Construction of phylogenetic trees for proteins and nucleic acids: Empirical evaluation of alternative matrix methods

Summary The methods of Fitch and Margoliash and of Farris for the construction of phylogenetic trees were compared. A phenetic clustering technique - the UPGMA method — was also considered.The three methods were applied to difference matrices obtained from comparison of macromolecules by immunological, DNA hybridization, electrophoretic, and amino acid sequencing techniques. To evaluate the results, we used the goodness-of-fit criterion. In some instances, the F-M and Farris methods gave a comparably good fit of the output to the input data, though in most cases the F-M procedure gave a much better fit. By the fit criterion, the UPGMA procedure was on the average better than the Farris method but not as good as the F-M procedure.On the basis of the results given in this report and the goodness-of-fit criterion, it is suggested that where input data are likely to include overestimates as well as true estimates and underestimates of the actual distances between taxonomic units, the F-M method is the most reasonable to use for constructing phylogenies from distance matrices. Immunological, DNA hybridization, and electrophoretic data fall into this category. By contrast, where it is known that each input datum is indeed either a true estimate or an underestimate of the actual distance between 2 taxonomic units, the Farris procedure appears, on theoretical grounds, to be the matrix method of choice. Amino acid and nucleotide sequence data are in this category.The following abbreviations are used in this work F-M Fitch-Margoliash - UPGMA unweighted pair-group method using arithmetic averages - SD percent standard deviation     

The ancestral distance test: what relatedness can reveal about correlated evolution in large lineages with missing character data and incomplete phylogenies

The ancestral distance test is introduced to detect correlated evolution between two binary traits in large phylogenies that may lack resolved subclades, branch lengths, and/or comparative data. We define the ancestral distance as the time separating a randomly sampled taxon from its most recent ancestor (MRA) with extant descendants that have an independent trait. The sampled taxon either has (target sample) or lacks (nontarget sample) a dependent trait. Modeled as a Markov process, we show that the distribution of ancestral distances for the target sample is identical to that of the nontarget sample when characters are uncorrelated, whereas ancestral distances are smaller on average for the target sample when characters are correlated. Simulations suggest that the ancestral distance can be estimated using the time, total branch length, taxonomic rank, or number of speciation events between a sampled taxon and the MRA. These results are shown to be robust to deviations from Markov assumptions. A Monte Carlo technique estimates P-values when fully resolved phylogenies with branch lengths are available, and we evaluate the Monte Carlo approach using a data set with known correlation. Measures of relatedness were found to provide a robust means to test hypotheses of correlated character evolution.     

Accuracy of estimated phylogenetic trees from molecular data

Summary The accuracies and efficiencies of four different methods for constructing phylogenetic trees from molecular data were examined by using computer simulation. The methods examined are UPGMA, Fitch and Margoliash's (1967) (F/M) method, Farris' (1972) method, and the modified Farris method (Tateno, Nei, and Tajima, this paper). In the computer simulation, eight OTUs (32 OTUs in one case) were assumed to evolve according to a given model tree, and the evolutionary change of a sequence of 300 nucleotides was followed. The nucleotide substitution in this sequence was assumed to occur following the Poisson distribution, negative binomial distribution or a model of temporally varying rate. Estimates of nucleotide substitutions (genetic distances) were then computed for all pairs of the nucleotide sequences that were generated at the end of the evolution considered, and from these estimates a phylogenetic tree was reconstructed and compared with the true model tree. The results of this comparison indicate that when the coefficient of variation of branch length is large the Farris and modified Farris methods tend to be better than UPGMA and the F/M method for obtaining a good topology. For estimating the number of nucleotide substitutions for each branch of the tree, however, the modified Farris method shows a better performance than the Farris method. When the coefficient of variation of branch length is small, however, UPGMA shows the best performance among the four methods examined. Nevertheless, any tree-making method is likely to make errors in obtaining the correct topology with a high probability, unless all branch lengths of the true tree are sufficiently long. It is also shown that the agreement between patristic and observed genetic distances is not a good indicator of the goodness of the tree obtained.     

