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while the standard deviation is estimated to be image = 1.49. In contrast to Table 4.1, there is one tRNA, that for cystine, that scores exceptionally high. The tails of the extremal distributions in the logarithmic region probably behave like exp(-lt), where t is the test value as in the section "Local Sequence Comparisons" and l is a constant, but this has not yet been proven rigorously. The usual intuition informed by the tail of a normal distribution has the probabilities behaving like exp(-t2)/2, which converges to 0 much more rapidly than the Poisson or exponential tails. Thus except for the cystine score, the remaining scores look very much like scores from random sequences. Simulations were performed, and the score 21.0 has an approximate p-value of 10-3, so that it is not possible to dismiss this matching for statistical reasons alone. As far as we know, no one has offered a biological explanation of this interesting match. As to the hypothesis of Bloch et al. (1983), while their work concluded that "matches are too frequent and extensive to be attributed to coincidence," it is not supported by the data but is instead the result of incorrect estimation of p-values. This data set received their most extensive analysis, and they concluded that over 30 percent of the matchings between E. coli 16S rRNA and tRNAs were significant at the level a = 0.10. Correct estimates show about 10 percent of the matching at the level a = 0.10. While the origin of life may be hiding in tRNA and 16S rRNA, it remains elusive.

References

Aldous, D.J., 1989, Probability Approximations via the Poisson Clumping Heuristic, New York: Springer-Verlag.

Arratia, R.A., L. Goldstein, and L. Gordon, 1989, "Two moments suffice for Poisson approximation: The Chen-Stein method," Annals of Probability 17, 9-25.

Arratia, R.A., L. Goldstein, and L. Gordon, 1990, "Poisson approximation and the Chen-Stein method," Statistical Science 5, 403-434.

Arratia, R.A., and M.S. Waterman, 1994, "A phase transition for the score in matching random sequences allowing deletions," Annals of Applied Probability 4, 200-225.

Bloch, D.P., B. McArthur, R. Widdowson, D. Spector, R.C. Guimaraes, and J. Smith, 1983, "tRNA-rRNA sequence homologies: Evidence for a common evolutionary origin?," Journal of Molecular Evolution 19, 420-428.

Chung, K.L., 1974, A Course in Probability Theory, 2nd ed, San Diego, CA: Academic Press.



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