From what I can tell, the "ecological integrative approach" is referring to the approach used in the research of that paper, not on how Vitamin D acts in relation to COVID

> Following an ecological integrative approach, we examined the associations between published representative and standardized European population vitamin D data and the Worldometer COVID-19 data at two completely different time points of the first wave of this pandemic.

and

> Thus, a major limitation of our ecological approach is that we had to rely on published - but perhaps not always completely representative - data on the vitamin D status of the populations in Europe.