The consistency of several phylogeny-inference methods under varying evolutionary rates.

A phylogenetic method is a consistent estimator of phylogeny if and only if it is guaranteed to give the correct tree, given that sufficient (possibly infinite) independent data are examined. The following methods are examined for consistency: UPGMA (unweighted pair-group method, averages), NJ (neighbor joining), MF (modified Farris), and P (parsimony). A two-parameter model of nucleotide sequence substitution is used, and the expected distribution of character states is calculated. Without perfect correction for superimposed substitutions, all four methods may be inconsistent if there is but one branch evolving at a faster rate than the other branches. Partial correction of observed distances improves the robustness of the NJ method to rate variation, and perfect correction makes the NJ method a consistent estimator for all combinations of rates that were examined. The sensitivity of all the methods to unequal rates varies over a wide range, so relative-rate tests are unlikely to be a reliable guide for accepting or rejecting phylogenies based on parsimony analysis.     

Accuracy of estimated phylogenetic trees from molecular data

The accuracies and efficiencies of three different methods of making phylogenetic trees from gene frequency data were examined by using computer simulation. The methods examined are UPGMA, Farris' (1972) method, and Tateno et al.'s (1982) modified Farris method. In the computer simulation eight species (or populations) were assumed to evolve according to a given model tree, and the evolutionary changes of allele frequencies were followed by using the infinite-allele model. At the end of the simulated evolution five genetic distance measures (Nei's standard and minimum distances, Rogers' distance, Cavalli-Sforza's f theta, and the modified Cavalli-Sforza distance) were computed for all pairs of species, and the distance matrix obtained for each distance measure was used for reconstructing a phylogenetic tree. The phylogenetic tree obtained was then compared with the model tree. The results obtained indicate that in all tree-making methods examined the accuracies of both the topology and branch lengths of a reconstructed tree (rooted tree) are very low when the number of loci used is less than 20 but gradually increase with increasing number of loci. When the expected number of gene substitutions (M) for the shortest branch is 0.1 or more per locus and 30 or more loci are used, the topological error as measured by the distortion index (dT) is not great, but the probability of obtaining the correct topology (P) is less than 0.5 even with 60 loci. When M is as small as 0.004, P is substantially lower. In obtaining a good topology (small dT and high P) UPGMA and the modified Farris method generally show a better performance than the Farris method. The poor performance of the Farris method is observed even when Rogers' distance which obeys the triangle inequality is used. The main reason for this seems to be that the Farris method often gives overestimates of branch lengths. For estimating the expected branch lengths of the true tree UPGMA shows the best performance. For this purpose Nei's standard distance gives a better result than the others because of its linear relationship with the number of gene substitutions. Rogers' or Cavalli-Sforza's distance gives a phylogenetic tree in which the parts near the root are condensed and the other parts are elongated. It is recommended that more than 30 loci, including both polymorphic and monomorphic loci, be used for making phylogenetic trees. The conclusions from this study seem to apply also to data on nucleotide differences obtained by the restriction enzyme techniques.     

An information-based sequence distance and its application to whole mitochondrial genome phylogeny

MOTIVATION: Traditional sequence distances require an alignment and therefore are not directly applicable to the problem of whole genome phylogeny where events such as rearrangements make full length alignments impossible. We present a sequence distance that works on unaligned sequences using the information theoretical concept of Kolmogorov complexity and a program to estimate this distance. RESULTS: We establish the mathematical foundations of our distance and illustrate its use by constructing a phylogeny of the Eutherian orders using complete unaligned mitochondrial genomes. This phylogeny is consistent with the commonly accepted one for the Eutherians. A second, larger mammalian dataset is also analyzed, yielding a phylogeny generally consistent with the commonly accepted one for the mammals. AVAILABILITY: The program to estimate our sequence distance, is available at http://www.cs.cityu.edu.hk/~cssamk/gencomp/GenCompress1.htm. The distance matrices used to generate our phylogenies are available at http://www.math.uwaterloo.ca/~mli/distance.html.     

