I wish to delete all submissions prior to 2016. I can't figure out how.

You can follow this guide on how to delete your submissions: https://www.jotform.com/help/377-How-to-Delete-Form-Submission-Data. You can specify what group of submissions to delete by simply changing the "Time Frame" option in the settings.

Please note that deleting submissions is irreversible, they cannot be recovered after. It would be best to download your submissions for backup purposes. 

I hope that helps.