Tree roots react to their surrounding underground environment. If your sewer pipe leaks in the slightest, roots from nearby trees will seek out the water and "fertilizer" they need to thrive. One the tiny, seemingly harmless feeder roots work their way into pipe seams and / or holes, they will slowly but surely grow into bigger roots and will eventually fill the inside of the pipe with more and more roots until your sewer no longer drains at all.
The best warning sign is slow household drains. If you notice that your shower, tub and kitchen sink plumbing / drains appear to be extra slow, first try to use a natural enzyme-based drain care product like Roto-Rooter Pipe Shield(available from any Roto-Rooter office or service technician). Treat the drains and watch for improvement in drainage. If you don't see improvement, you may need a professional sewer cleaning or even a sewer repair.
Residential plumbing takes a hit this time of year because of so much use with guests and all. Thanksgiving is the height of the busy season for plumbers. You would be well advised to address these problems now before you begin your holiday entertaining. You won't be sorry if you plan ahead now for the unexpected.