On investigating the statistical properties of the populous path algorithm by computer simulation

Summary Goodman et al.'s (1974) populous path algorithm for estimating hidden mutational change in protein evolution is designed to be used as an adjunct to the maximum parsimony method. When the algorithm is so used, the augmented maximum parsimony distances, far from being overestimates, are underestimates of the actual number of nucleotide substitutions which occur in Tateno and Nei's (1978) computer simulation by the Poisson process model, even when the simulation is carried out at two and a half times the sequence density. Although underestimates, our evidence shows that they are nevertheless more accurate than estimates obtained by a Poisson correction. In the maximum parsimony reconstruction, there is a bias towards overrepresenting the number of shared nucleotide identities between adjacent ancestral and descendant nodal sequences with the bias being stronger in those portions of the evolutionary tree sparser in sequence data. Because of this particular property of maximum parsimony reconstructed sequences, the conclusions of Tateno and Nei concerning the statistical properties of the populous path algorithm are invalid. We conclude that estimates of protein evolutionary rates by the maximum parsimony - populous path approach will become more accurate rather than less as larger numbers of closely related species are included in the analysis.     

Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences: II. Four taxa without a molecular clock

Summary The statistical properties of sample estimation and bootstrap estimation of phylogenetic variability from a sample of nucleotide sequences were studied by considering model trees of three taxa with an outgroup. The cases of constant and varying rates of nucleotide substitution were compared. From sequences obtained by simulation, phylogenetic trees were constructed by using the maximum parsimony (MP) and neighbor joining (NJ) methods. The effectiveness and consistency of the MP method were studied in terms of proportions of informative sites. The results of simulation showed that bootstrap estimation of the confidence level for an inferred phylogeny can be used even under unequal rates of evolution if the rate differences are not large so that the MP method is not misleading. The condition under which the MP method becomes misleading (inconsistent) is more stringent for slowly evolving sequences than for rapidly evolving ones, and it also depends on the length of the internal branch. If the rate differences are large so that the MP method becomes consistently misleading, then bootstrap estimation will reinforce an erroneous conclusion on topology. Similar conclusions apply to the NJ method with uncorrected distances. The NJ method with corrected distances performs poorly when the sequence length is short but can avoid the inconsistency problem if the sequence length is long and if the distances can be estimated accurately.Offprint requests to: W.-H. Li     

Phylogenetic analysis using parsimony and likelihood methods

The assumptions underlying the maximum-parsimony (MP) method of phylogenetic tree reconstruction were intuitively examined by studying the way the method works. Computer simulations were performed to corroborate the intuitive examination. Parsimony appears to involve very stringent assumptions concerning the process of sequence evolution, such as constancy of substitution rates between nucleotides, constancy of rates across nucleotide sites, and equal branch lengths in the tree. For practical data analysis, the requirement of equal branch lengths means similar substitution rates among lineages (the existence of an approximate molecular clock), relatively long interior branches, and also few species in the data. However, a small amount of evolution is neither a necessary nor a sufficient requirement of the method. The difficulties involved in the application of current statistical estimation theory to tree reconstruction were discussed, and it was suggested that the approach proposed by Felsenstein (1981,J. Mol. Evol. 17: 368–376) for topology estimation, as well as its many variations and extensions, differs fundamentally from the maximum likelihood estimation of a conventional statistical parameter. Evidence was presented showing that the Felsenstein approach does not share the asymptotic efficiency of the maximum likelihood estimator of a statistical parameter. Computer simulations were performed to study the probability that MP recovers the true tree under a hierarchy of models of nucleotide substitution; its performance relative to the likelihood method was especially noted. The results appeared to support the intuitive examination of the assumptions underlying MP. When a simple model of nucleotide substitution was assumed to generate data, the probability that MP recovers the true topology could be as high as, or even higher than, that for the likelihood method. When the assumed model became more complex and realistic, e.g., when substitution rates were allowed to differ between nucleotides or across sites, the probability that MP recovers the true topology, and especially its performance relative to that of the likelihood method, generally deteriorates. As the complexity of the process of nucleotide substitution in real sequences is well recognized, the likelihood method appears preferable to parsimony. However, the development of a statistical methodology for the efficient estimation of the tree topology remains a difficult open problem.     

