The planetary boundaries framework attempts to set limits for biodiversity loss within which ecological function is relatively unaffected. In a recent article in Science Newbold et al. present a quantitative global analysis of the extent to which the proposed planetary boundary has been crossed. 

Abstract: 

Land use and related pressures have reduced local terrestrial biodiversity, but it is unclear how the magnitude of change relates to the recently proposed planetary boundary ("safe limit"). We estimate that land use and related pressures have already reduced local biodiversity intactness—the average proportion of natural biodiversity remaining in local ecosystems—beyond its recently proposed planetary boundary across 58.1% of the world’s land surface, where 71.4% of the human population live. Biodiversity intactness within most biomes (especially grassland biomes), most biodiversity hotspots, and even some wilderness areas is inferred to be beyond the boundary. Such widespread transgression of safe limits suggests that biodiversity loss, if unchecked, will undermine efforts toward long-term sustainable development.

The study is available at http://dx.doi/10.1126/science.aaf2201