A predictive model of avian natal dispersal distance provides prior information for investigating response to landscape change

1. Informative Bayesian priors can improve the precision of estimates in ecological studies or estimate parameters for which little or no information is available. While Bayesian analyses are becoming more popular in ecology, the use of strongly informative priors remains rare, perhaps because examples of informative priors are not readily available in the published literature. 2. Dispersal distance is an important ecological parameter, but is difficult to measure and estimates are scarce. General models that provide informative prior estimates of dispersal distances will therefore be valuable. 3. Using a world-wide data set on birds, we develop a predictive model of median natal dispersal distance that includes body mass, wingspan, sex and feeding guild. This model predicts median dispersal distance well when using the fitted data and an independent test data set, explaining up to 53% of the variation. 4. Using this model, we predict a priori estimates of median dispersal distance for 57 woodland-dependent bird species in northern Victoria, Australia. These estimates are then used to investigate the relationship between dispersal ability and vulnerability to landscape-scale changes in habitat cover and fragmentation. 5. We find evidence that woodland bird species with poor predicted dispersal ability are more vulnerable to habitat fragmentation than those species with longer predicted dispersal distances, thus improving the understanding of this important phenomenon. 6. The value of constructing informative priors from existing information is also demonstrated. When used as informative priors for four example species, predicted dispersal distances reduced the 95% credible intervals of posterior estimates of dispersal distance by 8-19%. Further, should we have wished to collect information on avian dispersal distances and relate it to species' responses to habitat loss and fragmentation, data from 221 individuals across 57 species would have been required to obtain estimates with the same precision as those provided by the general model.     

Euclidean nature of phylogenetic distance matrices

Phylogenies are fundamental to comparative biology as they help to identify independent events on which statistical tests rely. Two groups of phylogenetic comparative methods (PCMs) can be distinguished: those that take phylogenies into account by introducing explicit models of evolution and those that only consider phylogenies as a statistical constraint and aim at partitioning trait values into a phylogenetic component (phylogenetic inertia) and one or multiple specific components related to adaptive evolution. The way phylogenetic information is incorporated into the PCMs depends on the method used. For the first group of methods, phylogenies are converted into variance-covariance matrices of traits following a given model of evolution such as Brownian motion (BM). For the second group of methods, phylogenies are converted into distance matrices that are subsequently transformed into Euclidean distances to perform principal coordinate analyses. Here, we show that simply taking the elementwise square root of a distance matrix extracted from a phylogenetic tree ensures having a Euclidean distance matrix. This is true for any type of distances between species (patristic or nodal) and also for trees harboring multifurcating nodes. Moreover, we illustrate that this simple transformation using the square root imposes less geometric distortion than more complex transformations classically used in the literature such as the Cailliez method. Given the Euclidean nature of the elementwise square root of phylogenetic distance matrices, the positive semidefinitiveness of the phylogenetic variance-covariance matrix of a trait following a BM model, or related models of trait evolution, can be established. In that way, we build a bridge between the two groups of statistical methods widely used in comparative analysis. These results should be of great interest for ecologists and evolutionary biologists performing statistical analyses incorporating phylogenies.     

Genetic Distances Based on Quantitative Traits

Morphological data showing continuous distributions, polygenically controlled, may be particularly useful in intergroup classification below the species level; an appropriate distance analysis based on these traits is an important tool in evolutionary biology and in plant and animal breeding.--The interpretation of morphological distances in genetic terms is not easy because simple phenotypic data may lead to biased estimates of genetic distances. Convenient estimates can be obtained whenever it is possible to breed populations according to a suitable crossing design and to derive information from genetic parameters.--A general method for determining genetic distances is proposed. The procedure of multivariate analysis of variance is extended to estimate appropriate genetic parameters (genetic effects). Not only are optimal statistical estimates of parameters obtained but also the procedure allows the measurement of genetic distances between populations as linear functions of the estimated parameters, providing an appropriate distance matrix that can be defined in terms of these parameters. The use of the T2 statistic, defined in terms of the vector of contrasts specifying the distance, permits the testing of the significance of any distance between any pair of populations that may be of interest from a genetic point of view.--A numerical example from maize diallel data is reported in order to illustrate the procedure. In particular, heterosis effects are used as the basis for estimates of genetic divergence between populations.     