Molecular phylogeny of the New World monkeys (Platyrrhini,primates) based on two unlinked nuclear genes: IRBP intron 1 and ϵ-globin sequences

Nuclear sequences of the 1.8 kilobase (kb) long intron 1 of the interstitial retinol-binding protein gene (IRBP), previously determined for 11 of the 16 extant genera of New World monkeys (superfamily Ceboidea, infraorder Platyrrhini), have now been determined for the remaining 5 genera. The maximum parsimony trees found, first with IRBP sequences alone and then with tandemly combined IRBP and ϵ-globin gene sequences from the same species, supported a provisional cladistic classification with the following clusters. Subtribes Callitrichina (Callithrix, Cebuella), Callimiconina (Callimico), Leontopithecina (Leontopithecus) and Saguina (Saguinus) constitute subfamily Callitrichinae, and subfamilies Callitrichinae, Aotinae (Aotus), and Cebinae (Cebus, Saimiri) constitute family Cebidae. Subtribes Chiropotina (Chiropotes, Cacajao) and Pitheciina (Pithecia) constitute tribe Pitheciini; and tribes Pitheciini and Callicebini (Callicebus) constitute subfamily Pitheciinae. Subtribes Brachytelina (Brachyteles, Lagothrix) and Atelina (Ateles) constitute tribe Atelini, and tribes Atelini and Alouattini (Alouatta) constitute subfamily Atelinae. The parsimony results were equivocal as to whether Pitheciinae should be grouped with Atelinae in family Atelidae or have its own family Pitheciidae. The cladistic groupings of extant ceboids were also examined by different stochastic evolutionary models that employed the same stochastic process of nucleotide substitutions but alternative putative phylogenetic trees on which the nucleotide substitutions occurred. Each model, i.e., each different tree, predicted a different multinomial distribution of nucleotide character patterns for the contemporary sequences. The predicted distributions that were closest to the actual observed distributions identified the best fitting trees. The cladistic relationships depicted in these best fitting trees agreed in almost all cases with those depicted in the maximum parsimony trees. © 1996 Wiley-Liss, Inc.     

Nucleotide sequence of the beta-globin genes in gorilla and macaque: The origin of nucleotide polymorphisms in human

Summary Part of the beta-globin genes ofMacaca cynomolgus andGorilla gorilla has been cloned and sequenced. Ten putatively neutral nucleotide polymorphisms have been described at the beta-globin locus in humans. They are associated in seven combinations, which define seven different haplotypes of the beta-globin gene: four major frameworks—1, 2, 3, and 3^*—and three minor frameworks, which we term KI1, KA1, and OR1. The nucleotide sequences of these frameworks are compared with those of homologous sequences in chimpanzee, colobus, macaque, and gorilla. This comparison provides strong evidence that framework 2 was the earliest framework in the human lineage. From framework 2, a rooted parsimonious tree for the six other frameworks is constructed. This phylogenetic tree is discussed in terms of the evolution of nucleotide polymorphisms as well as in terms of genetic affinities between human populations.For each position at which there is base difference in comparing human, gorilla, and chimpanzee beta-globin genes, the phyletic lineage where the corresponding substitution occurred has been identified using the maximum parsimony procedure. The data provide evidence that polymorphisms may represent a significant component of differences between closely related species. If so, nucleotide polymorphisms may strongly bias estimates of small evolutionary distances.     

