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Biomedical subjects

M D Hendy

Publications and source records attributed to M D Hendy.

18 recordsLinked to original sources
PubMed1996

Complete families of linear invariants for some stochastic models of sequence evolution, with and without the molecular clock assumption.

For various models of sequence evolution, the set of linear functions of the frequencies of the nucleotide patterns forms a vector space, the invariant space. Here we distinguish between the model of nucleotide substitution, and the phylogenetic tree T describing the paths on which these changes occur. We describe a procedure to construct a basis of the invariant space for those models that are extensions of models incorporating Kimura's three substitution model of nucleotide change, including both the Jukes-Cantor and Cavender-Farris models. The dimension of the invariant space is determined, for those models where it is independent of the tree topology, as a function of the number of sequences. These are calculated where the nucleotide distribution at the root is unspecified, and both with, and without, the assumption of the molecular clock hypothesis. The invariants have a number of potential applications, including tree identification, and testing the fit of models (which could include the molecular clock) to sequence data.

Biological Evolution↗
PubMed1995

Improved analyses of human mtDNA sequences support a recent African origin for Homo sapiens.

New quantitative methods are applied to the 135 human mitochondrial sequences from the Vigilant et al. data set. General problems in analyzing large numbers of short sequences are discussed, and an improved strategy is suggested. A key feature is to focus not on individual trees but on the general "landscape" of trees. Over 1,000 searches were made from random starting trees with only one tree (a local optimum) being retained each time, thereby ensuring optima were found independently. A new tree comparison metric was developed that is unaffected by rearrangements of trees around many very short internal edges. Use of this metric showed that downweighting hypervariable sites revealed more evolutionary structure than studies that weighted all sites equally. Our results are consistent with convergence toward a global optimum. Crucial features are that the best optima show very strong regional differentiation, a common group of 49 African sequences is found in all the best optima, and the best optima contain the 16 !Kung sequences in a separate group of San people. The other 86 sequences form a heterogeneous mixture of Africans, Europeans, Australopapuans, and Asians. Thus all major human lineages occur in Africa, but only a subset occurs in the rest of the world. The existence of these African-only groups strongly contradicts multiregional theories for the origin of Homo sapiens that require widespread migration and interbreeding over the entire range of H. erectus. Only when the multiregional model is rejected is it appropriate to consider the root, based on a single locus, to be the center of origin of a population (otherwise different loci could give alternative geographic positions for the root). For this data, several methods locate the root within the group of 49 African sequences and are thus consistent with the recent African origin of H. sapiens. We demonstrate that the time of the last common ancestor cannot be the time of major expansion in human numbers, and our results are thus also consistent with recent models that differentiate between the last common ancestor, expansion out of Africa, and the major expansion in human populations. Such a two-phase model is consistent with a wide range of molecular and archeological evidence.

Africa↗
PubMed1994

A discrete Fourier analysis for evolutionary trees.

Discrete Fourier transformations have recently been developed to model the evolution of two-state characters (the Cavender/Farris model). We report here the extension of these transformations to provide invertible relationships between a phylogenetic tree T (with three probability parameters of nucleotide substitution on each edge corresponding to Kimura's 3ST model) and the expected frequencies of the nucleotide patterns in the sequences. We refer to these relationships as spectral analysis. In either model with independent and identically distributed site substitutions, spectral analysis allows a global correction for all multiple substitutions (second- and higher-order interactions), independent of any particular tree. From these corrected data we use a least-squares selection procedure, the closest tree algorithm, to infer an evolutionary tree. Other selection criteria such as parsimony or compatibility analysis could also be used; each of these criteria will be statistically consistent for these models. The closest tree algorithm selects a unique best-fit phylogenetic tree together with independent edge length parameters for each edge. The method is illustrated with an analysis of some primate hemoglobin sequences.

Animals↗
PubMed1994

The effects of sequence length, tree topology, and number of taxa on the performance of phylogenetic methods.

