Terry, you are so mean making us make these tough choices
No matter the bow, in this situation for me, it would have to be 50-55#, to be able to handle anything that it may have to encounter. Apocalypses means all those critters in zoo's are out and worst enemy will have armor on.
My second choice for a "survival" bow, would be one on the rack now of course, Northern Mist American 66" long, 55@28".
This bow is built bomb tough by Steve, being an ASL it is a little finicky with arrows (love heavy) but can shoot wide span (see bottom). It is very shootable in my hands. It is a one piece, but a 2 piece would be ideal in situation, for concealability and hiking. Spare String on bow, with spare in pack, set up ready to go.
My First choice, would be what Pat said, a solid fiberglass longbow, 50-55#. Years ago, I had an old one from Ben Pearson, that was 55#, 2 piece, and that bow was actually bomb proof, shot accurately within 18 yards for me, weather would not be an issue.
Arrows are the biggest challenge I see. So a bow that can handle a wide variety of arrow spine and material would be crucial. There would be plenty of material still around, but having the ability to get it tuned effectively would be the challenge. Why I see a wide span of handling shaft spine critical. Making our own shafts from dogwood now it easy and fun, but in this situation, our very lives depend on it. Plus, we all know that we will need to be able to replenish our ammunition supply, sooner or later.