A tree reconstruction method that is economical in the number of pairwise comparisons used

A fast method for reconstructing phylogenies from distance data is presented. The method is economical in the number of pairwise comparisons needed. It can be combined with a new phylogenetic alignment procedure to yield an algorithm that gives a complete history of a set of homologous sequences. The method is applicable to very large distance matrices. An auxiliary program was developed that simplifies large phylogenies without ignoring biologically essential features. A set of 213 globins from vertebrates, plants, and Vitreoscilla (a prokaryote) were analyzed using this method.      

A new simplified method for constructing Wagner networks and the cladistics of Pentachaeta (Compositae,Astereae)

The new procedure for constructing a Wagner network presented differs from Farris’s (1970) method in that the amount of computation required is reduced. The usefulness of this procedure was examined by applying it to the 20 characters considered in a recent monograph of the seven OTUs of the genusPentachaeta. A single network was derived from some 945 or more networks possible for this group. A comparison of the network constructed by this simplified method to that constructed by Farris’ procedure revealed no differences. An attempt to reconstruct the cladistic history of this group by generating a Wagner tree based on the network resulted in four equally possible trees, suggesting that further data are needed before cladogenesis in this group is resolved.     

Flies on thistles: support for synchronous speciation?

Synchronous speciation of hosts and herbivorous insects predicts a congruent topology of host and insect phylogenies and similar evolutionary ages of host and insect taxa. To test these predictions for the specialized herbivorous fly genus Urophora (Diptera: Tephritidae), we used three different approaches. (i) We generated a phylogenetic tree of 11 European Urophora species from allozyme data and constructed a phylogeny of their hosts from published sources. Superimposing the Urophora tree on the host-plant tree we found no evidence for general congruence. (ii) We correlated genetic distances (Nei distances) of the host plants vs. the genetic distances of associated Urophora species. Overall, the relationship was not positive. Nevertheless, for some pairs of Urophora species and host plants genetic distances were in the same order of magnitude. (iii) We collected allozyme data for pairs of thistle taxa and pairs of herbivores on thistles together with independent time estimates. With these data we calibrated a molecular clock. There was a non-linear relationship between phylogenetic age and genetic distance, rendering the dating of deep events in thistle–insect evolution difficult. Nevertheless the derived molecular clock showed that the split of insect taxa lagged behind the split of hosts.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 84 , 775–783.     

Intraordinal relationships of the Pelecaniformes and Cuculiformes: electrophoresis of feather keratins

Electrophoresis of soluble feather keratins was performed in Gradipore gels under two pH conditions. The taxa of two diverse orders, the Pelecaniformes and Cuculiformes, were compared. Dendograms based on identity indices and genetic distances were constructed by the Fitch-Margoliash and unweighed pair-group algorithms (UPGMA). Differences within taxa were influenced by both pH conditions and the algorithm used for analysis.
Values of identity indices at each pH were compared within and between taxa. Dendograms for the Pelecaniform consistently group species within genera and placed families within the traditional arrangements. One notable exception was Nannopterum. The Cuculiformes, with many monotypic genera, were more resistant to constant clustering.
The problems of relating genetic distance to phylogenies are discussed. The relationship of systematic, ecological and molecular diversity is still unresolved. Genetic distance of feather keratins consistently correlated with other estimates of divergence times. The values indicate the systematic equivalence of taxa within orders.     

