Data from: Clines arc through multivariate morphospace

Evolutionary biologists typically represent clines as spatial gradients in a univariate character (or a principal-component axis) whose mean changes as a function of location along a transect spanning an environmental gradient or ecotone. This univariate approach may obscure the multivariate nature of phenotypic evolution across a landscape. Clines might instead be plotted as a series of vectors in multidimensional morphospace, connecting sequential geographic sites. We present a model showing that clines may trace nonlinear paths that arc through morphospace rather than elongating along a single major trajectory. Arcing clines arise because different characters diverge at different rates or locations along a geographic transect. We empirically confirm that some clines arc through morphospace, using morphological data from threespine stickleback sampled along eight independent transects from lakes down their respective outlet streams. In all eight clines, successive vectors of lake-stream divergence fluctuate in direction and magnitude in trait space, rather than pointing along a single phenotypic axis. Most clines exhibit surprisingly irregular directions of divergence as one moves downstream, although a few clines exhibit more directional arcs through morphospace. Our results highlight the multivariate complexity of clines that cannot be captured with the traditional graphical framework. We discuss hypotheses regarding the causes, and implications, of such arcing multivariate clines.

进化生物学家通常将渐变群（cline）表示为单变量性状（univariate character，或主成分轴（principal-component axis））上的空间梯度，其均值随跨越环境梯度或生态交错带（ecotone）的样带（transect）上的采样位置变化而变化。这种单变量研究方法可能会掩盖跨景观表型演化的多变量本质。与之相对，渐变群可被绘制为多维形态空间（morphospace）中的一系列向量，用以连接连续的地理采样点。我们提出了一个模型，表明渐变群可能会沿着穿过形态空间的弧形非线性路径延伸，而非仅沿单一主要轨迹（trajectory）拉长。弧形渐变群的产生，是因为不同性状在地理样带的不同位置以不同速率发生分化。我们利用沿8条独立样带（从湖泊至其各自出水口溪流）采集的三刺鱼（threespine stickleback）形态学数据，实证证实了部分渐变群确实会在形态空间中呈弧形分布。在全部8条渐变群中，湖-溪分化的连续向量在性状空间（trait space）中的方向与大小均存在波动，而非始终沿单一表型轴延伸。尽管少数渐变群在形态空间中呈现出较为规整的弧形轨迹，但多数渐变群在沿溪流向下游移动时，其分化方向表现出出人意料的不规则性。我们的研究结果凸显了渐变群的多变量复杂性，而这类复杂性是传统图形框架无法捕捉的。我们还讨论了关于这类弧形多变量渐变群的成因与影响的相关假说。