Fig. 2: A synthesized example of the SORD vector-direction comparison methodology.
From: Forest fires and climate-induced tree range shifts in the western US
After scaling the environmental variables across the study area, we plotted the SORD vectors (exemplified here by \(\vec{{{{{{\rm{A}}}}}}}\) and \(\vec{{{{{{\rm{B}}}}}}}\)) with the initial point of each vector at the centroid of the source population and the terminal point of each vector at the centroid of the seedling-only population (a). We then translocated the vectors to the origin and found the angle θ between them (b) and calculated the cosine of θ which is equivalent to \(\frac{|\vec{{{{{{{\rm{A}}}}}}}_{{{{{{\rm{j}}}}}}}}|}{\left|\vec{{{{{{\rm{A}}}}}}}\right|}\), i.e., the component of the normalized \(\vec{{{{{{\rm{A}}}}}}}\) that lies along normalized \(\vec{{{{{{\rm{B}}}}}}}\) (c).
