How important is Sahara dust for the Amazon?
Lovett (2010) describe that as the soils in the Amazon Basin are actually nutrient poor, due to nutrients such as the phosphorous and iron supplied by the Saharan dust, being leached out via the higher rainfall.  The Saharan sediment is rich in nutrients as, according to Lovett (2010), it is essentially dried up lake bed sediments, mostly (56%, according to Fisher, 2007) coming from the Bodélé depression in Chad, Africa, which is composed of diatom shells which have significant (but not excessive) amounts of phosphorous and iron - this is a finite source.

Mahowald et al. (2014) explain that phosphorus availability constrains both carbon uptake and loss, hence, the amount of phosphorus in a forest is a limiting factor for rainforests (and other environments).  Atmospheric phosphorus, such as that from the Sahara is linked with the long term productivity of the Amazon.  Mahowald et al. also state that biomass burning is also a source of aerosol phosphorus.

In terms of variability, Lovett also explains that these plumes are seasonal - during summer, they go across the Caribbean and winter, traversing south to the Amazon.  It is believed that at current rates of dust dispersal, this nutrient input could last for another millennia - however, there is considerable uncertainty due to uncertainty in the climate models about the Sahara becoming wetter or drier in future.

If drier, Lovett asserts that there would be more dust, allowing the continued input to the Amazon, whereas increased precipitation, i.e. a wetter Sahara would result in less dust, hence less nutrient input to the Amazon.  Miller et al. (2014) explain that many climate models predict that enhanced dust aerosol loading would reduce precipitation due to the dimming effect reducing evaporation, hence making the environment drier.  However, aerosols, including dust, are a major source of uncertainty in climate modelling.

Anthropogenic activity is also a significant source of uncertainty in long term climate modelling, it is suggested by Mahowald et al. that current land use changes in the Amazon itself is having a significant effect on the phosphorus input in the Amazon and surrounding forests.

A generalised view of the phosphorus cycle is provided below (from Wikipedia):



For the Amazon, the important differences are that atmospheric deposition is a vital input, and that leaching and runoff are more important loss mechanisms. (Crop harvest is also relevant due to human activity in the basin).

References

Fisher, 2007, Amazon forest relies on dust from one Saharan valley, New Scientist

Lovett, 2010, African dust keeps Amazon blooming, Nature News

Mahowald et al. 2014, Impacts of biomass burning emissions and land use change on Amazonian atmospheric phosphorus cycling and deposition, Global Geochemical Cycles

Miller et al. 2014, Impact of Dust Radiative Forcing upon Climate, Mineral Dust