Was globin evolution very rapid in its early stages?: A dubious case against the rate-constancy hypothesis

Summary Goodman et al's (1975) claim of accelerated evolution in the early stages of globin evolution is based on an erroneous assignment of the time of divergence of vertebrate myoglobin and hemoglobin. When this is corrected, there is no basis for their claim. The data are much more consistent with the nearly constant rate expected on the neutral mutation-random drift hypothesis than with the uneven rates expected if most amino acid changes were caused by substitution of favorable mutants through Darwinian selection. In addition, the majority of the codons determined by their maximum parsimony method have turned out to be wrong when compared to the actual nucleotide sequences of rabbit and human hemoglobins determined by direct sequencing.Contribution No. 1314 from the National Institute of Genetics, Mishima, 411 Japan.     

Estimating the pattern of nucleotide substitution

Knowledge of the pattern of nucleotide substitution is important both to our understanding of molecular sequence evolution and to reliable estimation of phylogenetic relationships. The method of parsimony analysis, which has been used to estimate substitution patterns in real sequences, has serious drawbacks and leads to results difficult to interpret. In this paper a model-based maximum likelihood approach is proposed for estimating substitution patterns in real sequences. Nucleotide substitution is assumed to follow a homogeneous Markov process, and the general reversible process model (REV) and the unrestricted model without the reversibility assumption are used. These models are also applied to examine the adequacy of the model of Hasegawa et al. (J. Mol. Evol. 1985;22:160–174) (HKY85). Two data sets are analyzed. For the -globin pseudogenes of six primate species, the REV model fits the data much better than HKY85, while, for a segment of mtDNA sequences from nine primates, REV cannot provide a significantly better fit than HKY85 when rate variation over sites is taken into account in the models. It is concluded that the use of the REV model in phylogenetic analysis can be recommended, especially for large data sets or for sequences with extreme substitution patterns, while HKY85 may be expected to provide a good approximation. The use of the unrestricted model does not appear to be worthwhile.     

Should we be worried about long-branch attraction in real data sets? Investigations using metazoan 18S rDNA

Although long-branch attraction (LBA) is frequently cited as the cause of anomalous phylogenetic groupings, few examples of LBA involving real sequence data are known. We have found several cases of probable LBA by analyzing subsamples from an alignment of 18S rDNA sequences for 133 metazoans. In one example, maximum parsimony analysis of sequences from two rotifers, a ctenophore, and a polychaete annelid resulted in strong support for a tree grouping two "long-branch taxa" (a rotifer and the ctenophore). Maximum-likelihood analysis of the same sequences yielded strong support for a more biologically reasonable "rotifer monophyly" tree. Attempts to break up long branches for problematic subsamples through increased taxon sampling reduced, but did not eliminate, LBA problems. Exhaustive analyses of all quartets for a subset of 50 sequences were performed in order to compare the performance of maximum likelihood, equal-weights parsimony, and two additional variants of parsimony; these methods do differ substantially in their rates of failure to recover trees consistent with well established, but highly unresolved phylogenies. Power analyses using simulations suggest that some incorrect inferences by maximum parsimony are due to statistical inconsistency and that when estimates of central branch lengths for certain quartets are very low, maximum-likelihood analyses have difficulty recovering accepted phylogenies even with large amounts of data. These examples demonstrate that LBA problems can occur in real data sets, and they provide an opportunity to investigate causes of incorrect inferences.     

Testing Introgressive Hybridization Hypotheses Using Statistical Network Analysis of Nuclear and Cytoplasmic Haplotypes in the Leaf Beetle Timarcha goettingensis Species Complex

