"随季节而移居" can be translated into English as "migrate seasonally" or "relocate according to the seasons".
"Migrate seasonally" is a concise and commonly used expression, directly conveying the idea of moving from one place to another in response to seasonal changes.
"Relocate according to the seasons" provides a slightly more detailed description, emphasizing the act of moving and the seasonal basis for that movement.
Both translations are accurate and can be used depending on the context and desired level of detail.