Challenges in the estimation of extinction from molecular phylogenies: A response to Beaulieu and O'Meara

Time‐calibrated phylogenies that contain only living species have been widely used to study the dynamics of speciation and extinction. Concerns about the reliability of phylogenetic extinction estimates were raised by Rabosky (2010), where I suggested that unaccommodated heterogeneity in speciation rate could lead to positively biased extinction estimates. In a recent article, Beaulieu and O'Meara (2015a) correctly point out several technical errors in the execution of my 2010 study and concluded that phylogenetic extinction estimates are robust to speciation rate heterogeneity under a range of model parameters. I demonstrate that Beaulieu and O'Meara underestimated the magnitude of speciation rate variation in real phylogenies and consequently did not incorporate biologically meaningful levels of rate heterogeneity into their simulations. Using parameter values drawn from the recent literature, I find that modest levels of heterogeneity in speciation rate result in a consistent, positive bias in extinction estimates that are exacerbated by phylogenetic tree size. This bias, combined with the inherent lack of information about extinction in molecular phylogenies, suggests that extinction rate estimates from phylogenies of extant taxa only should be treated with caution.     

A Report on "One Day Symposium on Numerical Cladistics"

A recent symposium on numerical cladistics held at the American Museum of Natural History in New York City, addressed novel methods for searching tree space, applications of randomizations in cladistic analysis, and data management. One of the major concerns in systematics is that of finding the global optimum in tree length. The space to search is complex because it includes many local optima. It is a difficult task to escape local optima without a great loss in efficiency. The ideal is to search among suboptimal topologies and still obtain an answer in a reasonable amount of time. Nixon presented a new family of methods called "parsimony ratchet," which are successful at escaping local optima. Moilanen presented a new program which may have similar advantages. Two presentations, one by Goloboff and Farris and another by Farris, Goloboff, Källersjö, and Oxelman, introduced modifications to parsimony jackknifing that improved its accuracy when compared to normal heuristic searches. Wheeler discussed the advantages of new methods of analyzing DNA and protein sequence data, which eliminate multiple alignment; the most recent one packs nucleotides into strings which constitute the new characters. Siddall discussed different applications of randomization in cladistics and their logical consistency, finding some more acceptable than others. Nixon and Carpenter presented a new program for managing data. This symposium will probably be a landmark judging from the originality and practicality of the points presented.     

Divergence time uncertainty and historical biogeography reconstruction – an example from Urophylleae (Rubiaceae)

Aim When hypotheses of historical biogeography are evaluated, age estimates of individual nodes in a phylogeny often have a direct impact on what explanation is concluded to be most likely. Confidence intervals of estimated divergence times obtained in molecular dating analyses are usually very large, but the uncertainty is rarely incorporated in biogeographical analyses. The aim of this study is to use the group Urophylleae, which has a disjunct pantropical distribution, to explore how the uncertainty in estimated divergence times affects conclusions in biogeographical analysis. Two hypotheses are evaluated: (1) long‐distance dispersal from Africa to Asia and the Neotropics, and (2) a continuous distribution in the boreotropics, probably involving migration across the North Atlantic Land Bridge, followed by isolation in equatorial refugia. Location Tropical and subtropical Asia, tropical Africa, and central and southern tropical America. Methods This study uses parsimony and Bayesian phylogenetic analyses of chloroplast DNA and nuclear ribosomal DNA data from 56 ingroup species, beast molecular dating and a Bayesian approach to dispersal–vicariance analysis (Bayes‐DIVA) to reconstruct the ancestral area of the group, and the dispersal–extinction–cladogenesis method to test biogeographical hypotheses. Results When the two models of geographic range evolution were compared using the maximum likelihood (ML) tree with mean estimates of divergence times, boreotropical migration was indicated to be much more likely than long‐distance dispersal. Analyses of a large sample of dated phylogenies did, however, show that this result was not consistent. The age estimate of one specific node had a major impact on likelihood values and on which model performed best. The results show that boreotropical migration provides a slightly better explanation of the geographical distribution patterns of extant Urophylleae than long‐distance dispersal. Main conclusions This study shows that results from biogeographical analyses based on single phylogenetic trees, such as a ML or consensus tree, can be misleading, and that it may be very important to take the uncertainty in age estimates into account. Methods that account for the uncertainty in topology, branch lengths and estimated divergence times are not commonly used in biogeographical inference today but should definitely be preferred in order to avoid unwarranted conclusions.     

