, 2nd edition
2926:I. J. Wilson, D. Weale, D.Balding
2895:Bayesian concordance of gene trees
2399:. The acceptance probability is:
2317:{\displaystyle t^{\star }=|t+U|\ }
1128:
1125:
14:
5022:Trends in Ecology & Evolution
2350:is uniformly distributed between
805:{\displaystyle j=1,2,\ldots ,m\ }
447:{\displaystyle j=2,3,\ldots ,m\ }
334:{\displaystyle j=1,2,\ldots ,m\ }
5908:
5897:
5896:
5749:Phylogenetic comparative methods
5573:
5371:The Annals of Applied Statistics
4889:10.1111/j.1365-2699.2011.02594.x
3682:Proceedings. Biological Sciences
3619:10.1111/j.0006-341x.1999.00001.x
3567:Larget B, Simon DL (June 1999).
3189:10.1111/j.0006-341x.1999.00001.x
2930:http://www.maths.abdn.ac.uk/Ëśijw
1464:is a uniform random variable on
193:is accepted as the current tree.
5754:Phylogenetic niche conservatism
4648:Molecular Biology and Evolution
4563:Molecular Biology and Evolution
4455:Molecular Biology and Evolution
4371:(12). Oxford, England: 1572–4.
4324:Molecular Biology and Evolution
4240:10.1093/bioinformatics/17.8.754
4086:Molecular Biology and Evolution
4018:Molecular Biology and Evolution
3977:Molecular Biology and Evolution
3573:Molecular Biology and Evolution
3465:The Journal of Chemical Physics
3293:10.1093/bioinformatics/17.8.754
3135:Molecular Biology and Evolution
2269:centered at the current value:
735:{\displaystyle \theta ^{(j)}\ }
574:so that the first chain is the
370:{\displaystyle \pi _{1}=\pi \ }
178:is computed as follows: R = f(T
126:Markov Chain Monte Carlo (MCMC)
20:Bayesian inference in phylogeny
5424:"Phylogenetic Factor Analysis"
4305:Evolution of Protein Molecules
3374:Nature Ecology & Evolution
3317:L'Académie Royale des Sciences
3245:10.1080/01621459.2000.10474227
3077:Journal of Molecular Evolution
2764:List of phylogenetics software
2758:List of phylogenetics software
2442:
2436:
2425:
2412:
2307:
2293:
2227:
2205:
2124:
2118:
1960:
1954:
1711:
1705:
1535:
1529:
1521:
1515:
1483:
1471:
1418:
1415:
1396:
1390:
1074:
1068:
1050:
1044:
1004:
999:
993:
985:
972:
967:
961:
953:
938:
933:
927:
919:
906:
901:
895:
887:
858:is accepted with probability:
742:be the current state in chain
724:
718:
632:
626:
535:
532:
520:
508:
496:
489:
480:
474:
278:
272:
1:
4836:10.1093/bioinformatics/btn575
4617:10.1093/bioinformatics/btl175
4378:10.1093/bioinformatics/btg180
4233:(8). Oxford, England: 754–5.
3046:Inference of ancestral areas.
609:{\displaystyle 2,3,\ldots ,m}
377:is the target density, while
287:{\displaystyle \pi _{j}(.)\ }
150:Metropolis–Hastings algorithm
144:Metropolis–Hastings algorithm
5333:10.1371/journal.pcbi.1000520
4786:10.1371/journal.pone.0029903
4525:10.1371/journal.pcbi.1003537
4303:Jukes TH, Cantor CR (1969).
4067:10.1080/15659801.2014.937900
1598:To estimate a branch length
5937:Computational phylogenetics
5674:Phylogenetic reconciliation
5581:Evolutionary biology portal
5537:Computational phylogenetics
5136:10.1016/j.ympev.2012.02.026
2962:Armadillo Workflow Platform
2854:PhyloBayes / PhyloBayes MPI
706:Metropolis-type step. Let
5958:
5312:PLOS Computational Biology
5034:10.1016/j.tree.2004.07.002
4504:PLOS Computational Biology
4080:Yang, Z. (18 April 2007).
3049:Molecular dating analysis.
3009:I.Milne, D.Lindner, et al.
3006:GUI wrapper around MrBayes
2987:GUI wrapper around MrBayes
2968:GUI wrapper around MrBayes
2761:
2714:Pitfalls and controversies
2526:{\displaystyle n_{2}=30\ }
2490:{\displaystyle n_{1}=70\ }
1688:{\displaystyle \lambda \ }
400:{\displaystyle \pi _{j}\ }
5892:
5864:Phylogenetic nomenclature
5568:
4199:10.1080/10635150390235485
3394:10.1038/s41559-017-0280-x
3037:Inference of phylogenies.
2981:Geneious (MrBayes plugin)
54:
45:Optimally search criteria
5482:MrBayes official website
5225:10.1186/1471-2148-13-214
5204:BMC Evolutionary Biology
5082:10.1186/1471-2148-10-246
5061:BMC Evolutionary Biology
4988:10.1186/1471-2148-12-102
4967:BMC Evolutionary Biology
4318:Yang Z (November 1993).
2882:Suchard MA, Redelings BD
2754:and other tree viewers.
1845:for unvaried sites, and
698:{\displaystyle T>1\ }
5744:Molecular phylogenetics
5694:Distance-matrix methods
5542:Molecular phylogenetics
4869:Journal of Biogeography
4718:The American Naturalist
4702:10.1111/1467-985X.00264
4281:10.1093/sysbio/46.4.590
4148:10.1073/pnas.1712673115
3663:10.1093/sysbio/27.4.401
3333:English translation by
2994:http://www.geneious.com
2886:http://www.bali-phy.org
2823:https://beast.community
2607:{\displaystyle w=0.5\ }
2578:{\displaystyle w=0.1\ }
1645:sites are unvaried and
1492:{\displaystyle (0,1)\ }
1457:{\displaystyle U_{1}\ }
1292:{\displaystyle t_{9}\ }
1262:{\displaystyle t_{1}\ }
1186:{\displaystyle t_{8}\ }
638:{\displaystyle \pi (.)}
341:, where the first one,
250:Metropolis-coupled MCMC
160:, is randomly selected.
