"随季节而移居" can be translated into English as "migrate seasonally" or "seasonal migration" (depending on the context, with the former as a verb phrase and the latter as a noun phrase).
For example:
Some birds migrate seasonally to find warmer climates. （一些鸟类随季节而移居，以寻找更温暖的气候。）
Seasonal migration is a common phenomenon among certain animal species. （随季节而移居在某些动物物种中是一种常见现象。）