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M Hendy

Publications and source records attributed to M Hendy.

5 recordsLinked to original sources
PubMed1990

Distribution of the number of matches between nucleotide sequences.

When two strings of symbols are aligned it is important to know whether the observed number of matches is better than that expected between two independent sequences with the same frequency of symbols. When strings are of different lengths, nulls need to be inserted in order to align the sequences. One approach is to use simple approximations of sampling for replacement. We describe an algorithm for exactly determining the frequencies of given numbers of matches, sampling without replacement. This does not lead to a simple closed form expression. However, we show examples where sampling with, or without, replacement give very similar results and the simple approach may be adequate for all but the smallest cases.

Base Sequence↗
PubMed1990

Minimally colored trees.

Each edge in a weighted colored tree has a nonnegative weight corresponding to the colors of its incident vertices. The sum of these weights is the weight of the tree. Algorithms of O(n) are known to find minimal colorings, that is, to assign colors from a given finite set to the vertices of a tree so as to minimize the weight of the tree. In this paper generating functions are used to find the number of minimal colorings and the average weight of each edge over such colorings, also using O(n) operations. Applications to evolutionary trees are given.

Algorithms↗
PubMed1986

Estimating the reliability of evolutionary trees.

Six protein sequences from the same 11 mammalian taxa were used to estimate the accuracy and reliability of phylogenetic trees using real, rather than simulated, data. A tree comparison metric was used to measure the increase in similarity of minimal trees as larger, randomly selected subsets of nucleotide positions were taken. The ratio of the observed to the expected number of incompatibilities for each nucleotide position (character) is a good predictor of the number of changes required at that position on the minimal (most-parsimonious) tree. This allows a higher weighting of nucleotide positions that have changed more slowly and should result in the minimal length tree converging to the correct tree as more sequences are obtained. An estimate was made of the smallest subset of trees that need to be considered to include the actual historical tree for a given set of data. It was concluded that it is possible to give a reasonable estimate of the reliability of the final tree, at least when several sequences are combined. With the present data, resolving the rodent-primate-lagomorph (rabbit) trichotomy is the least certain aspect of the final tree, followed then by establishing the position of dog. In our opinion, it is unreasonable to publish an evolutionary tree derived from sequence data without giving an idea of the reliability of the tree.

Animals↗