There is an interesting baraita towards the end of chapter 1 of Yerushalmi Shabbat which seems to talk about certain creatures turning in to other creatures. In order to prove this, another baraita is quoted:
דמר ר' יוסה בר ר' בון בשם רב זביד אחת לשבע שנים הקב"ה מחלף את עולמו.
(As) Rabbi Yosa son of Rabbi Bun said in the name of Rav Zavid: Once every seven years, HaKadosh Baruch Hu "switches" the world.That is to imply a cyclical nature to the world. Shmita is not mentioned.