Cis4elk, I have not found any literature discussing FMV, or any of the other viruses that cause mottling disease in figs, persistence in soil. There are a number of studies looking at tobacco & tomato mosaic virus persistence in soil. One example is:
http://link.springer.com/article/10.1007%2Fs10661-007-0075-7
This study is pretty typical of what I have found in the literature. TMV belongs to the genus Tobamovirus. These viruses are known to persist in soil as you point out. These viruses are not transmitted by insects, fungi or nematodes, unlike the various viruses that cause FMD (fig mosaic disease). TMV and the other Tobamoviruses are easily transmitted by rub-inoculation. The FMD causing viruses appear to be only transmitted by insect vectors, certain mites. Additionally grafting or budding with an infect branch on an uninfected tree will cause transmission of FMD. A recent paper, which is attached below, indicates that 3 viruses causing FMD can not be transmitted mechanically. Before everyone gets too excited about “uninfected” trees in Turkey, please note there are some technical flaws in their testing that clearly give false negative results in terms of whether they detect virus in a tree. Mechanical transmission would be the primary reason to be concerned about viral persistence in the soil and/or vegetative material near your trees. If you have erophyid mites around, they will easily move from tree to tree well beyond usual yard dimensions. I am attaching a mite review for those interested.
As to the organic matter left over after pulling your trees, there is almost certainly virus in the fig tissue (roots, leaves, etc.) left in or on the ground. Transmission of FMD causing viruses by the insects and other organisms left in the ground has not been reported to my knowledge. Mites that transmit FMD viruses over-winter in the buds of dormant fig trees. It is not apparent that removing left over roots, dropped leaves, etc. serves any useful purpose. It certainly won’t hurt. If you have trees that are showing FMD and some that are not, my guess is your energy is better spent trying to eliminate/reduce any mite population you may have around when they start to reappear in April & May.
Dieseler, I have not seen any study demonstrating transmission through shears or other physical means. My bias is to follow the “better safe than sorry” adage on this one, but would be interested to see any publications you have seen on this issue.
Like Mike and many others on this forum, I have accepted that all my trees likely are infected by one or more FMD causing viruses. I am interested in approaches that give me healthier trees. Some of the members of this forum work hard to find examples of each cultivar which show few, if any, FMD symptoms. That approach requires a little more work, but it is loaded with common sense. A second approach I am trying is to look at whether a nutritional strategy can impact FMD. Also, there are molecules that activate a plant’s innate immune system. I have started looking to see if using any of those molecules can impact my trees’ health.