Population synthesis models are based on two main components. The first component is a planet formation and evolution model, which provides, starting from a protoplanetary disk, the properties of the planetary system that can be formed in it. These properties can be the ones of the system at the end of the disc lifetime (in the case of formation models) or after a few Gyr (in the case of formation-evolution models). The second component is a distribution of the properties of protoplanetary discs, in particular their mass, thermal structure, lifetime and composition.
From these two components, a large number of planetary systems are computed, each assuming different properties of the disc. The distribution of these properties is taken at random, following some observed distribution. The ensemble of planetary systems obtained this way constitutes the theoretical planetary population. By taking into account the observational bias related to a given observational technique (for example by selecting planets producing a Doppler semi-amplitude larger than a given threshold), one obtains the theoretically observable population. Finally, this population is compared to the actually observed population (taking into account only planets detectable with the same observational bias). By trying to match the two population, one can gain knownledge on the physics at work during planet formation.
In case the two populations match, the full theoretical population can be ‘observed’ with another technique (e.g. with Transit) in order to predict what another observational method would yield.