Statistical methods for biological applications

My thesis consists of four distinct statistical issues occurring in biology. Each chapter discusses one issue at length and provides the code needed to implement the statistical methodology.;Chapter 1 deals with testing the randomness of gene duplications in the genome of a specific fern species. Standard Chi-square testing does not apply because the expected cell counts are too low and because gene duplicates place unique restrictions on the table. We develop and discuss appropriate methods for handling these issues in this biological context.;Chapter 2 deals with developing the appropriate multivariate test to determine if there is segregation distortion along the chromosomes of the same fern species. Methods for determining the locations contributing to the segregation distortion are discussed as well.;Chapter 3 deals with developing a pooled-variance estimator for hypothesis testing using cDNA microarrays. Such methods were previously developed for oglionucleotide arrays and the chapter discusses the problems of extending these results to cDNA arrays as well as presenting a statistical technique appropriate to the new problem.;Chapter 4 deals with correcting the bias in Tajima's D statistic, a popular statistic in Biology used for detecting selection under the assumption of constant population sizes and detecting changes in population sizes under the assumption of neutral gene evolution.