If these holes are all about 1" in diameter and there is little to no excavated dirt around each opening, it most likely is the work of meadow voles (Microtus pennsylvanicus) (see https://en.wikipedia.org/wiki/Meadow_vole).  These small rodents (about 4-5" long) are voracious feeders on plant roots, selected bulbs and tubers, seeds, and the inner bark of landscape shrubs and trees (which they gnaw off at or just above the ground line, called "girdling").  Their high reproductive output often leads to periodic population eruptions - - they can produce a new litter about once a month with 4-7 pups per litter, so numbers multiply quickly in favorable habitats.  Thankfully, they are subject to relative high mortality (about 80%) and individual survival can be low - - the typical vole lives no more than several months to a maximum of 2 years.

Treatment often can be difficult, given that these critters spend much of their life underground.  Their presence also may be difficult to detect, particularly in lush habitats with thick or abundant ground cover and especially where synthetic weed barriers have been installed (voles thrive under these covers).  In beds that do not contain weed barriers, reducing the amount of plant cover that affords protection is a key starting point.  Also, reducing the amount of mulch in landscape beds to no more than 1 - 1.5" in depth reduces the attractiveness and protection afforded to voles, thereby helping natural predators to find vole activity areas.  Given their high reproductive output, trapping (either with small live-capture box traps or baited mouse snap traps) typically is not effective in staying ahead of the numbers being produced.  As a result, many cases of vole eruptions require some form of rodenticide treatment to knock down numbers.  Professional assistance often is needed as the materials used to perform this treatment are "restricted use materials" and require those doing the work to acquire special training and certification; many home landscaping and lawn care vendors now have someone on staff who possesses the necessary certification to perform the task.  That said, such treatments can become a regular ongoing and costly repetitive process if nothing else is done to modify the habitat and the amount of available resources that initially attracted voles to the area.  Thus, the entire property should be examined to assess the status of the vole population and to determine where centers of vole activity might be located; then, a well-reasoned landscape management plan should be crafted and implemented to reduce the potential of future infestations. 

Thank you very much! They appear to all be in a 10 x 10 area in the middle of our backyard with no weeds or mulch within 2o feet in any direction. So it sounds like it’s best to let nature take its course?

I would be cautious in assuming that the problem is isolated and would allow you to simply walk away.  I would suggest that you monitor this area and any adjoining areas that support landscaping so as to detect new movement and to be ready to take action, if necessary.  Although they may seem to be out in the open and away from anything else right now, new activity centers can spring up quickly, so rigorous monitoring to detect changes in the population would be encouraged strongly.