Asked March 13, 2017, 1:58 PM EDT
Deschutes County Oregon
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Sounds like you have a vole issue. Voles (Microtus spp) are rodents that make the characteristic holes and runways which you describe. The presence really becomes noticeable after snow. These little guys are capable of causing a lot of damage to cultivated crops, orchards, and lawns. Trees are most often damaged (girdled) in the winter so now is the time to check them as well.
Tree girdling caused by voles is characterized by non-uniform gnaw marks that are about 1/8 inch in width and 3/8 inch in length which occur at various angles and in irregular patches. And because of the small size of voles this girdling occurs close to the ground.
The most prominent damage by voles is their extensive runway system through grassy areas including lawns. Runways are 1 to 2 inches in width and the vegetation is often clipped close to the ground next to well-traveled routes.
Control falls into 3 categories - habitat modification, exclusion, and population reduction. For effective long-term control all three measures will probably be needed.
The elimination of weeds and ground cover around lawns and flower beds can reduce habitat suitability - voles do not like open ground. Lawns should be mowed regularly to two inches and mulch should be cleared three feet from the base of trees. In addition, if you live in an area where you can modify the habitat to encourage natural vole predators, that will help. These include snakes, hawks, owls, weasels and shrews.
Cylinders made of hardware cloth (with a mesh size no larger than 1/4 inch) are often effective in excluding voles and protecting individual plants and trees. You will need to burry part of the cylinder at least 6 inches below the ground surface to ensure that voles will not burrow under it. Protecting large areas such as your lawn is cost prohibitive.
You do not say what your trapping method has been but simple snap traps baited with peanut butter is fairly effective if the population is not too large. Make sure you cover the traps somehow so other critters such as birds do not get caught in them.
I usually do not recommend rodenticides (rodent poisons) because of the possibility of poisoning other animals such as hawks and owls, which will often eat the poisoned rodents. However, if that is the direction you want to go, here are two links to some information regarding elimination and control:
It is very important to put the poison down in the burrow so birds do not eat it off the ground and read and follow the label carefully.