The topic of my diploma thesis is the statistical evaluation of biological sequences with the help of phylogenic trees. In the theoretical part we will create a literary recherche of estimation methodology concerning the course of phylogeny on the basis of the similarity of biological sequences (DNA and proteins) and we will focus on the inaccuracies of the estimation, their causes and the possibilities of their elimination. Afterwards, we will compare the methods for the statistical evaluation of the correctness of the course of phylogeny. In the practical part of the thesis we will suggest algorithms that will be used for testing the correctness of the phylogenic trees on the basis of bootstrapping, jackknifing, OTU jackknifing and PTP test which are able to the capture phylogenic tree with the method neighbor joining from the biological sequences in FASTA code. It is also possible to change the distance model and the substitution matrix. To be able to use these algorithms for the statistical support of phylogenic trees we have to verify their right function. This verification will be evaluated on the theoretical sequences of the amino acids. For the verification of the correct function of the algorithms, we will carry out single statistical tests on real 10 sequences of mammalian ubiquitin. These results will be analysed and appropriately discussed.

The master's thesis provides a comprehensive overview of resampling methods for testing the correctness topology of the phylogenetic trees which estimate the process of phylogeny on the bases of biological sequences similarity. We focused on the possibility of errors creation in this estimate and the possibility of their removal and detection. These methods were implemented in Matlab for Bootstrapping, jackknifing, OTU jackknifing and PTP test (Permutation tail probability). The work aims to test their applicability to various biological sequences and also to assess the impact of the choice of input analysis parameters on the results of these statistical tests.

Like coral reefs worldwide, the Florida Reef Tract has dramatically declined within the past two decades. Monitoring of 40 sites throughout the Florida Keys National Marine Sanctuary has undertaken a multiple-parameter approach to assess spatial and temporal changes in the status of the ecosystem. The objectives of the present study consist of the following: In chapter one, we review past coral reef studies; emphasis is placed on recent studies on the stony corals of reefs in the lower Florida Keys. We also review the economic impact of coral reefs on the state of Florida. In chapter two, we identify the underlying probability distribution function of the stony coral cover proportions and we obtain better estimates of the statistical properties of stony coral cover proportions. Furthermore, we improve present procedures in constructing confidence intervals of the true median and mean for the underlying probability distribution. In chapter three, we investigate the applicability of the normal probability distribution assumption made on the pseudovalues obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies. We investigate a new and more effective approach to estimating the Shannon-Wiener and Simpson's diversity index. In chapter four, we develop the best possible estimate of the probability distribution function of the jackknifing pseudovalues, obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies, using the xi nonparametric kernel density estimate method. This nonparametric procedure gives very effective estimates of the statistical measures for the jackknifing pseudovalues. Lastly, the present study develops a predictive statistical model for stony coral cover. In addition to identifying the attributable variables that influence the stony coral cover data of the lower Florida Keys, we investigate the possible interactions present. The final form of the developed statistical model gives good estimates of the stony coral cover given some information of the attributable variables. Our nonparametric and parametric approach to analyzing coral reef data provides a sound basis for developing efficient ecosystem models that estimate future trends in coral reef diversity. This will give the scientists and managers another tool to help monitor and maintain a healthy ecosystem.

The estimated bias and variance of commonly applied and jackknife variance estimators and observed significance level and power of standardised generalized Wilcoxon linear rank sum test statistics and tests, respectively, of Gehan and Prentice are compared in a Monte Carlo simulation study. The variance estimators are the permutational-, the conditional permutational- and the jackknife variance estimators of the test statistic of Gehan, and the asymptotic- and the jackknife variance estimators of the test statistic of Prentice. In unbalanced small sample size problems with right censoring, the commonly applied variance estimators for the generalized Wilcoxon rank test statistics of Gehan and Prentice may be biased. In the simulation study it appears that variance properties and observed level and power may be improved by using the jackknife variance estimator. To establish the sensitivity to gross errors and misclassifications for standardised generalized Wilcoxon linear rank sum statistics in small samples with right censoring, the sensitivity curves of Tukey are used. For a certain combined sample, which might contain gross errors, a relatively simple method is needed to establish the applicability of the inference drawn from the selected rank test. One way is to use the change of decision point, which in this thesis is defined as the smallest proportion of altered positions resulting in an opposite decision. When little is known about the shape of a distribution function, non-parametric estimates for the location parameter are found by making use of censored one-sample- and two-sample rank statistics. Methods for constructing censored small sample confidence intervals and asymptotic confidence intervals for a location parameter are also considered. Generalisations of the solutions from uncensored one-sample and two-sample rank tests are utilised. A Monte-Carlo simulation study indicates that rank estimators may have smaller absolute estimated bias and smaller estimated mean squared error than a location estimator derived from the Product-Limit estimator of the survival distribution function. The ideas described and discussed are illustrated with data from a clinical trial of Head and Neck cancer. / digitalisering@umu