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The arrows indicate the potential direction of range expansion from putative glacial refugia.
For wedge-billed woodcreepers in the Andes, the most likely direction of range expansion since the LGM is from lower to higher altitudes (Fig. S7).
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The two-dimensional SAR image formed is interpreted in the directions of range and azimuth.
For each of these groups the probable directions of range expansion from the putative glacial refugia in which they are likely to have differentiated could be inferred from decreasing diversity trends when moving away from the putative refugia.
That no ecological differences have been found between these species, and that replacement of hermit warblers by Townsend's warblers is proceeding downward in latitude and elevation – opposite the directions of range shifts predicted by recent climate change – further support that this movement is not being driven by alternative environmental factors.
Results of our simulation analyses generally illustrated that pairwise genetic distances become reduced in the direction of the range expansion (Fig. 3e, Table 1).
We investigated here the phylogeography of this land snail to reassess the evolutionary scenario we previously considered for explaining its scattered distribution in the western Mediterranean, and to help to resolve the question of the direction of its range expansion (from north Africa to Europe or vice versa).
Mr. Apatow's film taps into an easily recognizable strain of Jewish-American male identity, one that nods not only in the direction of comedians ranging from Milton Berle to Lenny Bruce to Larry David, but also at a broader tradition of sexual insecurity and worldly ambition that zigzags from Saul Bellow to Woody Allen by way of Paul Mazursky and Philip Roth.
Using such a composite estimate would be critical if the goal was to project the direction and extent of range shifts for each of the subunits separately (which is not our focus).
These results are comparable to those from a similar study in terms of the direction and range of IRRs estimates.
This method was based on the cumulant domain data and adopted the total least squares (TLS) solution to obtain the direction-of-arrival (DOA) and range estimations, which avoided the computationally inefficient 2-D spectral search.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com