39:Molecular phylogenetics
5764:Phylogenetics software
5678:Probabilistic methods
5627:Long branch attraction
5487:BEAST official website
3939:10.1073/pnas.212646199
3852:10.1093/sysbio/syaa012
3743:10.1098/rsbl.2016.0081
3694:10.1098/rspb.2016.2086
3514:Felsenstein J (2004).
3447:10.1093/biomet/57.1.97
3033:
3003:Phylogenetic inference
2794:Phylogenetic inference
2704:long branch attraction
2685:
2682:long branch attraction
2673:
2654:
2653:{\displaystyle 2000\ }
2637:and update the length
2631:
2608:
2579:
2550:
2527:
2491:
2452:
2393:
2370:
2344:
2318:
2263:
2237:
2096:
1932:
1836:
1743:
1689:
1666:
1639:
1612:
1584:
1493:
1458:
1428:
1355:
1293:
1263:
1233:
1210:
1187:
1145:
1110:
1084:
1017:
852:
829:
806:
759:
736:
699:
670:
639:
610:
565:
448:
401:
371:
335:
288:
113:
105:
88:inference of phylogeny
5557:Evolutionary taxonomy
5440:10.1093/sysbio/syx066
5275:10.1093/sysbio/syu006
5176:10.1093/sysbio/syr123
4929:10.1093/sysbio/syr062
4661:10.1093/molbev/msl170
4576:10.1093/molbev/msh112
4467:10.1093/molbev/mss075
4418:10.1093/sysbio/sys029
4099:10.1093/molbev/msm081
4031:10.1093/molbev/msg042
3990:10.1093/molbev/msg028
3516:Inferring phylogenies
3354:10.1214/ss/1177013620
3031:
3013:http://www.topali.org
2848:http://www.beast2.org
2679:
2671:
2655:
2632:
2609:
2580:
2551:
2528:
2492:
2453:
2394:
2371:
2345:
2319:
2264:
2238:
2097:
1933:
1837:
1744:
1690:
1667:
1665:{\displaystyle n_{2}}
1640:
1638:{\displaystyle n_{1}}
1613:
1594:Assessing convergence
1585:
1494:
1459:
1429:
1356:
1294:
1264:
1234:
1211:
1193:that separates taxa
1188:
1146:
1111:
1085:
1018:
853:
830:
807:
760:
737:
700:
671:
669:{\displaystyle 1/T\ }
640:
611:
566:
449:
402:
372:
336:
289:
111:
103:
5716:Three-taxon analysis
5622:Phylogenetic network
2837:Bayesian inference,
2641:
2618:
2589:
2560:
2537:
2501:
2465:
2406:
2380:
2369:{\displaystyle -w\ }
2354:
2331:
2276:
2250:
2112:
1948:
1852:
1756:
1699:
1676:
1649:
1622:
1602:
1506:
1468:
1438:
1365:
1303:
1273:
1243:
1220:
1197:
1167:
1120:
1097:
1031:
865:
839:
816:
769:
746:
710:
680:
649:
620:
582:
461:
411:
381:
345:
298:
259:
29:Evolutionary biology
5759:Phylogenetic signal
5324:2009PLSCB...5E0520L
5216:2013BMCEE..13..214S
5128:2012MolPE..64....1F
5073:2010BMCEE..10..246S
4979:2012BMCEE..12..102V
4881:2012JBiog..39..434A
4777:2012PLoSO...729903L
4516:2014PLSCB..10E3537B
4139:2018PNAS..115.1854Y
3930:2002PNAS...9916138S
3477:1953JChPh..21.1087M
3439:1970Bimka..57...97H
3386:2017NatEE...1.1446N
3341:Statistical Science
3335:Stigler SM (1986).
3089:1996JMolE..43..304R
2630:{\displaystyle 5\ }
2549:{\displaystyle w\ }
2392:{\displaystyle w\ }
2343:{\displaystyle U\ }
2262:{\displaystyle w\ }
1232:{\displaystyle B\ }
1209:{\displaystyle A\ }
1109:{\displaystyle m\ }
851:{\displaystyle j\ }
828:{\displaystyle i\ }
758:{\displaystyle j\ }
163:A neighbour tree, T
21:
5687:Bayesian inference
5682:Maximum likelihood
5428:Systematic Biology
5383:10.1214/15-AOAS821
5263:Systematic Biology
5163:Systematic Biology
4916:Systematic Biology
4406:Systematic Biology
4268:Systematic Biology
4186:Systematic Biology
3839:Systematic Biology
3688:(1847): 20162086.
3651:Systematic Zoology
3097:10.1007/BF02338839
3034:
2954:2020-02-19 at the
2945:M. Pagel, A. Meade
2686:
2674:
2650:
2627:
2604:
2575:
2546:
2523:
2487:
2448:
2389:
2366:
2340:
2314:
2259:
2233:
2092:
1928:
1832:
1739:
1685:
1662:
1635:
1608:
1580:
1489:
1454:
1424:
1351:
1289:
1259:
1229:
1206:
1183:
1141:
1106:
1080:
1013:
848:
825:
802:
755:
732:
695:
666:
635:
606:
561:
444:
397:
367:
331:
284:
156:An initial tree, T
114:
106:
49:Bayesian inference
5924:
5923:
5669:Maximum parsimony
5662:Inference methods
5610:Phylogenetic tree
3793:10.1111/cla.12205
3485:10.1063/1.1699114
3380:(10): 1446–1454.
