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.