Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2009

A method was developed to apply double principal coordinate analysis to compositional data with zeros. This method was then applied to the fish gut content data of some important fishes in Lake Mihaba, Agusan Marsh. The developed method involved applying rounded zero replacement to the original compositional distribution matrix. After zero replacement, centered logarithmic-ratio transformation was applied to the new matrix in order to transformation the compositional distribution matrix from the constrained simplex space to the unconstrained real number space. To address this one, the absolute value of the minimum element in each row of the clr-transformed matrix was added to every element in each row where that minimum belong, resulting in a new modified clr-transformed distribution matrix. The DPCoA produced with this were also compared with using the nonzero compositional data as the distribution matrix. Computations of Rao DVIC using modified clr-transformed matrix reflected better not only the compositional abundance among variables compared to when nonzero compositional matrix was used, but also the dissimilarities between samples. In addition, DPCoA based on Rao DIVC and Rao DISC presented a better typology on the dietary behavior of fish species and the consumption pattern of food items by various fish species when modified clr-transformed distribution matrix was used. The better results produced by the developed method reflect the use of the principles of compositional data analysis.