3018:
3017:
2936:Bayes Phylogenies
2841:, multiple models
2649:
2626:
2603:
2574:
2545:
2522:
2486:
2447:
2388:
2365:
2339:
2313:
2258:
2232:
2105:or, alternately,
2091:
1927:
1831:
1738:
1695:. The density is
1684:
1611:{\displaystyle t}
1579:
1575:
1539:
1488:
1453:
1423:
1350:
1288:
1258:
1228:
1205:
1182:
1140:
1105:
1079:
1012:
1008:
847:
824:
801:
754:
731:
694:
665:
548:
545:
443:
396:
366:
330:
283:
83:
82:
35:Subclassification
5949:
5912:
5911:
5900:
5899:
5699:Neighbor-joining
5653:Ghost population
5583:
5578:
5577:
5516:
5509:
5502:
5493:
5470:
5469:
5459:
5419:
5413:
5412:
5402:
5362:
5356:
5355:
5345:
5335:
5303:
5297:
5296:
5286:
5254:
5248:
5247:
5237:
5227:
5195:
5189:
5188:
5178:
5154:
5148:
5147:
5111:
5105:
5104:
5094:
5084:
5052:
5046:
5045:
5017:
5011:
5010:
5000:
4990:
4958:
4952:
4951:
4941:
4931:
4907:
4901:
4900:
4864:
4858:
4857:
4847:
4815:
4809:
4808:
4798:
4788:
4756:
4750:
4749:
4713:
4707:
4706:
4704:
4680:
4674:
4673:
4663:
4636:
4630:
4629:
4619:
4595:
4589:
4588:
4578:
4554:
4548:
4547:
4537:
4527:
4495:
4489:
4488:
4478:
4446:
4440:
4439:
4429:
4397:
4391:
4390:
4380:
4356:
4350:
4349:
4339:
4315:
4309:
4308:
4300:
4294:
4293:
4283:
4259:
4253:
4252:
4242:
4218:
4212:
4211:
4201:
4177:
4171:
4170:
4160:
4150:
4133:(8): 1854–1859.
4118:
4112:
4111:
4101:
4092:(8): 1639–1655.
4077:
4071:
4070:
4050:
4044:
4043:
4033:
4009:
4003:
4002:
3992:
3968:
3962:
3961:
3951:
3941:
3924:(25): 16138–43.
3909:
3900:
3899:
3881:
3875:
3874:
3864:
3854:
3830:
3824:
3823:
3805:
3795:
3771:
3765:
3764:
3754:
3722:
3716:
3715:
3705:
3673:
3667:
3666:
3646:
3640:
3639:
3621:
3597:
3591:
3590:
3588:
3564:
3558:
3557:
3541:
3535:
3534:
3526:
3520:
3519:
3511:
3505:
3504:
3460:
3451:
3450:
3422:
3416:
3415:
3405:
3365:
3359:
3358:
3356:
3332:
3312:
3306:
3305:
3295:
3271:
3265:
3264:
3239:(450): 493–508.
3224:
3218:
3217:
3191:
3167:
3161:
3160:
3150:
3126:
3117:
3116:
3072:
2771:
2733:MrBayes software
2659:
2657:
2656:
2651:
2647:
2636:
2634:
2633:
2628:
2624:
2613:
2611:
2610:
2605:
2601:
2584:
2582:
2581:
2576:
2572:
2555:
2553:
2552:
2547:
2543:
2532:
2530:
2529:
2524:
2520:
2513:
2512:
2496:
2494:
2493:
2488:
2484:
2477:
2476:
2457:
2455:
2454:
2449:
2445:
2432:
2424:
2423:
2398:
2396:
2395:
2390:
2386:
2375:
2373:
2372:
2367:
2363:
2349:
2347:
2346:
2341:
2337:
2323:
2321:
2320:
2315:
2311:
2310:
2296:
2288:
2287:
2268:
2266:
2265:
2260:
2256:
2242:
2240:
2239:
2234:
2230:
2226:
2225:
2204:
2200:
2199:
2198:
2197:
2196:
2186:
2185:
2184:
2177:
2156:
2142:
2101:
2099:
2098:
2093:
2089:
2088:
2084:
2083:
2082:
2081:
2080:
2070:
2069:
2068:
2061:
2040:
2026:
2013:
2012:
2011:
2010:
1998:
1997:
1987:
1983:
1979:
1937:
1935:
1934:
1929:
1925:
1924:
1920:
1919:
1918:
1911:
1892:
1878:
1862:
1841:
1839:
1838:
1833:
1829:
1828:
1824:
1823:
1822:
1815:
1796:
1782:
1766:
1748:
1746:
1745:
1740:
1736:
1735:
1734:
1694:
1692:
1691:
1686:
1682:
1671:
1669:
1668:
1663:
1661:
1660:
1644:
1642:
1641:
1636:
1634:
1633:
1617:
1615:
1614:
1609:
1589:
1587:
1586:
1581:
1577:
1576:
1574:
1573:
1564:
1563:
1558:
1557:
1556:
1545:
1540:
1538:
1524:
1510:
1498:
1496:
1495:
1490:
1486:
1463:
1461:
1460:
1455:
1451:
1450:
1449:
1433:
1431:
1430:
1425:
1421:
1408:
1407:
1377:
1376:
1360:
1358:
1357:
1352:
1348:
1347:
1346:
1334:
1333:
1321:
1320:
1298:
1296:
1295:
1290:
1286:
1285:
1284:
1268:
1266:
1265:
1260:
1256:
1255:
1254:
1238:
1236:
1235:
1230:
1226:
1215:
1213:
1212:
1207:
1203:
1192:
1190:
1189:
1184:
1180:
1179:
1178:
1150:
1148:
1147:
1142:
1138:
1137:
1136:
1131:
1115:
1113:
1112:
1107:
1103:
1089:
1087:
1086:
1081:
1077:
1067:
1066:
1057:
1043:
1042:
1022:
1020:
1019:
1014:
1010:
1009:
1007:
1003:
1002:
984:
983:
971:
970:
952:
951:
941:
937:
936:
918:
917:
905:
904:
886:
885:
875:
857:
855:
854:
849:
845:
834:
832:
831:
826:
822:
811:
809:
808:
803:
799:
764:
762:
761:
756:
752:
741:
739:
738:
733:
729:
728:
727:
704:
702:
701:
696:
692:
675:
673:
672:
667:
663:
659:
644:
642:
641:
636:
615:
613:
612:
607:
570:
568:
567:
562:
546:
543:
539:
538:
507:
473:
472:
453:
451:
450:
445:
441:
406:
404:
403:
398:
394:
393:
392:
376:
374:
373:
368:
364:
357:
356:
340:
338:
337:
332:
328:
293:
291:
290:
285:
281:
271:
270:
223:when we are at T
75:
68:
61:
22:
5957:
5956:
5952:
5951:
5950:
5948:
5947:
5946:
5927:
5926:
5925:
5920:
5888:
5852:
5826:
5800:Symplesiomorphy
5778:
5720:
5657:
5586:
5579:
5572:
5566:
5530:Relevant fields
5525:
5520:
5478:
5473:
5421:
5420:
5416:
5364:
5363:
5359:
5318:(9): e1000520.
