Taxonomic analysis of marine phytoplankton

Samples of sea water contain phytoplankton taxa in varying amounts, and marine scientists are interested in the relative abundance of each taxa. Their relative biomass can be ascertained indirectly by measuring the quantity of various pigments using high performance liquid chromatography. However, the conversion from pigment to taxa is mathematically non trivial as it is a positive matrix factorisation problem where both matrices are unknown beyond the level of initial estimates. The prior information on the pigment to taxa conversion matrix is used to give the problem a unique solution. An iteration of two non-negative least squares algorithms gives satisfactory results. Some sample analysis of data indicates prospects for this type of analysis. An alternative more computationally intensive approach using Bayesian methods is discussed. References Efron, B., and Tibirani, R. J., 1993. An introduction to the Bootstrap, Chapman and Hall, New York. Hastings, W. K., 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika, 57:97--109. doi:10.1093/biomet/57.1.97 Lawson C. L., and Hanson R. L. 1995. Solving Least Squares Problems, SIAM, Philadelphia, Ch 23. Lee D. D., and Seung H. S. 2001. Algorithms for Non-negative Matrix Factorization, Advances in Neural Information Processing Systems, 13:556--562. http://luthuli.cs.uiuc.edu/ daf/courses/Optimization/Papers/lee01algorithms.pdf Mackey, M. D., Mackey, D. J., Higgins, H. W. and Wright, S. W., 1996. CHEMTAX---A program for estimating class abundances from chemical markers: application to HPLC measurement of phytoplankton, Marine Ecology - Progress Series, 144:266--283. doi:10.3354/meps144265 van den Meersche, K., Soetaert, K., and Middleburg, J. J., 2008. A Bayesian computational estimator for microbial taxonomy based on biomarkers, Limnol. Oceanogr. Methods 6: 190--199. doi:10.4319/lom.2008.6.190 Robert, C. P. and Casella, G., 2004. Monte Carlo statistical methods, Springer, New York. Roberts, G. O. and Rosenthal, J. S., 2001. Optimal Scaling for Various Metropolis--Hastings Algorithms, Statistical Science 16:351--367. doi:10.1214/ss/1015346320 Wikipedia, 2011. Basic linear algebra subprograms, http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms Wright, S. W., van den Enden, R. L., Pearce, I., Davidson, A. T. Scott, F. J., and Westwood, K. J., 2010. Phytoplankton community structure and stocks in the Southern Ocean (30-80E) determined by CHEMTAX analysis of HPLC pigment signatures Deep-Sea Research II 57:758--778. doi:10.1016/j.dsr2.2009.06.01