Biodiversity can be impacted by a multitude of factors, and different factors can operate at different scales. Even large-scale changes, such as global climate change, have different effects in different habitats, so in a sense all change is local.
In addition, impacts interact. For example, habitat fragmentation resulting from development can exacerbate the effects of fire and invasive species. Because biodiversity promotes resilience, loss of biodiversity takes it away, so that smaller impacts can have greater effects.
A fourth impact, regional air quality, is very instructive of the complexity of interactions. During the 1970s and 1980s, air quality in southern California was at its worst, with improvements beginning in the 1990s as a result of improved emission controls for automobiles, factories, and other sources. Air pollution directly effects many organisms: lichens were effectively eliminated from campus, and many plants suffered reduced health. With improved air quality, many of these effects went away (although it is not inconceivable that some plant or lichen species were eliminated from the area and have never returned).
But air pollution also adds nitrogen to soils, through oxides of nitrogen being dissolved in raindrops. In some areas, the amount of nitrogen added each year to natural environments was roughly the amount added as fertilizer to crop fields. The increased nitrogen is known to favor certain invasive species over native plants, and it can remain in soils, and be recycled from vegetation, for many years after the source is eliminated. In addition, fire can either increase or decrease available soil nitrogen, depending on a number of factors. So, although the air is better, natural habitats are still being affected.