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Issue No.02 - March/April (2011 vol.8)
pp: 551-556
Glenn Hickey , McGill University, Montreal
Mathieu Blanchette , McGill University, Montreal
Paz Carmi , Ben-Gurion University of the Negev, Beer-Sheva
Anil Maheshwari , Carleton University, Ottawa
Norbert Zeh , Dalhousie University, Halifax
The phylogenetic diversity (PD) of a set of species is a measure of their evolutionary distinctness based on a phylogenetic tree. PD is increasingly being adopted as an index of biodiversity in ecological conservation projects. The Noah's Ark Problem (NAP) is an NP-Hard optimization problem that abstracts a fundamental conservation challenge in asking to maximize the expected PD of a set of taxa given a fixed budget, where each taxon is associated with a cost of conservation and a probability of extinction. Only simplified instances of the problem, where one or more parameters are fixed as constants, have as of yet been addressed in the literature. Furthermore, it has been argued that PD is not an appropriate metric for models that allow information to be lost along paths in the tree. We therefore generalize the NAP to incorporate a proposed model of feature loss according to an exponential distribution and term this problem NAP with Loss (NAPL). In this paper, we present a pseudopolynomial time approximation scheme for NAPL.
Noah's ark problem, phylogenetic diversity, approximation algorithm.
Glenn Hickey, Mathieu Blanchette, Paz Carmi, Anil Maheshwari, Norbert Zeh, "An Approximation Algorithm for the Noah's Ark Problem with Random Feature Loss", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 2, pp. 551-556, March/April 2011, doi:10.1109/TCBB.2010.37
[1] S. Nee and R. May, "Extinction and the Loss of Evolutionary History," Science, vol. 278, no. 5338, p. 692-694, 1997.
[2] A. Magurran, Measuring Biological Diversity. Blackwell Publishing, 2004.
[3] D. Faith, "Conservation Evaluation and Phylogenetic Diversity," Biological Conservation, vol. 61, pp. 1-10, 1992.
[4] S. Heard and A. Mooers, "Phylogenetically Patterned Speciation Rates and Extinction Risks Change the Loss of Evolutionary History during Extinctions," Proc. Royal Soc. of London B, vol. 267, pp. 613-620, 2000.
[5] Phylogeny and Conservation, A. Pruvis, L.L. Gittleman, and T. Brooks, eds. Cambridge Univ. Press, 2005.
[6] F. Pardi and N. Goldman, "Species Choice for Comparative Genomics: Being Greedy Works," PLoS Genetics, vol. 1, no. 6,e71, 2005.
[7] M. Weitzman, "The Noah's Ark Problem," Econometrica, vol. 66, pp. 1279-1298, 1998.
[8] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, 1979.
[9] M. Bordewich, A. Rodrigo, and C. Semple, "Selecting Taxa to Save or Sequence: Desirable Criteria and a Greedy Solution," Systematic Biology, vol. 57, no. 6, pp. 825-834, 2008.
[10] K. Hartmann and M. Steel, "Maximizing Phylogenetic Diversity in Biodiversity Conservation: Greedy Solutions to the Noah's Ark Problem," Systematic Biology, vol. 55, no. 4, pp. 644-651, 2006.
[11] F. Pardi and N. Goldman, "Resource-Aware Taxon Selection for Maximizing Phylogenetic Diversity," Systematic Biology, vol. 56, no. 3, pp. 431-44, 2007.
[12] B. Minh, S. Klaere, and A.von Haeseler, "Phylogenetic Diversity within Seconds," Systematic Biology, vol. 55, no. 5, pp. 769-773, 2006.
[13] M. Steel, "Phylogenetic Diversity and the Greedy Algorithm," Systematic Biology, vol. 54, no. 4, pp. 527-529, 2005.
[14] M. Bordewich, C. Semple, and A. Spillner, "Optimizing Phylogenetic Diversity across Two Trees," Applied Math. Letters, vol. 22, no. 5, pp. 638-641, 2009.
[15] B. Minh, F. Pardi, S. Klaere, and A. von Haeseler, "Budgeted Phylogenetic Diversity on Circular Split Systems," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 6, no. 1, pp. 22-29, Jan.-Mar. 2009.
[16] A. Spillner, B. Nguyen, and V. Moulton, "Computing Phylogenetic Diversity for Split Systems," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 5, no. 2, pp. 235-244, Apr.-June 2008.
[17] M. Bender and M. Colton, "The LCA Problem Revisited," Proc. Fourth Latin Am. Symp. Theoretical Informatics (LATIN '00), pp. 10-14, Apr. 2000.
[18] E. Harding, "The Probabilities of Rooted Tree-Shapes Generated by Random Bifurcation," Advances in Applied Probability, vol. 3, no. 1, pp. 44-77, 1971.
[19] G. Yule, "A Mathematical Theory of Evolution, Based on the Conclusions of Dr. JC Willis, FRS," Philosophical Trans. Royal Soc. of London. Series B, Containing Papers of a Biological Character, vol. 213, pp. 21-87, 1925.
[20] P. Erdos, M. Steel, L. Szekely, and T. Warnow, "A Few Logs Suffice to Build (Almost) All Trees: Part II," Theoretical Computer Science, vol. 221, no. 1, pp. 77-118, 1999.
[21] V. Moulton, C. Semple, and M. Steel, "Optimizing Phylogenetic Diversity under Constraints," J. Theoretical Biology, vol. 246, no. 1, pp. 186-194, 2007.
[22] M. Bordewich and C. Semple, "Nature Reserve Selection Problem: A Tight Approximation Algorithm," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 5, no. 2, pp. 275-280, Apr.-June 2008.
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