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Simulation remains a very important approach to testing the robustness and accuracy of phylogenetic inference methods. However, current simulation programs are limited, especially concerning realistic models for simulating insertions and deletions (indels). In this thesis I implement a new, portable and flexible application, named INDELible, which can be used to generate nucleotide, amino acid and codon sequence data by simulating indels (under several models of indel length distribution) as well as substitutions (under a rich repertoire of substitution models). In particular, I introduce a simulation study that makes use of one of INDELible’s many unique features to simulate data with indels under codon models that allow the nonsynonymous/synonymous substitution rate ratio to vary among sites and branches. This data is used to quantify, for the first time, the precise effects of indels and alignment errors on the false-positive rate and power of the widely used branch-site test of positive selection. Several alignment programs are used and assessed in this context. Through the simulation experiment, I show that insertions and deletions do not cause the test to generate excessive false positives if the alignment is correct, but alignment errors can lead to unacceptably high false positives. Previous selection studies that use inferior alignment programs are revisited to demonstrate the applicability of my results in real world situations. Further work uses simulated data from INDELible to examine the effects of tree-shape and branch length on the alignment accuracy of several alignment programs, and the impact of alignment errors on different methods of phylogeny reconstruction. In particular, analysis is performed to explore which programs avoid generating the kind of alignment errors that are most detrimental to the process of phylogeny reconstruction.

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

published_or_final_version / Business Administration / Master / Master of Business Administration

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In this thesis analytical and simulation techniques are applied to problems in biological evolution. The thesis is divided into four parts. Firstly, chapter two investigates anomalies that occur in the Penna bit-string model of ageing, an influential model of mutation accumulation and selection. These anomalies result in unusual demographic distributions and can lead to the so-called Eve effect. The anomalies are characterised along with their associated demographic distributions. It is argued that the anomalies are similar in nature to the well known first-passage problem. Secondly, chapter three uses evolutionary game theory to investigate the evolution of harmful mating tactics in hermaphrodites. These tactics benefit the function of the sperm donor at the expense of sperm recipient. The model predicts evolutionary stable values of resource allocation between sexual functions, and the level of harm. The analysis provides support for empirical observations and makes predictions about the effects of harmful mating tactics on population evolution. Thirdly, chapter four considers the sustainability of the two main types of sexual reproduction; hermaphroditism and dioecy (male and female individuals). By use of stochastic spatial simulations it is demonstrated that hermaphroditism can have an even greater advantage over dioecy than predicted by mean-field analysis. This result provides support for the observation that hermaphroditism is associated with sedentary species. Finally, chapter five considers the evolution of gynodioecy, a breeding system of plants in which populations consist of hermaphrodite and female individuals. It is both a common and widespread polymorphism, and has been identified in many species of ecological and economic interest. Mean-field calculations and stochastic spatial simulations are used to identify the conditions necessary for gynodioecy to evolve.

We propose using statistical regular pavings (SRPs) as an efficient and adaptive statistical data structure for processing massive, multi-dimensional data. A regular paving (RP) is an ordered binary tree that recursively bisects a box in $\Rz^{d}$ along the first widest side. An SRP is extended from an RP by allowing mutable caches of recursively computable statistics of the data. In this study we use SRPs for two major applications: estimating histogram densities and summarising large spatio-temporal datasets. The SRP histograms produced are $L_1$-consistent density estimators driven by a randomised priority queue that adaptively grows the SRP tree, and formalised as a Markov chain over the space of SRPs. A way to select an estimate is to run a Markov chain over the space of SRP trees, also initialised by the randomised priority queue, but here the SRP tree either shrinks or grows adaptively through pruning or splitting operations. The stationary distribution of the Markov chain is then the posterior distribution over the space of all possible histograms. We then take advantage of the recursive nature of SRPs to make computationally efficient arithmetic averages, and take the average of the states sampled from the stationary distribution to obtain the posterior mean histogram estimate. We also show that SRPs are capable of summarizing large datasets by working with a dataset containing high frequency aircraft position information. Recursively computable statistics can be stored for variable-sized regions of airspace. The regions themselves can be created automatically to reflect the varying density of aircraft observations, dedicating more computational resources and providing more detailed information in areas with more air traffic. In particular, SRPs are able to very quickly aggregate or separate data with different characteristics so that data describing individual aircraft or collected using different technologies (reflecting different levels of precision) can be stored separately and yet also very quickly combined using standard arithmetic operations.

No description available.