5305:
5304:
5300:
5256:
5255:
5251:
5197:
5196:
5192:
5156:
5155:
5151:
5113:
5112:
5108:
5054:
5053:
5049:
5019:
5018:
5014:
4960:
4959:
4955:
4909:
4908:
4904:
4866:
4865:
4861:
4817:
4816:
4812:
4758:
4757:
4753:
4715:
4714:
4710:
4682:
4681:
4677:
4638:
4637:
4633:
4597:
4596:
4592:
4569:(6): 1095–109.
4556:
4555:
4551:
4510:(4): e1003537.
4497:
4496:
4492:
4448:
4447:
4443:
4399:
4398:
4394:
4358:
4357:
4353:
4330:(6): 1396–401.
4317:
4316:
4312:
4302:
4301:
4297:
4261:
4260:
4256:
4220:
4219:
4215:
4179:
4178:
4174:
4120:
4119:
4115:
4079:
4078:
4074:
4052:
4051:
4047:
4011:
4010:
4006:
3970:
3969:
3965:
3911:
3910:
3903:
3896:
3883:
3882:
3878:
3832:
3831:
3827:
3773:
3772:
3768:
3737:(4): 20160081.
3731:Biology Letters
3724:
3723:
3719:
3675:
3674:
3670:
3648:
3647:
3643:
3599:
3598:
3594:
3566:
3565:
3561:
3543:
3542:
3538:
3529:Yang Z (2014).
3528:
3527:
3523:
3513:
3512:
3508:
3462:
3461:
3454:
3424:
3423:
3419:
3367:
3366:
3362:
3334:
3314:
3313:
3309:
3273:
3272:
3268:
3226:
3225:
3221:
3169:
3168:
3164:
3128:
3127:
3120:
3074:
3073:
3069:
3065:
3023:
2956:Wayback Machine
2766:
2760:
2735:
2716:
2666:
2639:
2638:
2616:
2615:
2587:
2586:
2558:
2557:
2535:
2534:
2504:
2499:
2498:
2468:
2463:
2462:
2415:
2404:
2403:
2378:
2377:
2352:
2351:
2329:
2328:
2279:
2274:
2273:
2248:
2247:
2211:
2188:
2162:
2160:
2134:
2130:
2110:
2109:
2072:
2046:
2044:
2018:
2014:
2002:
1989:
1971:
1967:
1966:
1946:
1945:
1896:
1870:
1866:
1850:
1849:
1800:
1774:
1770:
1754:
1753:
1720:
1697:
1696:
1674:
1673:
1652:
1647:
1646:
1625:
1620:
1619:
1600:
1599:
1596:
1565:
1548:
1546:
1525:
1511:
1504:
1503:
1466:
1465:
1441:
1436:
1435:
1399:
1368:
1363:
1362:
1338:
1325:
1312:
1301:
1300:
1276:
1271:
1270:
1246:
1241:
1240:
1218:
1217:
1195:
1194:
1170:
1165:
1164:
1157:
1123:
1118:
1117:
1095:
1094:
1058:
1034:
1029:
1028:
988:
975:
956:
943:
942:
922:
909:
890:
877:
876:
863:
862:
837:
836:
814:
813:
767:
766:
744:
743:
713:
708:
707:
678:
677:
647:
646:
618:
617:
580:
579:
495:
464:
459:
458:
409:
408:
384:
379:
378:
348:
343:
342:
296:
295:
262:
257:
256:
252:
244:
240:
234:
226:
222:
218:
214:
203:
199:
192:
185:
181:
177:
173:
166:
159:
146:
98:
79:
17:
12:
11:
5:
5955:
5953:
5945:
5944:
5939:
5929:
5928:
5922:
5921:
5919:
5918:
5906:
5893:
5890:
5889:
5887:
5886:
5881:
5876:
5871:
5866:
5860:
5858:
5854:
5853:
5851:
5850:
5845:
5840:
5834:
5832:
5828:
5827:
5825:
5824:
5823:
5822:
5817:
5812:
5804:
5803:
5802:
5797:
5786:
5784:
5780:
5779:
5777:
5776:
5774:Phylogeography
5771:
5766:
5761:
5756:
5751:
5746:
5741:
5736:
5728:
5726:
5725:Current topics
5722:
5721:
5719:
5718:
5713:
5712:
5711:
5706:
5701:
5691:
5690:
5689:
5684:
5676:
5671:
5665:
5663:
5659:
5658:
5656:
5655:
5650:
5649:
5648:
5638:
5629:
5624:
5619:
5618:
5617:
5607:
5606:
5605:
5594:
5592:
5591:Basic concepts
5588:
5587:
5585:
5584:
5569:
5567:
5565:
5564:
5559:
5554:
5549:
5544:
5539:
5533:
5531:
5527:
5526:
5521:
5519:
5518:
5511:
5504:
5496:
5490:
5489:
5484:
5477:
5476:External links
5474:
5472:
5471:
5434:(3): 384–399.
