Pick Shortest Path and Select -> Checker Deselect are your friends
Select one edge ring along the torus (ring, not loop), Select -> Checker Deselect, Select -> Select Loops -> Edge Loops, dissolve edges.
With default keymap (and on a cylinder instead of torus) selecting the ring can be done by clicking one edge at the top, ctrl+clicking one at the bottom and in options checking both Face Stepping and Topology Distance; dissolution is, in edge mode, ctrl+x.
Options for both Checker Deselect and Pick Shortest Path can let you define a pattern other than every other edge.
Another way is to, in edge mode, select one edge in the ring, select one after next in the same ring (have to be done with click-selection to set active), do a bunch of Select -> Select More/Less -> Next Active, then convert to loops and dissolve.