A growing number of empirical studies have quantified the degree to which evolution is geometrically parallel by estimating and interpreting pairwise angles between multiple replicate lineages’ evolutionary change vectors in multivariate trait space. Similar comparisons, of distance in trait space, are used to assess the degree of convergence. These approaches amount to element‐by‐element interpretation of distance matrices, typically testing for differences among replicate evolutionary vectors, compared to a null hypothesis of perfect parallelism. We suggest a complimentary set of approaches, co‐opted from evolutionary quantitative genetics, involving eigen analysis and comparison of among‐lineage covariance matrices. Such approaches allow one to identify multiple major axes of evolutionary change (e.g., alternative adaptive solutions), and also allow for the definition of biologically tenable null hypotheses, such as drift, against which empirical patterns can be tested. Reanalysis of a dataset of multivariate evolution across a replicated lake/stream gradient in threespine stickleback reveals that most of the variation in the direction of evolutionary change can be captured in just a few dimensions, indicating a greater extent of parallelism than previously appreciated. We suggest that applying such multivariate approaches may often be necessary to fully understand the extent and form of parallel and convergent evolution.

中文翻译：

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平行进化的多元观点

越来越多的实证研究通过估计和解释多元性状空间中多个复制谱系的进化变化向量之间的成对角度来量化进化几何平行的程度。特征空间中距离的类似比较用于评估收敛程度。这些方法相当于对距离矩阵的逐元素解释，通常测试重复进化向量之间的差异，与完美并行的零假设相比。我们建议从进化数量遗传学中选择一套互补的方法，包括特征分析和谱系间协方差矩阵的比较。这种方法允许人们识别进化变化的多个主轴（例如，替代的适应性解决方案），并且还允许定义生物学上站得住脚的零假设，例如可以测试经验模式的漂移。对三脊棘鱼中复制的湖泊/河流梯度的多元进化数据集的重新分析表明，进化变化方向的大部分变化都可以在几个维度上捕捉到，这表明比以前认识到的更大程度的并行性。我们建议应用这种多变量方法对于充分理解并行和收敛进化的程度和形式通常是必要的。对三脊棘鱼中复制的湖泊/河流梯度的多元进化数据集的重新分析表明，进化变化方向的大部分变化都可以在几个维度上捕捉到，这表明比以前认识到的更大程度的并行性。我们建议应用这种多变量方法对于充分理解并行和收敛进化的程度和形式通常是必要的。对三脊棘鱼中复制的湖泊/河流梯度的多元进化数据集的重新分析表明，进化变化方向的大部分变化都可以在几个维度上捕捉到，这表明比以前认识到的更大程度的并行性。我们建议应用这种多变量方法对于充分理解并行和收敛进化的程度和形式通常是必要的。