Molecular genetic divergence of orang utan (Pongo pygmaeus) subspecies based on isozyme and two-dimensional gel electrophoresis

The orang utan (Pongo pygmaeus), as currently recognized, includes two geographically separated subspecies: Pongo pygmaeus pygmaeus, which resides on Borneo, and P. p. abelii, which inhabits Sumatra. At present, there is no known route of gene flow between the two populations except through captive individuals which have been released back into the wild over the last several decades. The two subspecies are differentiated by morphological and behavioral characters, and they can be distinguished by a subspecies specific pericentric chromosomal inversion. Nei-genetic distances were estimated between orang utan subspecies, gorilla, chimpanzee and humans using 44 isozyme loci and using 458 soluble fibroblast proteins which were resolved by two-dimensional gel electrophoresis. Phenetic analysis of both data sets supports the following conclusions: the orang utan subspecies distances are approximately 10 times closer to each other than they are to the African apes, and the orang utan subspecies are approximately as divergent as are the two chimpanzee species. Comparison of the genetic distances to genetic distance estimates done in the same laboratory under identical conditions reveals that the distance between Bornean vs. Sumatran orang utans is 5-10 times the distance measured between several pairs of subspecies including lions, cheetahs, and tigers. Near species level molecular genetic distances between orang utan subspecies would support the separate management of Bornean and Sumatran orang utans as evolutionary significant units (Ryder 1987). Evolutionary topologies were constructed from the distance data using both cladistic and phenetic methods. The majority of resulting trees affirmed previous molecular evolutionary studies that indicated that man and chimpanzee diverged from a common ancestor subsequent to the divergence of gorilla from the common ancestor.     

Empirical Bayes procedure for estimating genetic distance between populations and effective population size

We developed an empirical Bayes procedure to estimate genetic distances between populations using allele frequencies. This procedure makes it possible to describe the skewness of the genetic distance while taking full account of the uncertainty of the sample allele frequencies. Dirichlet priors of the allele frequencies are specified, and the posterior distributions of the various composite parameters are obtained by Monte Carlo simulation. To avoid overdependence on subjective priors, we adopt a hierarchical model and estimate hyperparameters by maximizing the joint marginal-likelihood function. Taking advantage of the empirical Bayesian procedure, we extend the method to estimate the effective population size using temporal changes in allele frequencies. The method is applied to data sets on red sea bream, herring, northern pike, and ayu broodstock. It is shown that overdispersion overestimates the genetic distance and underestimates the effective population size, if it is not taken into account during the analysis. The joint marginal-likelihood function also estimates the rate of gene flow into island populations.     

The quality of the fossil record and the accuracy of phylogenetic inferences about sampling and diversity

Because phylogenies can be estimated without stratigraphic data and because estimated phylogenies also infer gaps in sampling, some workers have used phylogeny estimates as templates for evaluating sampling from the fossil record and for "correcting" historical diversity patterns. However, it is not known how sampling intensity (the probability of sampling taxa per unit time) and completeness (the proportion of taxa sampled) affect the accuracy of phylogenetic inferences, nor how phylogenetically inferred estimates of sampling and diversity respond to inaccurate estimates of phylogeny. Both issues are addressed with a series of simulations using simple models of character evolution, varying speciation patterns, and various rates of speciation, extinction, character change, and preservation. Parsimony estimates of simulated phylogenies become less accurate as sampling decreases, and inaccurate trees chronically underestimate sampling. Biotic factors such as rates of morphologic change and extinction both affect the accuracy of phylogenetic estimates and thus affect estimated gaps in sampling, indicating that differences in implied sampling need not reflect actual differences in sampling. Errors in inferred diversity are concentrated early in the history of a clade. This, coupled with failure to account for true extinction times (i.e., the Signor-Lipps effect), inflates relative diversity levels early in clade histories. Because factors other than differences in sampling predict differences in the numbers of gaps implied by phylogeny estimates, inferred phylogenies can be misleading templates for evaluating sampling or historical diversity patterns.