Is there a way to merge or collapse a row of verts or edges into a new row with a single operation as shown in the attached picture?
Hi Esemkay! This might not be the best way, but I would select the two lines as you have done above. Then I would scale them both on the Y-axis to 0. To do this just press ‘S’ then ‘Y’ and then ‘0’. Both these lines will now be in the exact same position, but they will still be two separate rows. To fix this, with the two rows still selected press ‘W’ and select ‘Remove Doubles’.
Hope it helps!
Collapse partial edge ring, from left:
- select faces (shortest path selection)
- edge select mode with contract selection (ctrl+click)
- collapse edges (x).
Thanks for both your replies.
JA12 your method best suits what I need as it averages the edges to collapse so if the lines are not parallel then the collapsed lines shape best follows the average of the two lines.
Following on from my last question what if there are no edges to collapse (see picture). Would it be best to grid fill and then choose the edges to collapse?
JA12 beat me to it 
I’ll still make my post as it’s a touch different and has an extra bit of info (customizing the PathSelectRing hotkey).
And this is the operator for PathSelectRing. This basically selects shortest path, but in Ring fassion.
In the screenshot you can also see how to use Search in the InputEditor (ring). On the left from the Search is the Search Filter (Name (is default), and Key-Biding). You can use the combo of these to filter out the InputEditor and hunt down conflicts and operrators when customizing blender hotkeys.
Thanks for the extra info 0rAngE.
Could do it like that, or W -> bridge edge loops and enable merge from the operator panel, which collapses the edge ring in between and gives a control to position the joined loop.
JA12 thanks for that last tip regarding the merge checkbox with the bridge edgeloops it was very helpful.