Simulations were used to study the performance of several character-based and distance-based phylogenetic methods in obtaining the correct tree from pseudo-randomly generated input data. The study included all the topologies of unrooted binary trees with from 4 to 10 pendant vertices (taxa) inclusive. The length of the character sequences used ranged from 10 to 10(5) characters exponentially. The methods studied include Closest Tree, Compatibility, Li's method, Maximum Parsimony, Neighbor-joining, Neighborliness, and UPGMA. We also provide a modification to Li's method (SimpLi) which is consistent with additive data. We give estimations of the sequence lengths required for given confidence in the output of these methods under the assumptions of molecular evolution used in this study. A notation for characterizing all tree topologies is described. We show that when the number of taxa, the maximum path length, and the minimum edge length are held constant, there it little but significant dependence of the performance of the methods on the tree topology. We show that those methods that are consistent with the model used perform similarly, whereas the inconsistent methods, UPGMA and Li's method, perform very poorly.

Base Sequence↗
PubMed1994

Reconstructing trees when sequence sites evolve at variable rates.

For a sequence of colors independently evolving on a tree under a simple Markov model, we consider conditions under which the tree can be uniquely recovered from the "sequence spectrum"-the expected frequencies of the various leaf colorations. This is relevant for phylogenetic analysis (where colors represent nucleotides or amino acids; leaves represent extant taxa) as the sequence spectrum is estimated directly from a collection of aligned sequences. Allowing the rate of the evolutionary process to vary across sites is an important extension over most previous studies-we show that, given suitable restrictions on the rate distribution, the true tree (up to the placement of its root) is uniquely identified by its sequence spectrum. However, if the rate distribution is unknown and arbitrary, then, for simple models, it is possible for every tree to produce the same sequence spectrum. Hence there is a logical barrier to accurate, consistent phylogenetic inference for these models when assumptions about the rate distribution are not made. This result exploits a novel theorem on the action of polynomials with non-negative coefficients on sequences.

Markov Chains↗
PubMed1993

Neighbor-joining uses the optimal weight for net divergence.

A class of phylogenetic clustering methods which calculate net divergences from distance data, but assign differing weights to the net divergences, is defined. The class includes the Neighbor-Joining Method and the Unweighted Pair-Group Method with Arithmetic Mean. The accuracy of some of these methods is studied by computer simulation for the case of four taxa under the additive tree hypothesis. Of these methods and under this hypothesis, it is proved that Neighbor-Joining uses the only weighting for net divergence which is consistent, so that it is the only method in the class which is expected to converge to the correct tree as more data are added. Neighbor-Joining is then compared with Closest Tree on Distances for five taxa by simulation. It is proved that Closest Tree on Distances is equivalent to Neighbor-Joining for four taxa, though it is not when more than four taxa are considered.

Cluster Analysis↗
PubMed1992

Controversy on chloroplast origins.

Controversy exists over the origins of photosynthetic organelles in that contradictory trees arise from different sequence, biochemical and ultrastructural data sets. We propose a testable hypothesis which explains this inconsistency as a result of the differing GC contents of sequences. We report that current methods of tree reconstruction tend to group sequences with similar GC contents irrespective of whether the similar GC content is due to common ancestry or is independently acquired. Nuclear encoded sequences (high GC) give different trees from chloroplast encoded sequences (low GC). We find that current data is consistent with the hypothesis of multiple origins for photosynthetic organelles and single origins for each type of light harvesting complex.

Base Composition↗
PubMed1989

Influenza viruses, comets and the science of evolutionary trees.

The study of phylogeny is becoming increasing scientific in that hypotheses can be tested quantitatively. We report a method of estimating the probabilities of obtaining a tree of a given length from nucleic acid sequence data. The method is applied to the hypothesis of Hoyle & Wickramasinghe that the earth is being continually bombarded by influenza (and other) viruses which originate from comets. A quantitative analysis of sequences from the H1 strain of human influenza viruses contradicts three versions of the Hoyle-Wickramasinghe model. One non-evolutionary version of their model has less than one chance in 10(66) of being correct. A version that allowed extraterrestrial evolution has less than one change in 10(6) of being correct. The sequence data is in agreement with the biological (evolutionary) model. The results are discussed from the aspect of the falsifiability of evolutionary theory.