Previous studies of leaf beetles (Chrysomelidae) in the Timarcha goettingensis species complex using mitochondrial (cox2) and nuclear (ITS-2 rRNA) markers revealed two main clades confined to the Iberian Peninsula and the rest of Europe but showing incongruent distributions indicative of gene exchange between both groups. Because of the anastomosing nature of hybridization, which disrupts the cladistic structure of character variation, phylogenetic trees might be inappropriate to represent and study this process. Here we test for evidence of hybridization in the T. goettingensis complex by analyzing the extra homoplasy arising in hybrid genomes from the simultaneous analysis of genetically independent markers. Haplotype networks obtained by Templeton’s statistical parsimony analysis were generated for combined (concatenated) cox2 and ITS-2 sequences from 167 individuals of the T. goettingensis complex. Networks were used to detect runs of homoplasious characters physically clustered along a nucleotide sequence, as evidence for recombination between both gene partitions. A hypergeometric tail probability for the chance occurrence of physically clustered character changes on the connections linking networks of genotypes was applied. The test recognized two instances of statistically significant clustering, indicating the presence of cox2–ITS-2 mosaic genotypes and reticulation of both main T. goettingensis clades, supporting the reticulate origin of samples of T. maritima in southwestern France and T. sinuatocollis/T. monserratensis in the eastern Pyrenees. Although the assessment of reticulation in DNA sequences does not provide direct proof for hybridization, the geographical distribution of mosaic genotypes in the vicinity of “pure” genotypes supports the effect of gene flow between the two divergent lineages. The study demonstrates the utility of statistical parsimony networks for the detection of hybrids in the growing number of phylogeographic studies based on multiple gene markers. [Reviewing Editor: Dr. Rafael Zardoya]     

A phylogenetic study of the palm family (Palmae) based on chloroplast DNA sequences from thetrnL —trnF region

Phylogenies of the palm family based on DNA sequences from thetrnL —trnF region of the chloroplast genome are presented. Although the region is highly conserved in palms and relatively few sites in the aligned data matrix are parsimony informative, a variety of relationships among members of the family are revealed by the analyses, some of which are congruent with the current classification of the palms, and others which are not. However, consensus trees contain high levels of ambiguosity, partly due to the inadequate numbers of informative characters in the dataset. Additional data are required before well resolved palm phylogenies can be generated.     

The evolution of muscular parvalbumins investigated by the maximum parsimony method

Summary Phylogenetic trees requiring the lowest sum of nucleotide replacements and gene duplicative events were constructed from the amino acid sequence data on ten gnathostome parvalbumins (PAR) and two related myofibrillar proteins troponin-C (TNC) and myosin alkali-light-chain (ALC). The origin and differentiation of the structural domains within these proteins were also investigated by the maximum parsimony method and by an alignment statistic for identifying evolutionarily related protein sequences. The results suggest, in agreement with the Weeds-McLachlan model, that tandem duplications in a precursor gene caused a primordial one-domain polypeptide (consisting of two helices with a calcium binding region in between) to double and then quadruple in size. Duplications of the gene coding for this four domain (I–II–III–IV) protein in an early metazoan, pre-gnathostome lineage gave rise to the separate loci for TNC, ALC, and PAR. TNC, which alone retained the Ca-binding function in each of its four domains, evolved much more slowly than either the ALC or PAR lineages. In the PAR lineage the I–II–III–IV structure was degraded, presumably by a partial gene deletion, to the II–III–IV structure during descent to the gnathostome ancestor of parvalbumins. Also during this period the mid region in domain II lost its Ca-binding function and, as it did so, evolved at an accelerated rate over other regions, a pattern indicative of positive selection for a change in function. In turn, from the gnathostome ancestor to the present, the mid regions of domains III and IV, which each retained Ca-bindung function, evolved much more slowly than other regions, a pattern indicative of stabilizing selection for preservation of function. Between the gnathostome and teleost-tetrapod ancestor a gene duplication separated the parvalbumins into an-lineage and a-lineage. During this early vertebrate period PAR genes evolved at the extremely fast rate of 89 nucleotide replacements per 100 codons per 10⁸ years (i.e. 89 NR %), but from the teleost-tetrapod ancestor to the present, both- and-PAR lineages evolved at a much slower rate, about 8 NR %. The use of-parvalbumins as phylogenetic markers was complicated by presumptive evidence that paralogous (i.e. duplication dependent) gene lineages occur within this group. As a final point, in the genealogy of TNC, ALC, and PAR lineages, a non-random pattern of nucleotide replacements was observed between the reconstructed ancestral and descendant mRNA sequences. The pattern was similar to that observed for other protein genealogies and seems to reflect a bias in the genetic code for guanine to adenine and adenine to guanine transitions (especially at the first nucleotide position of the RNA codons) to produce amino acid substitutions which are compatible with the preservation of protein three-dimensional structure.     

