Data from: On measurements of phenotypic parallel evolution

Several metrics have been proposed to measure phenotypic parallel
evolution.  All of these metrics stem from a geometric definition
of parallel evolution in which two evolutionary trajectories are,
literally, parallel or non-parallel to each other.  Two metrics
fit this definition: the interaction term between population and habitat
in a two-factor ANOVA and a measure of the angle between two multivariate
trajectories of evolution.  A third metric is derived from the
general direction of multivariate trajectories; although this might fit
our intuition about parallel evolution, it does not fit the geometric
definition.  A fourth metric is based on the amount of variation
explained by the habitat variable in a one-factor ANOVA (i.e., the
R2).  We show here that the R2 metric does not reliably measure
any aspect of parallelism and should be avoided.  We also discuss
the importance of establishing proper ancestor-descendent relationships in
attempting to use any of the valid metrics to quantify parallel
evolution.  Finally, because different metrics measure different
aspects of evolutionary trajectories, we recommend being explicit about
what one is trying to measure (angle, direction, or length of
trajectories).

目前已有多种度量指标被提出用于衡量表型平行进化（phenotypic parallel evolution）。所有这些指标均源于平行进化的几何定义——在此定义中，两条进化轨迹（evolutionary trajectories）在字面意义上要么平行，要么不平行。有两种指标符合这一定义：双因素方差分析（two-factor ANOVA）中种群与栖息地的交互项，以及两条多变量进化轨迹间的夹角度量。第三种指标源于多变量轨迹的总体方向；尽管这可能符合我们对平行进化的直觉认知，但它并不满足上述几何定义。第四种指标基于单因素方差分析（one-factor ANOVA）中栖息地变量所解释的变异量（即R²）。本文表明，R²指标无法可靠地衡量平行性（parallelism）的任何方面，因此应避免使用。我们还讨论了在尝试使用任何有效指标量化平行进化时，建立恰当的祖先-后代关系（ancestor-descendent relationships）的重要性。最后，由于不同指标衡量进化轨迹的不同方面，我们建议明确说明拟测量的具体内容（轨迹的夹角、方向或长度）。