Base Sequence↗
PubMed1987

TurboTree: a fast algorithm for minimal trees.

A branch and bound algorithm is described for searching rapidly for minimal length trees from biological data. The algorithm adds characters one at a time, rather than adding taxa, as in previous branch and bound methods. The algorithm has been programmed and is available from the authors. A worked example is given with 33 characters and 15 taxa. About 8 x 10(12) binary trees are possible with 15 taxa but the branch and bound program finds the minimal tree in less than 5 min on an IBM PC.

Algorithms↗
PubMed1980

Techniques for the verification of minimal phylogenetic trees illustrated with ten mammalian haemoglobin sequences.

We have recently reported a method to identify the shortest possible phylogenetic tree for a set of protein sequences [Foulds Hendy & Penny (1979) J. Mol. Evol. 13. 127--150; Foulds, Penny & Hendy (1979) J. Mol. Evol. 13, 151--166]. The present paper discusses issues that arise during the construction of minimal phylogenetic trees from protein-sequence data. The conversion of the data from amino acid sequences into nucleotide sequences is shown to be advantageous. A new variation of a method for constructing a minimal tree is presented. Our previous methods have involved first constructing a tree and then either proving that it is minimal or transforming it into a minimal tree. The approach presented in the present paper progressively builds up a tree, taxon by taxon. We illustrate this approach by using it to construct a minimal tree for ten mammalian haemoglobin alpha-chain sequences. Finally we define a measure of the complexity of the data and illustrate a method to derive a directed phylogenetic tree from the minimal tree.

Amino Acid Sequence↗
PubMed1979

A graph theoretic approach to the development of minimal phylogenetic trees.

The problem of determining the minimal phylogenetic tree is discussed in relation to graph theory. It is shown that this problem is an example of the Steiner problem in graphs which is to connect a set of points by a minimal length network where new points can be added. There is no reported method of solving realistically-sized Steiner problems in reasonable computing time. A heuristic method of approaching the phylogenetic problem is presented, together with a worked example with 7 mammalian cytochrome c sequences. It is shown in this case that the method develops a phylogenetic tree that has the smallest possible number of amino acid replacements. The potential and limitations of the method are discussed. It is stressed that objective methods must be used for comparing different trees. In particular it should be determined how close a given tree is to a mathematically determined lower bound. A theorem is proved which is used to establish a lower bound on the lenghtof any tree and if a tree is found with a length equal to the lower bound, then no shorter tree can exist.

Mathematics↗
PubMed1979

A general approach to proving the minimality of phylogenetic trees illustrated by an example with a set of 23 vertebrates.

We have recently described a method of building phylogenetic trees and have outlined an approach for proving whether a particular tree is optimal for the data used. In this paper we describe in detail the method of establishing lower bounds on the length of a minimal tree by partitioning the data set into subsets. All characters that could be involved in duplications in the data are paired with all other such characters. A matching algorithm is then used to obtain the pairing of characters that reveals the most duplications in the data. This matching may still not account for all nucleotide substitutions on the tree. The structure of the tree is then used to help select subsets of three or more characters until the lower bound found by partitioning is equal to the length of the tree. The tree must then be a minimal tree since no tree can exist with a length less than that of the lower bound. The method is demonstrated using a set of 23 vertebrate cytochrome c sequences with the criterion of minimizing the total number of nucleotide substitutions. There are 131130 7045768798 96033440625 topologically distinct trees that can be constructed from this data set. The method described in this paper does identify 144 minimal tree variants. The method is general in the sense that it can be used for other data and other criteria of length. It need not however always be possible to prove a treee minimal but the method will give an upper and lower bound on the length of minimal trees.

Amino Acid Sequence↗