5414:
5377:(2): 969–991.
5357:
5298:
5249:
5190:
5149:
5106:
5047:
5012:
4953:
4922:(5): 596–615.
4902:
4859:
4824:Bioinformatics
4810:
4751:
4730:10.1086/503444
4708:
4675:
4631:
4610:(16): 2047–8.
4604:Bioinformatics
4590:
4549:
4490:
4461:(8): 1969–73.
4441:
4392:
4365:Bioinformatics
4351:
4310:
4295:
4274:(4): 590–621.
4254:
4227:Bioinformatics
4213:
4172:
4113:
4072:
4045:
4004:
3963:
3901:
3894:
3876:
3845:(5): 897–912.
3825:
3786:(4): 407–437.
3766:
3717:
3668:
3641:
3592:
3559:
3536:
3521:
3506:
3471:(6): 1087–92.
3452:
3417:
3360:
3347:(3): 359–378.
3307:
3286:(8): 754–755.
3280:Bioinformatics
3266:
3219:
3162:
3141:(7): 717–724.
3118:
3083:(3): 304–311.
3066:
3064:
3061:
3060:
3059:
3056:
3053:
3050:
3047:
3044:
3041:
3038:
3022:
3019:
3016:
3015:
3010:
3007:
3004:
3001:
2997:
2996:
2991:
2988:
2985:
2982:
2978:
2977:
2972:
2969:
2966:
2963:
2959:
2958:
2946:
2943:
2940:
2937:
2933:
2932:
2927:
2924:
2921:
2918:
2914:
2913:
2908:
2899:
2896:
2893:
2889:
2888:
2883:
2880:
2877:
2874:
2870:
2869:
2864:
2861:
2858:
2855:
2851:
2850:
2845:
2842:
2835:
2832:
2826:
2825:
2820:
2817:
2814:
2811:
2807:
2806:
2801:
2798:
2795:
2792:
2788:
2787:
2784:
2781:
2778:
2775:
2762:Main article:
2759:
2756:
2734:
2731:
2730:
2729:
2725:
2721:
2715:
2712:
2665:
2662:
2646:
2623:
2600:
2597:
2594:
2571:
2568:
2565:
2542:
2519:
2516:
2511:
2507:
2483:
2480:
2475:
2471:
2459:
2458:
2444:
2441:
2438:
2435:
2431:
2427:
2422:
2418:
2414:
2411:
2385:
2362:
2359:
2336:
2325:
2324:
2309:
2305:
2302:
2299:
2295:
2291:
2286:
2282:
2255:
2244:
2243:
2229:
2224:
2221:
2218:
2214:
2210:
2207:
2203:
2195:
2191:
2183:
2180:
2176:
2172:
2169:
2165:
2159:
2155:
2151:
2148:
2145:
2141:
2137:
2133:
2129:
2126:
2123:
2120:
2117:
2103:
2102:
2087:
2079:
2075:
2067:
2064:
2060:
2056:
2053:
2049:
2043:
2039:
2035:
2032:
2029:
2025:
2021:
2017:
2009:
2005:
2001:
1996:
1992:
1986:
1982:
1978:
1974:
1970:
1965:
1962:
1959:
1956:
1953:
1939:
1938:
1923:
1917:
1914:
1910:
1906:
1903:
1899:
1895:
1891:
1887:
1884:
1881:
1877:
1873:
1869:
1865:
1861:
1857:
1843:
1842:
1827:
1821:
1818:
1814:
1810:
1807:
1803:
1799:
1795:
1791:
1788:
1785:
1781:
1777:
1773:
1769:
1765:
1761:
1733:
1730:
1727:
1723:
1719:
1716:
1713:
1710:
1707:
1704:
1681:
1659:
1655:
1632:
1628:
1607:
1595:
1592:
1591:
1590:
1572:
1568:
1562:
1555:
1551:
1543:
1537:
1534:
1531:
1528:
1523:
1520:
1517:
1514:
1485:
1482:
1479:
1476:
1473:
1448:
1444:
1420:
1417:
1414:
1411:
1406:
1402:
1398:
1395:
1392:
1389:
1386:
1383:
1380:
1375:
1371:
1345:
1341:
1337:
1332:
1328:
1324:
1319:
1315:
1311:
1308:
1283:
1279:
1253:
1249:
1225:
1202:
1177:
1173:
1156:
1153:
1135:
1130:
1127:
1102:
1076:
1073:
1070:
1065:
1061:
1056:
1052:
1049:
1046:
1041:
1037:
1024:
1023:
1006:
1001:
998:
995:
991:
987:
982:
978:
974:
969:
966:
963:
959:
955:
950:
946:
940:
935:
932:
929:
925:
921:
916:
912:
908:
903:
900:
897:
893:
889:
884:
880:
873:
870:
844:
821:
798:
795:
792:
789:
786:
783:
780:
777:
774:
751:
726:
723:
720:
716:
691:
688:
685:
662:
658:
654:
634:
631:
628:
625:
605:
602:
599:
596:
593:
590:
587:
572:
571:
560:
557:
554:
551:
542:
537:
534:
531:
528:
525:
522:
519:
516:
513:
510:
506:
502:
498:
494:
491:
488:
485:
482:
479:
476:
471:
467:
440:
437:
434:
431:
428:
425:
422:
419:
416:
391:
387:
363:
360:
355:
351:
327:
324:
321:
318:
315:
312:
309:
306:
303:
280:
277:
274:
269:
265:
251:
248:
247:
246:
242:
238:
235:
232:
224:
220:
216:
212:
209:
208:
205:
201:
197:
196:If R < 1, T
194:
190:
