A dense overgrown forest provides poor quality wildlife habitat. See, e.g., Knapp et al. 2013. Dead wood such as snags and coarse woody debris are increasingly seen as critical to healthy forest ecosystems. Bottorff 2009. Girdling a tree to create a snag accomplishes two goals: it thins a stand of trees, and it provides the dead wood essential to many species. I also believe it is a much easier way to thin a stand of trees than conventional logging methods, especially for the land manager with minimal heavy equipment.
In this presentation, Girdling Trees to Create Snags and Coarse Woody Debris, I describe how we have managed a small woodland for the past several years where snag creation is a critical component of the management. This is not scientific research, but the experience we have gained may be helpful to others.
What does this have to do with invasive plants? Not much. I have tried girdling invasive trees like buckthorn (Rhamnus cathartica) with limited success. In fact, I would generally not recommend girdling invasive plants because girdling usually kills a tree slowly and may allow ongoing seed production. Nonetheless, just like invasives removal, snag and coarse woody debris creation is another way to improve habitat.