Heterogeneity of nucleotide frequencies among evolutionary lineages and phylogenetic inference

A major assumption of many molecular phylogenetic methods is the homogeneity of nucleotide frequencies among taxa, which refers to the equality of the nucleotide frequency bias among species. Changes in nucleotide frequency among different lineages in a data set are thought to lead to erroneous phylogenetic inference because unrelated clades may appear similar because of evolutionarily unrelated similarities in nucleotide frequencies. We tested the effects of the heterogeneity of nucleotide frequency bias on phylogenetic inference, along with the interaction between this heterogeneity and stratified taxon sampling, by means of computer simulations using evolutionary parameters derived from genomic databases. We found that the phylogenetic trees inferred from data sets simulated under realistic, observed levels of heterogeneity for mammalian genes were reconstructed with accuracy comparable to those simulated with homogeneous nucleotide frequencies; the results hold for Neighbor-Joining, minimum evolution, maximum parsimony, and maximum-likelihood methods. The LogDet distance method, specifically designed to deal with heterogeneous nucleotide frequencies, does not perform better than distance methods that assume substitution pattern homogeneity among sequences. In these specific simulation conditions, we did not find a significant interaction between phylogenetic accuracy and substitution pattern heterogeneity among lineages, even when the taxon sampling is increased.     

Reconstruction of ancestral sequences by the inferential method,a tool for protein engineering studies

This paper describes the inferential method, an approach for reconstructing protein and nucleotide sequences of ancestral species, starting from known, homologous, contemporary sequences. The method requires knowledge of the topology of the phylogenetic tree, whose nodes are the species to whom the reconstructed sequences belong.The method has been tested by computer simulation of speciation and nucleotide substitutions, starting from a single ancestral sequence, and by subsequent reconstruction of nodal sequences. Results have shown that reconstructions obtained by the inferential method are affected by limited error frequencies, which (1) are proportional to the squares of nucleotide substitution rates and of internodal distances, and (2) are little influenced by non-uniformity of transformation rates of nucleotides.Furthermore, good agreement of the results has been obtained by comparing protein-sequence reconstructions carried out with the inferential method with those obtained using the maximum parsimony method in two different cases: e.g., a reconstruction of simulated sequences and a reconstruction of mammalian ribonuclease sequences.Abbreviations used MP maximum parsimony method - ML maximum likelihood method - IM inferential method - MY millions of years - N-tree natural-like phylogenetic tree - E-tree equibranched phylogenetic tree - EA percentage number of erroneous amino acids in a reconstructed sequence - EC percentage number of erroneous codons in a reconstructed sequence - t _n time interval between a P- and its - F-sequence nucleotides and amino acids are indicated by their I.U.B. codes (N.C.-I.U.B., 1985) Correspondence to: A. Di Donato     

Relative efficiencies of the maximum parsimony and distance-matrix methods in obtaining the correct phylogenetic tree

The relative efficiencies of the maximum parsimony (MP) and distance-matrix methods in obtaining the correct tree (topology) were studied by using computer simulation. The distance-matrix methods examined are the neighbor-joining, distance-Wagner, Tateno et al. modified Farris, Faith, and Li methods. In the computer simulation, six or eight DNA sequences were assumed to evolve following a given model tree, and the evolutionary changes of the sequences were followed. Both constant and varying rates of nucleotide substitution were considered. From the sequences thus obtained, phylogenetic trees were constructed using the six tree-making methods and compared with the model (true) tree. This process was repeated 300 times for each different set of parameters. The results obtained indicate that when the number of nucleotide substitutions per site is small and a relatively small number of nucleotides are used, the probability of obtaining the correct topology (P1) is generally lower in the MP method than in the distance-matrix methods. The P1 value for the MP method increases with increasing number of nucleotides but is still generally lower than the value for the NJ or DW method. Essentially the same conclusion was obtained whether or not the rate of nucleotide substitution was constant or whether or not a transition bias in nucleotide substitution existed. The relatively poor performance of the MP method for these cases is due to the fact that information from singular sites is not used in this method. The MP method also showed a relatively low P1 value when the model of varying rate of nucleotide substitution was used and the number of substitutions per site was large. However, the MP method often produced cases in which the correct tree was one of several equally parsimonious trees. When these cases were included in the class of "success," the MP method performed better than the other methods, provided that the number of nucleotide substitutions per site was small.     