187:
183:
179:
175:
171:
168:
164:
161:
157:
145:
142:
118:Bayes' theorem
104:Bayes' Theorem
97:
94:
81:
80:
78:
77:
70:
63:
55:
52:
51:
46:
42:
41:
36:
32:
31:
26:
25:Classification
15:
13:
10:
9:
6:
4:
3:
2:
5954:
5943:
5940:
5938:
5935:
5934:
5932:
5917:
5916:
5907:
5905:
5904:
5895:
5894:
5891:
5885:
5882:
5880:
5877:
5875:
5872:
5870:
5867:
5865:
5862:
5861:
5859:
5855:
5849:
5846:
5844:
5841:
5839:
5836:
5835:
5833:
5829:
5821:
5818:
5816:
5813:
5811:
5808:
5807:
5805:
5801:
5798:
5796:
5793:
5792:
5791:
5788:
5787:
5785:
5781:
5775:
5772:
5770:
5769:Phylogenomics
5767:
5765:
5762:
5760:
5757:
5755:
5752:
5750:
5747:
5745:
5742:
5740:
5739:DNA barcoding
5737:
5735:
5734:
5730:
5729:
5727:
5723:
5717:
5714:
5710:
5709:Least squares
5707:
5705:
5702:
5700:
5697:
5696:
5695:
5692:
5688:
5685:
5683:
5680:
5679:
5677:
5675:
5672:
5670:
5667:
5666:
5664:
5660:
5654:
5651:
5647:
5646:Ghost lineage
5644:
5643:
5642:
5639:
5637:
5633:
5630:
5628:
5625:
5623:
5620:
5616:
5613:
5612:
5611:
5608:
5604:
5601:
5600:
5599:
5596:
5595:
5593:
5589:
5582:
5576:
5571:
5563:
5560:
5558:
5555:
5553:
5550:
5548:
5545:
5543:
5540:
5538:
5535:
5534:
5532:
5528:
5524:
5523:Phylogenetics
5517:
5512:
5510:
5505:
5503:
5498:
5497:
5494:
5488:
5485:
5483:
5480:
5479:
5475:
5467:
5463:
5458:
5453:
5449:
5445:
5441:
5437:
5433:
5429:
5425:
5418:
5415:
5410:
5406:
5401:
5396:
5392:
5388:
5384:
5380:
5376:
5372:
5368:
5361:
5358:
5353:
5349:
5344:
5339:
5334:
5329:
5325:
5321:
5317:
5313:
5309:
5302:
5299:
5294:
5290:
5285:
5280:
5276:
5272:
5269:(3): 349–67.
5268:
5264:
5260:
5253:
5250:
5245:
5241:
5236:
5231:
5226:
5221:
5217:
5213:
5209:
5205:
5201:
5194:
5191:
5186:
5182:
5177:
5172:
5169:(3): 426–42.
5168:
5164:
5160:
5153:
5150:
5145:
5141:
5137:
5133:
5129:
5125:
5121:
5117:
5110:
5107:
5102:
5098:
5093:
5088:
5083:
5078:
5074:
5070:
5066:
5062:
5058:
5051:
5048:
5043:
5039:
5035:
5031:
5028:(9): 475–81.
5027:
5023:
5016:
5013:
5008:
5004:
4999:
4994:
4989:
4984:
4980:
4976:
4972:
4968:
4964:
4957:
4954:
4949:
4945:
4940:
4935:
4930:
4925:
4921:
4917:
4913:
4906:
4903:
4898:
4894:
4890:
4886:
4882:
4878:
4875:(3): 434–51.
4874:
4870:
4863:
4860:
4855:
4851:
4846:
4841:
4837:
4833:
4829:
4825:
4821:
4814:
4811:
4806:
4802:
4797:
4792:
4787:
4782:
4778:
4774:
4771:(1): e29903.
4770:
4766:
4762:
4755:
4752:
4747:
4743:
4739:
4735:
4731:
4727:
4724:(6): 808–25.
4723:
4719:
4712:
4709:
4703:
4698:
4695:(2): 155–88.
4694:
4690:
4686:
4679:
4676:
4671:
4667:
4662:
4657:
4654:(2): 412–26.
4653:
4649:
4645:
4641:
4635:
4632:
4627:
4623:
4618:
4613:
4609:
4605:
4601:
4594:
4591:
4586:
4582:
4577:
4572:
4568:
4564:
4560:
4553:
4550:
4545:
4541:
4536:
4531:
4526:
4521:
4517:
4513:
4509:
4505:
4501:
4494:
4491:
4486:
4482:
4477:
4472:
4468:
4464:
4460:
4456:
4452:
4445:
4442:
4437:
4433:
4428:
4423:
4419:
4415:
4412:(3): 539–42.
4411:
4407:
4403:
4396:
4393:
4388:
4384:
4379:
4374:
4370:
4366:
4362:
4355:
4352:
4347:
4343:
4338:
4333:
4329:
4325:
4321:
4314:
4311:
4306:
4299:
4296:
4291:
4287:
4282:
4277:
4273:
4269:
4265:
4258:
4255:
4250:
4246:
4241:
4236:
4232:
4228:
4224:
4217:
4214:
4209:
4205:
4200:
4195:
4192:(5): 665–73.
4191:
4187:
4183:
4176:
4173:
4168:
4164:
4159:
4154:
4149:
4144:
4140:
4136:
4132:
4128:
4124:
4117:
4114:
4109:
4105:
4100:
4095:
4091:
4087:
4083:
4076:
4073:
4068:
4064:
4060:
4056:
4049:
4046:
4041:
4037:
4032:
4027:
4024:(2): 248–54.
4023:
4019:
4015:
4008:
4005:
4000:
3996:
3991:
3986:
3983:(2): 255–66.
