Phylogenetic comparative methods are well established tools for using inter-species variation to analyse phenotypic evolution and adaptation. They are generally hampered, however, by predominantly univariate approaches and failure to include uncertainty and measurement error in the phylogeny as well as the measured traits. This thesis addresses all these three issues. First, by investigating the effects of correlated measurement errors on a phylogenetic regression. Second, by developing a multivariate Ornstein-Uhlenbeck model combined with a maximum-likelihood estimation package in R. This model allows, uniquely, a direct way of testing adaptive coevolution. Third, accounting for the often substantial phylogenetic uncertainty in comparative studies requires an explicit model for the tree. Based on recently developed conditioned branching processes, with Brownian and Ornstein-Uhlenbeck evolution on top, expected species similarities are derived, together with phylogenetic confidence intervals for the optimal trait value. Finally, inspired by these developments, the phylogenetic framework is illustrated by an exploration of questions concerning "time since hybridization", the distribution of which proves to be asymptotically exponential. [COMMENT: Please note that this abstract and thesis is from 2013]

翻译：系统发育比较方法是通过物种间变异分析表型演化与适应的成熟工具。然而，这些方法通常受限于以单变量分析为主，且未能充分考虑系统发育树及测量性状中的不确定性与测量误差。本论文针对这三个问题展开研究。首先，探究了相关测量误差对系统发育回归的影响。其次，开发了结合R语言最大似然估计程序包的多变量Ornstein-Uhlenbeck模型，该模型首次提供了检验适应性协同演化的直接方法。第三，为解决比较研究中常存在的显著系统发育不确定性，需要建立明确的树模型。基于近期发展的条件分支过程（以布朗运动和Ornstein-Uhlenbeck演化过程为基础），推导出物种相似度的期望值，并给出最优性状值的系统发育置信区间。最后，受这些进展启发，通过探索关于"杂交后时间"的问题（其分布被证明具有渐近指数特性）来阐释系统发育分析框架。