"From a quarter to half of Earth’s vegetated lands has shown significant greening over the last 35 years largely due to rising levels of atmospheric carbon dioxide, according to a new study published in the journal Nature Climate Change on April 25."
This information is based on observational study, not theoretical modeling.
Published April 26th, 2016
Source: https://www.nasa.gov/feature/goddard/2016/carbon-dioxide-fertilization-greening-earth