3982:
3978:
3974:
3967:
3964:
3959:
3955:
3950:
3945:
3940:
3935:
3931:
3927:
3923:
3919:
3915:
3908:
3906:
3902:
3897:
3895:9780878932825
3891:
3887:
3880:
3877:
3872:
3868:
3863:
3858:
3853:
3848:
3844:
3840:
3836:
3829:
3826:
3821:
3817:
3813:
3809:
3804:
3799:
3794:
3789:
3785:
3781:
3777:
3770:
3767:
3762:
3758:
3753:
3748:
3744:
3740:
3736:
3732:
3728:
3721:
3718:
3713:
3709:
3704:
3699:
3695:
3691:
3687:
3683:
3679:
3672:
3669:
3664:
3660:
3657:(4): 401–10.
3656:
3652:
3645:
3642:
3637:
3633:
3629:
3625:
3620:
3615:
3611:
3607:
3603:
3596:
3593:
3587:
3582:
3578:
3574:
3570:
3563:
3560:
3555:
3551:
3547:
3540:
3537:
3532:
3525:
3522:
3517:
3510:
3507:
3502:
3498:
3494:
3490:
3486:
3482:
3478:
3474:
3470:
3466:
3459:
3457:
3453:
3448:
3444:
3440:
3436:
3433:(1): 97–109.
3432:
3428:
3421:
3418:
3413:
3409:
3404:
3399:
3395:
3391:
3387:
3383:
3379:
3375:
3371:
3364:
3361:
3355:
3350:
3346:
3342:
3338:
3330:
3326:
3322:
3318:
3311:
3308:
3303:
3299:
3294:
3289:
3285:
3281:
3277:
3270:
3267:
3262:
3258:
3254:
3250:
3246:
3242:
3238:
3234:
3230:
3223:
3220:
3215:
3211:
3207:
3203:
3199:
3195:
3190:
3185:
3181:
3177:
3173:
3166:
3163:
3158:
3154:
3149:
3144:
3140:
3136:
3132:
3125:
3123:
3119:
3114:
3110:
3106:
3102:
3098:
3094:
3090:
3086:
3082:
3078:
3071:
3068:
3062:
3057:
3054:
3051:
3048:
3045:
3042:
3039:
3036:
3035:
3030:
3026:
3020:
3014:
3011:
3008:
3005:
3002:
2999:
2998:
2995:
2992:
2989:
2986:
2983:
2980:
2979:
2976:
2973:
2970:
2967:
2964:
2961:
2960:
2957:
2953:
2950:
2947:
2944:
2941:
2938:
2935:
2934:
2931:
2928:
2925:
2922:
2919:
2916:
2915:
2912:
2909:
2907:
2903:
2900:
2897:
2894:
2891:
2890:
2887:
2884:
2881:
2878:
2875:
2872:
2871:
2868:
2865:
2862:
2859:
2856:
2853:
2852:
2849:
2846:
2843:
2840:
2836:
2833:
2831:
2828:
2827:
2824:
2821:
2818:
2815:
2812:
2809:
2808:
2805:
2802:
2799:
2796:
2793:
2790:
2789:
2786:Website link
2785:
2782:
2779:
2776:
2773:
2772:
2769:
2765:
2757:
2755:
2751:
2747:
2743:
2741:
2732:
2726:
2722:
2718:
2717:
2713:
2711:
2707:
2705:
2700:
2695:
2690:
2683:
2678:
2670:
2663:
2661:
2644:
2621:
2598:
2595:
2592:
2569:
2566:
2563:
2540:
2517:
2514:
2509:
2505:
2481:
2478:
2473:
2469:
2439:
2433:
2429:
2420:
2416:
2409:
2402:
2401:
2400:
2383:
2360:
2357:
2334:
2303:
2300:
2297:
2289:
2284:
2280:
2272:
2271:
2270:
2253:
2222:
2219:
2216:
2212:
2208:
2201:
2193:
2189:
2181:
2178:
2174:
2170:
2167:
2163:
2157:
2153:
2149:
2146:
2143:
2139:
2135:
2131:
2127:
2121:
2115:
2108:
2107:
2106:
2085:
2077:
2073:
2065:
2062:
2058:
2054:
2051:
2047:
2041:
2037:
2033:
2030:
2027:
2023:
2019:
2015:
2007:
2003:
1999:
1994:
1990:
1984:
1980:
1976:
1972:
1968:
1963:
1957:
1951:
1944:
1943:
1942:
1921:
1915:
1912:
1908:
1904:
1901:
1897:
1893:
1889:
1885:
1882:
1879:
1875:
1871:
1867:
1863:
1859:
1855:
1848:
1847:
1846:
1825:
1819:
1816:
1812:
1808:
1805:
1801:
1797:
1793:
1789:
1786:
1783:
1779:
1775:
1771:
1767:
1763:
1759:
1752:
1751:
1750:
1731:
1728:
1725:
1721:
1717:
1714:
1708:
1702:
1679:
1657:
1653:
1630:
1626:
1605:
1593:
1570:
1566:
1560:
1553:
1549:
1541:
1532:
1526:
1518:
1512:
1502:
1501:
1500:
1480:
1477:
1474:
1446:
1442:
1412:
1409:
1404:
1400:
1393:
1387:
1384:
1381:
1378:
1373:
1369:
1343:
1339:
1335:
1330:
1326:
1322:
1317:
1313:
1309:
1306:
1281:
1277:
1251:
1247:
1223:
1200:
1175:
1171:
1161:
1154:
1152:
1133:
1100:
1091:
1071:
1063:
1059:
1054:
1047:
1039:
1035:
996:
989:
980:
976:
964:
957:
948:
944:
930:
923:
914:
910:
898:
891:
882:
878:
871:
868:
861:
860:
859:
842:
819:
796:
793:
790:
787:
784:
781:
778:
775:
772:
749:
721:
714:
689:
686:
683:
660:
656:
652:
645:to the power
629:
623:
603:
600:
597:
594:
591:
588:
585:
577:
558:
555:
552:
549:
540:
529:
526:
523:
517:
514:
511:
504:
500:
492:
486:
483:
477:
469:
465:
457:
456:
455:
438:
435:
432:
429:
426:
423:
420:
417:
414:
389:
385:
361:
358:
353:
349:
325:
322:
319:
316:
313:
310:
307:
304:
301:
275:
267:
263:
249:
236:
230:
229:
228:
206:
195:
188:
169:
162:
155:
154:
153:
151:
143:
141:
138:
133:
129:
127:
121:
119:
110:
102:
95:
93:
90:
89:
76:
71:
69:
64:
62:
57:
56:
53:
50:
47:
43:
40:
37:
33:
30:
27:
23:
5913:
5901:
5874:Sister group
5857:Nomenclature
5820:Autapomorphy
5815:Synapomorphy
5795:Plesiomorphy
5783:Group traits
5731:
5686:
5603:Cladogenesis
5598:Phylogenesis
5431:
5427:
5417:
5374:
5370:
5360:
5315:
5311:
5301:
5266:
5262:
5252:
5207:
5203:
5193:
5166:
5162:
5152:
5119:
5115:
5109:
5064:
5060:
5050:
5025:
5021:
5015:
4970:
4966:
4956:
4919:
4915:
4905:
4872:
4868:
4862:
4830:(1): 126–7.
