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L R Foulds

Publications and source records attributed to L R Foulds.

5 recordsLinked to original sources
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↗