Several investigators reported that soil suppressiveness mainly affected the soilborne pathogens and that this phenomena is returned to soil microorganisms and demonstrated that compost and organic amendments enhanced the suppression of the soil.
There are a lot of indirect measurements (for instance, the density or proportion of colonies on a soil dilution plate that are antagonistic toward pathogens), though I think it is better to try to measure something that's as close to actual disease as you can get. A good assay would be to measure disease severity in response to a defined inoculum dose and under controlled environmental conditions. For fungi, I have seen papers where people measure the physical distance that hyphae disperse through the soil.
I think what the supresive soil can be measured through indicator plants, which certainly will give us an idea of the current state of the soil; and certainly the application of organic materials can improve soil conditions as already mentioned
Suppressiveness explicitly refers to the ability of a soil to prevent the expression of disease in a soil where inoculum is present. The classical measure of soil suppressiveness is thus linked to infectious potential - i.e., the ability of a given amount of inoculum introduced in that soil to cause disease. it is often measured through inoculum dilution series in the soil, planting/sowing susceptible hosts and measuring the amount of disease after appropriate inculbation. This can be done in microcosm experiments (potted soil). Be aware though that you need to measure also the infectious potential of the 'control' soil (i.e., have pots with the original soil, without any extra inoculum introduced). Else, the results might be confused by the inoculum already present in the soil before artificial sdoil infection. You also need a conducive soil as another controil, just to make sure that it is not the inoculum quality, inoculation protocol or incubation conditions that prevented the development of disease in the suppressive soil.
There are many papers from the 1970s and early 1980s (in particular from the INRA group in Dijon & Nancy - Louvet, Alabouvette, Rouxel, Bouhot, Lemanceau, etc..., but also from the UK and USA) which developed the concept of infectious potential and described how to use it to assess suppressiveness. They're still very good reading!
Great answers! Even with recent advances in understanding the mechanisms of disease suppression in soil, there is no universal biomarker that is associated with suppression. So the classic work Didier mentions from INRA is still highly relevant, and it is important to note that INRA groups in Dijon and Nancy are still at the forefront of current research on suppressive soils.
Disease suppression bioassays where field soil is taken into a greenhouse or growth chamber situation, a susceptible host is sown, the pathogen is added and disease is monitored are still the best way to measure if a soil is suppressive or not. You also need to have a conducive control to make sure that the combination of the susceptible host and the virulent pathogen does actually result in disease in other soils. The closer the conducive soil is to the suppressive soil in type, texture and chemical composition, the better the comparison.
If you want to test if compost amendments enhance suppressiveness, you can compare field soil to compost-amended field soil in the disease suppression bioassays. You could also add a treatment of sterile (autoclaved) compost-amended soil.
For disease suppressive soils, along with the French groups, I would recommend checking out Jos Raaijmakers' work in The Netherlands and David Weller's work in the US. For disease suppressive composts, Eric Nelson in the US and the relatively recent review from Bonanomi in Italy.
There is only one parameter, in my opinion, to determine if a soil is suppressive.
If a pathogen is present in the soil and a susceptible host (plant) is grown under optimum conditions. If the plant is not diseased, then that soil is suppressive. Therefore, if the disease is not expressed in the presence of pathogen, then the soil is suppressive. It is a simple thing to do.
Yes, in principle you're right. However, I disagree with your last statement - it's not always a simple thing to do to assess suppressiveness. As in all biological systems, there are many factors that could make a soil suppressiveness assay go wrong: temperature, moisture, host development, inoculum type and concentration,etc.. are only a few of them. Therefore, setting up a proper trial usually requires more than a little tinkering before the assay works reliably well.