Rate acceleration and long-branch attraction in a conserved gene of cryptic daphniid (Crustacea) species.

The nuclear large subunit (LSU) rRNA gene is a rich source of phylogenetic characters because of its large size, mosaic of slowly and rapidly evolving regions, and complex secondary structure variation. Nevertheless, many studies have indicated that inconsistency, bias, and gene-specific error (e.g., within-individual gene family variation, cryptic sequence simplicity, and sequence coevolution) can complicate animal phylogenies based on LSU rDNA sequences. However, most of these studies sampled small gene fragments from expansion segments--among animals only five nonchordate complete LSU sequences are published. In this study, we sequenced near-complete nuclear LSU genes from 11 representative daphniids (Crustacea). The daphniid expansion segment V6 was larger and showed more length variation (90-351 bp) than is found in all other reported LSU V6 sequences. Daphniid LSU (without the V6 region) phylogenies generally agreed with the existing phylogenies based on morphology and mtDNA sequences. Nevertheless, a major disagreement between the LSU and the expected trees involved a positively misleading association between the two taxa with the longest branches, Daphnia laevis and D. occidentalis. Both maximum parsimony (MP) and maximum likelihood (ML) optimality criteria recovered this association, but parametric simulations indicated that MP was markedly more sensitive to this bias than ML. Examination of data partitions indicated that the inconsistency was caused by increased nucleotide substitution rates in the branches leading to D. laevis and D. occidentalis rather than among-taxon differences in base composition or distribution of sites that are free to vary. These results suggest that lineage-specific rate acceleration can lead to long-branch attraction even in the conserved genes of animal species that are almost morphologically indistinguishable.     

Frequent inconsistency of parsimony under a simple model of cladogenesis

Although the conditions under which the parsimony method becomes inconsistent have been studied for almost two decades, the probability that the parsimony method would encounter conditions causing inconsistency under simple models of cladogenesis is unknown. Here, we examine the statistical behavior of the parsimony method under a birth-death model of cladogenesis, when the molecular clock holds. The parsimony method can become inconsistent a high proportion of the time even under this simple model of cladogenesis. When taxon sampling is poor or rates of evolution are high, the probability that parsimony will become inconsistent increases.     

Globin evolution was apparently very rapid in early vertebrates: A reasonable case against the rate-constancy hypothesis

Kimura mistook ambiguous maximum parsimony codons for wrong codons. The maximum parsimony method performed well as judged by the two classes of serine codons (which can not be connected by silent mutations) on comparing the parsimony codons for serines in human, rabbit, and mouse hemoglobin chains to actual codons determined by nucleotide sequencing. In genealogical reconstructions involving 247 eucaryotic globins, the maximum parsimony distances separating the contemporary sequences show that Kimura's Poisson and Dayhoff's PAM estimates of rate of globin evolution miss most of the superimposed replacements and are therefore seriously in error. Nor is Kimura's constant rate assumption and his belief in a single origin of myoglobin supported. Lamprey myoglobin appears to be most like lamprey hemoglobin, while gnathostome myoglobin seems closest to gnathostome hemoglobin. It was found that the three types of gnathostome globins (Mb, Hb, Hb) evolved between the shark-boney vertebrate and bird-mammal ancestors at a much faster rate than from the latter ancestor to the present. The data indicate that rates were exceedingly fast during the origin of these globin chains because a high proportion of substitutions were adaptive. It was concluded that wherever strong stabilizing selection acts on a protein, somewhere in the past positive Darwinian selection must have spread the amino acid substitutions now being preserved.     