4827:
4823:
4813:
4768:
4764:
4754:
4721:
4717:
4711:
4692:
4688:
4678:
4651:
4647:
4634:
4607:
4603:
4593:
4566:
4562:
4552:
4507:
4503:
4493:
4458:
4454:
4444:
4409:
4405:
4395:
4368:
4364:
4354:
4327:
4323:
4313:
4304:
4298:
4271:
4267:
4257:
4230:
4226:
4216:
4189:
4185:
4175:
4130:
4126:
4116:
4089:
4085:
4075:
4058:
4054:
4048:
4021:
4017:
4007:
3980:
3976:
3966:
3921:
3917:
3885:
3879:
3842:
3838:
3828:
3783:
3779:
3769:
3734:
3730:
3720:
3685:
3681:
3671:
3654:
3650:
3644:
3609:
3605:
3595:
3579:(6): 750–9.
3576:
3572:
3562:
3545:
3539:
3530:
3524:
3515:
3509:
3468:
3464:
3430:
3426:
3420:
3377:
3373:
3363:
3344:
3340:
3320:
3316:
3310:
3283:
3279:
3269:
3236:
3232:
3222:
3179:
3175:
3165:
3138:
3134:
3080:
3076:
3070:
3024:
3021:Applications
2767:
2752:
2748:
2744:
2740:NEXUS format
2736:
2708:
2691:
2687:
2460:
2326:
2245:
2104:
1940:
1844:
1597:
1162:
1158:
1092:
1027:However, if
1025:
573:
253:
210:
147:
137:Markov chain
134:
130:
122:
115:
85:
84:
5869:Crown group
5831:Group types
5562:Systematics
5122:(1): 1–11.
4939:10261/34829
4061:(1): 41–4.
3803:11336/57822
3612:(1): 1–12.
3329:10010866843
3323:: 621–656.
3182:(1): 1–12.
2777:Description
2680:Example of
189:If R ≥ 1, T
5931:Categories
5547:Cladistics
5210:(1): 214.
5067:(1): 246.
4973:(1): 102.
3780:Cladistics
3606:Biometrics
3427:Biometrika
3176:Biometrics
3063:References
2461:Example:
576:cold chain
5884:Supertree
5848:Polyphyly
5843:Paraphyly
5838:Monophyly
5810:Apomorphy
5790:Primitive
5733:PhyloCode
5615:Cladogram
5448:1063-5157
5391:1932-6157
4746:205984494
3812:0748-3007
3261:122459537
2699:bootstrap
2421:⋆
2358:−
2285:⋆
2220:λ
2217:−
2209:λ
2168:−
2147:−
2052:−
1902:−
1883:−
1806:−
1729:λ
1726:−
1718:λ
1680:λ
1554:⋆
1542:×
1410:−
1394:λ
1388:
1374:⋆
1072:θ
1060:π
1048:θ
1036:π
990:θ
977:π
958:θ
945:π
924:θ
911:π
892:θ
879:π
869:α
791:…
715:θ
624:π
598:…
550:λ
527:−
518:λ
493:θ
487:π
478:θ
466:π
433:…
386:π
362:π
350:π
320:…
264:π
86:Bayesian
5903:Category
5806:Derived
5552:Taxonomy
5466:28950376
5409:27053974
5352:19779555
5293:24510972
5244:24283922
5185:22223444
5144:22425729
5101:20701742
5042:16701310
5007:22741602
4948:21856636
4854:18984599
4805:22253821
4765:PLOS ONE
4738:16685633
4670:17095535
4626:16679334
4585:15014145
4544:24722319
4485:22367748
4436:22357727
4387:12912839
4290:11975335
4249:11524383
4208:14530133
4167:29432193
4108:17488737
4040:12598692
3999:12598693
3958:12451182
3871:32073641
3820:34649370
3761:27095266
3712:28123088
3628:11318142
3554:26603816
3412:28983516
3302:11524383
3206:11318142
2952:Archived
2873:Bali-Phy
2839:packages
1434:, where
204:is kept.
5915:Commons
5641:Lineage
5457:5920329
5400:4820077
5343:2740835
5320:Bibcode
5284:4361715
5235:3850475
5212:Bibcode
5124:Bibcode
5092:2930640
5069:Bibcode
4998:3582467
4975:Bibcode
4897:4152245
4877:Bibcode
4845:2638937
4796:3256230
4773:Bibcode
4535:3985171
4512:Bibcode
4476:3408070
4427:3329765
4346:8277861
4158:5828583
4135:Bibcode
3926:Bibcode
3862:7440746
3752:4881353
3703:5310032
3501:1046577
3493:4390578
3473:Bibcode
3435:Bibcode
3403:5624502
3382:Bibcode
3253:2669394
3198:2533889
3157:9214744
3113:8269826
3105:8703097
3085:Bibcode
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