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A maximum likelihood approach for testing and calibrating the molecular clock using temporally dispersed sequences

Roald Forsberg, Anne-Mette Krabbe Pedersen, Jotun Hein, Martin Oleksiewicz¹ and Torben Storgaard¹
Institute of Biological Sciences, Department of Genetics and Ecology, University of Aarhus DK-8000
¹Danish Veterinary Institute of Virology, Lindholm DK-4571

Testing the hypothesis of equal evolutionary rates in the evolutionary pathways connecting different lineages is of great interest in studies of molecular evolution. The existence of equal evolutionary rates, i.e. a molecular clock between lineages, is a central prediction of the neutral theory (Kimura 1983). The finding of a molecular clock may therefore serve as an indication of neutrality dominating the evolution of the gene in question, and a calibrated clock may be used to date important evolutionary events such as speciation or epidemiological events. Alternatively, the rejection of the hypothesis may aid in the formulation and testing of hypotheses which seek to establish the biological basis of rate variation such as taxonomical differences in generation times, DNA repair rates, variation in gene function and selective pressures (Sorhannus 1999).

Tests of the molecular clock hypothesis may be based on at least three major different approaches.

The first one is comprised of the relative-rate tests which use reference information in the form of a designated outgroup, to test the equality of evolutionary rates in the ingroup in question. These tests may be based on the statistical comparison of distance measures (Sarich and Wilson 1973) or on likelihood ratio tests of different hypotheses (Muse and Weir 1992).

The second major approach constitutes tests based on the equal sum of branch lengths in a phylogeny relating a group of lineages under the hypothesis of a molecular clock. The likelihood ratio test of the molecular clock proposed by Felsenstein (1981) is an example of such a test. A common feature of the two above mentioned approaches is that they assume data to be sampled at the same time and that they rely on additional information such as paleological data or experimental determination of the absolute rate of evolution for the calibration of the molecular clock.

In contrast to this, the third approach uses information of evolutionary events in the form of dated temporally dispersed isolates, to simultaneously test the hypothesis of a clock and to determine the absolute rate of evolution (Leitner and Albert 1999, Gorman et al. 1991). This approach is as such dependent upon the availability of "historical" sequence data, i.e. sequences sampled before the present which cover a significant span of the evolutionary history of the group of organisms in question. Such data are hard to obtain for slowly evolving species such as eukaryotes, and the approach is therefore in practice restricted to rapidly evolving species such as RNA viruses. By plotting genetic distances in the form of pairwise distances, distances to an estimated ancestral sequence or phylogenetic branch lengths against the known time of isolation, a linear regression may be developed where a significant degree of linearity implies a molecular clock with the absolute rate of substitution determined by the slope of the regression line. Several problems are evident with this approach. In order to obtain a temporal frame of reference distances must either be plotted as distance to an outgroup strain or to an estimated ancestral sequence of the most recent common ancestor of the sample sequences. If no sequences are positioned close to the root of the phylogeny ancestral sequences may not be correctly inferred (Cunningham et al. 1998) and such error will bias all measured distances. Furthermore, the test or linearity assumes independence among data points whereas evolutionary distances are correlated by shared phylogeny. The consequence of this violation of the statistical assumptions is unknown (Leitner and Albert 1999).

We have developed an extension to Felsenstein's maximum likelihood procedure for inferring evolutionary trees with clocks which allows for the proper analysis of temporally dispersed sequences. This extension combines the latter two of the above approaches by incorporating information of sequencing dates in the likelihood function. This allows for the likelihood ratio testing of the molecular clock hypothesis even when sequences are temporally dispersed and provides simultaneous maximum likelihood estimation of the absolute rate of evolution and the times of evolutionary events. This testing and estimation procedure employs the full phylogenetic information as well as information of sampling times and has the well-defined statistical properties of likelihood theory. The test is of special relevance to the analysis of rapidly evolving species such as RNA viruses, where appropriate data are available. A computer program is under development which will include standard sequence format and substitution models. The program will be available via the World Wide Web, at: http://www.biology.au.dk/~bioroald.

References
Cunningham C.W., Omland K.E., Oakley T.H. 1998. Reconstructing ancestral character states: a critical reappraisal. TREE 13, 361-366.

Felsenstein J. 1981. Evolutionary trees from DNA sequences: A maximum likelihood approach. Journal of Molecular Evolution. 17, 368-376.

Gorman O.T., Bean W.J., Kawaoka Y., Donatelli I., Guo Y., Webster R.G. 1991. Evolution of Influenza A Virus Nucleoprotein Genes:Implications for the Origins of H1N1 Human and Classical Swine Viruses. Journal of Virology 65:3704-3714.

Kimura M. 1983. The neutral theory of molecular evolution. Cambridge University Press, Cambridge pp.269-276.

Leitner T, Albert J. 1999. The molecular clock of HIV-1 unveiled through analysis of a known transmission history. Proc. Natl. Acad. Sci. USA. 96 10752-10757.

Muse S. V. and Weir B.S. 1992. Testing for equality of evolutionary rates. Genetics. 132,

Sarich V.M., Wilson A.C. 1973. Generration time and genomic evolution in primates. Science. 179, 1144-1147.

Abstract - Presented at the Virus Evolution Workshop
Ardmore, OK
October 21 - 24th, 1999

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Dr. Marilyn Roossinck
Plant Biology Division
The Noble Foundation
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phone: 580 224-6630