Repeated sequences in the DNA of Drosophila and their localization in giant chromosomes

It is shown by isopycnic density gradient centrifugation that the DNAs of the sibling species Drosophila hydei, Drosophila neohydei and Drosophila pseudoneohydei differ regarding the numbers and proportions of satellite DNA bands. An overwhelming proportion of all repetitive nucleotide sequences of the DNA is contained in these satellite fractions. The majority of the satellites are species specific despite the close phylogenetic and cytological relationship between the three species studied. — By in situ hybridization experiments it is demonstrated that the various satellite sequences occupy different positions within the chromosomes. All types of localization patterns, from a wide spread occurrence in all chromosomes to an apparent restriction to kinetochore regions of single chromosomes, have been observed. Main band DNA, on the other hand, in its hybridization behavior reflects the DNA distribution according to the banding pattern in giant chromosomes. Generally satellite sequences seem to be included in -heterochromatic chromosome regions but no relation to the heterochromatin of the Y-chromosome was found. — Renaturation studies support various evidence that satellite sequences occur in tandemly repetitious units. At least some of this repetitious material seems to be linked to non-satellite DNA sequences or to DNA of other satellites.     

Maximum parsimony on subsets of taxa

In this paper we investigate mathematical questions concerning the reliability (reconstruction accuracy) of Fitch's maximum parsimony algorithm for reconstructing the ancestral state given a phylogenetic tree and a character. In particular, we consider the question whether the maximum parsimony method applied to a subset of taxa can reconstruct the ancestral state of the root more accurately than when applied to all taxa, and we give an example showing that this indeed is possible. A surprising feature of our example is that ignoring a taxon closer to the root improves the reliability of the method. On the other hand, in the case of the two-state symmetric substitution model, we answer affirmatively a conjecture of Li, Steel and Zhang which states that under a molecular clock the probability that the state at a single taxon is a correct guess of the ancestral state is a lower bound on the reconstruction accuracy of Fitch's method applied to all taxa.     

Ancestral Population Sizes and Species Divergence Times in the Primate Lineage on the Basis of Intron and BAC End Sequences

The effective sizes of ancestral populations and species divergence times of six primate species (humans, chimpanzees, gorillas, orangutans, and representatives of Old World monkeys and New World monkeys) are estimated by applying the two-species maximum likelihood (ML) method to intron sequences of 20 different loci. Examination of rate heterogeneity of nucleotide substitutions and intragenic recombination identifies five outrageous loci (ODC1, GHR, HBE, INS, and HBG). The estimated ancestral polymorphism ranges from 0.21 to 0.96% at major divergences in primate evolution. One exceptionally low polymorphism occurs when African and Asian apes diverged. However, taking into consideration the possible short generation times in primate ancestors, it is concluded that the ancestral population size in the primate lineage was no smaller than that of extant humans. Furthermore, under the assumption of 6 million years (myr) divergence between humans and chimpanzees, the divergence time of humans from gorillas, orangutans, Old World monkeys, and New World monkeys is estimated as 7.2, 18, 34, and 65 myr ago, respectively, which are generally older than traditional estimates. Beside the intron sequences, three other data sets of orthologous sequences are used between the human and the chimpanzee comparison. The ML application to these data sets including 58,156 random BAC end sequences (BES) shows that the nucleotide substitution rate is as low as 0.6–0.8 × 10^–9 per site per year and the extent of ancestral polymorphism is 0.33–0.51%. With such a low substitution rate and short generation time, the relatively high extent of polymorphism suggests a fairly large effective population size in the ancestral lineage common to humans and chimpanzees.[Reviewing Editor: Dr. Magnus Nordborg]